Research ArticleA Numerical Study for Flow Excitation and Performance ofRampressor Inlet considering Rotor Motion

Weijia Kang Zhansheng Liu Jiangbo Lu Yu Wang and Yanyang Dong

School of Energy Science and Engineering Harbin Institute of Technology Harbin Heilongjiang 150001 China

Correspondence should be addressed to Weijia Kang kwj1221163com

Received 21 February 2014 Revised 1 July 2014 Accepted 2 July 2014 Published 24 July 2014

Academic Editor Longjun Dong

Copyright copy 2014 Weijia Kang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A unique supersonic compressor rotor with high pressure ratio termed the Rampressor is presented by Ramgen Power SystemsInc (RPS) In order to obtain the excitation characteristic and performance of Rampressor inlet flow field under external excitationcompression inlet flow of Rampressor is studied with considering Rampressor rotor whirling Flow excitation characteristics andperformance of Rampressor inlet are analyzed under different frequency and amplitude of Rampressor rotor whirling The resultsindicate that the rotor whirling has a significant effect for flow excitation characteristics and performance of Rampressor inletThe effect of rotor whirling on the different inlet location excitation has a definite phase difference Inlet excitation becomes morecomplex along with the inlet flow path More frequency components appear in the excitation spectrum of Rampressor inlet withconsidering Rampressor rotor whirlingThemain frequency component is the fundamental frequency which is caused by the rotorwhirling Besides the fundamental frequency the double frequency components are generated due to the coupling between inletcompression flow of Rampressor rotor and rotor whirling especially in the subsonic diffuser of Rampressor rotor inlet With theincrement of rotor whirling frequency and whirling amplitude the complexity of Rampressor inlet excitation increases and thestability of Rampressor inlet performance deteriorates

1 Introduction

Ramgen engine with a proof-of-concept version of a newtype of compression system has been proposed by AmericanRamgen Power Systems Inc [1 2] The core part of Ramgenengine is Rampressor Rampressor inlet is formed of therotor compression ramp and engine casing Shock wavecompression system is employed in the Rampressor inletCompared with traditional axial or centrifugal compressorRamgen engine has some distinct technical characteristics[3ndash5] such as a higher stage pressure ratio greater com-pression efficiency higher operational reliability and smallervolume and compact structure

Ramgen Power Systems Inc has developed the relatednumerical simulation of Rampressor inlet which providedthe advantageous validation for the design of inlet flow-pathstructure and supersonic shock wave compression system[6] A two-dimensional model of Rampressor rotor inlet wasdesigned and established byHan et al [7] and thismodel wasnumerically studied by CFDThe effects of rotational speed of

Rampressor rotor and exit back pressure on the shock wavestructure flow field distributions and flow performance ofthe two-dimensional inletmodel were given in their researchBased on the previous research of two-dimensional model ofRampressor inlet a three-dimensional model of Rampressorrotor inlet was also designed and numerically studied by Hanet al [8] Yang et al [9] also numerically analyzed the flowfield of Rampressor inlet in different geometrical parameterssuch as strake section shape throat length-height ratio strakestagger angle compression ramp angle subsonic divergentangle and throat contraction ratio The effects of thesegeometrical parameters on the flowfield distributions and theflowperformance of Rampressor inlet have been given to pro-vide the foundation for the subsequent optimization of inletstructure and performance In order to promote the wholeperformance of Rampressor inlet the research of flow controltechnology and the tip clearance control technology has alsobeen presented and tested by Ramgen Power Systems IncBasing on these design techniques an industrial CO

2com-

pressor has been proposed and implemented which offers

Hindawi Publishing CorporationShock and VibrationVolume 2014 Article ID 963234 16 pageshttpdxdoiorg1011552014963234

2 Shock and Vibration

XCYCZC

Strake wall

Compression ramp

Throat Subsonic diffuser

ldquoPre-inletrdquo flow surface

Figure 1 Model of Rampressor rotor

Compression ramp

Throat

Subsonic diffuser

Straight flow path

ldquoPreinletrdquo flow path

Figure 2 Two-dimensional simplified model of Rampressor inlet

significant cost savings and efficiency advantages over othertypical CO

2compressor systems used for industrial applica-

tions and its highest pressure ratio can achieve 200 1 [10] Atpresent a 13000 horsepower carbon dioxide Rampressor wasconstructed and tested in New York and significant progresshad been achieved in the design and test of the advancedvortex combustor (AVC) system until the spring of 2011 [11]

Operational condition of Rampressor rotor is determinedby the inlet excitation characteristic that causes the rotorwhirl simultaneously inlet flow distribution and excitationcharacteristic are affected by rotor whirl However mostof the previous researches emphasized on Rampressor inletstructural design based on aerodynamic performance andRampressor inlet excitation characteristics had not beenreported in the references Therefore it is necessary to studythe effect of rotor whirl on flow excitation characteristics andperformance of Rampressor inlet

Models of Rampressor rotor and inlet are established inthis study and the effects of exit back pressure on the shockwave structure flow field distribution and flow performanceof Rampressor inlet are numerically studied Then thispaper emphatically analyzes the inlet flow field considering

Wall condition

Flow zone

Rotor rim surface

Stationary engine case

Pressure-inlet

Pressure-outlet

Figure 3 Specific boundary conditions of Rampressor inlet

00 02 04 06 08 1000

05

10

15

20

25

(S)

Result in this paperRamgen result (Grosvenor et al (2006))

Ma r

el

Figure 4 Comparison of relative centerline Mach number versusnormalized streamwise distance (S) between result in this paper andresult in Ramgen

Rampressor rotor whirling The variations of inlet excitationcharacteristic and performance under rotor whirling areobtained and discussed in this paper

2 Numerical Modeling

The Rampressor rotor impeller can be developed with twothree four or more inlets according to the Rampressor flowThe Rampressor rotor model in this study is established withthree inlet flow paths as shown in Figure 1 The supersonicrotor flow path is formed by three strakes mounted on therim of the rotor These strakes are mounted on the rotor at ashallow angle typically 8∘ and formed the axial boundariesof each of the three flow paths Figure 1 shows that eachflow path includes ldquopreinletrdquo surface compression rampthroat and subsonic diffuser The principal shock system isgenerated by the compression ramp integrated into the rim ofthe rotorThe compression ramp is designed to create a seriesof oblique shock waves

Shock and Vibration 3

12 15 19 22 25

(a) Gird size = 11636

12 15 19 22 25

(b) Gird size = 20249

12 15 19 22 25

(c) Gird size = 45439

12 15 19 22 25

(d) Gird size = 84590

Figure 5 Comparison of Mach number contour of Rampressor inlet in different grid sizes

00 02 04 06 08 10

16

24

32

40

48

56

64

Pres

sure

dist

ribut

ions

(Pa)

(S)

Grid size = 11 363

Grid size = 20 249

Grid size = 45 439

Grid size = 84 590

08

times105

Figure 6 Comparison of pressure distribution of stationary enginecase versus normalized streamwise distance in different grid sizes

The three inlets of the designed Rampressor are thesymmetric periodic layout on the rotor If Rampressor rotordoes not whirl the flows of the three inlets are of centralsymmetry so one of the three inlets can be used for numericalstudy of the flow field Beside this the rotor whirl is generallygenerated in the radial direction but the difference betweenthree-dimensional and two-dimensional models is in theaxial direction Because the rotor whirling almost has noeffect on the axial structure of three-dimensional model theaxial flow gradient of the inlet can be ignored Therefore itis accepted to use the two-dimensional model for studyingthe excitation characteristic and performance of Rampressorinlet with considering Rampressor rotor whirling

The two-dimensional simplified model of Rampressorinlet is established for numerical study of flow excitation andperformance as shown in Figure 2 It consists of ldquopreinletrdquo

A

D

CB

Figure 7 Schematic diagram of key point in Rampressor inlet

flow path compression ramp throat subsonic diffuser andstraight flow path

Solution of the compressible form of the Euler equationsfor the simulations presented herein is conducted using afinite-volume and density based scheme in the fluent simula-tion of this study So the two-dimensional simplified modeldoes not take into account the boundary layer developedupward but the centrifugal force is taken into considerationin the calculation The calculation formulation is implicitand the convection flux type is Roe averaged flux differencesplitting (Roe-FDS) Figure 3 shows boundary conditions ofRampressor rotor inletThe exact boundary conditions are asfollows

(a) Inflow boundary condition the Mach number is0348 the total pressure is 119875

119905= 108676 times 10

5 Pa thestatic pressure is 119875

0= 101325 times 10

5 Pa and the totaltemperature is 119879

119905= 306K

(b) Wall boundary condition the no-slip and adiabaticwall boundary conditions are placed on the wallsurfaces The engine case is the stationary adiabaticwall The rotor rim is also adiabatic wall and the

4 Shock and Vibration

11 15 18 22 25079 21 33 46 58

times105(Pa)

Pressure contour Mach number contour

(a) 119875119903 = 80

035 089 14 20 25079 33 59 84

times105(Pa)

Pressure contour Mach number contour

11

(b) 119875119903 = 90

013 072 13 19 25079 36 63 91 12

times105(Pa)

Pressure contour Mach number contour

(c) 119875119903 = 100

013 072 13 19 25079 36 63 91 12

times105(Pa)

Pressure contour Mach number contour

(d) 119875119903 = 106

Figure 8 Flow distribution of Rampressor inlet in different 119875119903

direction of rotation of the rim shown in Figure 3 isright to left In the present case proposed in this paperthe designed Rampressor rotor speed is 40600 rpm

(c) Subsonic outlet boundary condition the exit condi-tion is set to the pressure outlet in order to generatenormal shock waves within internal inlet flow field

3 Validation of Numerical Method

The numerical method of this paper is validated by compar-ing the numerical results of Rampressor inlet flow field of

American Ramgen Power Systems Inc [6] which is based onthe same calculation parameters such as the initial conditionsthe boundary conditions and the Rampressor rotor speedThe variation of relative centerline Mach number versusnormalized streamwise distance (S) in the numerical studyshows a good agreement with the Ramgen results (as shownin Figure 4)The numerical method proposed in this paper isfeasible to solve supersonic compressible flow of Rampressorinlet

In this paper high quality grid of two-dimensionalsimplified model of Rampressor inlet is calculated by using

Shock and Vibration 5

0 02 04 06 08 10

2

4

6

8

10

12

Normalized streamwise distance (S)

Load

(Pa)

Normal shock wave location

times105

Pr = 8

Pr = 9

Pr = 10

Pr = 106

(a) Stationary engine case

0

2

4

6

8

10

12

Load

(Pa)

Normal shock wave location

times105

0 02 04 06 08 1Normalized streamwise distance (S)

Pr = 8

Pr = 9

Pr = 10

Pr = 106

(b) Rotor rim surface

Figure 9 Pressure distribution of Rampressor inlet in different 119875119903

Rampressor under no rotor whirl

Casing

Rampressor under rotor whirl

X

Y

O

O998400

e

Flow path 3

Flow path 1

Flow path 2

Figure 10 Structure schematic diagram of inlet flow path on Rampressor rotor

the structured grid technology The computational grid den-sity of Rampressor inlet model should be examined Machnumber distributions of Rampressor inlet are computed indifferent grid sizes Comparison of Mach number contour ofRampressor inlet in different grid sizes is given in Figure 5The grid density has some influence on the flow field butthe distribution of the shock waves is essentially similarWith the increment of grid size the Mach number contoursof Rampressor inlet gradually tend to be same The Machnumber distribution of the grid size 45439 is basicallyidentical to that of the grid size 84590 Therefore flow field

distribution of Rampressor inlet can be calculated accuratelyby the computational gird sizes 45439 and 84590

Figure 6 shows comparison of pressure distribution of thestationary engine case versus normalized streamwise distancein different grid sizesThegrid density also has a few effects onthe pressure distribution along the stationary engine case butthe location of the shock waves and the pressure fluctuationare basically identical With the increment of grid size thepressure distributions of stationary engine case graduallyhave a tendency to coincide The pressure distribution of thestationary engine case in the numerical simulation of the grid

6 Shock and Vibration

0 0005 001 00151021

10215

1022

10225

1023

10235

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

1020304050607080

Frequency (Hz)

Exci

tatio

n (P

a)

times105

6764Hz

(a) Point A

0 0005 001 0015503

5035

504

5045

505

5055

506

5065

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

times105

(b) Point B

0 0005 001 0015419

4195

42

4205

421

4215

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

100200300400500600700800

Frequency (Hz)

Exci

tatio

n (P

a)

times105

13528Hz

6764Hz

(c) Point C

0 0005 001 00151143114411451146114711481149

1151151

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

times106

(d) Point D

Figure 11 Pressure pulsation time history and spectrogram on every key point of Rampressor rotor inlet

Shock and Vibration 7

0 05 1 150995

1

1005

Time (s)

Point APoint B

Point CPoint D

Non

dim

ensio

nal e

xcita

tion

(Pa)

times10minus3

Figure 12 Time history of nondimensional excitation

size 45439 shows a good agreement with that of the grid size84590 (Figure 6)

The computational model of grid size 45439 is chosenfor the latter Rampressor inlet simulation in comprehensiveconsideration with computational accuracy and computa-tional complexity The grid employed 781 nodes (maximumnumber) in the streamwise direction and 88 (maximumnumber) in the radial

4 Simulation Results and Analysis

The following parameters are defined to analyze the perfor-mances of Rampressor inlet flow path for different operatingconditions [4 7]

Static pressure ratio of flow path can be obtained asfollows

119901119904=119901outlet119901inlet (1)

where 119901outlet and 119901inlet are the static pressure of entrance andexit of flow path respectively

Total-pressure recovery coefficient of flow path

119901119877=119901lowast

outlet119901lowast

inlet (2)

where 119901lowastoutlet and 119901lowast

inlet are the total pressure of entrance andexit of flow path respectively

Pressurization ratio in flow path

119901119911=119901lowast

outlet119901inlet= 119901119877(1 +120581 minus 1

2Ma2inlet)

120581(120581minus1)

(3)

Loss coefficient in flow path

120596 =1 minus 119901119877

1 minus 119901119904(Mainlet)

(4)

where 119901119877is total-pressure recovery coefficient 119901

119904is static

pressure ratio and Mainlet is airflow Mach numberKinetic energy efficiency in flow path

120578 = 1 minus2

(120581 minus 1)Ma2inlet[(1

119901119877

)

(120581minus1)120581

minus 1] (5)

where 120581 is adiabatic exponentNondimensional total pressure distortion of flow-path

exit is defined as

Δ =119875119905MAX minus 119875119905MIN

119875119905avg

(6)

where 119875119905MAX and 119875

119905MIN are maximum total-pressure andminimum total-pressure of flow-path exit respectively and119875119905avg is average total pressure of flow-path exitIn order to study the excitation characteristic of Rampres-

sor inlet well pressure pulsation of key points in Rampressorinlet should be measured The arrangement of key points isshown in Figure 7 The points A B C and D are located inthe middle part of the compression ramp the entrance ofthe throat entrance of subsonic diffuser and the entrance ofstraight flow path respectively

41 Performance and Excitation Characteristic of Inlet underno Rotor Whirling The equation 119875

119903= 1198751198871198750is defined

where 119875119887is the exit back pressure of Rampressor inlet so

119875119903is the nondimensional back pressure Figure 8 shows the

static pressure contour and theMach number contour of two-dimensional inlet in different 119875

119903= 80 90 100 and 1060

when the design rotor speed is 40600 rpmA series of oblique shock waves is generated by the

compression ramp of inlet flow path to achieve airflowcompression and the airflow pressure after the shock waveincreases abruptly as shown in Figure 8 Several reflections ofthe oblique shock waves are produced between the stationaryengine case and the Rampressor rotor rim surface followedby a terminal normal shock The Mach number contoursshow that the airflow speed after a normal shock wavereduces to be subsonic When 119875

119903increases from 9 to 106

the position where the normal shock wave appears graduallymoves towards the inlet throat The position of the normalshock wave just locates in the throat when 119875

119903equals 1060

and Rampressor inlet reaches the critical statePressure distributions along stationary engine case and

rotor rim surface of Rampressor inlet are given in Figure 9The pressure distribution curves of the stationary engine

case and rotor rim surface are completely overlapped beforenormal shock wave in the different 119875

119903as shown in Figure 9

Therefore aerodynamic loading of inlet supersonic compres-sion section is accordant in the different 119875

119903and is not affected

by the exit condition (combustor) Figure 9 illustrates that theloading of the stationary engine case and rotor rim surfaceafter normal shock wave suddenly rises and then tends to bea certain value along inlet flow path The results indicate thatalong with the increment of 119875

119903 the position of the normal

shock wave gradually moves forward and then aerodynamicloading of the stationary engine case and rotor rim surfacealso increases

8 Shock and Vibration

00 02 04 06 08 100

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

Point A

Point B

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Stationary engine case

00 02 04 06 08 1000

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Rotor rim surface

Figure 13 Pressure distributions along stationary engine case and rotor rim surface in a whirling motion cycle

0460 0461 0462 0463 0464 0465570

575

580

585

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Point A

05313 05314 0531588

89

90

91

92

93

94

95

96

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Point B

Figure 14 Partial enlarged drawing of pressure distributions along stationary engine case

The consequences of Rampressor inlet flow performancein different pressure ratios are shown in Table 1 With theincrease of 119875

119903(back pressure) static pressure ratio 119901

119904

total-pressure recovery coefficient 119901119877 pressurization ratio

119901119911 and kinetic energy efficiency 120578 gradually enhance but

nondimensional total pressure distortion and loss coefficientdecrease by degrees and exit stability of Rampressor inletameliorates As a result appropriate enhancement of exitback pressure is advantageous to pressure ratio compressionefficiency and other performance indices when inlet can

Shock and Vibration 9

0 02 04 06 08 10843

0844

0845

0846

0847

0848

0849

0850

Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 15 Flow performance of Rampressor inlet in a whirling motion cycle

Table 1 Flow performance parameters in the different 119875119903

119901119904

119901119877

119901119911

120596 120578 Δ ()9 07649 1148 00116 09292 367310 08294 1244 00075 09512 4339106 08483 1273 00063 09572 2546

start and normally work and meanwhile beneficial toimprovement of Rampressor overall efficiency

42 Performance and Excitation Characteristic of Inlet underRotor Whirling Rampressor inlet flow may be affected byRampressor rotor whirl in the work process When the inletpressure regularly changes which is caused by rotor whirlRampressor rotor bears the inconstant pressure load and thenvibrates

Structure schematic diagram of inlet flow path underRampressor rotor whirl is illustrated in Figure 10 The dottedline represents the state of Rampressor rotor without whirl

and the solid line curve represents the state of Rampressorrotor whirl

Because the three inlets of the designed Rampressor arethe symmetric periodic layout on the rotor the flow excitationcharacteristics and flow performance of inlet flow path 1 arestudied under Rampressor rotor periodic whirl in this paperExpression of rotor periodic whirl is given as follows

119890 = 119886 sin (Ω119905 + 120593) (7)

where 119890 represents the displacement between Rampressorcenter1198741015840 under rotor whirl andRampressor center119874withoutrotor whirl 119886 is rotor whirl amplitude Ω is rotor whirlfrequency (whirl speed) and120593 is initial phase In otherwordsthe trajectory of the Rampressor rotor is assumed as a circlein different whirl frequencies and whirl amplitudes so theeffect of the damping on the rotor whirl is not taken intoconsideration in the calculation

Result of steady flow is taken as the initial result in theunsteady calculation of this paper Time step size is set to1478 times 10minus5 s in the design rotor speed The unsteady flow ofRampressor inlet under rotor whirl is studied when 119875

119903equals

10 Shock and Vibration

0 200 400 600 800 1000 12000

500

1000

1500

2000

2500

3000

3500

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

3382Hz

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764 Hz

13528 Hz

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

500

1000

1500

2000

Frequency (Hz)

Exci

tatio

n (P

a)

13528Hz

27056Hz40584Hz

(c) Ω = 8500 rads

Figure 16 Calculation results of point D in different rotor whirling frequencies

106 Flow excitation characteristics of Rampressor inlet willbe analyzed under different frequencies and amplitudes ofRampressor whirl

Pressure pulsation time history and spectrogramon everykey point of Rampressor rotor inlet are shown in Figure 11when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads (the design Rampressor rotor speed)

Figure 11 indicates that excitation spectrogram of point Alocated in inlet supersonic compression of Rampressor is rel-atively simple The main frequency component is the funda-mental frequency which is caused by the rotor whirling Thevalue of rotor whirling frequency (fundamental frequency)is 6764Hz and excitation amplitude is small Comparedwith point A more frequency components appear in thefrequency spectrogram of Rampressor inlet point B point Cand point D Not only rotor whirling frequency 6764Hz butalso its double frequency component 13528Hz is obtainedin excitation spectrogram The double frequency 13528Hzis generated due to the coupling between inlet compressionflow of Rampressor rotor and rotor whirling especially in

the subsonic diffuser of Rampressor rotor inlet The ampli-tude of the double frequency component is smaller thanthat of the fundamental frequency component As shownin the frequency spectrum the excitation amplitudes of thefundamental frequency and double frequency componentsall gradually increase along with inlet flow pathThis happensbecause the subsonic flow in Rampressor inlet is easilyaffected by the external excitation It follows from above thatthe inlet excitation becomes more complex along with inletflow path

Time history of nondimensional excitation in a pulsationcycle is given (as shown in Figure 12) on every key point ofRampressor rotor inlet when rotor whirl amplitude equals100 120583m and whirl speed (Ω) is 4250 rads Figure 12 showsthat phases of nondimensional excitation in differentmeasurepoints are greatly different Among them phase differencebetween point B located on the entrance of the inlet throatand point C located on exit of the inlet throat is close to 180degrees Thus it can be seen that rotor whirl effect on inletdifferent location excitation has a certain phase difference

Shock and Vibration 11

0 200 400 600 800 1000 12000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

Frequency (Hz)

Exci

tatio

n (P

a)

(c) Ω = 8500 rads

Figure 17 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling frequencies

Pressure distributions along stationary engine case androtor rim surface of Rampressor inlet in a whirling motioncycle are shown in Figure 13 when rotor whirl amplitudeequals 100 120583m and whirl speed (Ω) is 4250 rads

Figure 14 shows partial enlarged drawing of pressuredistributions along the stationary engine case of Rampressorinlet (as shown in Figure 13(a) point A and point B) Periodicoscillation phenomenon of the inlet pressure distribution isobtained under Rampressor rotor whirl

The curves of flow performance parameters of Rampres-sor inlet in a whirling motion cycle are shown in Figure 15when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads Figure 15 indicates that the variations oftotal-pressure recovery coefficient pressure ratio and kineticenergy efficiency for Rampressor inlet are also periodic in awhirling motion cycle

421 Results and Discussion in Different Frequencies of Ram-pressor Rotor Whirl Pressure pulsation spectrograms of key

point D (shown in Figure 6) are respectively obtained indifferent whirling frequencies such as Ω = 2125 rads4250 rads and 8500 rads (shown in Figure 16) when rotorwhirl amplitude is 100 120583m

Figure 17 shows the spectrograms of airflow excitingforce on Rampressor rotor rim surface when rotor whirlingamplitude equals 100120583m and rotor whirl frequencies are2125 rads 4250 rads and 8500 rads respectively

Figure 16 indicates that the excitation characteristic ofpoint D is rather complex As shown in the frequencyspectrum besides the fundamental frequency componentthe higher order frequency component is also generatedwhere the amplitude of the fundamental frequency compo-nent is the highest The amplitude of the double frequencycomponent is smaller than that of the fundamental frequencybut greater than those of other frequency componentsCompared with excitation spectrum of Ω = 2125 radsthe amplitude of the double frequency component rela-tively increses when the whirl frequency (Ω) is 4250 rads

12 Shock and Vibration

0843

0844

0845

0846

0847

0848

0849

0850To

tal-p

ress

ure r

ecov

ery

coeffi

cien

t

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

(a) Total-pressure recovery coefficient

1264

1266

1268

1270

1272

1274

1276

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

2125 rads4250 rads8500 rads

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 18 Flow performance in different whirling frequencies during a whirling motion cycle

(as shown in Figure 16(b)) In Figure 16(c) more frequencycomponents appear in the excitation spectrum In additionto the fundamental frequency and double frequency compo-nent the third harmonic frequency component simultane-ously emerges when the whirl frequency (Ω) is 8500 radswhich is caused by the coupling between inlet compressionflow of Rampressor rotor and rotor whirling With theincrement of rotor whirling frequency the amplitude of thefundamental frequency component in the frequency spec-trum gradually decreases but the amplitude of the doublefrequency component increases by degrees It follows fromabove that the complexity of Rampressor inlet excitationincreases along with the increase of rotor whirling frequencyThe above results are also illustrated in the frequency

spectrum of airflow exciting force on the rotor rim surfaceof Rampressor inlet as shown in Figure 17

The curves of flow performance parameters of Rampres-sor inlet in a whirlingmotion cycle are respectively obtainedin different whirl frequencies such as Ω = 2125 rads4250 rads and 8500 rads (illustrated in Figure 18) whenrotor whirl amplitude is 100120583m Figure 18 shows that waveamplitudes of total-pressure recovery coefficient pressuriza-tion ratio and kinetic energy efficiency of Rampressor inletare not affected by rotor whirling frequency which onlyinfluences the wave frequency of inlet flow performanceparameters The wave frequency of inlet flow performanceparameters becomes higher with the increment of rotor whirlfrequency Therefore the stability of inlet performance is

Shock and Vibration 13

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

3500

4000

Frequency (Hz)

Exci

tatio

n (P

a)

20292Hz

6764Hz

13528Hz

(c) 119886 = 150 120583m

Figure 19 Calculation results of point D in different rotor whirling amplitudes

better in the practical engineering when Rampressor rotorwhirling frequency is less

422 Results and Discussion in Different Amplitudes of Ram-pressor RotorWhirl Excitation characteristics of Rampressorinlet are analyzed in different rotor whirling amplitudes suchas 119886 = 50 120583m 119886 = 100 120583m and 119886 = 150 120583m whenrotor whirling frequency Ω = 4250 rads Figure 19 showspressure pulsation spectrogramof Rampressor inlet key pointD (shown in Figure 6) in different rotor whirl amplitudes

The spectrograms of airflow exciting force onRampressorrotor rim surface are respectively obtained in different rotorwhirling amplitudes such as 119886 = 50 120583m 119886 = 100 120583m and 119886 =150 120583m (shown in Figure 20) when the rotor whirl frequencyΩ = 4250 rads

As shown in Figure 19 more frequency componentsemerge in the excitation spectrum such as the fundamentalfrequency component double frequency component andthird harmonic frequency component where the amplitude

of the fundamental frequency component is the highest Theamplitude of the double frequency component is smallerthan that of the fundamental frequency component buthigher than that of the third harmonic frequency componentCompared with point D excitation of 119886 = 50 120583m besides thefundamental frequency and double frequency componentsthe third harmonic component in excitation spectrum isalso generated when the rotor whirl amplitudes are 100 120583mand 150 120583m (as shown in Figures 19(b) and 19(c)) andthe amplitude of the double frequency component in theexcitation spectrum of inlet point D relatively increasesWiththe increment of rotor whirling amplitude the amplitude ofthe fundamental frequency component and double frequencycomponent in the excitation spectrum of inlet wall allgradually increases It follows from above that the complexityof Rampressor inlet excitation also increases along with theincrease of rotor whirling amplitude The above results arealso illustrated in the spectrumof airflow exciting force on therotor rim surface of Rampressor inlet as shown in Figure 20

14 Shock and Vibration

0 500 1000 1500 2000 25000

10

20

30

40

50

60

70

80

Frequency (Hz)

Exci

tatio

n (P

a)

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

50

100

150

200

Frequency (Hz)

Exci

tatio

n (P

a)

(c) 119886 = 150 120583m

Figure 20 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling amplitudes

Flow performance of Rampressor inlet is studied indifferent rotor whirling amplitudes such as 119886 = 50 120583m 119886 =100 120583m and 119886 = 150 120583mwhen rotor whirling frequencyΩ =4250 rads Figure 21 shows the curves of flow performanceparameters of Rampressor inlet during a whirling motioncycle in different rotor whirling amplitudes Along with theincrease of rotor whirling amplitude wave amplitudes oftotal-pressure recovery coefficient pressurization ratio andkinetic energy efficiency of Rampressor inlet enlarge and thestability of inlet performance reduces Therefore the stabilityof inlet performance is better in the practical engineeringwhen Rampressor rotor whirling amplitude is less

5 Conclusions

Based on Rampressor rotor model and inlet flow modelthe compression inlet flow field of Rampressor rotor isnumerically studied with consideration of Rampressor rotorwhirling Flow excitation characteristics and performance

of Rampressor inlet are analyzed and discussed under thedifferent frequencies and amplitudes of Rampressor rotorwhirling The following conclusions are obtained

Alongwith the increment of119875119903 the position of the normal

shock wave gradually moves forward and aerodynamic load-ing of the inlet wall also increases Appropriate enhancementof inlet back pressure is advantageous to the pressure ratiocompression efficiency and other performance indices wheninlet can start and normally work

More frequency components appear in the excitationspectrum of Rampressor inlet with considering Rampressorrotor whirling The main frequency component is the fun-damental frequency which is caused by the rotor whirlingBesides the fundamental frequency the double frequencycomponents emerge because of the coupling between inletcompression flow of Rampressor rotor and rotor whirlingespecially in the subsonic diffuser of Rampressor rotor inletThe effect of rotor whirling on the excitation of Rampressorinlet wall has a definite phase difference Inlet excitation

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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2 Shock and Vibration

XCYCZC

Strake wall

Compression ramp

Throat Subsonic diffuser

ldquoPre-inletrdquo flow surface

Figure 1 Model of Rampressor rotor

Compression ramp

Throat

Subsonic diffuser

Straight flow path

ldquoPreinletrdquo flow path

Figure 2 Two-dimensional simplified model of Rampressor inlet

significant cost savings and efficiency advantages over othertypical CO

2compressor systems used for industrial applica-

tions and its highest pressure ratio can achieve 200 1 [10] Atpresent a 13000 horsepower carbon dioxide Rampressor wasconstructed and tested in New York and significant progresshad been achieved in the design and test of the advancedvortex combustor (AVC) system until the spring of 2011 [11]

Operational condition of Rampressor rotor is determinedby the inlet excitation characteristic that causes the rotorwhirl simultaneously inlet flow distribution and excitationcharacteristic are affected by rotor whirl However mostof the previous researches emphasized on Rampressor inletstructural design based on aerodynamic performance andRampressor inlet excitation characteristics had not beenreported in the references Therefore it is necessary to studythe effect of rotor whirl on flow excitation characteristics andperformance of Rampressor inlet

Models of Rampressor rotor and inlet are established inthis study and the effects of exit back pressure on the shockwave structure flow field distribution and flow performanceof Rampressor inlet are numerically studied Then thispaper emphatically analyzes the inlet flow field considering

Wall condition

Flow zone

Rotor rim surface

Stationary engine case

Pressure-inlet

Pressure-outlet

Figure 3 Specific boundary conditions of Rampressor inlet

00 02 04 06 08 1000

05

10

15

20

25

(S)

Result in this paperRamgen result (Grosvenor et al (2006))

Ma r

el

Figure 4 Comparison of relative centerline Mach number versusnormalized streamwise distance (S) between result in this paper andresult in Ramgen

Rampressor rotor whirling The variations of inlet excitationcharacteristic and performance under rotor whirling areobtained and discussed in this paper

2 Numerical Modeling

The Rampressor rotor impeller can be developed with twothree four or more inlets according to the Rampressor flowThe Rampressor rotor model in this study is established withthree inlet flow paths as shown in Figure 1 The supersonicrotor flow path is formed by three strakes mounted on therim of the rotor These strakes are mounted on the rotor at ashallow angle typically 8∘ and formed the axial boundariesof each of the three flow paths Figure 1 shows that eachflow path includes ldquopreinletrdquo surface compression rampthroat and subsonic diffuser The principal shock system isgenerated by the compression ramp integrated into the rim ofthe rotorThe compression ramp is designed to create a seriesof oblique shock waves

Shock and Vibration 3

12 15 19 22 25

(a) Gird size = 11636

12 15 19 22 25

(b) Gird size = 20249

12 15 19 22 25

(c) Gird size = 45439

12 15 19 22 25

(d) Gird size = 84590

Figure 5 Comparison of Mach number contour of Rampressor inlet in different grid sizes

00 02 04 06 08 10

16

24

32

40

48

56

64

Pres

sure

dist

ribut

ions

(Pa)

(S)

Grid size = 11 363

Grid size = 20 249

Grid size = 45 439

Grid size = 84 590

08

times105

Figure 6 Comparison of pressure distribution of stationary enginecase versus normalized streamwise distance in different grid sizes

The three inlets of the designed Rampressor are thesymmetric periodic layout on the rotor If Rampressor rotordoes not whirl the flows of the three inlets are of centralsymmetry so one of the three inlets can be used for numericalstudy of the flow field Beside this the rotor whirl is generallygenerated in the radial direction but the difference betweenthree-dimensional and two-dimensional models is in theaxial direction Because the rotor whirling almost has noeffect on the axial structure of three-dimensional model theaxial flow gradient of the inlet can be ignored Therefore itis accepted to use the two-dimensional model for studyingthe excitation characteristic and performance of Rampressorinlet with considering Rampressor rotor whirling

The two-dimensional simplified model of Rampressorinlet is established for numerical study of flow excitation andperformance as shown in Figure 2 It consists of ldquopreinletrdquo

A

D

CB

Figure 7 Schematic diagram of key point in Rampressor inlet

flow path compression ramp throat subsonic diffuser andstraight flow path

Solution of the compressible form of the Euler equationsfor the simulations presented herein is conducted using afinite-volume and density based scheme in the fluent simula-tion of this study So the two-dimensional simplified modeldoes not take into account the boundary layer developedupward but the centrifugal force is taken into considerationin the calculation The calculation formulation is implicitand the convection flux type is Roe averaged flux differencesplitting (Roe-FDS) Figure 3 shows boundary conditions ofRampressor rotor inletThe exact boundary conditions are asfollows

(a) Inflow boundary condition the Mach number is0348 the total pressure is 119875

119905= 108676 times 10

5 Pa thestatic pressure is 119875

0= 101325 times 10

5 Pa and the totaltemperature is 119879

119905= 306K

(b) Wall boundary condition the no-slip and adiabaticwall boundary conditions are placed on the wallsurfaces The engine case is the stationary adiabaticwall The rotor rim is also adiabatic wall and the

4 Shock and Vibration

11 15 18 22 25079 21 33 46 58

times105(Pa)

Pressure contour Mach number contour

(a) 119875119903 = 80

035 089 14 20 25079 33 59 84

times105(Pa)

Pressure contour Mach number contour

11

(b) 119875119903 = 90

013 072 13 19 25079 36 63 91 12

times105(Pa)

Pressure contour Mach number contour

(c) 119875119903 = 100

013 072 13 19 25079 36 63 91 12

times105(Pa)

Pressure contour Mach number contour

(d) 119875119903 = 106

Figure 8 Flow distribution of Rampressor inlet in different 119875119903

direction of rotation of the rim shown in Figure 3 isright to left In the present case proposed in this paperthe designed Rampressor rotor speed is 40600 rpm

(c) Subsonic outlet boundary condition the exit condi-tion is set to the pressure outlet in order to generatenormal shock waves within internal inlet flow field

3 Validation of Numerical Method

The numerical method of this paper is validated by compar-ing the numerical results of Rampressor inlet flow field of

American Ramgen Power Systems Inc [6] which is based onthe same calculation parameters such as the initial conditionsthe boundary conditions and the Rampressor rotor speedThe variation of relative centerline Mach number versusnormalized streamwise distance (S) in the numerical studyshows a good agreement with the Ramgen results (as shownin Figure 4)The numerical method proposed in this paper isfeasible to solve supersonic compressible flow of Rampressorinlet

In this paper high quality grid of two-dimensionalsimplified model of Rampressor inlet is calculated by using

Shock and Vibration 5

0 02 04 06 08 10

2

4

6

8

10

12

Normalized streamwise distance (S)

Load

(Pa)

Normal shock wave location

times105

Pr = 8

Pr = 9

Pr = 10

Pr = 106

(a) Stationary engine case

0

2

4

6

8

10

12

Load

(Pa)

Normal shock wave location

times105

0 02 04 06 08 1Normalized streamwise distance (S)

Pr = 8

Pr = 9

Pr = 10

Pr = 106

(b) Rotor rim surface

Figure 9 Pressure distribution of Rampressor inlet in different 119875119903

Rampressor under no rotor whirl

Casing

Rampressor under rotor whirl

X

Y

O

O998400

e

Flow path 3

Flow path 1

Flow path 2

Figure 10 Structure schematic diagram of inlet flow path on Rampressor rotor

the structured grid technology The computational grid den-sity of Rampressor inlet model should be examined Machnumber distributions of Rampressor inlet are computed indifferent grid sizes Comparison of Mach number contour ofRampressor inlet in different grid sizes is given in Figure 5The grid density has some influence on the flow field butthe distribution of the shock waves is essentially similarWith the increment of grid size the Mach number contoursof Rampressor inlet gradually tend to be same The Machnumber distribution of the grid size 45439 is basicallyidentical to that of the grid size 84590 Therefore flow field

distribution of Rampressor inlet can be calculated accuratelyby the computational gird sizes 45439 and 84590

Figure 6 shows comparison of pressure distribution of thestationary engine case versus normalized streamwise distancein different grid sizesThegrid density also has a few effects onthe pressure distribution along the stationary engine case butthe location of the shock waves and the pressure fluctuationare basically identical With the increment of grid size thepressure distributions of stationary engine case graduallyhave a tendency to coincide The pressure distribution of thestationary engine case in the numerical simulation of the grid

6 Shock and Vibration

0 0005 001 00151021

10215

1022

10225

1023

10235

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

1020304050607080

Frequency (Hz)

Exci

tatio

n (P

a)

times105

6764Hz

(a) Point A

0 0005 001 0015503

5035

504

5045

505

5055

506

5065

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

times105

(b) Point B

0 0005 001 0015419

4195

42

4205

421

4215

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

100200300400500600700800

Frequency (Hz)

Exci

tatio

n (P

a)

times105

13528Hz

6764Hz

(c) Point C

0 0005 001 00151143114411451146114711481149

1151151

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

times106

(d) Point D

Figure 11 Pressure pulsation time history and spectrogram on every key point of Rampressor rotor inlet

Shock and Vibration 7

0 05 1 150995

1

1005

Time (s)

Point APoint B

Point CPoint D

Non

dim

ensio

nal e

xcita

tion

(Pa)

times10minus3

Figure 12 Time history of nondimensional excitation

size 45439 shows a good agreement with that of the grid size84590 (Figure 6)

The computational model of grid size 45439 is chosenfor the latter Rampressor inlet simulation in comprehensiveconsideration with computational accuracy and computa-tional complexity The grid employed 781 nodes (maximumnumber) in the streamwise direction and 88 (maximumnumber) in the radial

4 Simulation Results and Analysis

The following parameters are defined to analyze the perfor-mances of Rampressor inlet flow path for different operatingconditions [4 7]

Static pressure ratio of flow path can be obtained asfollows

119901119904=119901outlet119901inlet (1)

where 119901outlet and 119901inlet are the static pressure of entrance andexit of flow path respectively

Total-pressure recovery coefficient of flow path

119901119877=119901lowast

outlet119901lowast

inlet (2)

where 119901lowastoutlet and 119901lowast

inlet are the total pressure of entrance andexit of flow path respectively

Pressurization ratio in flow path

119901119911=119901lowast

outlet119901inlet= 119901119877(1 +120581 minus 1

2Ma2inlet)

120581(120581minus1)

(3)

Loss coefficient in flow path

120596 =1 minus 119901119877

1 minus 119901119904(Mainlet)

(4)

where 119901119877is total-pressure recovery coefficient 119901

119904is static

pressure ratio and Mainlet is airflow Mach numberKinetic energy efficiency in flow path

120578 = 1 minus2

(120581 minus 1)Ma2inlet[(1

119901119877

)

(120581minus1)120581

minus 1] (5)

where 120581 is adiabatic exponentNondimensional total pressure distortion of flow-path

exit is defined as

Δ =119875119905MAX minus 119875119905MIN

119875119905avg

(6)

where 119875119905MAX and 119875

119905MIN are maximum total-pressure andminimum total-pressure of flow-path exit respectively and119875119905avg is average total pressure of flow-path exitIn order to study the excitation characteristic of Rampres-

sor inlet well pressure pulsation of key points in Rampressorinlet should be measured The arrangement of key points isshown in Figure 7 The points A B C and D are located inthe middle part of the compression ramp the entrance ofthe throat entrance of subsonic diffuser and the entrance ofstraight flow path respectively

41 Performance and Excitation Characteristic of Inlet underno Rotor Whirling The equation 119875

119903= 1198751198871198750is defined

where 119875119887is the exit back pressure of Rampressor inlet so

119875119903is the nondimensional back pressure Figure 8 shows the

static pressure contour and theMach number contour of two-dimensional inlet in different 119875

119903= 80 90 100 and 1060

when the design rotor speed is 40600 rpmA series of oblique shock waves is generated by the

compression ramp of inlet flow path to achieve airflowcompression and the airflow pressure after the shock waveincreases abruptly as shown in Figure 8 Several reflections ofthe oblique shock waves are produced between the stationaryengine case and the Rampressor rotor rim surface followedby a terminal normal shock The Mach number contoursshow that the airflow speed after a normal shock wavereduces to be subsonic When 119875

119903increases from 9 to 106

the position where the normal shock wave appears graduallymoves towards the inlet throat The position of the normalshock wave just locates in the throat when 119875

119903equals 1060

and Rampressor inlet reaches the critical statePressure distributions along stationary engine case and

rotor rim surface of Rampressor inlet are given in Figure 9The pressure distribution curves of the stationary engine

case and rotor rim surface are completely overlapped beforenormal shock wave in the different 119875

119903as shown in Figure 9

Therefore aerodynamic loading of inlet supersonic compres-sion section is accordant in the different 119875

119903and is not affected

by the exit condition (combustor) Figure 9 illustrates that theloading of the stationary engine case and rotor rim surfaceafter normal shock wave suddenly rises and then tends to bea certain value along inlet flow path The results indicate thatalong with the increment of 119875

119903 the position of the normal

shock wave gradually moves forward and then aerodynamicloading of the stationary engine case and rotor rim surfacealso increases

8 Shock and Vibration

00 02 04 06 08 100

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

Point A

Point B

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Stationary engine case

00 02 04 06 08 1000

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Rotor rim surface

Figure 13 Pressure distributions along stationary engine case and rotor rim surface in a whirling motion cycle

0460 0461 0462 0463 0464 0465570

575

580

585

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Point A

05313 05314 0531588

89

90

91

92

93

94

95

96

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Point B

Figure 14 Partial enlarged drawing of pressure distributions along stationary engine case

The consequences of Rampressor inlet flow performancein different pressure ratios are shown in Table 1 With theincrease of 119875

119903(back pressure) static pressure ratio 119901

119904

total-pressure recovery coefficient 119901119877 pressurization ratio

119901119911 and kinetic energy efficiency 120578 gradually enhance but

nondimensional total pressure distortion and loss coefficientdecrease by degrees and exit stability of Rampressor inletameliorates As a result appropriate enhancement of exitback pressure is advantageous to pressure ratio compressionefficiency and other performance indices when inlet can

Shock and Vibration 9

0 02 04 06 08 10843

0844

0845

0846

0847

0848

0849

0850

Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 15 Flow performance of Rampressor inlet in a whirling motion cycle

Table 1 Flow performance parameters in the different 119875119903

119901119904

119901119877

119901119911

120596 120578 Δ ()9 07649 1148 00116 09292 367310 08294 1244 00075 09512 4339106 08483 1273 00063 09572 2546

start and normally work and meanwhile beneficial toimprovement of Rampressor overall efficiency

42 Performance and Excitation Characteristic of Inlet underRotor Whirling Rampressor inlet flow may be affected byRampressor rotor whirl in the work process When the inletpressure regularly changes which is caused by rotor whirlRampressor rotor bears the inconstant pressure load and thenvibrates

Structure schematic diagram of inlet flow path underRampressor rotor whirl is illustrated in Figure 10 The dottedline represents the state of Rampressor rotor without whirl

and the solid line curve represents the state of Rampressorrotor whirl

Because the three inlets of the designed Rampressor arethe symmetric periodic layout on the rotor the flow excitationcharacteristics and flow performance of inlet flow path 1 arestudied under Rampressor rotor periodic whirl in this paperExpression of rotor periodic whirl is given as follows

119890 = 119886 sin (Ω119905 + 120593) (7)

where 119890 represents the displacement between Rampressorcenter1198741015840 under rotor whirl andRampressor center119874withoutrotor whirl 119886 is rotor whirl amplitude Ω is rotor whirlfrequency (whirl speed) and120593 is initial phase In otherwordsthe trajectory of the Rampressor rotor is assumed as a circlein different whirl frequencies and whirl amplitudes so theeffect of the damping on the rotor whirl is not taken intoconsideration in the calculation

Result of steady flow is taken as the initial result in theunsteady calculation of this paper Time step size is set to1478 times 10minus5 s in the design rotor speed The unsteady flow ofRampressor inlet under rotor whirl is studied when 119875

119903equals

10 Shock and Vibration

0 200 400 600 800 1000 12000

500

1000

1500

2000

2500

3000

3500

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

3382Hz

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764 Hz

13528 Hz

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

500

1000

1500

2000

Frequency (Hz)

Exci

tatio

n (P

a)

13528Hz

27056Hz40584Hz

(c) Ω = 8500 rads

Figure 16 Calculation results of point D in different rotor whirling frequencies

106 Flow excitation characteristics of Rampressor inlet willbe analyzed under different frequencies and amplitudes ofRampressor whirl

Pressure pulsation time history and spectrogramon everykey point of Rampressor rotor inlet are shown in Figure 11when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads (the design Rampressor rotor speed)

Figure 11 indicates that excitation spectrogram of point Alocated in inlet supersonic compression of Rampressor is rel-atively simple The main frequency component is the funda-mental frequency which is caused by the rotor whirling Thevalue of rotor whirling frequency (fundamental frequency)is 6764Hz and excitation amplitude is small Comparedwith point A more frequency components appear in thefrequency spectrogram of Rampressor inlet point B point Cand point D Not only rotor whirling frequency 6764Hz butalso its double frequency component 13528Hz is obtainedin excitation spectrogram The double frequency 13528Hzis generated due to the coupling between inlet compressionflow of Rampressor rotor and rotor whirling especially in

the subsonic diffuser of Rampressor rotor inlet The ampli-tude of the double frequency component is smaller thanthat of the fundamental frequency component As shownin the frequency spectrum the excitation amplitudes of thefundamental frequency and double frequency componentsall gradually increase along with inlet flow pathThis happensbecause the subsonic flow in Rampressor inlet is easilyaffected by the external excitation It follows from above thatthe inlet excitation becomes more complex along with inletflow path

Time history of nondimensional excitation in a pulsationcycle is given (as shown in Figure 12) on every key point ofRampressor rotor inlet when rotor whirl amplitude equals100 120583m and whirl speed (Ω) is 4250 rads Figure 12 showsthat phases of nondimensional excitation in differentmeasurepoints are greatly different Among them phase differencebetween point B located on the entrance of the inlet throatand point C located on exit of the inlet throat is close to 180degrees Thus it can be seen that rotor whirl effect on inletdifferent location excitation has a certain phase difference

Shock and Vibration 11

0 200 400 600 800 1000 12000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

Frequency (Hz)

Exci

tatio

n (P

a)

(c) Ω = 8500 rads

Figure 17 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling frequencies

Pressure distributions along stationary engine case androtor rim surface of Rampressor inlet in a whirling motioncycle are shown in Figure 13 when rotor whirl amplitudeequals 100 120583m and whirl speed (Ω) is 4250 rads

Figure 14 shows partial enlarged drawing of pressuredistributions along the stationary engine case of Rampressorinlet (as shown in Figure 13(a) point A and point B) Periodicoscillation phenomenon of the inlet pressure distribution isobtained under Rampressor rotor whirl

The curves of flow performance parameters of Rampres-sor inlet in a whirling motion cycle are shown in Figure 15when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads Figure 15 indicates that the variations oftotal-pressure recovery coefficient pressure ratio and kineticenergy efficiency for Rampressor inlet are also periodic in awhirling motion cycle

421 Results and Discussion in Different Frequencies of Ram-pressor Rotor Whirl Pressure pulsation spectrograms of key

point D (shown in Figure 6) are respectively obtained indifferent whirling frequencies such as Ω = 2125 rads4250 rads and 8500 rads (shown in Figure 16) when rotorwhirl amplitude is 100 120583m

Figure 17 shows the spectrograms of airflow excitingforce on Rampressor rotor rim surface when rotor whirlingamplitude equals 100120583m and rotor whirl frequencies are2125 rads 4250 rads and 8500 rads respectively

Figure 16 indicates that the excitation characteristic ofpoint D is rather complex As shown in the frequencyspectrum besides the fundamental frequency componentthe higher order frequency component is also generatedwhere the amplitude of the fundamental frequency compo-nent is the highest The amplitude of the double frequencycomponent is smaller than that of the fundamental frequencybut greater than those of other frequency componentsCompared with excitation spectrum of Ω = 2125 radsthe amplitude of the double frequency component rela-tively increses when the whirl frequency (Ω) is 4250 rads

12 Shock and Vibration

0843

0844

0845

0846

0847

0848

0849

0850To

tal-p

ress

ure r

ecov

ery

coeffi

cien

t

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

(a) Total-pressure recovery coefficient

1264

1266

1268

1270

1272

1274

1276

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

2125 rads4250 rads8500 rads

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 18 Flow performance in different whirling frequencies during a whirling motion cycle

(as shown in Figure 16(b)) In Figure 16(c) more frequencycomponents appear in the excitation spectrum In additionto the fundamental frequency and double frequency compo-nent the third harmonic frequency component simultane-ously emerges when the whirl frequency (Ω) is 8500 radswhich is caused by the coupling between inlet compressionflow of Rampressor rotor and rotor whirling With theincrement of rotor whirling frequency the amplitude of thefundamental frequency component in the frequency spec-trum gradually decreases but the amplitude of the doublefrequency component increases by degrees It follows fromabove that the complexity of Rampressor inlet excitationincreases along with the increase of rotor whirling frequencyThe above results are also illustrated in the frequency

spectrum of airflow exciting force on the rotor rim surfaceof Rampressor inlet as shown in Figure 17

The curves of flow performance parameters of Rampres-sor inlet in a whirlingmotion cycle are respectively obtainedin different whirl frequencies such as Ω = 2125 rads4250 rads and 8500 rads (illustrated in Figure 18) whenrotor whirl amplitude is 100120583m Figure 18 shows that waveamplitudes of total-pressure recovery coefficient pressuriza-tion ratio and kinetic energy efficiency of Rampressor inletare not affected by rotor whirling frequency which onlyinfluences the wave frequency of inlet flow performanceparameters The wave frequency of inlet flow performanceparameters becomes higher with the increment of rotor whirlfrequency Therefore the stability of inlet performance is

Shock and Vibration 13

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

3500

4000

Frequency (Hz)

Exci

tatio

n (P

a)

20292Hz

6764Hz

13528Hz

(c) 119886 = 150 120583m

Figure 19 Calculation results of point D in different rotor whirling amplitudes

better in the practical engineering when Rampressor rotorwhirling frequency is less

422 Results and Discussion in Different Amplitudes of Ram-pressor RotorWhirl Excitation characteristics of Rampressorinlet are analyzed in different rotor whirling amplitudes suchas 119886 = 50 120583m 119886 = 100 120583m and 119886 = 150 120583m whenrotor whirling frequency Ω = 4250 rads Figure 19 showspressure pulsation spectrogramof Rampressor inlet key pointD (shown in Figure 6) in different rotor whirl amplitudes

The spectrograms of airflow exciting force onRampressorrotor rim surface are respectively obtained in different rotorwhirling amplitudes such as 119886 = 50 120583m 119886 = 100 120583m and 119886 =150 120583m (shown in Figure 20) when the rotor whirl frequencyΩ = 4250 rads

As shown in Figure 19 more frequency componentsemerge in the excitation spectrum such as the fundamentalfrequency component double frequency component andthird harmonic frequency component where the amplitude

of the fundamental frequency component is the highest Theamplitude of the double frequency component is smallerthan that of the fundamental frequency component buthigher than that of the third harmonic frequency componentCompared with point D excitation of 119886 = 50 120583m besides thefundamental frequency and double frequency componentsthe third harmonic component in excitation spectrum isalso generated when the rotor whirl amplitudes are 100 120583mand 150 120583m (as shown in Figures 19(b) and 19(c)) andthe amplitude of the double frequency component in theexcitation spectrum of inlet point D relatively increasesWiththe increment of rotor whirling amplitude the amplitude ofthe fundamental frequency component and double frequencycomponent in the excitation spectrum of inlet wall allgradually increases It follows from above that the complexityof Rampressor inlet excitation also increases along with theincrease of rotor whirling amplitude The above results arealso illustrated in the spectrumof airflow exciting force on therotor rim surface of Rampressor inlet as shown in Figure 20

14 Shock and Vibration

0 500 1000 1500 2000 25000

10

20

30

40

50

60

70

80

Frequency (Hz)

Exci

tatio

n (P

a)

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

50

100

150

200

Frequency (Hz)

Exci

tatio

n (P

a)

(c) 119886 = 150 120583m

Figure 20 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling amplitudes

Flow performance of Rampressor inlet is studied indifferent rotor whirling amplitudes such as 119886 = 50 120583m 119886 =100 120583m and 119886 = 150 120583mwhen rotor whirling frequencyΩ =4250 rads Figure 21 shows the curves of flow performanceparameters of Rampressor inlet during a whirling motioncycle in different rotor whirling amplitudes Along with theincrease of rotor whirling amplitude wave amplitudes oftotal-pressure recovery coefficient pressurization ratio andkinetic energy efficiency of Rampressor inlet enlarge and thestability of inlet performance reduces Therefore the stabilityof inlet performance is better in the practical engineeringwhen Rampressor rotor whirling amplitude is less

5 Conclusions

Based on Rampressor rotor model and inlet flow modelthe compression inlet flow field of Rampressor rotor isnumerically studied with consideration of Rampressor rotorwhirling Flow excitation characteristics and performance

of Rampressor inlet are analyzed and discussed under thedifferent frequencies and amplitudes of Rampressor rotorwhirling The following conclusions are obtained

Alongwith the increment of119875119903 the position of the normal

shock wave gradually moves forward and aerodynamic load-ing of the inlet wall also increases Appropriate enhancementof inlet back pressure is advantageous to the pressure ratiocompression efficiency and other performance indices wheninlet can start and normally work

More frequency components appear in the excitationspectrum of Rampressor inlet with considering Rampressorrotor whirling The main frequency component is the fun-damental frequency which is caused by the rotor whirlingBesides the fundamental frequency the double frequencycomponents emerge because of the coupling between inletcompression flow of Rampressor rotor and rotor whirlingespecially in the subsonic diffuser of Rampressor rotor inletThe effect of rotor whirling on the excitation of Rampressorinlet wall has a definite phase difference Inlet excitation

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Journal of

Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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International Journal of

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International Journal of

Shock and Vibration 3

12 15 19 22 25

(a) Gird size = 11636

12 15 19 22 25

(b) Gird size = 20249

12 15 19 22 25

(c) Gird size = 45439

12 15 19 22 25

(d) Gird size = 84590

Figure 5 Comparison of Mach number contour of Rampressor inlet in different grid sizes

00 02 04 06 08 10

16

24

32

40

48

56

64

Pres

sure

dist

ribut

ions

(Pa)

(S)

Grid size = 11 363

Grid size = 20 249

Grid size = 45 439

Grid size = 84 590

08

times105

Figure 6 Comparison of pressure distribution of stationary enginecase versus normalized streamwise distance in different grid sizes

The three inlets of the designed Rampressor are thesymmetric periodic layout on the rotor If Rampressor rotordoes not whirl the flows of the three inlets are of centralsymmetry so one of the three inlets can be used for numericalstudy of the flow field Beside this the rotor whirl is generallygenerated in the radial direction but the difference betweenthree-dimensional and two-dimensional models is in theaxial direction Because the rotor whirling almost has noeffect on the axial structure of three-dimensional model theaxial flow gradient of the inlet can be ignored Therefore itis accepted to use the two-dimensional model for studyingthe excitation characteristic and performance of Rampressorinlet with considering Rampressor rotor whirling

The two-dimensional simplified model of Rampressorinlet is established for numerical study of flow excitation andperformance as shown in Figure 2 It consists of ldquopreinletrdquo

A

D

CB

Figure 7 Schematic diagram of key point in Rampressor inlet

flow path compression ramp throat subsonic diffuser andstraight flow path

Solution of the compressible form of the Euler equationsfor the simulations presented herein is conducted using afinite-volume and density based scheme in the fluent simula-tion of this study So the two-dimensional simplified modeldoes not take into account the boundary layer developedupward but the centrifugal force is taken into considerationin the calculation The calculation formulation is implicitand the convection flux type is Roe averaged flux differencesplitting (Roe-FDS) Figure 3 shows boundary conditions ofRampressor rotor inletThe exact boundary conditions are asfollows

(a) Inflow boundary condition the Mach number is0348 the total pressure is 119875

119905= 108676 times 10

5 Pa thestatic pressure is 119875

0= 101325 times 10

5 Pa and the totaltemperature is 119879

119905= 306K

(b) Wall boundary condition the no-slip and adiabaticwall boundary conditions are placed on the wallsurfaces The engine case is the stationary adiabaticwall The rotor rim is also adiabatic wall and the

4 Shock and Vibration

11 15 18 22 25079 21 33 46 58

times105(Pa)

Pressure contour Mach number contour

(a) 119875119903 = 80

035 089 14 20 25079 33 59 84

times105(Pa)

Pressure contour Mach number contour

11

(b) 119875119903 = 90

013 072 13 19 25079 36 63 91 12

times105(Pa)

Pressure contour Mach number contour

(c) 119875119903 = 100

013 072 13 19 25079 36 63 91 12

times105(Pa)

Pressure contour Mach number contour

(d) 119875119903 = 106

Figure 8 Flow distribution of Rampressor inlet in different 119875119903

direction of rotation of the rim shown in Figure 3 isright to left In the present case proposed in this paperthe designed Rampressor rotor speed is 40600 rpm

(c) Subsonic outlet boundary condition the exit condi-tion is set to the pressure outlet in order to generatenormal shock waves within internal inlet flow field

3 Validation of Numerical Method

The numerical method of this paper is validated by compar-ing the numerical results of Rampressor inlet flow field of

American Ramgen Power Systems Inc [6] which is based onthe same calculation parameters such as the initial conditionsthe boundary conditions and the Rampressor rotor speedThe variation of relative centerline Mach number versusnormalized streamwise distance (S) in the numerical studyshows a good agreement with the Ramgen results (as shownin Figure 4)The numerical method proposed in this paper isfeasible to solve supersonic compressible flow of Rampressorinlet

In this paper high quality grid of two-dimensionalsimplified model of Rampressor inlet is calculated by using

Shock and Vibration 5

0 02 04 06 08 10

2

4

6

8

10

12

Normalized streamwise distance (S)

Load

(Pa)

Normal shock wave location

times105

Pr = 8

Pr = 9

Pr = 10

Pr = 106

(a) Stationary engine case

0

2

4

6

8

10

12

Load

(Pa)

Normal shock wave location

times105

0 02 04 06 08 1Normalized streamwise distance (S)

Pr = 8

Pr = 9

Pr = 10

Pr = 106

(b) Rotor rim surface

Figure 9 Pressure distribution of Rampressor inlet in different 119875119903

Rampressor under no rotor whirl

Casing

Rampressor under rotor whirl

X

Y

O

O998400

e

Flow path 3

Flow path 1

Flow path 2

Figure 10 Structure schematic diagram of inlet flow path on Rampressor rotor

the structured grid technology The computational grid den-sity of Rampressor inlet model should be examined Machnumber distributions of Rampressor inlet are computed indifferent grid sizes Comparison of Mach number contour ofRampressor inlet in different grid sizes is given in Figure 5The grid density has some influence on the flow field butthe distribution of the shock waves is essentially similarWith the increment of grid size the Mach number contoursof Rampressor inlet gradually tend to be same The Machnumber distribution of the grid size 45439 is basicallyidentical to that of the grid size 84590 Therefore flow field

distribution of Rampressor inlet can be calculated accuratelyby the computational gird sizes 45439 and 84590

Figure 6 shows comparison of pressure distribution of thestationary engine case versus normalized streamwise distancein different grid sizesThegrid density also has a few effects onthe pressure distribution along the stationary engine case butthe location of the shock waves and the pressure fluctuationare basically identical With the increment of grid size thepressure distributions of stationary engine case graduallyhave a tendency to coincide The pressure distribution of thestationary engine case in the numerical simulation of the grid

6 Shock and Vibration

0 0005 001 00151021

10215

1022

10225

1023

10235

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

1020304050607080

Frequency (Hz)

Exci

tatio

n (P

a)

times105

6764Hz

(a) Point A

0 0005 001 0015503

5035

504

5045

505

5055

506

5065

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

times105

(b) Point B

0 0005 001 0015419

4195

42

4205

421

4215

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

100200300400500600700800

Frequency (Hz)

Exci

tatio

n (P

a)

times105

13528Hz

6764Hz

(c) Point C

0 0005 001 00151143114411451146114711481149

1151151

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

times106

(d) Point D

Figure 11 Pressure pulsation time history and spectrogram on every key point of Rampressor rotor inlet

Shock and Vibration 7

0 05 1 150995

1

1005

Time (s)

Point APoint B

Point CPoint D

Non

dim

ensio

nal e

xcita

tion

(Pa)

times10minus3

Figure 12 Time history of nondimensional excitation

size 45439 shows a good agreement with that of the grid size84590 (Figure 6)

The computational model of grid size 45439 is chosenfor the latter Rampressor inlet simulation in comprehensiveconsideration with computational accuracy and computa-tional complexity The grid employed 781 nodes (maximumnumber) in the streamwise direction and 88 (maximumnumber) in the radial

4 Simulation Results and Analysis

The following parameters are defined to analyze the perfor-mances of Rampressor inlet flow path for different operatingconditions [4 7]

Static pressure ratio of flow path can be obtained asfollows

119901119904=119901outlet119901inlet (1)

where 119901outlet and 119901inlet are the static pressure of entrance andexit of flow path respectively

Total-pressure recovery coefficient of flow path

119901119877=119901lowast

outlet119901lowast

inlet (2)

where 119901lowastoutlet and 119901lowast

inlet are the total pressure of entrance andexit of flow path respectively

Pressurization ratio in flow path

119901119911=119901lowast

outlet119901inlet= 119901119877(1 +120581 minus 1

2Ma2inlet)

120581(120581minus1)

(3)

Loss coefficient in flow path

120596 =1 minus 119901119877

1 minus 119901119904(Mainlet)

(4)

where 119901119877is total-pressure recovery coefficient 119901

119904is static

pressure ratio and Mainlet is airflow Mach numberKinetic energy efficiency in flow path

120578 = 1 minus2

(120581 minus 1)Ma2inlet[(1

119901119877

)

(120581minus1)120581

minus 1] (5)

where 120581 is adiabatic exponentNondimensional total pressure distortion of flow-path

exit is defined as

Δ =119875119905MAX minus 119875119905MIN

119875119905avg

(6)

where 119875119905MAX and 119875

119905MIN are maximum total-pressure andminimum total-pressure of flow-path exit respectively and119875119905avg is average total pressure of flow-path exitIn order to study the excitation characteristic of Rampres-

sor inlet well pressure pulsation of key points in Rampressorinlet should be measured The arrangement of key points isshown in Figure 7 The points A B C and D are located inthe middle part of the compression ramp the entrance ofthe throat entrance of subsonic diffuser and the entrance ofstraight flow path respectively

41 Performance and Excitation Characteristic of Inlet underno Rotor Whirling The equation 119875

119903= 1198751198871198750is defined

where 119875119887is the exit back pressure of Rampressor inlet so

119875119903is the nondimensional back pressure Figure 8 shows the

static pressure contour and theMach number contour of two-dimensional inlet in different 119875

119903= 80 90 100 and 1060

when the design rotor speed is 40600 rpmA series of oblique shock waves is generated by the

compression ramp of inlet flow path to achieve airflowcompression and the airflow pressure after the shock waveincreases abruptly as shown in Figure 8 Several reflections ofthe oblique shock waves are produced between the stationaryengine case and the Rampressor rotor rim surface followedby a terminal normal shock The Mach number contoursshow that the airflow speed after a normal shock wavereduces to be subsonic When 119875

119903increases from 9 to 106

the position where the normal shock wave appears graduallymoves towards the inlet throat The position of the normalshock wave just locates in the throat when 119875

119903equals 1060

and Rampressor inlet reaches the critical statePressure distributions along stationary engine case and

rotor rim surface of Rampressor inlet are given in Figure 9The pressure distribution curves of the stationary engine

case and rotor rim surface are completely overlapped beforenormal shock wave in the different 119875

119903as shown in Figure 9

Therefore aerodynamic loading of inlet supersonic compres-sion section is accordant in the different 119875

119903and is not affected

by the exit condition (combustor) Figure 9 illustrates that theloading of the stationary engine case and rotor rim surfaceafter normal shock wave suddenly rises and then tends to bea certain value along inlet flow path The results indicate thatalong with the increment of 119875

119903 the position of the normal

shock wave gradually moves forward and then aerodynamicloading of the stationary engine case and rotor rim surfacealso increases

8 Shock and Vibration

00 02 04 06 08 100

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

Point A

Point B

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Stationary engine case

00 02 04 06 08 1000

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Rotor rim surface

Figure 13 Pressure distributions along stationary engine case and rotor rim surface in a whirling motion cycle

0460 0461 0462 0463 0464 0465570

575

580

585

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Point A

05313 05314 0531588

89

90

91

92

93

94

95

96

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Point B

Figure 14 Partial enlarged drawing of pressure distributions along stationary engine case

The consequences of Rampressor inlet flow performancein different pressure ratios are shown in Table 1 With theincrease of 119875

119903(back pressure) static pressure ratio 119901

119904

total-pressure recovery coefficient 119901119877 pressurization ratio

119901119911 and kinetic energy efficiency 120578 gradually enhance but

nondimensional total pressure distortion and loss coefficientdecrease by degrees and exit stability of Rampressor inletameliorates As a result appropriate enhancement of exitback pressure is advantageous to pressure ratio compressionefficiency and other performance indices when inlet can

Shock and Vibration 9

0 02 04 06 08 10843

0844

0845

0846

0847

0848

0849

0850

Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 15 Flow performance of Rampressor inlet in a whirling motion cycle

Table 1 Flow performance parameters in the different 119875119903

119901119904

119901119877

119901119911

120596 120578 Δ ()9 07649 1148 00116 09292 367310 08294 1244 00075 09512 4339106 08483 1273 00063 09572 2546

start and normally work and meanwhile beneficial toimprovement of Rampressor overall efficiency

42 Performance and Excitation Characteristic of Inlet underRotor Whirling Rampressor inlet flow may be affected byRampressor rotor whirl in the work process When the inletpressure regularly changes which is caused by rotor whirlRampressor rotor bears the inconstant pressure load and thenvibrates

Structure schematic diagram of inlet flow path underRampressor rotor whirl is illustrated in Figure 10 The dottedline represents the state of Rampressor rotor without whirl

and the solid line curve represents the state of Rampressorrotor whirl

Because the three inlets of the designed Rampressor arethe symmetric periodic layout on the rotor the flow excitationcharacteristics and flow performance of inlet flow path 1 arestudied under Rampressor rotor periodic whirl in this paperExpression of rotor periodic whirl is given as follows

119890 = 119886 sin (Ω119905 + 120593) (7)

where 119890 represents the displacement between Rampressorcenter1198741015840 under rotor whirl andRampressor center119874withoutrotor whirl 119886 is rotor whirl amplitude Ω is rotor whirlfrequency (whirl speed) and120593 is initial phase In otherwordsthe trajectory of the Rampressor rotor is assumed as a circlein different whirl frequencies and whirl amplitudes so theeffect of the damping on the rotor whirl is not taken intoconsideration in the calculation

Result of steady flow is taken as the initial result in theunsteady calculation of this paper Time step size is set to1478 times 10minus5 s in the design rotor speed The unsteady flow ofRampressor inlet under rotor whirl is studied when 119875

119903equals

10 Shock and Vibration

0 200 400 600 800 1000 12000

500

1000

1500

2000

2500

3000

3500

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

3382Hz

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764 Hz

13528 Hz

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

500

1000

1500

2000

Frequency (Hz)

Exci

tatio

n (P

a)

13528Hz

27056Hz40584Hz

(c) Ω = 8500 rads

Figure 16 Calculation results of point D in different rotor whirling frequencies

106 Flow excitation characteristics of Rampressor inlet willbe analyzed under different frequencies and amplitudes ofRampressor whirl

Pressure pulsation time history and spectrogramon everykey point of Rampressor rotor inlet are shown in Figure 11when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads (the design Rampressor rotor speed)

Figure 11 indicates that excitation spectrogram of point Alocated in inlet supersonic compression of Rampressor is rel-atively simple The main frequency component is the funda-mental frequency which is caused by the rotor whirling Thevalue of rotor whirling frequency (fundamental frequency)is 6764Hz and excitation amplitude is small Comparedwith point A more frequency components appear in thefrequency spectrogram of Rampressor inlet point B point Cand point D Not only rotor whirling frequency 6764Hz butalso its double frequency component 13528Hz is obtainedin excitation spectrogram The double frequency 13528Hzis generated due to the coupling between inlet compressionflow of Rampressor rotor and rotor whirling especially in

the subsonic diffuser of Rampressor rotor inlet The ampli-tude of the double frequency component is smaller thanthat of the fundamental frequency component As shownin the frequency spectrum the excitation amplitudes of thefundamental frequency and double frequency componentsall gradually increase along with inlet flow pathThis happensbecause the subsonic flow in Rampressor inlet is easilyaffected by the external excitation It follows from above thatthe inlet excitation becomes more complex along with inletflow path

Time history of nondimensional excitation in a pulsationcycle is given (as shown in Figure 12) on every key point ofRampressor rotor inlet when rotor whirl amplitude equals100 120583m and whirl speed (Ω) is 4250 rads Figure 12 showsthat phases of nondimensional excitation in differentmeasurepoints are greatly different Among them phase differencebetween point B located on the entrance of the inlet throatand point C located on exit of the inlet throat is close to 180degrees Thus it can be seen that rotor whirl effect on inletdifferent location excitation has a certain phase difference

Shock and Vibration 11

0 200 400 600 800 1000 12000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

Frequency (Hz)

Exci

tatio

n (P

a)

(c) Ω = 8500 rads

Figure 17 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling frequencies

Pressure distributions along stationary engine case androtor rim surface of Rampressor inlet in a whirling motioncycle are shown in Figure 13 when rotor whirl amplitudeequals 100 120583m and whirl speed (Ω) is 4250 rads

Figure 14 shows partial enlarged drawing of pressuredistributions along the stationary engine case of Rampressorinlet (as shown in Figure 13(a) point A and point B) Periodicoscillation phenomenon of the inlet pressure distribution isobtained under Rampressor rotor whirl

The curves of flow performance parameters of Rampres-sor inlet in a whirling motion cycle are shown in Figure 15when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads Figure 15 indicates that the variations oftotal-pressure recovery coefficient pressure ratio and kineticenergy efficiency for Rampressor inlet are also periodic in awhirling motion cycle

421 Results and Discussion in Different Frequencies of Ram-pressor Rotor Whirl Pressure pulsation spectrograms of key

point D (shown in Figure 6) are respectively obtained indifferent whirling frequencies such as Ω = 2125 rads4250 rads and 8500 rads (shown in Figure 16) when rotorwhirl amplitude is 100 120583m

Figure 17 shows the spectrograms of airflow excitingforce on Rampressor rotor rim surface when rotor whirlingamplitude equals 100120583m and rotor whirl frequencies are2125 rads 4250 rads and 8500 rads respectively

Figure 16 indicates that the excitation characteristic ofpoint D is rather complex As shown in the frequencyspectrum besides the fundamental frequency componentthe higher order frequency component is also generatedwhere the amplitude of the fundamental frequency compo-nent is the highest The amplitude of the double frequencycomponent is smaller than that of the fundamental frequencybut greater than those of other frequency componentsCompared with excitation spectrum of Ω = 2125 radsthe amplitude of the double frequency component rela-tively increses when the whirl frequency (Ω) is 4250 rads

12 Shock and Vibration

0843

0844

0845

0846

0847

0848

0849

0850To

tal-p

ress

ure r

ecov

ery

coeffi

cien

t

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

(a) Total-pressure recovery coefficient

1264

1266

1268

1270

1272

1274

1276

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

2125 rads4250 rads8500 rads

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 18 Flow performance in different whirling frequencies during a whirling motion cycle

(as shown in Figure 16(b)) In Figure 16(c) more frequencycomponents appear in the excitation spectrum In additionto the fundamental frequency and double frequency compo-nent the third harmonic frequency component simultane-ously emerges when the whirl frequency (Ω) is 8500 radswhich is caused by the coupling between inlet compressionflow of Rampressor rotor and rotor whirling With theincrement of rotor whirling frequency the amplitude of thefundamental frequency component in the frequency spec-trum gradually decreases but the amplitude of the doublefrequency component increases by degrees It follows fromabove that the complexity of Rampressor inlet excitationincreases along with the increase of rotor whirling frequencyThe above results are also illustrated in the frequency

spectrum of airflow exciting force on the rotor rim surfaceof Rampressor inlet as shown in Figure 17

The curves of flow performance parameters of Rampres-sor inlet in a whirlingmotion cycle are respectively obtainedin different whirl frequencies such as Ω = 2125 rads4250 rads and 8500 rads (illustrated in Figure 18) whenrotor whirl amplitude is 100120583m Figure 18 shows that waveamplitudes of total-pressure recovery coefficient pressuriza-tion ratio and kinetic energy efficiency of Rampressor inletare not affected by rotor whirling frequency which onlyinfluences the wave frequency of inlet flow performanceparameters The wave frequency of inlet flow performanceparameters becomes higher with the increment of rotor whirlfrequency Therefore the stability of inlet performance is

Shock and Vibration 13

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

3500

4000

Frequency (Hz)

Exci

tatio

n (P

a)

20292Hz

6764Hz

13528Hz

(c) 119886 = 150 120583m

Figure 19 Calculation results of point D in different rotor whirling amplitudes

better in the practical engineering when Rampressor rotorwhirling frequency is less

422 Results and Discussion in Different Amplitudes of Ram-pressor RotorWhirl Excitation characteristics of Rampressorinlet are analyzed in different rotor whirling amplitudes suchas 119886 = 50 120583m 119886 = 100 120583m and 119886 = 150 120583m whenrotor whirling frequency Ω = 4250 rads Figure 19 showspressure pulsation spectrogramof Rampressor inlet key pointD (shown in Figure 6) in different rotor whirl amplitudes

The spectrograms of airflow exciting force onRampressorrotor rim surface are respectively obtained in different rotorwhirling amplitudes such as 119886 = 50 120583m 119886 = 100 120583m and 119886 =150 120583m (shown in Figure 20) when the rotor whirl frequencyΩ = 4250 rads

As shown in Figure 19 more frequency componentsemerge in the excitation spectrum such as the fundamentalfrequency component double frequency component andthird harmonic frequency component where the amplitude

of the fundamental frequency component is the highest Theamplitude of the double frequency component is smallerthan that of the fundamental frequency component buthigher than that of the third harmonic frequency componentCompared with point D excitation of 119886 = 50 120583m besides thefundamental frequency and double frequency componentsthe third harmonic component in excitation spectrum isalso generated when the rotor whirl amplitudes are 100 120583mand 150 120583m (as shown in Figures 19(b) and 19(c)) andthe amplitude of the double frequency component in theexcitation spectrum of inlet point D relatively increasesWiththe increment of rotor whirling amplitude the amplitude ofthe fundamental frequency component and double frequencycomponent in the excitation spectrum of inlet wall allgradually increases It follows from above that the complexityof Rampressor inlet excitation also increases along with theincrease of rotor whirling amplitude The above results arealso illustrated in the spectrumof airflow exciting force on therotor rim surface of Rampressor inlet as shown in Figure 20

14 Shock and Vibration

0 500 1000 1500 2000 25000

10

20

30

40

50

60

70

80

Frequency (Hz)

Exci

tatio

n (P

a)

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

50

100

150

200

Frequency (Hz)

Exci

tatio

n (P

a)

(c) 119886 = 150 120583m

Figure 20 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling amplitudes

Flow performance of Rampressor inlet is studied indifferent rotor whirling amplitudes such as 119886 = 50 120583m 119886 =100 120583m and 119886 = 150 120583mwhen rotor whirling frequencyΩ =4250 rads Figure 21 shows the curves of flow performanceparameters of Rampressor inlet during a whirling motioncycle in different rotor whirling amplitudes Along with theincrease of rotor whirling amplitude wave amplitudes oftotal-pressure recovery coefficient pressurization ratio andkinetic energy efficiency of Rampressor inlet enlarge and thestability of inlet performance reduces Therefore the stabilityof inlet performance is better in the practical engineeringwhen Rampressor rotor whirling amplitude is less

5 Conclusions

Based on Rampressor rotor model and inlet flow modelthe compression inlet flow field of Rampressor rotor isnumerically studied with consideration of Rampressor rotorwhirling Flow excitation characteristics and performance

of Rampressor inlet are analyzed and discussed under thedifferent frequencies and amplitudes of Rampressor rotorwhirling The following conclusions are obtained

Alongwith the increment of119875119903 the position of the normal

shock wave gradually moves forward and aerodynamic load-ing of the inlet wall also increases Appropriate enhancementof inlet back pressure is advantageous to the pressure ratiocompression efficiency and other performance indices wheninlet can start and normally work

More frequency components appear in the excitationspectrum of Rampressor inlet with considering Rampressorrotor whirling The main frequency component is the fun-damental frequency which is caused by the rotor whirlingBesides the fundamental frequency the double frequencycomponents emerge because of the coupling between inletcompression flow of Rampressor rotor and rotor whirlingespecially in the subsonic diffuser of Rampressor rotor inletThe effect of rotor whirling on the excitation of Rampressorinlet wall has a definite phase difference Inlet excitation

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

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4 Shock and Vibration

11 15 18 22 25079 21 33 46 58

times105(Pa)

Pressure contour Mach number contour

(a) 119875119903 = 80

035 089 14 20 25079 33 59 84

times105(Pa)

Pressure contour Mach number contour

11

(b) 119875119903 = 90

013 072 13 19 25079 36 63 91 12

times105(Pa)

Pressure contour Mach number contour

(c) 119875119903 = 100

013 072 13 19 25079 36 63 91 12

times105(Pa)

Pressure contour Mach number contour

(d) 119875119903 = 106

Figure 8 Flow distribution of Rampressor inlet in different 119875119903

direction of rotation of the rim shown in Figure 3 isright to left In the present case proposed in this paperthe designed Rampressor rotor speed is 40600 rpm

(c) Subsonic outlet boundary condition the exit condi-tion is set to the pressure outlet in order to generatenormal shock waves within internal inlet flow field

3 Validation of Numerical Method

The numerical method of this paper is validated by compar-ing the numerical results of Rampressor inlet flow field of

American Ramgen Power Systems Inc [6] which is based onthe same calculation parameters such as the initial conditionsthe boundary conditions and the Rampressor rotor speedThe variation of relative centerline Mach number versusnormalized streamwise distance (S) in the numerical studyshows a good agreement with the Ramgen results (as shownin Figure 4)The numerical method proposed in this paper isfeasible to solve supersonic compressible flow of Rampressorinlet

In this paper high quality grid of two-dimensionalsimplified model of Rampressor inlet is calculated by using

Shock and Vibration 5

0 02 04 06 08 10

2

4

6

8

10

12

Normalized streamwise distance (S)

Load

(Pa)

Normal shock wave location

times105

Pr = 8

Pr = 9

Pr = 10

Pr = 106

(a) Stationary engine case

0

2

4

6

8

10

12

Load

(Pa)

Normal shock wave location

times105

0 02 04 06 08 1Normalized streamwise distance (S)

Pr = 8

Pr = 9

Pr = 10

Pr = 106

(b) Rotor rim surface

Figure 9 Pressure distribution of Rampressor inlet in different 119875119903

Rampressor under no rotor whirl

Casing

Rampressor under rotor whirl

X

Y

O

O998400

e

Flow path 3

Flow path 1

Flow path 2

Figure 10 Structure schematic diagram of inlet flow path on Rampressor rotor

the structured grid technology The computational grid den-sity of Rampressor inlet model should be examined Machnumber distributions of Rampressor inlet are computed indifferent grid sizes Comparison of Mach number contour ofRampressor inlet in different grid sizes is given in Figure 5The grid density has some influence on the flow field butthe distribution of the shock waves is essentially similarWith the increment of grid size the Mach number contoursof Rampressor inlet gradually tend to be same The Machnumber distribution of the grid size 45439 is basicallyidentical to that of the grid size 84590 Therefore flow field

distribution of Rampressor inlet can be calculated accuratelyby the computational gird sizes 45439 and 84590

Figure 6 shows comparison of pressure distribution of thestationary engine case versus normalized streamwise distancein different grid sizesThegrid density also has a few effects onthe pressure distribution along the stationary engine case butthe location of the shock waves and the pressure fluctuationare basically identical With the increment of grid size thepressure distributions of stationary engine case graduallyhave a tendency to coincide The pressure distribution of thestationary engine case in the numerical simulation of the grid

6 Shock and Vibration

0 0005 001 00151021

10215

1022

10225

1023

10235

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

1020304050607080

Frequency (Hz)

Exci

tatio

n (P

a)

times105

6764Hz

(a) Point A

0 0005 001 0015503

5035

504

5045

505

5055

506

5065

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

times105

(b) Point B

0 0005 001 0015419

4195

42

4205

421

4215

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

100200300400500600700800

Frequency (Hz)

Exci

tatio

n (P

a)

times105

13528Hz

6764Hz

(c) Point C

0 0005 001 00151143114411451146114711481149

1151151

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

times106

(d) Point D

Figure 11 Pressure pulsation time history and spectrogram on every key point of Rampressor rotor inlet

Shock and Vibration 7

0 05 1 150995

1

1005

Time (s)

Point APoint B

Point CPoint D

Non

dim

ensio

nal e

xcita

tion

(Pa)

times10minus3

Figure 12 Time history of nondimensional excitation

size 45439 shows a good agreement with that of the grid size84590 (Figure 6)

The computational model of grid size 45439 is chosenfor the latter Rampressor inlet simulation in comprehensiveconsideration with computational accuracy and computa-tional complexity The grid employed 781 nodes (maximumnumber) in the streamwise direction and 88 (maximumnumber) in the radial

4 Simulation Results and Analysis

The following parameters are defined to analyze the perfor-mances of Rampressor inlet flow path for different operatingconditions [4 7]

Static pressure ratio of flow path can be obtained asfollows

119901119904=119901outlet119901inlet (1)

where 119901outlet and 119901inlet are the static pressure of entrance andexit of flow path respectively

Total-pressure recovery coefficient of flow path

119901119877=119901lowast

outlet119901lowast

inlet (2)

where 119901lowastoutlet and 119901lowast

inlet are the total pressure of entrance andexit of flow path respectively

Pressurization ratio in flow path

119901119911=119901lowast

outlet119901inlet= 119901119877(1 +120581 minus 1

2Ma2inlet)

120581(120581minus1)

(3)

Loss coefficient in flow path

120596 =1 minus 119901119877

1 minus 119901119904(Mainlet)

(4)

where 119901119877is total-pressure recovery coefficient 119901

119904is static

pressure ratio and Mainlet is airflow Mach numberKinetic energy efficiency in flow path

120578 = 1 minus2

(120581 minus 1)Ma2inlet[(1

119901119877

)

(120581minus1)120581

minus 1] (5)

where 120581 is adiabatic exponentNondimensional total pressure distortion of flow-path

exit is defined as

Δ =119875119905MAX minus 119875119905MIN

119875119905avg

(6)

where 119875119905MAX and 119875

119905MIN are maximum total-pressure andminimum total-pressure of flow-path exit respectively and119875119905avg is average total pressure of flow-path exitIn order to study the excitation characteristic of Rampres-

sor inlet well pressure pulsation of key points in Rampressorinlet should be measured The arrangement of key points isshown in Figure 7 The points A B C and D are located inthe middle part of the compression ramp the entrance ofthe throat entrance of subsonic diffuser and the entrance ofstraight flow path respectively

41 Performance and Excitation Characteristic of Inlet underno Rotor Whirling The equation 119875

119903= 1198751198871198750is defined

where 119875119887is the exit back pressure of Rampressor inlet so

119875119903is the nondimensional back pressure Figure 8 shows the

static pressure contour and theMach number contour of two-dimensional inlet in different 119875

119903= 80 90 100 and 1060

when the design rotor speed is 40600 rpmA series of oblique shock waves is generated by the

compression ramp of inlet flow path to achieve airflowcompression and the airflow pressure after the shock waveincreases abruptly as shown in Figure 8 Several reflections ofthe oblique shock waves are produced between the stationaryengine case and the Rampressor rotor rim surface followedby a terminal normal shock The Mach number contoursshow that the airflow speed after a normal shock wavereduces to be subsonic When 119875

119903increases from 9 to 106

the position where the normal shock wave appears graduallymoves towards the inlet throat The position of the normalshock wave just locates in the throat when 119875

119903equals 1060

and Rampressor inlet reaches the critical statePressure distributions along stationary engine case and

rotor rim surface of Rampressor inlet are given in Figure 9The pressure distribution curves of the stationary engine

case and rotor rim surface are completely overlapped beforenormal shock wave in the different 119875

119903as shown in Figure 9

Therefore aerodynamic loading of inlet supersonic compres-sion section is accordant in the different 119875

119903and is not affected

by the exit condition (combustor) Figure 9 illustrates that theloading of the stationary engine case and rotor rim surfaceafter normal shock wave suddenly rises and then tends to bea certain value along inlet flow path The results indicate thatalong with the increment of 119875

119903 the position of the normal

shock wave gradually moves forward and then aerodynamicloading of the stationary engine case and rotor rim surfacealso increases

8 Shock and Vibration

00 02 04 06 08 100

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

Point A

Point B

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Stationary engine case

00 02 04 06 08 1000

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Rotor rim surface

Figure 13 Pressure distributions along stationary engine case and rotor rim surface in a whirling motion cycle

0460 0461 0462 0463 0464 0465570

575

580

585

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Point A

05313 05314 0531588

89

90

91

92

93

94

95

96

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Point B

Figure 14 Partial enlarged drawing of pressure distributions along stationary engine case

The consequences of Rampressor inlet flow performancein different pressure ratios are shown in Table 1 With theincrease of 119875

119903(back pressure) static pressure ratio 119901

119904

total-pressure recovery coefficient 119901119877 pressurization ratio

119901119911 and kinetic energy efficiency 120578 gradually enhance but

nondimensional total pressure distortion and loss coefficientdecrease by degrees and exit stability of Rampressor inletameliorates As a result appropriate enhancement of exitback pressure is advantageous to pressure ratio compressionefficiency and other performance indices when inlet can

Shock and Vibration 9

0 02 04 06 08 10843

0844

0845

0846

0847

0848

0849

0850

Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 15 Flow performance of Rampressor inlet in a whirling motion cycle

Table 1 Flow performance parameters in the different 119875119903

119901119904

119901119877

119901119911

120596 120578 Δ ()9 07649 1148 00116 09292 367310 08294 1244 00075 09512 4339106 08483 1273 00063 09572 2546

start and normally work and meanwhile beneficial toimprovement of Rampressor overall efficiency

42 Performance and Excitation Characteristic of Inlet underRotor Whirling Rampressor inlet flow may be affected byRampressor rotor whirl in the work process When the inletpressure regularly changes which is caused by rotor whirlRampressor rotor bears the inconstant pressure load and thenvibrates

Structure schematic diagram of inlet flow path underRampressor rotor whirl is illustrated in Figure 10 The dottedline represents the state of Rampressor rotor without whirl

and the solid line curve represents the state of Rampressorrotor whirl

Because the three inlets of the designed Rampressor arethe symmetric periodic layout on the rotor the flow excitationcharacteristics and flow performance of inlet flow path 1 arestudied under Rampressor rotor periodic whirl in this paperExpression of rotor periodic whirl is given as follows

119890 = 119886 sin (Ω119905 + 120593) (7)

where 119890 represents the displacement between Rampressorcenter1198741015840 under rotor whirl andRampressor center119874withoutrotor whirl 119886 is rotor whirl amplitude Ω is rotor whirlfrequency (whirl speed) and120593 is initial phase In otherwordsthe trajectory of the Rampressor rotor is assumed as a circlein different whirl frequencies and whirl amplitudes so theeffect of the damping on the rotor whirl is not taken intoconsideration in the calculation

Result of steady flow is taken as the initial result in theunsteady calculation of this paper Time step size is set to1478 times 10minus5 s in the design rotor speed The unsteady flow ofRampressor inlet under rotor whirl is studied when 119875

119903equals

10 Shock and Vibration

0 200 400 600 800 1000 12000

500

1000

1500

2000

2500

3000

3500

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

3382Hz

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764 Hz

13528 Hz

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

500

1000

1500

2000

Frequency (Hz)

Exci

tatio

n (P

a)

13528Hz

27056Hz40584Hz

(c) Ω = 8500 rads

Figure 16 Calculation results of point D in different rotor whirling frequencies

106 Flow excitation characteristics of Rampressor inlet willbe analyzed under different frequencies and amplitudes ofRampressor whirl

Pressure pulsation time history and spectrogramon everykey point of Rampressor rotor inlet are shown in Figure 11when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads (the design Rampressor rotor speed)

Figure 11 indicates that excitation spectrogram of point Alocated in inlet supersonic compression of Rampressor is rel-atively simple The main frequency component is the funda-mental frequency which is caused by the rotor whirling Thevalue of rotor whirling frequency (fundamental frequency)is 6764Hz and excitation amplitude is small Comparedwith point A more frequency components appear in thefrequency spectrogram of Rampressor inlet point B point Cand point D Not only rotor whirling frequency 6764Hz butalso its double frequency component 13528Hz is obtainedin excitation spectrogram The double frequency 13528Hzis generated due to the coupling between inlet compressionflow of Rampressor rotor and rotor whirling especially in

the subsonic diffuser of Rampressor rotor inlet The ampli-tude of the double frequency component is smaller thanthat of the fundamental frequency component As shownin the frequency spectrum the excitation amplitudes of thefundamental frequency and double frequency componentsall gradually increase along with inlet flow pathThis happensbecause the subsonic flow in Rampressor inlet is easilyaffected by the external excitation It follows from above thatthe inlet excitation becomes more complex along with inletflow path

Time history of nondimensional excitation in a pulsationcycle is given (as shown in Figure 12) on every key point ofRampressor rotor inlet when rotor whirl amplitude equals100 120583m and whirl speed (Ω) is 4250 rads Figure 12 showsthat phases of nondimensional excitation in differentmeasurepoints are greatly different Among them phase differencebetween point B located on the entrance of the inlet throatand point C located on exit of the inlet throat is close to 180degrees Thus it can be seen that rotor whirl effect on inletdifferent location excitation has a certain phase difference

Shock and Vibration 11

0 200 400 600 800 1000 12000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

Frequency (Hz)

Exci

tatio

n (P

a)

(c) Ω = 8500 rads

Figure 17 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling frequencies

Pressure distributions along stationary engine case androtor rim surface of Rampressor inlet in a whirling motioncycle are shown in Figure 13 when rotor whirl amplitudeequals 100 120583m and whirl speed (Ω) is 4250 rads

Figure 14 shows partial enlarged drawing of pressuredistributions along the stationary engine case of Rampressorinlet (as shown in Figure 13(a) point A and point B) Periodicoscillation phenomenon of the inlet pressure distribution isobtained under Rampressor rotor whirl

The curves of flow performance parameters of Rampres-sor inlet in a whirling motion cycle are shown in Figure 15when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads Figure 15 indicates that the variations oftotal-pressure recovery coefficient pressure ratio and kineticenergy efficiency for Rampressor inlet are also periodic in awhirling motion cycle

421 Results and Discussion in Different Frequencies of Ram-pressor Rotor Whirl Pressure pulsation spectrograms of key

point D (shown in Figure 6) are respectively obtained indifferent whirling frequencies such as Ω = 2125 rads4250 rads and 8500 rads (shown in Figure 16) when rotorwhirl amplitude is 100 120583m

Figure 17 shows the spectrograms of airflow excitingforce on Rampressor rotor rim surface when rotor whirlingamplitude equals 100120583m and rotor whirl frequencies are2125 rads 4250 rads and 8500 rads respectively

Figure 16 indicates that the excitation characteristic ofpoint D is rather complex As shown in the frequencyspectrum besides the fundamental frequency componentthe higher order frequency component is also generatedwhere the amplitude of the fundamental frequency compo-nent is the highest The amplitude of the double frequencycomponent is smaller than that of the fundamental frequencybut greater than those of other frequency componentsCompared with excitation spectrum of Ω = 2125 radsthe amplitude of the double frequency component rela-tively increses when the whirl frequency (Ω) is 4250 rads

12 Shock and Vibration

0843

0844

0845

0846

0847

0848

0849

0850To

tal-p

ress

ure r

ecov

ery

coeffi

cien

t

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

(a) Total-pressure recovery coefficient

1264

1266

1268

1270

1272

1274

1276

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

2125 rads4250 rads8500 rads

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 18 Flow performance in different whirling frequencies during a whirling motion cycle

(as shown in Figure 16(b)) In Figure 16(c) more frequencycomponents appear in the excitation spectrum In additionto the fundamental frequency and double frequency compo-nent the third harmonic frequency component simultane-ously emerges when the whirl frequency (Ω) is 8500 radswhich is caused by the coupling between inlet compressionflow of Rampressor rotor and rotor whirling With theincrement of rotor whirling frequency the amplitude of thefundamental frequency component in the frequency spec-trum gradually decreases but the amplitude of the doublefrequency component increases by degrees It follows fromabove that the complexity of Rampressor inlet excitationincreases along with the increase of rotor whirling frequencyThe above results are also illustrated in the frequency

spectrum of airflow exciting force on the rotor rim surfaceof Rampressor inlet as shown in Figure 17

The curves of flow performance parameters of Rampres-sor inlet in a whirlingmotion cycle are respectively obtainedin different whirl frequencies such as Ω = 2125 rads4250 rads and 8500 rads (illustrated in Figure 18) whenrotor whirl amplitude is 100120583m Figure 18 shows that waveamplitudes of total-pressure recovery coefficient pressuriza-tion ratio and kinetic energy efficiency of Rampressor inletare not affected by rotor whirling frequency which onlyinfluences the wave frequency of inlet flow performanceparameters The wave frequency of inlet flow performanceparameters becomes higher with the increment of rotor whirlfrequency Therefore the stability of inlet performance is

Shock and Vibration 13

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

3500

4000

Frequency (Hz)

Exci

tatio

n (P

a)

20292Hz

6764Hz

13528Hz

(c) 119886 = 150 120583m

Figure 19 Calculation results of point D in different rotor whirling amplitudes

better in the practical engineering when Rampressor rotorwhirling frequency is less

422 Results and Discussion in Different Amplitudes of Ram-pressor RotorWhirl Excitation characteristics of Rampressorinlet are analyzed in different rotor whirling amplitudes suchas 119886 = 50 120583m 119886 = 100 120583m and 119886 = 150 120583m whenrotor whirling frequency Ω = 4250 rads Figure 19 showspressure pulsation spectrogramof Rampressor inlet key pointD (shown in Figure 6) in different rotor whirl amplitudes

The spectrograms of airflow exciting force onRampressorrotor rim surface are respectively obtained in different rotorwhirling amplitudes such as 119886 = 50 120583m 119886 = 100 120583m and 119886 =150 120583m (shown in Figure 20) when the rotor whirl frequencyΩ = 4250 rads

As shown in Figure 19 more frequency componentsemerge in the excitation spectrum such as the fundamentalfrequency component double frequency component andthird harmonic frequency component where the amplitude

of the fundamental frequency component is the highest Theamplitude of the double frequency component is smallerthan that of the fundamental frequency component buthigher than that of the third harmonic frequency componentCompared with point D excitation of 119886 = 50 120583m besides thefundamental frequency and double frequency componentsthe third harmonic component in excitation spectrum isalso generated when the rotor whirl amplitudes are 100 120583mand 150 120583m (as shown in Figures 19(b) and 19(c)) andthe amplitude of the double frequency component in theexcitation spectrum of inlet point D relatively increasesWiththe increment of rotor whirling amplitude the amplitude ofthe fundamental frequency component and double frequencycomponent in the excitation spectrum of inlet wall allgradually increases It follows from above that the complexityof Rampressor inlet excitation also increases along with theincrease of rotor whirling amplitude The above results arealso illustrated in the spectrumof airflow exciting force on therotor rim surface of Rampressor inlet as shown in Figure 20

14 Shock and Vibration

0 500 1000 1500 2000 25000

10

20

30

40

50

60

70

80

Frequency (Hz)

Exci

tatio

n (P

a)

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

50

100

150

200

Frequency (Hz)

Exci

tatio

n (P

a)

(c) 119886 = 150 120583m

Figure 20 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling amplitudes

Flow performance of Rampressor inlet is studied indifferent rotor whirling amplitudes such as 119886 = 50 120583m 119886 =100 120583m and 119886 = 150 120583mwhen rotor whirling frequencyΩ =4250 rads Figure 21 shows the curves of flow performanceparameters of Rampressor inlet during a whirling motioncycle in different rotor whirling amplitudes Along with theincrease of rotor whirling amplitude wave amplitudes oftotal-pressure recovery coefficient pressurization ratio andkinetic energy efficiency of Rampressor inlet enlarge and thestability of inlet performance reduces Therefore the stabilityof inlet performance is better in the practical engineeringwhen Rampressor rotor whirling amplitude is less

5 Conclusions

Based on Rampressor rotor model and inlet flow modelthe compression inlet flow field of Rampressor rotor isnumerically studied with consideration of Rampressor rotorwhirling Flow excitation characteristics and performance

of Rampressor inlet are analyzed and discussed under thedifferent frequencies and amplitudes of Rampressor rotorwhirling The following conclusions are obtained

Alongwith the increment of119875119903 the position of the normal

shock wave gradually moves forward and aerodynamic load-ing of the inlet wall also increases Appropriate enhancementof inlet back pressure is advantageous to the pressure ratiocompression efficiency and other performance indices wheninlet can start and normally work

More frequency components appear in the excitationspectrum of Rampressor inlet with considering Rampressorrotor whirling The main frequency component is the fun-damental frequency which is caused by the rotor whirlingBesides the fundamental frequency the double frequencycomponents emerge because of the coupling between inletcompression flow of Rampressor rotor and rotor whirlingespecially in the subsonic diffuser of Rampressor rotor inletThe effect of rotor whirling on the excitation of Rampressorinlet wall has a definite phase difference Inlet excitation

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

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Shock and Vibration 5

0 02 04 06 08 10

2

4

6

8

10

12

Normalized streamwise distance (S)

Load

(Pa)

Normal shock wave location

times105

Pr = 8

Pr = 9

Pr = 10

Pr = 106

(a) Stationary engine case

0

2

4

6

8

10

12

Load

(Pa)

Normal shock wave location

times105

0 02 04 06 08 1Normalized streamwise distance (S)

Pr = 8

Pr = 9

Pr = 10

Pr = 106

(b) Rotor rim surface

Figure 9 Pressure distribution of Rampressor inlet in different 119875119903

Rampressor under no rotor whirl

Casing

Rampressor under rotor whirl

X

Y

O

O998400

e

Flow path 3

Flow path 1

Flow path 2

Figure 10 Structure schematic diagram of inlet flow path on Rampressor rotor

the structured grid technology The computational grid den-sity of Rampressor inlet model should be examined Machnumber distributions of Rampressor inlet are computed indifferent grid sizes Comparison of Mach number contour ofRampressor inlet in different grid sizes is given in Figure 5The grid density has some influence on the flow field butthe distribution of the shock waves is essentially similarWith the increment of grid size the Mach number contoursof Rampressor inlet gradually tend to be same The Machnumber distribution of the grid size 45439 is basicallyidentical to that of the grid size 84590 Therefore flow field

distribution of Rampressor inlet can be calculated accuratelyby the computational gird sizes 45439 and 84590

Figure 6 shows comparison of pressure distribution of thestationary engine case versus normalized streamwise distancein different grid sizesThegrid density also has a few effects onthe pressure distribution along the stationary engine case butthe location of the shock waves and the pressure fluctuationare basically identical With the increment of grid size thepressure distributions of stationary engine case graduallyhave a tendency to coincide The pressure distribution of thestationary engine case in the numerical simulation of the grid

6 Shock and Vibration

0 0005 001 00151021

10215

1022

10225

1023

10235

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

1020304050607080

Frequency (Hz)

Exci

tatio

n (P

a)

times105

6764Hz

(a) Point A

0 0005 001 0015503

5035

504

5045

505

5055

506

5065

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

times105

(b) Point B

0 0005 001 0015419

4195

42

4205

421

4215

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

100200300400500600700800

Frequency (Hz)

Exci

tatio

n (P

a)

times105

13528Hz

6764Hz

(c) Point C

0 0005 001 00151143114411451146114711481149

1151151

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

times106

(d) Point D

Figure 11 Pressure pulsation time history and spectrogram on every key point of Rampressor rotor inlet

Shock and Vibration 7

0 05 1 150995

1

1005

Time (s)

Point APoint B

Point CPoint D

Non

dim

ensio

nal e

xcita

tion

(Pa)

times10minus3

Figure 12 Time history of nondimensional excitation

size 45439 shows a good agreement with that of the grid size84590 (Figure 6)

The computational model of grid size 45439 is chosenfor the latter Rampressor inlet simulation in comprehensiveconsideration with computational accuracy and computa-tional complexity The grid employed 781 nodes (maximumnumber) in the streamwise direction and 88 (maximumnumber) in the radial

4 Simulation Results and Analysis

The following parameters are defined to analyze the perfor-mances of Rampressor inlet flow path for different operatingconditions [4 7]

Static pressure ratio of flow path can be obtained asfollows

119901119904=119901outlet119901inlet (1)

where 119901outlet and 119901inlet are the static pressure of entrance andexit of flow path respectively

Total-pressure recovery coefficient of flow path

119901119877=119901lowast

outlet119901lowast

inlet (2)

where 119901lowastoutlet and 119901lowast

inlet are the total pressure of entrance andexit of flow path respectively

Pressurization ratio in flow path

119901119911=119901lowast

outlet119901inlet= 119901119877(1 +120581 minus 1

2Ma2inlet)

120581(120581minus1)

(3)

Loss coefficient in flow path

120596 =1 minus 119901119877

1 minus 119901119904(Mainlet)

(4)

where 119901119877is total-pressure recovery coefficient 119901

119904is static

pressure ratio and Mainlet is airflow Mach numberKinetic energy efficiency in flow path

120578 = 1 minus2

(120581 minus 1)Ma2inlet[(1

119901119877

)

(120581minus1)120581

minus 1] (5)

where 120581 is adiabatic exponentNondimensional total pressure distortion of flow-path

exit is defined as

Δ =119875119905MAX minus 119875119905MIN

119875119905avg

(6)

where 119875119905MAX and 119875

119905MIN are maximum total-pressure andminimum total-pressure of flow-path exit respectively and119875119905avg is average total pressure of flow-path exitIn order to study the excitation characteristic of Rampres-

sor inlet well pressure pulsation of key points in Rampressorinlet should be measured The arrangement of key points isshown in Figure 7 The points A B C and D are located inthe middle part of the compression ramp the entrance ofthe throat entrance of subsonic diffuser and the entrance ofstraight flow path respectively

41 Performance and Excitation Characteristic of Inlet underno Rotor Whirling The equation 119875

119903= 1198751198871198750is defined

where 119875119887is the exit back pressure of Rampressor inlet so

119875119903is the nondimensional back pressure Figure 8 shows the

static pressure contour and theMach number contour of two-dimensional inlet in different 119875

119903= 80 90 100 and 1060

when the design rotor speed is 40600 rpmA series of oblique shock waves is generated by the

compression ramp of inlet flow path to achieve airflowcompression and the airflow pressure after the shock waveincreases abruptly as shown in Figure 8 Several reflections ofthe oblique shock waves are produced between the stationaryengine case and the Rampressor rotor rim surface followedby a terminal normal shock The Mach number contoursshow that the airflow speed after a normal shock wavereduces to be subsonic When 119875

119903increases from 9 to 106

the position where the normal shock wave appears graduallymoves towards the inlet throat The position of the normalshock wave just locates in the throat when 119875

119903equals 1060

and Rampressor inlet reaches the critical statePressure distributions along stationary engine case and

rotor rim surface of Rampressor inlet are given in Figure 9The pressure distribution curves of the stationary engine

case and rotor rim surface are completely overlapped beforenormal shock wave in the different 119875

119903as shown in Figure 9

Therefore aerodynamic loading of inlet supersonic compres-sion section is accordant in the different 119875

119903and is not affected

by the exit condition (combustor) Figure 9 illustrates that theloading of the stationary engine case and rotor rim surfaceafter normal shock wave suddenly rises and then tends to bea certain value along inlet flow path The results indicate thatalong with the increment of 119875

119903 the position of the normal

shock wave gradually moves forward and then aerodynamicloading of the stationary engine case and rotor rim surfacealso increases

8 Shock and Vibration

00 02 04 06 08 100

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

Point A

Point B

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Stationary engine case

00 02 04 06 08 1000

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Rotor rim surface

Figure 13 Pressure distributions along stationary engine case and rotor rim surface in a whirling motion cycle

0460 0461 0462 0463 0464 0465570

575

580

585

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Point A

05313 05314 0531588

89

90

91

92

93

94

95

96

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Point B

Figure 14 Partial enlarged drawing of pressure distributions along stationary engine case

The consequences of Rampressor inlet flow performancein different pressure ratios are shown in Table 1 With theincrease of 119875

119903(back pressure) static pressure ratio 119901

119904

total-pressure recovery coefficient 119901119877 pressurization ratio

119901119911 and kinetic energy efficiency 120578 gradually enhance but

nondimensional total pressure distortion and loss coefficientdecrease by degrees and exit stability of Rampressor inletameliorates As a result appropriate enhancement of exitback pressure is advantageous to pressure ratio compressionefficiency and other performance indices when inlet can

Shock and Vibration 9

0 02 04 06 08 10843

0844

0845

0846

0847

0848

0849

0850

Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 15 Flow performance of Rampressor inlet in a whirling motion cycle

Table 1 Flow performance parameters in the different 119875119903

119901119904

119901119877

119901119911

120596 120578 Δ ()9 07649 1148 00116 09292 367310 08294 1244 00075 09512 4339106 08483 1273 00063 09572 2546

start and normally work and meanwhile beneficial toimprovement of Rampressor overall efficiency

42 Performance and Excitation Characteristic of Inlet underRotor Whirling Rampressor inlet flow may be affected byRampressor rotor whirl in the work process When the inletpressure regularly changes which is caused by rotor whirlRampressor rotor bears the inconstant pressure load and thenvibrates

Structure schematic diagram of inlet flow path underRampressor rotor whirl is illustrated in Figure 10 The dottedline represents the state of Rampressor rotor without whirl

and the solid line curve represents the state of Rampressorrotor whirl

Because the three inlets of the designed Rampressor arethe symmetric periodic layout on the rotor the flow excitationcharacteristics and flow performance of inlet flow path 1 arestudied under Rampressor rotor periodic whirl in this paperExpression of rotor periodic whirl is given as follows

119890 = 119886 sin (Ω119905 + 120593) (7)

where 119890 represents the displacement between Rampressorcenter1198741015840 under rotor whirl andRampressor center119874withoutrotor whirl 119886 is rotor whirl amplitude Ω is rotor whirlfrequency (whirl speed) and120593 is initial phase In otherwordsthe trajectory of the Rampressor rotor is assumed as a circlein different whirl frequencies and whirl amplitudes so theeffect of the damping on the rotor whirl is not taken intoconsideration in the calculation

Result of steady flow is taken as the initial result in theunsteady calculation of this paper Time step size is set to1478 times 10minus5 s in the design rotor speed The unsteady flow ofRampressor inlet under rotor whirl is studied when 119875

119903equals

10 Shock and Vibration

0 200 400 600 800 1000 12000

500

1000

1500

2000

2500

3000

3500

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

3382Hz

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764 Hz

13528 Hz

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

500

1000

1500

2000

Frequency (Hz)

Exci

tatio

n (P

a)

13528Hz

27056Hz40584Hz

(c) Ω = 8500 rads

Figure 16 Calculation results of point D in different rotor whirling frequencies

106 Flow excitation characteristics of Rampressor inlet willbe analyzed under different frequencies and amplitudes ofRampressor whirl

Pressure pulsation time history and spectrogramon everykey point of Rampressor rotor inlet are shown in Figure 11when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads (the design Rampressor rotor speed)

Figure 11 indicates that excitation spectrogram of point Alocated in inlet supersonic compression of Rampressor is rel-atively simple The main frequency component is the funda-mental frequency which is caused by the rotor whirling Thevalue of rotor whirling frequency (fundamental frequency)is 6764Hz and excitation amplitude is small Comparedwith point A more frequency components appear in thefrequency spectrogram of Rampressor inlet point B point Cand point D Not only rotor whirling frequency 6764Hz butalso its double frequency component 13528Hz is obtainedin excitation spectrogram The double frequency 13528Hzis generated due to the coupling between inlet compressionflow of Rampressor rotor and rotor whirling especially in

the subsonic diffuser of Rampressor rotor inlet The ampli-tude of the double frequency component is smaller thanthat of the fundamental frequency component As shownin the frequency spectrum the excitation amplitudes of thefundamental frequency and double frequency componentsall gradually increase along with inlet flow pathThis happensbecause the subsonic flow in Rampressor inlet is easilyaffected by the external excitation It follows from above thatthe inlet excitation becomes more complex along with inletflow path

Time history of nondimensional excitation in a pulsationcycle is given (as shown in Figure 12) on every key point ofRampressor rotor inlet when rotor whirl amplitude equals100 120583m and whirl speed (Ω) is 4250 rads Figure 12 showsthat phases of nondimensional excitation in differentmeasurepoints are greatly different Among them phase differencebetween point B located on the entrance of the inlet throatand point C located on exit of the inlet throat is close to 180degrees Thus it can be seen that rotor whirl effect on inletdifferent location excitation has a certain phase difference

Shock and Vibration 11

0 200 400 600 800 1000 12000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

Frequency (Hz)

Exci

tatio

n (P

a)

(c) Ω = 8500 rads

Figure 17 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling frequencies

Pressure distributions along stationary engine case androtor rim surface of Rampressor inlet in a whirling motioncycle are shown in Figure 13 when rotor whirl amplitudeequals 100 120583m and whirl speed (Ω) is 4250 rads

Figure 14 shows partial enlarged drawing of pressuredistributions along the stationary engine case of Rampressorinlet (as shown in Figure 13(a) point A and point B) Periodicoscillation phenomenon of the inlet pressure distribution isobtained under Rampressor rotor whirl

The curves of flow performance parameters of Rampres-sor inlet in a whirling motion cycle are shown in Figure 15when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads Figure 15 indicates that the variations oftotal-pressure recovery coefficient pressure ratio and kineticenergy efficiency for Rampressor inlet are also periodic in awhirling motion cycle

421 Results and Discussion in Different Frequencies of Ram-pressor Rotor Whirl Pressure pulsation spectrograms of key

point D (shown in Figure 6) are respectively obtained indifferent whirling frequencies such as Ω = 2125 rads4250 rads and 8500 rads (shown in Figure 16) when rotorwhirl amplitude is 100 120583m

Figure 17 shows the spectrograms of airflow excitingforce on Rampressor rotor rim surface when rotor whirlingamplitude equals 100120583m and rotor whirl frequencies are2125 rads 4250 rads and 8500 rads respectively

Figure 16 indicates that the excitation characteristic ofpoint D is rather complex As shown in the frequencyspectrum besides the fundamental frequency componentthe higher order frequency component is also generatedwhere the amplitude of the fundamental frequency compo-nent is the highest The amplitude of the double frequencycomponent is smaller than that of the fundamental frequencybut greater than those of other frequency componentsCompared with excitation spectrum of Ω = 2125 radsthe amplitude of the double frequency component rela-tively increses when the whirl frequency (Ω) is 4250 rads

12 Shock and Vibration

0843

0844

0845

0846

0847

0848

0849

0850To

tal-p

ress

ure r

ecov

ery

coeffi

cien

t

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

(a) Total-pressure recovery coefficient

1264

1266

1268

1270

1272

1274

1276

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

2125 rads4250 rads8500 rads

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 18 Flow performance in different whirling frequencies during a whirling motion cycle

(as shown in Figure 16(b)) In Figure 16(c) more frequencycomponents appear in the excitation spectrum In additionto the fundamental frequency and double frequency compo-nent the third harmonic frequency component simultane-ously emerges when the whirl frequency (Ω) is 8500 radswhich is caused by the coupling between inlet compressionflow of Rampressor rotor and rotor whirling With theincrement of rotor whirling frequency the amplitude of thefundamental frequency component in the frequency spec-trum gradually decreases but the amplitude of the doublefrequency component increases by degrees It follows fromabove that the complexity of Rampressor inlet excitationincreases along with the increase of rotor whirling frequencyThe above results are also illustrated in the frequency

spectrum of airflow exciting force on the rotor rim surfaceof Rampressor inlet as shown in Figure 17

The curves of flow performance parameters of Rampres-sor inlet in a whirlingmotion cycle are respectively obtainedin different whirl frequencies such as Ω = 2125 rads4250 rads and 8500 rads (illustrated in Figure 18) whenrotor whirl amplitude is 100120583m Figure 18 shows that waveamplitudes of total-pressure recovery coefficient pressuriza-tion ratio and kinetic energy efficiency of Rampressor inletare not affected by rotor whirling frequency which onlyinfluences the wave frequency of inlet flow performanceparameters The wave frequency of inlet flow performanceparameters becomes higher with the increment of rotor whirlfrequency Therefore the stability of inlet performance is

Shock and Vibration 13

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

3500

4000

Frequency (Hz)

Exci

tatio

n (P

a)

20292Hz

6764Hz

13528Hz

(c) 119886 = 150 120583m

Figure 19 Calculation results of point D in different rotor whirling amplitudes

better in the practical engineering when Rampressor rotorwhirling frequency is less

422 Results and Discussion in Different Amplitudes of Ram-pressor RotorWhirl Excitation characteristics of Rampressorinlet are analyzed in different rotor whirling amplitudes suchas 119886 = 50 120583m 119886 = 100 120583m and 119886 = 150 120583m whenrotor whirling frequency Ω = 4250 rads Figure 19 showspressure pulsation spectrogramof Rampressor inlet key pointD (shown in Figure 6) in different rotor whirl amplitudes

The spectrograms of airflow exciting force onRampressorrotor rim surface are respectively obtained in different rotorwhirling amplitudes such as 119886 = 50 120583m 119886 = 100 120583m and 119886 =150 120583m (shown in Figure 20) when the rotor whirl frequencyΩ = 4250 rads

As shown in Figure 19 more frequency componentsemerge in the excitation spectrum such as the fundamentalfrequency component double frequency component andthird harmonic frequency component where the amplitude

of the fundamental frequency component is the highest Theamplitude of the double frequency component is smallerthan that of the fundamental frequency component buthigher than that of the third harmonic frequency componentCompared with point D excitation of 119886 = 50 120583m besides thefundamental frequency and double frequency componentsthe third harmonic component in excitation spectrum isalso generated when the rotor whirl amplitudes are 100 120583mand 150 120583m (as shown in Figures 19(b) and 19(c)) andthe amplitude of the double frequency component in theexcitation spectrum of inlet point D relatively increasesWiththe increment of rotor whirling amplitude the amplitude ofthe fundamental frequency component and double frequencycomponent in the excitation spectrum of inlet wall allgradually increases It follows from above that the complexityof Rampressor inlet excitation also increases along with theincrease of rotor whirling amplitude The above results arealso illustrated in the spectrumof airflow exciting force on therotor rim surface of Rampressor inlet as shown in Figure 20

14 Shock and Vibration

0 500 1000 1500 2000 25000

10

20

30

40

50

60

70

80

Frequency (Hz)

Exci

tatio

n (P

a)

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

50

100

150

200

Frequency (Hz)

Exci

tatio

n (P

a)

(c) 119886 = 150 120583m

Figure 20 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling amplitudes

Flow performance of Rampressor inlet is studied indifferent rotor whirling amplitudes such as 119886 = 50 120583m 119886 =100 120583m and 119886 = 150 120583mwhen rotor whirling frequencyΩ =4250 rads Figure 21 shows the curves of flow performanceparameters of Rampressor inlet during a whirling motioncycle in different rotor whirling amplitudes Along with theincrease of rotor whirling amplitude wave amplitudes oftotal-pressure recovery coefficient pressurization ratio andkinetic energy efficiency of Rampressor inlet enlarge and thestability of inlet performance reduces Therefore the stabilityof inlet performance is better in the practical engineeringwhen Rampressor rotor whirling amplitude is less

5 Conclusions

Based on Rampressor rotor model and inlet flow modelthe compression inlet flow field of Rampressor rotor isnumerically studied with consideration of Rampressor rotorwhirling Flow excitation characteristics and performance

of Rampressor inlet are analyzed and discussed under thedifferent frequencies and amplitudes of Rampressor rotorwhirling The following conclusions are obtained

Alongwith the increment of119875119903 the position of the normal

shock wave gradually moves forward and aerodynamic load-ing of the inlet wall also increases Appropriate enhancementof inlet back pressure is advantageous to the pressure ratiocompression efficiency and other performance indices wheninlet can start and normally work

More frequency components appear in the excitationspectrum of Rampressor inlet with considering Rampressorrotor whirling The main frequency component is the fun-damental frequency which is caused by the rotor whirlingBesides the fundamental frequency the double frequencycomponents emerge because of the coupling between inletcompression flow of Rampressor rotor and rotor whirlingespecially in the subsonic diffuser of Rampressor rotor inletThe effect of rotor whirling on the excitation of Rampressorinlet wall has a definite phase difference Inlet excitation

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

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6 Shock and Vibration

0 0005 001 00151021

10215

1022

10225

1023

10235

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

1020304050607080

Frequency (Hz)

Exci

tatio

n (P

a)

times105

6764Hz

(a) Point A

0 0005 001 0015503

5035

504

5045

505

5055

506

5065

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

times105

(b) Point B

0 0005 001 0015419

4195

42

4205

421

4215

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

100200300400500600700800

Frequency (Hz)

Exci

tatio

n (P

a)

times105

13528Hz

6764Hz

(c) Point C

0 0005 001 00151143114411451146114711481149

1151151

Time (s)

Exci

tatio

n (P

a)

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

times106

(d) Point D

Figure 11 Pressure pulsation time history and spectrogram on every key point of Rampressor rotor inlet

Shock and Vibration 7

0 05 1 150995

1

1005

Time (s)

Point APoint B

Point CPoint D

Non

dim

ensio

nal e

xcita

tion

(Pa)

times10minus3

Figure 12 Time history of nondimensional excitation

size 45439 shows a good agreement with that of the grid size84590 (Figure 6)

The computational model of grid size 45439 is chosenfor the latter Rampressor inlet simulation in comprehensiveconsideration with computational accuracy and computa-tional complexity The grid employed 781 nodes (maximumnumber) in the streamwise direction and 88 (maximumnumber) in the radial

4 Simulation Results and Analysis

The following parameters are defined to analyze the perfor-mances of Rampressor inlet flow path for different operatingconditions [4 7]

Static pressure ratio of flow path can be obtained asfollows

119901119904=119901outlet119901inlet (1)

where 119901outlet and 119901inlet are the static pressure of entrance andexit of flow path respectively

Total-pressure recovery coefficient of flow path

119901119877=119901lowast

outlet119901lowast

inlet (2)

where 119901lowastoutlet and 119901lowast

inlet are the total pressure of entrance andexit of flow path respectively

Pressurization ratio in flow path

119901119911=119901lowast

outlet119901inlet= 119901119877(1 +120581 minus 1

2Ma2inlet)

120581(120581minus1)

(3)

Loss coefficient in flow path

120596 =1 minus 119901119877

1 minus 119901119904(Mainlet)

(4)

where 119901119877is total-pressure recovery coefficient 119901

119904is static

pressure ratio and Mainlet is airflow Mach numberKinetic energy efficiency in flow path

120578 = 1 minus2

(120581 minus 1)Ma2inlet[(1

119901119877

)

(120581minus1)120581

minus 1] (5)

where 120581 is adiabatic exponentNondimensional total pressure distortion of flow-path

exit is defined as

Δ =119875119905MAX minus 119875119905MIN

119875119905avg

(6)

where 119875119905MAX and 119875

119905MIN are maximum total-pressure andminimum total-pressure of flow-path exit respectively and119875119905avg is average total pressure of flow-path exitIn order to study the excitation characteristic of Rampres-

sor inlet well pressure pulsation of key points in Rampressorinlet should be measured The arrangement of key points isshown in Figure 7 The points A B C and D are located inthe middle part of the compression ramp the entrance ofthe throat entrance of subsonic diffuser and the entrance ofstraight flow path respectively

41 Performance and Excitation Characteristic of Inlet underno Rotor Whirling The equation 119875

119903= 1198751198871198750is defined

where 119875119887is the exit back pressure of Rampressor inlet so

119875119903is the nondimensional back pressure Figure 8 shows the

static pressure contour and theMach number contour of two-dimensional inlet in different 119875

119903= 80 90 100 and 1060

when the design rotor speed is 40600 rpmA series of oblique shock waves is generated by the

compression ramp of inlet flow path to achieve airflowcompression and the airflow pressure after the shock waveincreases abruptly as shown in Figure 8 Several reflections ofthe oblique shock waves are produced between the stationaryengine case and the Rampressor rotor rim surface followedby a terminal normal shock The Mach number contoursshow that the airflow speed after a normal shock wavereduces to be subsonic When 119875

119903increases from 9 to 106

the position where the normal shock wave appears graduallymoves towards the inlet throat The position of the normalshock wave just locates in the throat when 119875

119903equals 1060

and Rampressor inlet reaches the critical statePressure distributions along stationary engine case and

rotor rim surface of Rampressor inlet are given in Figure 9The pressure distribution curves of the stationary engine

case and rotor rim surface are completely overlapped beforenormal shock wave in the different 119875

119903as shown in Figure 9

Therefore aerodynamic loading of inlet supersonic compres-sion section is accordant in the different 119875

119903and is not affected

by the exit condition (combustor) Figure 9 illustrates that theloading of the stationary engine case and rotor rim surfaceafter normal shock wave suddenly rises and then tends to bea certain value along inlet flow path The results indicate thatalong with the increment of 119875

119903 the position of the normal

shock wave gradually moves forward and then aerodynamicloading of the stationary engine case and rotor rim surfacealso increases

8 Shock and Vibration

00 02 04 06 08 100

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

Point A

Point B

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Stationary engine case

00 02 04 06 08 1000

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Rotor rim surface

Figure 13 Pressure distributions along stationary engine case and rotor rim surface in a whirling motion cycle

0460 0461 0462 0463 0464 0465570

575

580

585

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Point A

05313 05314 0531588

89

90

91

92

93

94

95

96

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Point B

Figure 14 Partial enlarged drawing of pressure distributions along stationary engine case

The consequences of Rampressor inlet flow performancein different pressure ratios are shown in Table 1 With theincrease of 119875

119903(back pressure) static pressure ratio 119901

119904

total-pressure recovery coefficient 119901119877 pressurization ratio

119901119911 and kinetic energy efficiency 120578 gradually enhance but

nondimensional total pressure distortion and loss coefficientdecrease by degrees and exit stability of Rampressor inletameliorates As a result appropriate enhancement of exitback pressure is advantageous to pressure ratio compressionefficiency and other performance indices when inlet can

Shock and Vibration 9

0 02 04 06 08 10843

0844

0845

0846

0847

0848

0849

0850

Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 15 Flow performance of Rampressor inlet in a whirling motion cycle

Table 1 Flow performance parameters in the different 119875119903

119901119904

119901119877

119901119911

120596 120578 Δ ()9 07649 1148 00116 09292 367310 08294 1244 00075 09512 4339106 08483 1273 00063 09572 2546

start and normally work and meanwhile beneficial toimprovement of Rampressor overall efficiency

42 Performance and Excitation Characteristic of Inlet underRotor Whirling Rampressor inlet flow may be affected byRampressor rotor whirl in the work process When the inletpressure regularly changes which is caused by rotor whirlRampressor rotor bears the inconstant pressure load and thenvibrates

Structure schematic diagram of inlet flow path underRampressor rotor whirl is illustrated in Figure 10 The dottedline represents the state of Rampressor rotor without whirl

and the solid line curve represents the state of Rampressorrotor whirl

Because the three inlets of the designed Rampressor arethe symmetric periodic layout on the rotor the flow excitationcharacteristics and flow performance of inlet flow path 1 arestudied under Rampressor rotor periodic whirl in this paperExpression of rotor periodic whirl is given as follows

119890 = 119886 sin (Ω119905 + 120593) (7)

where 119890 represents the displacement between Rampressorcenter1198741015840 under rotor whirl andRampressor center119874withoutrotor whirl 119886 is rotor whirl amplitude Ω is rotor whirlfrequency (whirl speed) and120593 is initial phase In otherwordsthe trajectory of the Rampressor rotor is assumed as a circlein different whirl frequencies and whirl amplitudes so theeffect of the damping on the rotor whirl is not taken intoconsideration in the calculation

Result of steady flow is taken as the initial result in theunsteady calculation of this paper Time step size is set to1478 times 10minus5 s in the design rotor speed The unsteady flow ofRampressor inlet under rotor whirl is studied when 119875

119903equals

10 Shock and Vibration

0 200 400 600 800 1000 12000

500

1000

1500

2000

2500

3000

3500

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

3382Hz

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764 Hz

13528 Hz

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

500

1000

1500

2000

Frequency (Hz)

Exci

tatio

n (P

a)

13528Hz

27056Hz40584Hz

(c) Ω = 8500 rads

Figure 16 Calculation results of point D in different rotor whirling frequencies

106 Flow excitation characteristics of Rampressor inlet willbe analyzed under different frequencies and amplitudes ofRampressor whirl

Pressure pulsation time history and spectrogramon everykey point of Rampressor rotor inlet are shown in Figure 11when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads (the design Rampressor rotor speed)

Figure 11 indicates that excitation spectrogram of point Alocated in inlet supersonic compression of Rampressor is rel-atively simple The main frequency component is the funda-mental frequency which is caused by the rotor whirling Thevalue of rotor whirling frequency (fundamental frequency)is 6764Hz and excitation amplitude is small Comparedwith point A more frequency components appear in thefrequency spectrogram of Rampressor inlet point B point Cand point D Not only rotor whirling frequency 6764Hz butalso its double frequency component 13528Hz is obtainedin excitation spectrogram The double frequency 13528Hzis generated due to the coupling between inlet compressionflow of Rampressor rotor and rotor whirling especially in

the subsonic diffuser of Rampressor rotor inlet The ampli-tude of the double frequency component is smaller thanthat of the fundamental frequency component As shownin the frequency spectrum the excitation amplitudes of thefundamental frequency and double frequency componentsall gradually increase along with inlet flow pathThis happensbecause the subsonic flow in Rampressor inlet is easilyaffected by the external excitation It follows from above thatthe inlet excitation becomes more complex along with inletflow path

Time history of nondimensional excitation in a pulsationcycle is given (as shown in Figure 12) on every key point ofRampressor rotor inlet when rotor whirl amplitude equals100 120583m and whirl speed (Ω) is 4250 rads Figure 12 showsthat phases of nondimensional excitation in differentmeasurepoints are greatly different Among them phase differencebetween point B located on the entrance of the inlet throatand point C located on exit of the inlet throat is close to 180degrees Thus it can be seen that rotor whirl effect on inletdifferent location excitation has a certain phase difference

Shock and Vibration 11

0 200 400 600 800 1000 12000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

Frequency (Hz)

Exci

tatio

n (P

a)

(c) Ω = 8500 rads

Figure 17 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling frequencies

Pressure distributions along stationary engine case androtor rim surface of Rampressor inlet in a whirling motioncycle are shown in Figure 13 when rotor whirl amplitudeequals 100 120583m and whirl speed (Ω) is 4250 rads

Figure 14 shows partial enlarged drawing of pressuredistributions along the stationary engine case of Rampressorinlet (as shown in Figure 13(a) point A and point B) Periodicoscillation phenomenon of the inlet pressure distribution isobtained under Rampressor rotor whirl

The curves of flow performance parameters of Rampres-sor inlet in a whirling motion cycle are shown in Figure 15when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads Figure 15 indicates that the variations oftotal-pressure recovery coefficient pressure ratio and kineticenergy efficiency for Rampressor inlet are also periodic in awhirling motion cycle

421 Results and Discussion in Different Frequencies of Ram-pressor Rotor Whirl Pressure pulsation spectrograms of key

point D (shown in Figure 6) are respectively obtained indifferent whirling frequencies such as Ω = 2125 rads4250 rads and 8500 rads (shown in Figure 16) when rotorwhirl amplitude is 100 120583m

Figure 17 shows the spectrograms of airflow excitingforce on Rampressor rotor rim surface when rotor whirlingamplitude equals 100120583m and rotor whirl frequencies are2125 rads 4250 rads and 8500 rads respectively

Figure 16 indicates that the excitation characteristic ofpoint D is rather complex As shown in the frequencyspectrum besides the fundamental frequency componentthe higher order frequency component is also generatedwhere the amplitude of the fundamental frequency compo-nent is the highest The amplitude of the double frequencycomponent is smaller than that of the fundamental frequencybut greater than those of other frequency componentsCompared with excitation spectrum of Ω = 2125 radsthe amplitude of the double frequency component rela-tively increses when the whirl frequency (Ω) is 4250 rads

12 Shock and Vibration

0843

0844

0845

0846

0847

0848

0849

0850To

tal-p

ress

ure r

ecov

ery

coeffi

cien

t

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

(a) Total-pressure recovery coefficient

1264

1266

1268

1270

1272

1274

1276

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

2125 rads4250 rads8500 rads

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 18 Flow performance in different whirling frequencies during a whirling motion cycle

(as shown in Figure 16(b)) In Figure 16(c) more frequencycomponents appear in the excitation spectrum In additionto the fundamental frequency and double frequency compo-nent the third harmonic frequency component simultane-ously emerges when the whirl frequency (Ω) is 8500 radswhich is caused by the coupling between inlet compressionflow of Rampressor rotor and rotor whirling With theincrement of rotor whirling frequency the amplitude of thefundamental frequency component in the frequency spec-trum gradually decreases but the amplitude of the doublefrequency component increases by degrees It follows fromabove that the complexity of Rampressor inlet excitationincreases along with the increase of rotor whirling frequencyThe above results are also illustrated in the frequency

spectrum of airflow exciting force on the rotor rim surfaceof Rampressor inlet as shown in Figure 17

The curves of flow performance parameters of Rampres-sor inlet in a whirlingmotion cycle are respectively obtainedin different whirl frequencies such as Ω = 2125 rads4250 rads and 8500 rads (illustrated in Figure 18) whenrotor whirl amplitude is 100120583m Figure 18 shows that waveamplitudes of total-pressure recovery coefficient pressuriza-tion ratio and kinetic energy efficiency of Rampressor inletare not affected by rotor whirling frequency which onlyinfluences the wave frequency of inlet flow performanceparameters The wave frequency of inlet flow performanceparameters becomes higher with the increment of rotor whirlfrequency Therefore the stability of inlet performance is

Shock and Vibration 13

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

3500

4000

Frequency (Hz)

Exci

tatio

n (P

a)

20292Hz

6764Hz

13528Hz

(c) 119886 = 150 120583m

Figure 19 Calculation results of point D in different rotor whirling amplitudes

better in the practical engineering when Rampressor rotorwhirling frequency is less

422 Results and Discussion in Different Amplitudes of Ram-pressor RotorWhirl Excitation characteristics of Rampressorinlet are analyzed in different rotor whirling amplitudes suchas 119886 = 50 120583m 119886 = 100 120583m and 119886 = 150 120583m whenrotor whirling frequency Ω = 4250 rads Figure 19 showspressure pulsation spectrogramof Rampressor inlet key pointD (shown in Figure 6) in different rotor whirl amplitudes

The spectrograms of airflow exciting force onRampressorrotor rim surface are respectively obtained in different rotorwhirling amplitudes such as 119886 = 50 120583m 119886 = 100 120583m and 119886 =150 120583m (shown in Figure 20) when the rotor whirl frequencyΩ = 4250 rads

As shown in Figure 19 more frequency componentsemerge in the excitation spectrum such as the fundamentalfrequency component double frequency component andthird harmonic frequency component where the amplitude

of the fundamental frequency component is the highest Theamplitude of the double frequency component is smallerthan that of the fundamental frequency component buthigher than that of the third harmonic frequency componentCompared with point D excitation of 119886 = 50 120583m besides thefundamental frequency and double frequency componentsthe third harmonic component in excitation spectrum isalso generated when the rotor whirl amplitudes are 100 120583mand 150 120583m (as shown in Figures 19(b) and 19(c)) andthe amplitude of the double frequency component in theexcitation spectrum of inlet point D relatively increasesWiththe increment of rotor whirling amplitude the amplitude ofthe fundamental frequency component and double frequencycomponent in the excitation spectrum of inlet wall allgradually increases It follows from above that the complexityof Rampressor inlet excitation also increases along with theincrease of rotor whirling amplitude The above results arealso illustrated in the spectrumof airflow exciting force on therotor rim surface of Rampressor inlet as shown in Figure 20

14 Shock and Vibration

0 500 1000 1500 2000 25000

10

20

30

40

50

60

70

80

Frequency (Hz)

Exci

tatio

n (P

a)

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

50

100

150

200

Frequency (Hz)

Exci

tatio

n (P

a)

(c) 119886 = 150 120583m

Figure 20 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling amplitudes

Flow performance of Rampressor inlet is studied indifferent rotor whirling amplitudes such as 119886 = 50 120583m 119886 =100 120583m and 119886 = 150 120583mwhen rotor whirling frequencyΩ =4250 rads Figure 21 shows the curves of flow performanceparameters of Rampressor inlet during a whirling motioncycle in different rotor whirling amplitudes Along with theincrease of rotor whirling amplitude wave amplitudes oftotal-pressure recovery coefficient pressurization ratio andkinetic energy efficiency of Rampressor inlet enlarge and thestability of inlet performance reduces Therefore the stabilityof inlet performance is better in the practical engineeringwhen Rampressor rotor whirling amplitude is less

5 Conclusions

Based on Rampressor rotor model and inlet flow modelthe compression inlet flow field of Rampressor rotor isnumerically studied with consideration of Rampressor rotorwhirling Flow excitation characteristics and performance

of Rampressor inlet are analyzed and discussed under thedifferent frequencies and amplitudes of Rampressor rotorwhirling The following conclusions are obtained

Alongwith the increment of119875119903 the position of the normal

shock wave gradually moves forward and aerodynamic load-ing of the inlet wall also increases Appropriate enhancementof inlet back pressure is advantageous to the pressure ratiocompression efficiency and other performance indices wheninlet can start and normally work

More frequency components appear in the excitationspectrum of Rampressor inlet with considering Rampressorrotor whirling The main frequency component is the fun-damental frequency which is caused by the rotor whirlingBesides the fundamental frequency the double frequencycomponents emerge because of the coupling between inletcompression flow of Rampressor rotor and rotor whirlingespecially in the subsonic diffuser of Rampressor rotor inletThe effect of rotor whirling on the excitation of Rampressorinlet wall has a definite phase difference Inlet excitation

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

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Shock and Vibration 7

0 05 1 150995

1

1005

Time (s)

Point APoint B

Point CPoint D

Non

dim

ensio

nal e

xcita

tion

(Pa)

times10minus3

Figure 12 Time history of nondimensional excitation

size 45439 shows a good agreement with that of the grid size84590 (Figure 6)

The computational model of grid size 45439 is chosenfor the latter Rampressor inlet simulation in comprehensiveconsideration with computational accuracy and computa-tional complexity The grid employed 781 nodes (maximumnumber) in the streamwise direction and 88 (maximumnumber) in the radial

4 Simulation Results and Analysis

The following parameters are defined to analyze the perfor-mances of Rampressor inlet flow path for different operatingconditions [4 7]

Static pressure ratio of flow path can be obtained asfollows

119901119904=119901outlet119901inlet (1)

where 119901outlet and 119901inlet are the static pressure of entrance andexit of flow path respectively

Total-pressure recovery coefficient of flow path

119901119877=119901lowast

outlet119901lowast

inlet (2)

where 119901lowastoutlet and 119901lowast

inlet are the total pressure of entrance andexit of flow path respectively

Pressurization ratio in flow path

119901119911=119901lowast

outlet119901inlet= 119901119877(1 +120581 minus 1

2Ma2inlet)

120581(120581minus1)

(3)

Loss coefficient in flow path

120596 =1 minus 119901119877

1 minus 119901119904(Mainlet)

(4)

where 119901119877is total-pressure recovery coefficient 119901

119904is static

pressure ratio and Mainlet is airflow Mach numberKinetic energy efficiency in flow path

120578 = 1 minus2

(120581 minus 1)Ma2inlet[(1

119901119877

)

(120581minus1)120581

minus 1] (5)

where 120581 is adiabatic exponentNondimensional total pressure distortion of flow-path

exit is defined as

Δ =119875119905MAX minus 119875119905MIN

119875119905avg

(6)

where 119875119905MAX and 119875

119905MIN are maximum total-pressure andminimum total-pressure of flow-path exit respectively and119875119905avg is average total pressure of flow-path exitIn order to study the excitation characteristic of Rampres-

sor inlet well pressure pulsation of key points in Rampressorinlet should be measured The arrangement of key points isshown in Figure 7 The points A B C and D are located inthe middle part of the compression ramp the entrance ofthe throat entrance of subsonic diffuser and the entrance ofstraight flow path respectively

41 Performance and Excitation Characteristic of Inlet underno Rotor Whirling The equation 119875

119903= 1198751198871198750is defined

where 119875119887is the exit back pressure of Rampressor inlet so

119875119903is the nondimensional back pressure Figure 8 shows the

static pressure contour and theMach number contour of two-dimensional inlet in different 119875

119903= 80 90 100 and 1060

when the design rotor speed is 40600 rpmA series of oblique shock waves is generated by the

compression ramp of inlet flow path to achieve airflowcompression and the airflow pressure after the shock waveincreases abruptly as shown in Figure 8 Several reflections ofthe oblique shock waves are produced between the stationaryengine case and the Rampressor rotor rim surface followedby a terminal normal shock The Mach number contoursshow that the airflow speed after a normal shock wavereduces to be subsonic When 119875

119903increases from 9 to 106

the position where the normal shock wave appears graduallymoves towards the inlet throat The position of the normalshock wave just locates in the throat when 119875

119903equals 1060

and Rampressor inlet reaches the critical statePressure distributions along stationary engine case and

rotor rim surface of Rampressor inlet are given in Figure 9The pressure distribution curves of the stationary engine

case and rotor rim surface are completely overlapped beforenormal shock wave in the different 119875

119903as shown in Figure 9

Therefore aerodynamic loading of inlet supersonic compres-sion section is accordant in the different 119875

119903and is not affected

by the exit condition (combustor) Figure 9 illustrates that theloading of the stationary engine case and rotor rim surfaceafter normal shock wave suddenly rises and then tends to bea certain value along inlet flow path The results indicate thatalong with the increment of 119875

119903 the position of the normal

shock wave gradually moves forward and then aerodynamicloading of the stationary engine case and rotor rim surfacealso increases

8 Shock and Vibration

00 02 04 06 08 100

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

Point A

Point B

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Stationary engine case

00 02 04 06 08 1000

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Rotor rim surface

Figure 13 Pressure distributions along stationary engine case and rotor rim surface in a whirling motion cycle

0460 0461 0462 0463 0464 0465570

575

580

585

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Point A

05313 05314 0531588

89

90

91

92

93

94

95

96

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Point B

Figure 14 Partial enlarged drawing of pressure distributions along stationary engine case

The consequences of Rampressor inlet flow performancein different pressure ratios are shown in Table 1 With theincrease of 119875

119903(back pressure) static pressure ratio 119901

119904

total-pressure recovery coefficient 119901119877 pressurization ratio

119901119911 and kinetic energy efficiency 120578 gradually enhance but

nondimensional total pressure distortion and loss coefficientdecrease by degrees and exit stability of Rampressor inletameliorates As a result appropriate enhancement of exitback pressure is advantageous to pressure ratio compressionefficiency and other performance indices when inlet can

Shock and Vibration 9

0 02 04 06 08 10843

0844

0845

0846

0847

0848

0849

0850

Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 15 Flow performance of Rampressor inlet in a whirling motion cycle

Table 1 Flow performance parameters in the different 119875119903

119901119904

119901119877

119901119911

120596 120578 Δ ()9 07649 1148 00116 09292 367310 08294 1244 00075 09512 4339106 08483 1273 00063 09572 2546

start and normally work and meanwhile beneficial toimprovement of Rampressor overall efficiency

42 Performance and Excitation Characteristic of Inlet underRotor Whirling Rampressor inlet flow may be affected byRampressor rotor whirl in the work process When the inletpressure regularly changes which is caused by rotor whirlRampressor rotor bears the inconstant pressure load and thenvibrates

Structure schematic diagram of inlet flow path underRampressor rotor whirl is illustrated in Figure 10 The dottedline represents the state of Rampressor rotor without whirl

and the solid line curve represents the state of Rampressorrotor whirl

Because the three inlets of the designed Rampressor arethe symmetric periodic layout on the rotor the flow excitationcharacteristics and flow performance of inlet flow path 1 arestudied under Rampressor rotor periodic whirl in this paperExpression of rotor periodic whirl is given as follows

119890 = 119886 sin (Ω119905 + 120593) (7)

where 119890 represents the displacement between Rampressorcenter1198741015840 under rotor whirl andRampressor center119874withoutrotor whirl 119886 is rotor whirl amplitude Ω is rotor whirlfrequency (whirl speed) and120593 is initial phase In otherwordsthe trajectory of the Rampressor rotor is assumed as a circlein different whirl frequencies and whirl amplitudes so theeffect of the damping on the rotor whirl is not taken intoconsideration in the calculation

Result of steady flow is taken as the initial result in theunsteady calculation of this paper Time step size is set to1478 times 10minus5 s in the design rotor speed The unsteady flow ofRampressor inlet under rotor whirl is studied when 119875

119903equals

10 Shock and Vibration

0 200 400 600 800 1000 12000

500

1000

1500

2000

2500

3000

3500

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

3382Hz

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764 Hz

13528 Hz

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

500

1000

1500

2000

Frequency (Hz)

Exci

tatio

n (P

a)

13528Hz

27056Hz40584Hz

(c) Ω = 8500 rads

Figure 16 Calculation results of point D in different rotor whirling frequencies

106 Flow excitation characteristics of Rampressor inlet willbe analyzed under different frequencies and amplitudes ofRampressor whirl

Pressure pulsation time history and spectrogramon everykey point of Rampressor rotor inlet are shown in Figure 11when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads (the design Rampressor rotor speed)

Figure 11 indicates that excitation spectrogram of point Alocated in inlet supersonic compression of Rampressor is rel-atively simple The main frequency component is the funda-mental frequency which is caused by the rotor whirling Thevalue of rotor whirling frequency (fundamental frequency)is 6764Hz and excitation amplitude is small Comparedwith point A more frequency components appear in thefrequency spectrogram of Rampressor inlet point B point Cand point D Not only rotor whirling frequency 6764Hz butalso its double frequency component 13528Hz is obtainedin excitation spectrogram The double frequency 13528Hzis generated due to the coupling between inlet compressionflow of Rampressor rotor and rotor whirling especially in

the subsonic diffuser of Rampressor rotor inlet The ampli-tude of the double frequency component is smaller thanthat of the fundamental frequency component As shownin the frequency spectrum the excitation amplitudes of thefundamental frequency and double frequency componentsall gradually increase along with inlet flow pathThis happensbecause the subsonic flow in Rampressor inlet is easilyaffected by the external excitation It follows from above thatthe inlet excitation becomes more complex along with inletflow path

Time history of nondimensional excitation in a pulsationcycle is given (as shown in Figure 12) on every key point ofRampressor rotor inlet when rotor whirl amplitude equals100 120583m and whirl speed (Ω) is 4250 rads Figure 12 showsthat phases of nondimensional excitation in differentmeasurepoints are greatly different Among them phase differencebetween point B located on the entrance of the inlet throatand point C located on exit of the inlet throat is close to 180degrees Thus it can be seen that rotor whirl effect on inletdifferent location excitation has a certain phase difference

Shock and Vibration 11

0 200 400 600 800 1000 12000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

Frequency (Hz)

Exci

tatio

n (P

a)

(c) Ω = 8500 rads

Figure 17 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling frequencies

Pressure distributions along stationary engine case androtor rim surface of Rampressor inlet in a whirling motioncycle are shown in Figure 13 when rotor whirl amplitudeequals 100 120583m and whirl speed (Ω) is 4250 rads

Figure 14 shows partial enlarged drawing of pressuredistributions along the stationary engine case of Rampressorinlet (as shown in Figure 13(a) point A and point B) Periodicoscillation phenomenon of the inlet pressure distribution isobtained under Rampressor rotor whirl

The curves of flow performance parameters of Rampres-sor inlet in a whirling motion cycle are shown in Figure 15when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads Figure 15 indicates that the variations oftotal-pressure recovery coefficient pressure ratio and kineticenergy efficiency for Rampressor inlet are also periodic in awhirling motion cycle

421 Results and Discussion in Different Frequencies of Ram-pressor Rotor Whirl Pressure pulsation spectrograms of key

point D (shown in Figure 6) are respectively obtained indifferent whirling frequencies such as Ω = 2125 rads4250 rads and 8500 rads (shown in Figure 16) when rotorwhirl amplitude is 100 120583m

Figure 17 shows the spectrograms of airflow excitingforce on Rampressor rotor rim surface when rotor whirlingamplitude equals 100120583m and rotor whirl frequencies are2125 rads 4250 rads and 8500 rads respectively

Figure 16 indicates that the excitation characteristic ofpoint D is rather complex As shown in the frequencyspectrum besides the fundamental frequency componentthe higher order frequency component is also generatedwhere the amplitude of the fundamental frequency compo-nent is the highest The amplitude of the double frequencycomponent is smaller than that of the fundamental frequencybut greater than those of other frequency componentsCompared with excitation spectrum of Ω = 2125 radsthe amplitude of the double frequency component rela-tively increses when the whirl frequency (Ω) is 4250 rads

12 Shock and Vibration

0843

0844

0845

0846

0847

0848

0849

0850To

tal-p

ress

ure r

ecov

ery

coeffi

cien

t

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

(a) Total-pressure recovery coefficient

1264

1266

1268

1270

1272

1274

1276

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

2125 rads4250 rads8500 rads

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 18 Flow performance in different whirling frequencies during a whirling motion cycle

(as shown in Figure 16(b)) In Figure 16(c) more frequencycomponents appear in the excitation spectrum In additionto the fundamental frequency and double frequency compo-nent the third harmonic frequency component simultane-ously emerges when the whirl frequency (Ω) is 8500 radswhich is caused by the coupling between inlet compressionflow of Rampressor rotor and rotor whirling With theincrement of rotor whirling frequency the amplitude of thefundamental frequency component in the frequency spec-trum gradually decreases but the amplitude of the doublefrequency component increases by degrees It follows fromabove that the complexity of Rampressor inlet excitationincreases along with the increase of rotor whirling frequencyThe above results are also illustrated in the frequency

spectrum of airflow exciting force on the rotor rim surfaceof Rampressor inlet as shown in Figure 17

The curves of flow performance parameters of Rampres-sor inlet in a whirlingmotion cycle are respectively obtainedin different whirl frequencies such as Ω = 2125 rads4250 rads and 8500 rads (illustrated in Figure 18) whenrotor whirl amplitude is 100120583m Figure 18 shows that waveamplitudes of total-pressure recovery coefficient pressuriza-tion ratio and kinetic energy efficiency of Rampressor inletare not affected by rotor whirling frequency which onlyinfluences the wave frequency of inlet flow performanceparameters The wave frequency of inlet flow performanceparameters becomes higher with the increment of rotor whirlfrequency Therefore the stability of inlet performance is

Shock and Vibration 13

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

3500

4000

Frequency (Hz)

Exci

tatio

n (P

a)

20292Hz

6764Hz

13528Hz

(c) 119886 = 150 120583m

Figure 19 Calculation results of point D in different rotor whirling amplitudes

better in the practical engineering when Rampressor rotorwhirling frequency is less

422 Results and Discussion in Different Amplitudes of Ram-pressor RotorWhirl Excitation characteristics of Rampressorinlet are analyzed in different rotor whirling amplitudes suchas 119886 = 50 120583m 119886 = 100 120583m and 119886 = 150 120583m whenrotor whirling frequency Ω = 4250 rads Figure 19 showspressure pulsation spectrogramof Rampressor inlet key pointD (shown in Figure 6) in different rotor whirl amplitudes

The spectrograms of airflow exciting force onRampressorrotor rim surface are respectively obtained in different rotorwhirling amplitudes such as 119886 = 50 120583m 119886 = 100 120583m and 119886 =150 120583m (shown in Figure 20) when the rotor whirl frequencyΩ = 4250 rads

As shown in Figure 19 more frequency componentsemerge in the excitation spectrum such as the fundamentalfrequency component double frequency component andthird harmonic frequency component where the amplitude

of the fundamental frequency component is the highest Theamplitude of the double frequency component is smallerthan that of the fundamental frequency component buthigher than that of the third harmonic frequency componentCompared with point D excitation of 119886 = 50 120583m besides thefundamental frequency and double frequency componentsthe third harmonic component in excitation spectrum isalso generated when the rotor whirl amplitudes are 100 120583mand 150 120583m (as shown in Figures 19(b) and 19(c)) andthe amplitude of the double frequency component in theexcitation spectrum of inlet point D relatively increasesWiththe increment of rotor whirling amplitude the amplitude ofthe fundamental frequency component and double frequencycomponent in the excitation spectrum of inlet wall allgradually increases It follows from above that the complexityof Rampressor inlet excitation also increases along with theincrease of rotor whirling amplitude The above results arealso illustrated in the spectrumof airflow exciting force on therotor rim surface of Rampressor inlet as shown in Figure 20

14 Shock and Vibration

0 500 1000 1500 2000 25000

10

20

30

40

50

60

70

80

Frequency (Hz)

Exci

tatio

n (P

a)

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

50

100

150

200

Frequency (Hz)

Exci

tatio

n (P

a)

(c) 119886 = 150 120583m

Figure 20 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling amplitudes

Flow performance of Rampressor inlet is studied indifferent rotor whirling amplitudes such as 119886 = 50 120583m 119886 =100 120583m and 119886 = 150 120583mwhen rotor whirling frequencyΩ =4250 rads Figure 21 shows the curves of flow performanceparameters of Rampressor inlet during a whirling motioncycle in different rotor whirling amplitudes Along with theincrease of rotor whirling amplitude wave amplitudes oftotal-pressure recovery coefficient pressurization ratio andkinetic energy efficiency of Rampressor inlet enlarge and thestability of inlet performance reduces Therefore the stabilityof inlet performance is better in the practical engineeringwhen Rampressor rotor whirling amplitude is less

5 Conclusions

Based on Rampressor rotor model and inlet flow modelthe compression inlet flow field of Rampressor rotor isnumerically studied with consideration of Rampressor rotorwhirling Flow excitation characteristics and performance

of Rampressor inlet are analyzed and discussed under thedifferent frequencies and amplitudes of Rampressor rotorwhirling The following conclusions are obtained

Alongwith the increment of119875119903 the position of the normal

shock wave gradually moves forward and aerodynamic load-ing of the inlet wall also increases Appropriate enhancementof inlet back pressure is advantageous to the pressure ratiocompression efficiency and other performance indices wheninlet can start and normally work

More frequency components appear in the excitationspectrum of Rampressor inlet with considering Rampressorrotor whirling The main frequency component is the fun-damental frequency which is caused by the rotor whirlingBesides the fundamental frequency the double frequencycomponents emerge because of the coupling between inletcompression flow of Rampressor rotor and rotor whirlingespecially in the subsonic diffuser of Rampressor rotor inletThe effect of rotor whirling on the excitation of Rampressorinlet wall has a definite phase difference Inlet excitation

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

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8 Shock and Vibration

00 02 04 06 08 100

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

Point A

Point B

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Stationary engine case

00 02 04 06 08 1000

20

40

60

80

100

120

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Rotor rim surface

Figure 13 Pressure distributions along stationary engine case and rotor rim surface in a whirling motion cycle

0460 0461 0462 0463 0464 0465570

575

580

585

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(a) Point A

05313 05314 0531588

89

90

91

92

93

94

95

96

Load

(Pa)

Normalized streamwise distance (S)

t = 01Tt = 02Tt = 03Tt = 04Tt = 05T

t = 06Tt = 07Tt = 08Tt = 09Tt = 10T

times105

(b) Point B

Figure 14 Partial enlarged drawing of pressure distributions along stationary engine case

The consequences of Rampressor inlet flow performancein different pressure ratios are shown in Table 1 With theincrease of 119875

119903(back pressure) static pressure ratio 119901

119904

total-pressure recovery coefficient 119901119877 pressurization ratio

119901119911 and kinetic energy efficiency 120578 gradually enhance but

nondimensional total pressure distortion and loss coefficientdecrease by degrees and exit stability of Rampressor inletameliorates As a result appropriate enhancement of exitback pressure is advantageous to pressure ratio compressionefficiency and other performance indices when inlet can

Shock and Vibration 9

0 02 04 06 08 10843

0844

0845

0846

0847

0848

0849

0850

Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 15 Flow performance of Rampressor inlet in a whirling motion cycle

Table 1 Flow performance parameters in the different 119875119903

119901119904

119901119877

119901119911

120596 120578 Δ ()9 07649 1148 00116 09292 367310 08294 1244 00075 09512 4339106 08483 1273 00063 09572 2546

start and normally work and meanwhile beneficial toimprovement of Rampressor overall efficiency

42 Performance and Excitation Characteristic of Inlet underRotor Whirling Rampressor inlet flow may be affected byRampressor rotor whirl in the work process When the inletpressure regularly changes which is caused by rotor whirlRampressor rotor bears the inconstant pressure load and thenvibrates

Structure schematic diagram of inlet flow path underRampressor rotor whirl is illustrated in Figure 10 The dottedline represents the state of Rampressor rotor without whirl

and the solid line curve represents the state of Rampressorrotor whirl

Because the three inlets of the designed Rampressor arethe symmetric periodic layout on the rotor the flow excitationcharacteristics and flow performance of inlet flow path 1 arestudied under Rampressor rotor periodic whirl in this paperExpression of rotor periodic whirl is given as follows

119890 = 119886 sin (Ω119905 + 120593) (7)

where 119890 represents the displacement between Rampressorcenter1198741015840 under rotor whirl andRampressor center119874withoutrotor whirl 119886 is rotor whirl amplitude Ω is rotor whirlfrequency (whirl speed) and120593 is initial phase In otherwordsthe trajectory of the Rampressor rotor is assumed as a circlein different whirl frequencies and whirl amplitudes so theeffect of the damping on the rotor whirl is not taken intoconsideration in the calculation

Result of steady flow is taken as the initial result in theunsteady calculation of this paper Time step size is set to1478 times 10minus5 s in the design rotor speed The unsteady flow ofRampressor inlet under rotor whirl is studied when 119875

119903equals

10 Shock and Vibration

0 200 400 600 800 1000 12000

500

1000

1500

2000

2500

3000

3500

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

3382Hz

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764 Hz

13528 Hz

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

500

1000

1500

2000

Frequency (Hz)

Exci

tatio

n (P

a)

13528Hz

27056Hz40584Hz

(c) Ω = 8500 rads

Figure 16 Calculation results of point D in different rotor whirling frequencies

106 Flow excitation characteristics of Rampressor inlet willbe analyzed under different frequencies and amplitudes ofRampressor whirl

Pressure pulsation time history and spectrogramon everykey point of Rampressor rotor inlet are shown in Figure 11when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads (the design Rampressor rotor speed)

Figure 11 indicates that excitation spectrogram of point Alocated in inlet supersonic compression of Rampressor is rel-atively simple The main frequency component is the funda-mental frequency which is caused by the rotor whirling Thevalue of rotor whirling frequency (fundamental frequency)is 6764Hz and excitation amplitude is small Comparedwith point A more frequency components appear in thefrequency spectrogram of Rampressor inlet point B point Cand point D Not only rotor whirling frequency 6764Hz butalso its double frequency component 13528Hz is obtainedin excitation spectrogram The double frequency 13528Hzis generated due to the coupling between inlet compressionflow of Rampressor rotor and rotor whirling especially in

the subsonic diffuser of Rampressor rotor inlet The ampli-tude of the double frequency component is smaller thanthat of the fundamental frequency component As shownin the frequency spectrum the excitation amplitudes of thefundamental frequency and double frequency componentsall gradually increase along with inlet flow pathThis happensbecause the subsonic flow in Rampressor inlet is easilyaffected by the external excitation It follows from above thatthe inlet excitation becomes more complex along with inletflow path

Time history of nondimensional excitation in a pulsationcycle is given (as shown in Figure 12) on every key point ofRampressor rotor inlet when rotor whirl amplitude equals100 120583m and whirl speed (Ω) is 4250 rads Figure 12 showsthat phases of nondimensional excitation in differentmeasurepoints are greatly different Among them phase differencebetween point B located on the entrance of the inlet throatand point C located on exit of the inlet throat is close to 180degrees Thus it can be seen that rotor whirl effect on inletdifferent location excitation has a certain phase difference

Shock and Vibration 11

0 200 400 600 800 1000 12000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

Frequency (Hz)

Exci

tatio

n (P

a)

(c) Ω = 8500 rads

Figure 17 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling frequencies

Pressure distributions along stationary engine case androtor rim surface of Rampressor inlet in a whirling motioncycle are shown in Figure 13 when rotor whirl amplitudeequals 100 120583m and whirl speed (Ω) is 4250 rads

Figure 14 shows partial enlarged drawing of pressuredistributions along the stationary engine case of Rampressorinlet (as shown in Figure 13(a) point A and point B) Periodicoscillation phenomenon of the inlet pressure distribution isobtained under Rampressor rotor whirl

The curves of flow performance parameters of Rampres-sor inlet in a whirling motion cycle are shown in Figure 15when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads Figure 15 indicates that the variations oftotal-pressure recovery coefficient pressure ratio and kineticenergy efficiency for Rampressor inlet are also periodic in awhirling motion cycle

421 Results and Discussion in Different Frequencies of Ram-pressor Rotor Whirl Pressure pulsation spectrograms of key

point D (shown in Figure 6) are respectively obtained indifferent whirling frequencies such as Ω = 2125 rads4250 rads and 8500 rads (shown in Figure 16) when rotorwhirl amplitude is 100 120583m

Figure 17 shows the spectrograms of airflow excitingforce on Rampressor rotor rim surface when rotor whirlingamplitude equals 100120583m and rotor whirl frequencies are2125 rads 4250 rads and 8500 rads respectively

Figure 16 indicates that the excitation characteristic ofpoint D is rather complex As shown in the frequencyspectrum besides the fundamental frequency componentthe higher order frequency component is also generatedwhere the amplitude of the fundamental frequency compo-nent is the highest The amplitude of the double frequencycomponent is smaller than that of the fundamental frequencybut greater than those of other frequency componentsCompared with excitation spectrum of Ω = 2125 radsthe amplitude of the double frequency component rela-tively increses when the whirl frequency (Ω) is 4250 rads

12 Shock and Vibration

0843

0844

0845

0846

0847

0848

0849

0850To

tal-p

ress

ure r

ecov

ery

coeffi

cien

t

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

(a) Total-pressure recovery coefficient

1264

1266

1268

1270

1272

1274

1276

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

2125 rads4250 rads8500 rads

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 18 Flow performance in different whirling frequencies during a whirling motion cycle

(as shown in Figure 16(b)) In Figure 16(c) more frequencycomponents appear in the excitation spectrum In additionto the fundamental frequency and double frequency compo-nent the third harmonic frequency component simultane-ously emerges when the whirl frequency (Ω) is 8500 radswhich is caused by the coupling between inlet compressionflow of Rampressor rotor and rotor whirling With theincrement of rotor whirling frequency the amplitude of thefundamental frequency component in the frequency spec-trum gradually decreases but the amplitude of the doublefrequency component increases by degrees It follows fromabove that the complexity of Rampressor inlet excitationincreases along with the increase of rotor whirling frequencyThe above results are also illustrated in the frequency

spectrum of airflow exciting force on the rotor rim surfaceof Rampressor inlet as shown in Figure 17

The curves of flow performance parameters of Rampres-sor inlet in a whirlingmotion cycle are respectively obtainedin different whirl frequencies such as Ω = 2125 rads4250 rads and 8500 rads (illustrated in Figure 18) whenrotor whirl amplitude is 100120583m Figure 18 shows that waveamplitudes of total-pressure recovery coefficient pressuriza-tion ratio and kinetic energy efficiency of Rampressor inletare not affected by rotor whirling frequency which onlyinfluences the wave frequency of inlet flow performanceparameters The wave frequency of inlet flow performanceparameters becomes higher with the increment of rotor whirlfrequency Therefore the stability of inlet performance is

Shock and Vibration 13

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

3500

4000

Frequency (Hz)

Exci

tatio

n (P

a)

20292Hz

6764Hz

13528Hz

(c) 119886 = 150 120583m

Figure 19 Calculation results of point D in different rotor whirling amplitudes

better in the practical engineering when Rampressor rotorwhirling frequency is less

422 Results and Discussion in Different Amplitudes of Ram-pressor RotorWhirl Excitation characteristics of Rampressorinlet are analyzed in different rotor whirling amplitudes suchas 119886 = 50 120583m 119886 = 100 120583m and 119886 = 150 120583m whenrotor whirling frequency Ω = 4250 rads Figure 19 showspressure pulsation spectrogramof Rampressor inlet key pointD (shown in Figure 6) in different rotor whirl amplitudes

The spectrograms of airflow exciting force onRampressorrotor rim surface are respectively obtained in different rotorwhirling amplitudes such as 119886 = 50 120583m 119886 = 100 120583m and 119886 =150 120583m (shown in Figure 20) when the rotor whirl frequencyΩ = 4250 rads

As shown in Figure 19 more frequency componentsemerge in the excitation spectrum such as the fundamentalfrequency component double frequency component andthird harmonic frequency component where the amplitude

of the fundamental frequency component is the highest Theamplitude of the double frequency component is smallerthan that of the fundamental frequency component buthigher than that of the third harmonic frequency componentCompared with point D excitation of 119886 = 50 120583m besides thefundamental frequency and double frequency componentsthe third harmonic component in excitation spectrum isalso generated when the rotor whirl amplitudes are 100 120583mand 150 120583m (as shown in Figures 19(b) and 19(c)) andthe amplitude of the double frequency component in theexcitation spectrum of inlet point D relatively increasesWiththe increment of rotor whirling amplitude the amplitude ofthe fundamental frequency component and double frequencycomponent in the excitation spectrum of inlet wall allgradually increases It follows from above that the complexityof Rampressor inlet excitation also increases along with theincrease of rotor whirling amplitude The above results arealso illustrated in the spectrumof airflow exciting force on therotor rim surface of Rampressor inlet as shown in Figure 20

14 Shock and Vibration

0 500 1000 1500 2000 25000

10

20

30

40

50

60

70

80

Frequency (Hz)

Exci

tatio

n (P

a)

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

50

100

150

200

Frequency (Hz)

Exci

tatio

n (P

a)

(c) 119886 = 150 120583m

Figure 20 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling amplitudes

Flow performance of Rampressor inlet is studied indifferent rotor whirling amplitudes such as 119886 = 50 120583m 119886 =100 120583m and 119886 = 150 120583mwhen rotor whirling frequencyΩ =4250 rads Figure 21 shows the curves of flow performanceparameters of Rampressor inlet during a whirling motioncycle in different rotor whirling amplitudes Along with theincrease of rotor whirling amplitude wave amplitudes oftotal-pressure recovery coefficient pressurization ratio andkinetic energy efficiency of Rampressor inlet enlarge and thestability of inlet performance reduces Therefore the stabilityof inlet performance is better in the practical engineeringwhen Rampressor rotor whirling amplitude is less

5 Conclusions

Based on Rampressor rotor model and inlet flow modelthe compression inlet flow field of Rampressor rotor isnumerically studied with consideration of Rampressor rotorwhirling Flow excitation characteristics and performance

of Rampressor inlet are analyzed and discussed under thedifferent frequencies and amplitudes of Rampressor rotorwhirling The following conclusions are obtained

Alongwith the increment of119875119903 the position of the normal

shock wave gradually moves forward and aerodynamic load-ing of the inlet wall also increases Appropriate enhancementof inlet back pressure is advantageous to the pressure ratiocompression efficiency and other performance indices wheninlet can start and normally work

More frequency components appear in the excitationspectrum of Rampressor inlet with considering Rampressorrotor whirling The main frequency component is the fun-damental frequency which is caused by the rotor whirlingBesides the fundamental frequency the double frequencycomponents emerge because of the coupling between inletcompression flow of Rampressor rotor and rotor whirlingespecially in the subsonic diffuser of Rampressor rotor inletThe effect of rotor whirling on the excitation of Rampressorinlet wall has a definite phase difference Inlet excitation

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 9

0 02 04 06 08 10843

0844

0845

0846

0847

0848

0849

0850

Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 15 Flow performance of Rampressor inlet in a whirling motion cycle

Table 1 Flow performance parameters in the different 119875119903

119901119904

119901119877

119901119911

120596 120578 Δ ()9 07649 1148 00116 09292 367310 08294 1244 00075 09512 4339106 08483 1273 00063 09572 2546

start and normally work and meanwhile beneficial toimprovement of Rampressor overall efficiency

42 Performance and Excitation Characteristic of Inlet underRotor Whirling Rampressor inlet flow may be affected byRampressor rotor whirl in the work process When the inletpressure regularly changes which is caused by rotor whirlRampressor rotor bears the inconstant pressure load and thenvibrates

Structure schematic diagram of inlet flow path underRampressor rotor whirl is illustrated in Figure 10 The dottedline represents the state of Rampressor rotor without whirl

and the solid line curve represents the state of Rampressorrotor whirl

Because the three inlets of the designed Rampressor arethe symmetric periodic layout on the rotor the flow excitationcharacteristics and flow performance of inlet flow path 1 arestudied under Rampressor rotor periodic whirl in this paperExpression of rotor periodic whirl is given as follows

119890 = 119886 sin (Ω119905 + 120593) (7)

where 119890 represents the displacement between Rampressorcenter1198741015840 under rotor whirl andRampressor center119874withoutrotor whirl 119886 is rotor whirl amplitude Ω is rotor whirlfrequency (whirl speed) and120593 is initial phase In otherwordsthe trajectory of the Rampressor rotor is assumed as a circlein different whirl frequencies and whirl amplitudes so theeffect of the damping on the rotor whirl is not taken intoconsideration in the calculation

Result of steady flow is taken as the initial result in theunsteady calculation of this paper Time step size is set to1478 times 10minus5 s in the design rotor speed The unsteady flow ofRampressor inlet under rotor whirl is studied when 119875

119903equals

10 Shock and Vibration

0 200 400 600 800 1000 12000

500

1000

1500

2000

2500

3000

3500

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

3382Hz

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764 Hz

13528 Hz

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

500

1000

1500

2000

Frequency (Hz)

Exci

tatio

n (P

a)

13528Hz

27056Hz40584Hz

(c) Ω = 8500 rads

Figure 16 Calculation results of point D in different rotor whirling frequencies

106 Flow excitation characteristics of Rampressor inlet willbe analyzed under different frequencies and amplitudes ofRampressor whirl

Pressure pulsation time history and spectrogramon everykey point of Rampressor rotor inlet are shown in Figure 11when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads (the design Rampressor rotor speed)

Figure 11 indicates that excitation spectrogram of point Alocated in inlet supersonic compression of Rampressor is rel-atively simple The main frequency component is the funda-mental frequency which is caused by the rotor whirling Thevalue of rotor whirling frequency (fundamental frequency)is 6764Hz and excitation amplitude is small Comparedwith point A more frequency components appear in thefrequency spectrogram of Rampressor inlet point B point Cand point D Not only rotor whirling frequency 6764Hz butalso its double frequency component 13528Hz is obtainedin excitation spectrogram The double frequency 13528Hzis generated due to the coupling between inlet compressionflow of Rampressor rotor and rotor whirling especially in

the subsonic diffuser of Rampressor rotor inlet The ampli-tude of the double frequency component is smaller thanthat of the fundamental frequency component As shownin the frequency spectrum the excitation amplitudes of thefundamental frequency and double frequency componentsall gradually increase along with inlet flow pathThis happensbecause the subsonic flow in Rampressor inlet is easilyaffected by the external excitation It follows from above thatthe inlet excitation becomes more complex along with inletflow path

Time history of nondimensional excitation in a pulsationcycle is given (as shown in Figure 12) on every key point ofRampressor rotor inlet when rotor whirl amplitude equals100 120583m and whirl speed (Ω) is 4250 rads Figure 12 showsthat phases of nondimensional excitation in differentmeasurepoints are greatly different Among them phase differencebetween point B located on the entrance of the inlet throatand point C located on exit of the inlet throat is close to 180degrees Thus it can be seen that rotor whirl effect on inletdifferent location excitation has a certain phase difference

Shock and Vibration 11

0 200 400 600 800 1000 12000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

Frequency (Hz)

Exci

tatio

n (P

a)

(c) Ω = 8500 rads

Figure 17 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling frequencies

Pressure distributions along stationary engine case androtor rim surface of Rampressor inlet in a whirling motioncycle are shown in Figure 13 when rotor whirl amplitudeequals 100 120583m and whirl speed (Ω) is 4250 rads

Figure 14 shows partial enlarged drawing of pressuredistributions along the stationary engine case of Rampressorinlet (as shown in Figure 13(a) point A and point B) Periodicoscillation phenomenon of the inlet pressure distribution isobtained under Rampressor rotor whirl

The curves of flow performance parameters of Rampres-sor inlet in a whirling motion cycle are shown in Figure 15when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads Figure 15 indicates that the variations oftotal-pressure recovery coefficient pressure ratio and kineticenergy efficiency for Rampressor inlet are also periodic in awhirling motion cycle

421 Results and Discussion in Different Frequencies of Ram-pressor Rotor Whirl Pressure pulsation spectrograms of key

point D (shown in Figure 6) are respectively obtained indifferent whirling frequencies such as Ω = 2125 rads4250 rads and 8500 rads (shown in Figure 16) when rotorwhirl amplitude is 100 120583m

Figure 17 shows the spectrograms of airflow excitingforce on Rampressor rotor rim surface when rotor whirlingamplitude equals 100120583m and rotor whirl frequencies are2125 rads 4250 rads and 8500 rads respectively

Figure 16 indicates that the excitation characteristic ofpoint D is rather complex As shown in the frequencyspectrum besides the fundamental frequency componentthe higher order frequency component is also generatedwhere the amplitude of the fundamental frequency compo-nent is the highest The amplitude of the double frequencycomponent is smaller than that of the fundamental frequencybut greater than those of other frequency componentsCompared with excitation spectrum of Ω = 2125 radsthe amplitude of the double frequency component rela-tively increses when the whirl frequency (Ω) is 4250 rads

12 Shock and Vibration

0843

0844

0845

0846

0847

0848

0849

0850To

tal-p

ress

ure r

ecov

ery

coeffi

cien

t

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

(a) Total-pressure recovery coefficient

1264

1266

1268

1270

1272

1274

1276

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

2125 rads4250 rads8500 rads

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 18 Flow performance in different whirling frequencies during a whirling motion cycle

(as shown in Figure 16(b)) In Figure 16(c) more frequencycomponents appear in the excitation spectrum In additionto the fundamental frequency and double frequency compo-nent the third harmonic frequency component simultane-ously emerges when the whirl frequency (Ω) is 8500 radswhich is caused by the coupling between inlet compressionflow of Rampressor rotor and rotor whirling With theincrement of rotor whirling frequency the amplitude of thefundamental frequency component in the frequency spec-trum gradually decreases but the amplitude of the doublefrequency component increases by degrees It follows fromabove that the complexity of Rampressor inlet excitationincreases along with the increase of rotor whirling frequencyThe above results are also illustrated in the frequency

spectrum of airflow exciting force on the rotor rim surfaceof Rampressor inlet as shown in Figure 17

The curves of flow performance parameters of Rampres-sor inlet in a whirlingmotion cycle are respectively obtainedin different whirl frequencies such as Ω = 2125 rads4250 rads and 8500 rads (illustrated in Figure 18) whenrotor whirl amplitude is 100120583m Figure 18 shows that waveamplitudes of total-pressure recovery coefficient pressuriza-tion ratio and kinetic energy efficiency of Rampressor inletare not affected by rotor whirling frequency which onlyinfluences the wave frequency of inlet flow performanceparameters The wave frequency of inlet flow performanceparameters becomes higher with the increment of rotor whirlfrequency Therefore the stability of inlet performance is

Shock and Vibration 13

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

3500

4000

Frequency (Hz)

Exci

tatio

n (P

a)

20292Hz

6764Hz

13528Hz

(c) 119886 = 150 120583m

Figure 19 Calculation results of point D in different rotor whirling amplitudes

better in the practical engineering when Rampressor rotorwhirling frequency is less

422 Results and Discussion in Different Amplitudes of Ram-pressor RotorWhirl Excitation characteristics of Rampressorinlet are analyzed in different rotor whirling amplitudes suchas 119886 = 50 120583m 119886 = 100 120583m and 119886 = 150 120583m whenrotor whirling frequency Ω = 4250 rads Figure 19 showspressure pulsation spectrogramof Rampressor inlet key pointD (shown in Figure 6) in different rotor whirl amplitudes

The spectrograms of airflow exciting force onRampressorrotor rim surface are respectively obtained in different rotorwhirling amplitudes such as 119886 = 50 120583m 119886 = 100 120583m and 119886 =150 120583m (shown in Figure 20) when the rotor whirl frequencyΩ = 4250 rads

As shown in Figure 19 more frequency componentsemerge in the excitation spectrum such as the fundamentalfrequency component double frequency component andthird harmonic frequency component where the amplitude

of the fundamental frequency component is the highest Theamplitude of the double frequency component is smallerthan that of the fundamental frequency component buthigher than that of the third harmonic frequency componentCompared with point D excitation of 119886 = 50 120583m besides thefundamental frequency and double frequency componentsthe third harmonic component in excitation spectrum isalso generated when the rotor whirl amplitudes are 100 120583mand 150 120583m (as shown in Figures 19(b) and 19(c)) andthe amplitude of the double frequency component in theexcitation spectrum of inlet point D relatively increasesWiththe increment of rotor whirling amplitude the amplitude ofthe fundamental frequency component and double frequencycomponent in the excitation spectrum of inlet wall allgradually increases It follows from above that the complexityof Rampressor inlet excitation also increases along with theincrease of rotor whirling amplitude The above results arealso illustrated in the spectrumof airflow exciting force on therotor rim surface of Rampressor inlet as shown in Figure 20

14 Shock and Vibration

0 500 1000 1500 2000 25000

10

20

30

40

50

60

70

80

Frequency (Hz)

Exci

tatio

n (P

a)

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

50

100

150

200

Frequency (Hz)

Exci

tatio

n (P

a)

(c) 119886 = 150 120583m

Figure 20 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling amplitudes

Flow performance of Rampressor inlet is studied indifferent rotor whirling amplitudes such as 119886 = 50 120583m 119886 =100 120583m and 119886 = 150 120583mwhen rotor whirling frequencyΩ =4250 rads Figure 21 shows the curves of flow performanceparameters of Rampressor inlet during a whirling motioncycle in different rotor whirling amplitudes Along with theincrease of rotor whirling amplitude wave amplitudes oftotal-pressure recovery coefficient pressurization ratio andkinetic energy efficiency of Rampressor inlet enlarge and thestability of inlet performance reduces Therefore the stabilityof inlet performance is better in the practical engineeringwhen Rampressor rotor whirling amplitude is less

5 Conclusions

Based on Rampressor rotor model and inlet flow modelthe compression inlet flow field of Rampressor rotor isnumerically studied with consideration of Rampressor rotorwhirling Flow excitation characteristics and performance

of Rampressor inlet are analyzed and discussed under thedifferent frequencies and amplitudes of Rampressor rotorwhirling The following conclusions are obtained

Alongwith the increment of119875119903 the position of the normal

shock wave gradually moves forward and aerodynamic load-ing of the inlet wall also increases Appropriate enhancementof inlet back pressure is advantageous to the pressure ratiocompression efficiency and other performance indices wheninlet can start and normally work

More frequency components appear in the excitationspectrum of Rampressor inlet with considering Rampressorrotor whirling The main frequency component is the fun-damental frequency which is caused by the rotor whirlingBesides the fundamental frequency the double frequencycomponents emerge because of the coupling between inletcompression flow of Rampressor rotor and rotor whirlingespecially in the subsonic diffuser of Rampressor rotor inletThe effect of rotor whirling on the excitation of Rampressorinlet wall has a definite phase difference Inlet excitation

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Shock and Vibration

0 200 400 600 800 1000 12000

500

1000

1500

2000

2500

3000

3500

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

3382Hz

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764 Hz

13528 Hz

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

500

1000

1500

2000

Frequency (Hz)

Exci

tatio

n (P

a)

13528Hz

27056Hz40584Hz

(c) Ω = 8500 rads

Figure 16 Calculation results of point D in different rotor whirling frequencies

106 Flow excitation characteristics of Rampressor inlet willbe analyzed under different frequencies and amplitudes ofRampressor whirl

Pressure pulsation time history and spectrogramon everykey point of Rampressor rotor inlet are shown in Figure 11when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads (the design Rampressor rotor speed)

Figure 11 indicates that excitation spectrogram of point Alocated in inlet supersonic compression of Rampressor is rel-atively simple The main frequency component is the funda-mental frequency which is caused by the rotor whirling Thevalue of rotor whirling frequency (fundamental frequency)is 6764Hz and excitation amplitude is small Comparedwith point A more frequency components appear in thefrequency spectrogram of Rampressor inlet point B point Cand point D Not only rotor whirling frequency 6764Hz butalso its double frequency component 13528Hz is obtainedin excitation spectrogram The double frequency 13528Hzis generated due to the coupling between inlet compressionflow of Rampressor rotor and rotor whirling especially in

the subsonic diffuser of Rampressor rotor inlet The ampli-tude of the double frequency component is smaller thanthat of the fundamental frequency component As shownin the frequency spectrum the excitation amplitudes of thefundamental frequency and double frequency componentsall gradually increase along with inlet flow pathThis happensbecause the subsonic flow in Rampressor inlet is easilyaffected by the external excitation It follows from above thatthe inlet excitation becomes more complex along with inletflow path

Time history of nondimensional excitation in a pulsationcycle is given (as shown in Figure 12) on every key point ofRampressor rotor inlet when rotor whirl amplitude equals100 120583m and whirl speed (Ω) is 4250 rads Figure 12 showsthat phases of nondimensional excitation in differentmeasurepoints are greatly different Among them phase differencebetween point B located on the entrance of the inlet throatand point C located on exit of the inlet throat is close to 180degrees Thus it can be seen that rotor whirl effect on inletdifferent location excitation has a certain phase difference

Shock and Vibration 11

0 200 400 600 800 1000 12000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

Frequency (Hz)

Exci

tatio

n (P

a)

(c) Ω = 8500 rads

Figure 17 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling frequencies

Pressure distributions along stationary engine case androtor rim surface of Rampressor inlet in a whirling motioncycle are shown in Figure 13 when rotor whirl amplitudeequals 100 120583m and whirl speed (Ω) is 4250 rads

Figure 14 shows partial enlarged drawing of pressuredistributions along the stationary engine case of Rampressorinlet (as shown in Figure 13(a) point A and point B) Periodicoscillation phenomenon of the inlet pressure distribution isobtained under Rampressor rotor whirl

The curves of flow performance parameters of Rampres-sor inlet in a whirling motion cycle are shown in Figure 15when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads Figure 15 indicates that the variations oftotal-pressure recovery coefficient pressure ratio and kineticenergy efficiency for Rampressor inlet are also periodic in awhirling motion cycle

421 Results and Discussion in Different Frequencies of Ram-pressor Rotor Whirl Pressure pulsation spectrograms of key

point D (shown in Figure 6) are respectively obtained indifferent whirling frequencies such as Ω = 2125 rads4250 rads and 8500 rads (shown in Figure 16) when rotorwhirl amplitude is 100 120583m

Figure 17 shows the spectrograms of airflow excitingforce on Rampressor rotor rim surface when rotor whirlingamplitude equals 100120583m and rotor whirl frequencies are2125 rads 4250 rads and 8500 rads respectively

Figure 16 indicates that the excitation characteristic ofpoint D is rather complex As shown in the frequencyspectrum besides the fundamental frequency componentthe higher order frequency component is also generatedwhere the amplitude of the fundamental frequency compo-nent is the highest The amplitude of the double frequencycomponent is smaller than that of the fundamental frequencybut greater than those of other frequency componentsCompared with excitation spectrum of Ω = 2125 radsthe amplitude of the double frequency component rela-tively increses when the whirl frequency (Ω) is 4250 rads

12 Shock and Vibration

0843

0844

0845

0846

0847

0848

0849

0850To

tal-p

ress

ure r

ecov

ery

coeffi

cien

t

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

(a) Total-pressure recovery coefficient

1264

1266

1268

1270

1272

1274

1276

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

2125 rads4250 rads8500 rads

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 18 Flow performance in different whirling frequencies during a whirling motion cycle

(as shown in Figure 16(b)) In Figure 16(c) more frequencycomponents appear in the excitation spectrum In additionto the fundamental frequency and double frequency compo-nent the third harmonic frequency component simultane-ously emerges when the whirl frequency (Ω) is 8500 radswhich is caused by the coupling between inlet compressionflow of Rampressor rotor and rotor whirling With theincrement of rotor whirling frequency the amplitude of thefundamental frequency component in the frequency spec-trum gradually decreases but the amplitude of the doublefrequency component increases by degrees It follows fromabove that the complexity of Rampressor inlet excitationincreases along with the increase of rotor whirling frequencyThe above results are also illustrated in the frequency

spectrum of airflow exciting force on the rotor rim surfaceof Rampressor inlet as shown in Figure 17

The curves of flow performance parameters of Rampres-sor inlet in a whirlingmotion cycle are respectively obtainedin different whirl frequencies such as Ω = 2125 rads4250 rads and 8500 rads (illustrated in Figure 18) whenrotor whirl amplitude is 100120583m Figure 18 shows that waveamplitudes of total-pressure recovery coefficient pressuriza-tion ratio and kinetic energy efficiency of Rampressor inletare not affected by rotor whirling frequency which onlyinfluences the wave frequency of inlet flow performanceparameters The wave frequency of inlet flow performanceparameters becomes higher with the increment of rotor whirlfrequency Therefore the stability of inlet performance is

Shock and Vibration 13

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

3500

4000

Frequency (Hz)

Exci

tatio

n (P

a)

20292Hz

6764Hz

13528Hz

(c) 119886 = 150 120583m

Figure 19 Calculation results of point D in different rotor whirling amplitudes

better in the practical engineering when Rampressor rotorwhirling frequency is less

422 Results and Discussion in Different Amplitudes of Ram-pressor RotorWhirl Excitation characteristics of Rampressorinlet are analyzed in different rotor whirling amplitudes suchas 119886 = 50 120583m 119886 = 100 120583m and 119886 = 150 120583m whenrotor whirling frequency Ω = 4250 rads Figure 19 showspressure pulsation spectrogramof Rampressor inlet key pointD (shown in Figure 6) in different rotor whirl amplitudes

The spectrograms of airflow exciting force onRampressorrotor rim surface are respectively obtained in different rotorwhirling amplitudes such as 119886 = 50 120583m 119886 = 100 120583m and 119886 =150 120583m (shown in Figure 20) when the rotor whirl frequencyΩ = 4250 rads

As shown in Figure 19 more frequency componentsemerge in the excitation spectrum such as the fundamentalfrequency component double frequency component andthird harmonic frequency component where the amplitude

of the fundamental frequency component is the highest Theamplitude of the double frequency component is smallerthan that of the fundamental frequency component buthigher than that of the third harmonic frequency componentCompared with point D excitation of 119886 = 50 120583m besides thefundamental frequency and double frequency componentsthe third harmonic component in excitation spectrum isalso generated when the rotor whirl amplitudes are 100 120583mand 150 120583m (as shown in Figures 19(b) and 19(c)) andthe amplitude of the double frequency component in theexcitation spectrum of inlet point D relatively increasesWiththe increment of rotor whirling amplitude the amplitude ofthe fundamental frequency component and double frequencycomponent in the excitation spectrum of inlet wall allgradually increases It follows from above that the complexityof Rampressor inlet excitation also increases along with theincrease of rotor whirling amplitude The above results arealso illustrated in the spectrumof airflow exciting force on therotor rim surface of Rampressor inlet as shown in Figure 20

14 Shock and Vibration

0 500 1000 1500 2000 25000

10

20

30

40

50

60

70

80

Frequency (Hz)

Exci

tatio

n (P

a)

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

50

100

150

200

Frequency (Hz)

Exci

tatio

n (P

a)

(c) 119886 = 150 120583m

Figure 20 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling amplitudes

Flow performance of Rampressor inlet is studied indifferent rotor whirling amplitudes such as 119886 = 50 120583m 119886 =100 120583m and 119886 = 150 120583mwhen rotor whirling frequencyΩ =4250 rads Figure 21 shows the curves of flow performanceparameters of Rampressor inlet during a whirling motioncycle in different rotor whirling amplitudes Along with theincrease of rotor whirling amplitude wave amplitudes oftotal-pressure recovery coefficient pressurization ratio andkinetic energy efficiency of Rampressor inlet enlarge and thestability of inlet performance reduces Therefore the stabilityof inlet performance is better in the practical engineeringwhen Rampressor rotor whirling amplitude is less

5 Conclusions

Based on Rampressor rotor model and inlet flow modelthe compression inlet flow field of Rampressor rotor isnumerically studied with consideration of Rampressor rotorwhirling Flow excitation characteristics and performance

of Rampressor inlet are analyzed and discussed under thedifferent frequencies and amplitudes of Rampressor rotorwhirling The following conclusions are obtained

Alongwith the increment of119875119903 the position of the normal

shock wave gradually moves forward and aerodynamic load-ing of the inlet wall also increases Appropriate enhancementof inlet back pressure is advantageous to the pressure ratiocompression efficiency and other performance indices wheninlet can start and normally work

More frequency components appear in the excitationspectrum of Rampressor inlet with considering Rampressorrotor whirling The main frequency component is the fun-damental frequency which is caused by the rotor whirlingBesides the fundamental frequency the double frequencycomponents emerge because of the coupling between inletcompression flow of Rampressor rotor and rotor whirlingespecially in the subsonic diffuser of Rampressor rotor inletThe effect of rotor whirling on the excitation of Rampressorinlet wall has a definite phase difference Inlet excitation

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 11

0 200 400 600 800 1000 12000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(a) Ω = 2125 rads

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) Ω = 4250 rads

0 1000 2000 3000 4000 50000

20

40

60

80

100

120

140

Frequency (Hz)

Exci

tatio

n (P

a)

(c) Ω = 8500 rads

Figure 17 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling frequencies

Pressure distributions along stationary engine case androtor rim surface of Rampressor inlet in a whirling motioncycle are shown in Figure 13 when rotor whirl amplitudeequals 100 120583m and whirl speed (Ω) is 4250 rads

Figure 14 shows partial enlarged drawing of pressuredistributions along the stationary engine case of Rampressorinlet (as shown in Figure 13(a) point A and point B) Periodicoscillation phenomenon of the inlet pressure distribution isobtained under Rampressor rotor whirl

The curves of flow performance parameters of Rampres-sor inlet in a whirling motion cycle are shown in Figure 15when rotor whirl amplitude equals 100 120583m and whirl speed(Ω) is 4250 rads Figure 15 indicates that the variations oftotal-pressure recovery coefficient pressure ratio and kineticenergy efficiency for Rampressor inlet are also periodic in awhirling motion cycle

421 Results and Discussion in Different Frequencies of Ram-pressor Rotor Whirl Pressure pulsation spectrograms of key

point D (shown in Figure 6) are respectively obtained indifferent whirling frequencies such as Ω = 2125 rads4250 rads and 8500 rads (shown in Figure 16) when rotorwhirl amplitude is 100 120583m

Figure 17 shows the spectrograms of airflow excitingforce on Rampressor rotor rim surface when rotor whirlingamplitude equals 100120583m and rotor whirl frequencies are2125 rads 4250 rads and 8500 rads respectively

Figure 16 indicates that the excitation characteristic ofpoint D is rather complex As shown in the frequencyspectrum besides the fundamental frequency componentthe higher order frequency component is also generatedwhere the amplitude of the fundamental frequency compo-nent is the highest The amplitude of the double frequencycomponent is smaller than that of the fundamental frequencybut greater than those of other frequency componentsCompared with excitation spectrum of Ω = 2125 radsthe amplitude of the double frequency component rela-tively increses when the whirl frequency (Ω) is 4250 rads

12 Shock and Vibration

0843

0844

0845

0846

0847

0848

0849

0850To

tal-p

ress

ure r

ecov

ery

coeffi

cien

t

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

(a) Total-pressure recovery coefficient

1264

1266

1268

1270

1272

1274

1276

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

2125 rads4250 rads8500 rads

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 18 Flow performance in different whirling frequencies during a whirling motion cycle

(as shown in Figure 16(b)) In Figure 16(c) more frequencycomponents appear in the excitation spectrum In additionto the fundamental frequency and double frequency compo-nent the third harmonic frequency component simultane-ously emerges when the whirl frequency (Ω) is 8500 radswhich is caused by the coupling between inlet compressionflow of Rampressor rotor and rotor whirling With theincrement of rotor whirling frequency the amplitude of thefundamental frequency component in the frequency spec-trum gradually decreases but the amplitude of the doublefrequency component increases by degrees It follows fromabove that the complexity of Rampressor inlet excitationincreases along with the increase of rotor whirling frequencyThe above results are also illustrated in the frequency

spectrum of airflow exciting force on the rotor rim surfaceof Rampressor inlet as shown in Figure 17

The curves of flow performance parameters of Rampres-sor inlet in a whirlingmotion cycle are respectively obtainedin different whirl frequencies such as Ω = 2125 rads4250 rads and 8500 rads (illustrated in Figure 18) whenrotor whirl amplitude is 100120583m Figure 18 shows that waveamplitudes of total-pressure recovery coefficient pressuriza-tion ratio and kinetic energy efficiency of Rampressor inletare not affected by rotor whirling frequency which onlyinfluences the wave frequency of inlet flow performanceparameters The wave frequency of inlet flow performanceparameters becomes higher with the increment of rotor whirlfrequency Therefore the stability of inlet performance is

Shock and Vibration 13

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

3500

4000

Frequency (Hz)

Exci

tatio

n (P

a)

20292Hz

6764Hz

13528Hz

(c) 119886 = 150 120583m

Figure 19 Calculation results of point D in different rotor whirling amplitudes

better in the practical engineering when Rampressor rotorwhirling frequency is less

422 Results and Discussion in Different Amplitudes of Ram-pressor RotorWhirl Excitation characteristics of Rampressorinlet are analyzed in different rotor whirling amplitudes suchas 119886 = 50 120583m 119886 = 100 120583m and 119886 = 150 120583m whenrotor whirling frequency Ω = 4250 rads Figure 19 showspressure pulsation spectrogramof Rampressor inlet key pointD (shown in Figure 6) in different rotor whirl amplitudes

The spectrograms of airflow exciting force onRampressorrotor rim surface are respectively obtained in different rotorwhirling amplitudes such as 119886 = 50 120583m 119886 = 100 120583m and 119886 =150 120583m (shown in Figure 20) when the rotor whirl frequencyΩ = 4250 rads

As shown in Figure 19 more frequency componentsemerge in the excitation spectrum such as the fundamentalfrequency component double frequency component andthird harmonic frequency component where the amplitude

of the fundamental frequency component is the highest Theamplitude of the double frequency component is smallerthan that of the fundamental frequency component buthigher than that of the third harmonic frequency componentCompared with point D excitation of 119886 = 50 120583m besides thefundamental frequency and double frequency componentsthe third harmonic component in excitation spectrum isalso generated when the rotor whirl amplitudes are 100 120583mand 150 120583m (as shown in Figures 19(b) and 19(c)) andthe amplitude of the double frequency component in theexcitation spectrum of inlet point D relatively increasesWiththe increment of rotor whirling amplitude the amplitude ofthe fundamental frequency component and double frequencycomponent in the excitation spectrum of inlet wall allgradually increases It follows from above that the complexityof Rampressor inlet excitation also increases along with theincrease of rotor whirling amplitude The above results arealso illustrated in the spectrumof airflow exciting force on therotor rim surface of Rampressor inlet as shown in Figure 20

14 Shock and Vibration

0 500 1000 1500 2000 25000

10

20

30

40

50

60

70

80

Frequency (Hz)

Exci

tatio

n (P

a)

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

50

100

150

200

Frequency (Hz)

Exci

tatio

n (P

a)

(c) 119886 = 150 120583m

Figure 20 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling amplitudes

Flow performance of Rampressor inlet is studied indifferent rotor whirling amplitudes such as 119886 = 50 120583m 119886 =100 120583m and 119886 = 150 120583mwhen rotor whirling frequencyΩ =4250 rads Figure 21 shows the curves of flow performanceparameters of Rampressor inlet during a whirling motioncycle in different rotor whirling amplitudes Along with theincrease of rotor whirling amplitude wave amplitudes oftotal-pressure recovery coefficient pressurization ratio andkinetic energy efficiency of Rampressor inlet enlarge and thestability of inlet performance reduces Therefore the stabilityof inlet performance is better in the practical engineeringwhen Rampressor rotor whirling amplitude is less

5 Conclusions

Based on Rampressor rotor model and inlet flow modelthe compression inlet flow field of Rampressor rotor isnumerically studied with consideration of Rampressor rotorwhirling Flow excitation characteristics and performance

of Rampressor inlet are analyzed and discussed under thedifferent frequencies and amplitudes of Rampressor rotorwhirling The following conclusions are obtained

Alongwith the increment of119875119903 the position of the normal

shock wave gradually moves forward and aerodynamic load-ing of the inlet wall also increases Appropriate enhancementof inlet back pressure is advantageous to the pressure ratiocompression efficiency and other performance indices wheninlet can start and normally work

More frequency components appear in the excitationspectrum of Rampressor inlet with considering Rampressorrotor whirling The main frequency component is the fun-damental frequency which is caused by the rotor whirlingBesides the fundamental frequency the double frequencycomponents emerge because of the coupling between inletcompression flow of Rampressor rotor and rotor whirlingespecially in the subsonic diffuser of Rampressor rotor inletThe effect of rotor whirling on the excitation of Rampressorinlet wall has a definite phase difference Inlet excitation

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Shock and Vibration

0843

0844

0845

0846

0847

0848

0849

0850To

tal-p

ress

ure r

ecov

ery

coeffi

cien

t

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

(a) Total-pressure recovery coefficient

1264

1266

1268

1270

1272

1274

1276

0 02 04 06 08 1Time (T)

Pres

suriz

atio

n ra

tio

2125 rads4250 rads8500 rads

(b) Pressurization ratio

0955

0956

0957

0958

0 02 04 06 08 1Time (T)

2125 rads4250 rads8500 rads

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 18 Flow performance in different whirling frequencies during a whirling motion cycle

(as shown in Figure 16(b)) In Figure 16(c) more frequencycomponents appear in the excitation spectrum In additionto the fundamental frequency and double frequency compo-nent the third harmonic frequency component simultane-ously emerges when the whirl frequency (Ω) is 8500 radswhich is caused by the coupling between inlet compressionflow of Rampressor rotor and rotor whirling With theincrement of rotor whirling frequency the amplitude of thefundamental frequency component in the frequency spec-trum gradually decreases but the amplitude of the doublefrequency component increases by degrees It follows fromabove that the complexity of Rampressor inlet excitationincreases along with the increase of rotor whirling frequencyThe above results are also illustrated in the frequency

spectrum of airflow exciting force on the rotor rim surfaceof Rampressor inlet as shown in Figure 17

The curves of flow performance parameters of Rampres-sor inlet in a whirlingmotion cycle are respectively obtainedin different whirl frequencies such as Ω = 2125 rads4250 rads and 8500 rads (illustrated in Figure 18) whenrotor whirl amplitude is 100120583m Figure 18 shows that waveamplitudes of total-pressure recovery coefficient pressuriza-tion ratio and kinetic energy efficiency of Rampressor inletare not affected by rotor whirling frequency which onlyinfluences the wave frequency of inlet flow performanceparameters The wave frequency of inlet flow performanceparameters becomes higher with the increment of rotor whirlfrequency Therefore the stability of inlet performance is

Shock and Vibration 13

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

3500

4000

Frequency (Hz)

Exci

tatio

n (P

a)

20292Hz

6764Hz

13528Hz

(c) 119886 = 150 120583m

Figure 19 Calculation results of point D in different rotor whirling amplitudes

better in the practical engineering when Rampressor rotorwhirling frequency is less

422 Results and Discussion in Different Amplitudes of Ram-pressor RotorWhirl Excitation characteristics of Rampressorinlet are analyzed in different rotor whirling amplitudes suchas 119886 = 50 120583m 119886 = 100 120583m and 119886 = 150 120583m whenrotor whirling frequency Ω = 4250 rads Figure 19 showspressure pulsation spectrogramof Rampressor inlet key pointD (shown in Figure 6) in different rotor whirl amplitudes

The spectrograms of airflow exciting force onRampressorrotor rim surface are respectively obtained in different rotorwhirling amplitudes such as 119886 = 50 120583m 119886 = 100 120583m and 119886 =150 120583m (shown in Figure 20) when the rotor whirl frequencyΩ = 4250 rads

As shown in Figure 19 more frequency componentsemerge in the excitation spectrum such as the fundamentalfrequency component double frequency component andthird harmonic frequency component where the amplitude

of the fundamental frequency component is the highest Theamplitude of the double frequency component is smallerthan that of the fundamental frequency component buthigher than that of the third harmonic frequency componentCompared with point D excitation of 119886 = 50 120583m besides thefundamental frequency and double frequency componentsthe third harmonic component in excitation spectrum isalso generated when the rotor whirl amplitudes are 100 120583mand 150 120583m (as shown in Figures 19(b) and 19(c)) andthe amplitude of the double frequency component in theexcitation spectrum of inlet point D relatively increasesWiththe increment of rotor whirling amplitude the amplitude ofthe fundamental frequency component and double frequencycomponent in the excitation spectrum of inlet wall allgradually increases It follows from above that the complexityof Rampressor inlet excitation also increases along with theincrease of rotor whirling amplitude The above results arealso illustrated in the spectrumof airflow exciting force on therotor rim surface of Rampressor inlet as shown in Figure 20

14 Shock and Vibration

0 500 1000 1500 2000 25000

10

20

30

40

50

60

70

80

Frequency (Hz)

Exci

tatio

n (P

a)

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

50

100

150

200

Frequency (Hz)

Exci

tatio

n (P

a)

(c) 119886 = 150 120583m

Figure 20 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling amplitudes

Flow performance of Rampressor inlet is studied indifferent rotor whirling amplitudes such as 119886 = 50 120583m 119886 =100 120583m and 119886 = 150 120583mwhen rotor whirling frequencyΩ =4250 rads Figure 21 shows the curves of flow performanceparameters of Rampressor inlet during a whirling motioncycle in different rotor whirling amplitudes Along with theincrease of rotor whirling amplitude wave amplitudes oftotal-pressure recovery coefficient pressurization ratio andkinetic energy efficiency of Rampressor inlet enlarge and thestability of inlet performance reduces Therefore the stabilityof inlet performance is better in the practical engineeringwhen Rampressor rotor whirling amplitude is less

5 Conclusions

Based on Rampressor rotor model and inlet flow modelthe compression inlet flow field of Rampressor rotor isnumerically studied with consideration of Rampressor rotorwhirling Flow excitation characteristics and performance

of Rampressor inlet are analyzed and discussed under thedifferent frequencies and amplitudes of Rampressor rotorwhirling The following conclusions are obtained

Alongwith the increment of119875119903 the position of the normal

shock wave gradually moves forward and aerodynamic load-ing of the inlet wall also increases Appropriate enhancementof inlet back pressure is advantageous to the pressure ratiocompression efficiency and other performance indices wheninlet can start and normally work

More frequency components appear in the excitationspectrum of Rampressor inlet with considering Rampressorrotor whirling The main frequency component is the fun-damental frequency which is caused by the rotor whirlingBesides the fundamental frequency the double frequencycomponents emerge because of the coupling between inletcompression flow of Rampressor rotor and rotor whirlingespecially in the subsonic diffuser of Rampressor rotor inletThe effect of rotor whirling on the excitation of Rampressorinlet wall has a definite phase difference Inlet excitation

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 13

0 500 1000 1500 2000 25000

200

400

600

800

1000

1200

1400

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

Frequency (Hz)

Exci

tatio

n (P

a)

6764Hz

13528Hz

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

500

1000

1500

2000

2500

3000

3500

4000

Frequency (Hz)

Exci

tatio

n (P

a)

20292Hz

6764Hz

13528Hz

(c) 119886 = 150 120583m

Figure 19 Calculation results of point D in different rotor whirling amplitudes

better in the practical engineering when Rampressor rotorwhirling frequency is less

422 Results and Discussion in Different Amplitudes of Ram-pressor RotorWhirl Excitation characteristics of Rampressorinlet are analyzed in different rotor whirling amplitudes suchas 119886 = 50 120583m 119886 = 100 120583m and 119886 = 150 120583m whenrotor whirling frequency Ω = 4250 rads Figure 19 showspressure pulsation spectrogramof Rampressor inlet key pointD (shown in Figure 6) in different rotor whirl amplitudes

The spectrograms of airflow exciting force onRampressorrotor rim surface are respectively obtained in different rotorwhirling amplitudes such as 119886 = 50 120583m 119886 = 100 120583m and 119886 =150 120583m (shown in Figure 20) when the rotor whirl frequencyΩ = 4250 rads

As shown in Figure 19 more frequency componentsemerge in the excitation spectrum such as the fundamentalfrequency component double frequency component andthird harmonic frequency component where the amplitude

of the fundamental frequency component is the highest Theamplitude of the double frequency component is smallerthan that of the fundamental frequency component buthigher than that of the third harmonic frequency componentCompared with point D excitation of 119886 = 50 120583m besides thefundamental frequency and double frequency componentsthe third harmonic component in excitation spectrum isalso generated when the rotor whirl amplitudes are 100 120583mand 150 120583m (as shown in Figures 19(b) and 19(c)) andthe amplitude of the double frequency component in theexcitation spectrum of inlet point D relatively increasesWiththe increment of rotor whirling amplitude the amplitude ofthe fundamental frequency component and double frequencycomponent in the excitation spectrum of inlet wall allgradually increases It follows from above that the complexityof Rampressor inlet excitation also increases along with theincrease of rotor whirling amplitude The above results arealso illustrated in the spectrumof airflow exciting force on therotor rim surface of Rampressor inlet as shown in Figure 20

14 Shock and Vibration

0 500 1000 1500 2000 25000

10

20

30

40

50

60

70

80

Frequency (Hz)

Exci

tatio

n (P

a)

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

50

100

150

200

Frequency (Hz)

Exci

tatio

n (P

a)

(c) 119886 = 150 120583m

Figure 20 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling amplitudes

Flow performance of Rampressor inlet is studied indifferent rotor whirling amplitudes such as 119886 = 50 120583m 119886 =100 120583m and 119886 = 150 120583mwhen rotor whirling frequencyΩ =4250 rads Figure 21 shows the curves of flow performanceparameters of Rampressor inlet during a whirling motioncycle in different rotor whirling amplitudes Along with theincrease of rotor whirling amplitude wave amplitudes oftotal-pressure recovery coefficient pressurization ratio andkinetic energy efficiency of Rampressor inlet enlarge and thestability of inlet performance reduces Therefore the stabilityof inlet performance is better in the practical engineeringwhen Rampressor rotor whirling amplitude is less

5 Conclusions

Based on Rampressor rotor model and inlet flow modelthe compression inlet flow field of Rampressor rotor isnumerically studied with consideration of Rampressor rotorwhirling Flow excitation characteristics and performance

of Rampressor inlet are analyzed and discussed under thedifferent frequencies and amplitudes of Rampressor rotorwhirling The following conclusions are obtained

Alongwith the increment of119875119903 the position of the normal

shock wave gradually moves forward and aerodynamic load-ing of the inlet wall also increases Appropriate enhancementof inlet back pressure is advantageous to the pressure ratiocompression efficiency and other performance indices wheninlet can start and normally work

More frequency components appear in the excitationspectrum of Rampressor inlet with considering Rampressorrotor whirling The main frequency component is the fun-damental frequency which is caused by the rotor whirlingBesides the fundamental frequency the double frequencycomponents emerge because of the coupling between inletcompression flow of Rampressor rotor and rotor whirlingespecially in the subsonic diffuser of Rampressor rotor inletThe effect of rotor whirling on the excitation of Rampressorinlet wall has a definite phase difference Inlet excitation

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

14 Shock and Vibration

0 500 1000 1500 2000 25000

10

20

30

40

50

60

70

80

Frequency (Hz)

Exci

tatio

n (P

a)

(a) 119886 = 50 120583m

0 500 1000 1500 2000 25000

20

40

60

80

100

120

140

160

Frequency (Hz)

Exci

tatio

n (P

a)

(b) 119886 = 100 120583m

0 500 1000 1500 2000 25000

50

100

150

200

Frequency (Hz)

Exci

tatio

n (P

a)

(c) 119886 = 150 120583m

Figure 20 Calculation results of airflow exciting force on the rotor rim surface of Rampressor inlet in different rotor whirling amplitudes

Flow performance of Rampressor inlet is studied indifferent rotor whirling amplitudes such as 119886 = 50 120583m 119886 =100 120583m and 119886 = 150 120583mwhen rotor whirling frequencyΩ =4250 rads Figure 21 shows the curves of flow performanceparameters of Rampressor inlet during a whirling motioncycle in different rotor whirling amplitudes Along with theincrease of rotor whirling amplitude wave amplitudes oftotal-pressure recovery coefficient pressurization ratio andkinetic energy efficiency of Rampressor inlet enlarge and thestability of inlet performance reduces Therefore the stabilityof inlet performance is better in the practical engineeringwhen Rampressor rotor whirling amplitude is less

5 Conclusions

Based on Rampressor rotor model and inlet flow modelthe compression inlet flow field of Rampressor rotor isnumerically studied with consideration of Rampressor rotorwhirling Flow excitation characteristics and performance

of Rampressor inlet are analyzed and discussed under thedifferent frequencies and amplitudes of Rampressor rotorwhirling The following conclusions are obtained

Alongwith the increment of119875119903 the position of the normal

shock wave gradually moves forward and aerodynamic load-ing of the inlet wall also increases Appropriate enhancementof inlet back pressure is advantageous to the pressure ratiocompression efficiency and other performance indices wheninlet can start and normally work

More frequency components appear in the excitationspectrum of Rampressor inlet with considering Rampressorrotor whirling The main frequency component is the fun-damental frequency which is caused by the rotor whirlingBesides the fundamental frequency the double frequencycomponents emerge because of the coupling between inletcompression flow of Rampressor rotor and rotor whirlingespecially in the subsonic diffuser of Rampressor rotor inletThe effect of rotor whirling on the excitation of Rampressorinlet wall has a definite phase difference Inlet excitation

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 15

0843

0844

0845

0846

0847

0848

0849

0850

0 02 04 06 08 1Time (T)

Tota

l-pre

ssur

e rec

over

y co

effici

ent

a = 50120583ma = 100120583ma = 150120583m

(a) Total-pressure recovery coefficient

1266

1268

1270

1272

1274

1276

Pres

suriz

atio

n ra

tio

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

(b) Pressurization ratio

09555

09560

09565

09570

09575

09580

0 02 04 06 08 1Time (T)

a = 50120583ma = 100120583ma = 150120583m

Kine

tic en

ergy

effici

ency

(c) Kinetic energy efficiency

Figure 21 Flow performance in different rotor whirling amplitudes during a whirling motion cycle

becomes more complex along with inlet flow path With theincrease of rotor whirling frequency and whirling amplitudethe complexity of Rampressor inlet excitation increases

With the increase of rotor whirling amplitude waveamplitudes of total-pressure recovery coefficient pressur-ization ratio and kinetic energy efficiency of Rampressorinlet gradually enlarge and the stability of inlet performancereduces But wave amplitudes of total-pressure recoverycoefficient pressurization ratio and kinetic energy efficiencyof Rampressor inlet are constant with the increment ofrotor whirling frequency and only wave frequency of inletflow performance parameters increases Stability of inletperformance is better in the practical engineering when

Rampressor rotor whirling frequency and amplitude are allless

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research presented here was supported by the NationalNatural Science Foundation of China (Grant no 51106035)

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

16 Shock and Vibration

The authors are grateful for the support providedThe authorswould like to thankDr Guanghui Zhang andMS Jianhua Lufor their constructive suggestions andor assistant provided

References

[1] S P Lawlor B J Hinkey and S G Mackin ldquoSupersoniccompressor stage design amp test resultsrdquo IMECE2004-599142004

[2] R Draper and R Steele Design of Diffuser for High Mach andHigh Swirl Applications[EBOL] 2003 httpwwwclemsonedusciesUTSRPeerReviewProceeding20contentPoster20-sessionPoster Draperpdf

[3] Ramgen Power Systems Inc ldquoRamgen engine technologyoverview briefing [EBOL]rdquo March 2002 httpwwwnetldoegovpublicationsproceedings02turbinessteelepdf

[4] R Steele P Baldwin and J Kesseli ldquoInsertion of shock wavecomp ression technology into micro turbines for increasedefficiency and reduced costsrdquo ASME Paper GT2005-682032008

[5] A D Grosvenor D A Taylor and J R Bucher ldquoMeasuredand predicted performance of a high pressure ratio supersoniccompressor rotorrdquo ASME Paper GT2008-50150 2008

[6] A D Grosvenor P M Brown and S P Lawlor ldquoDesignMethodology and Predicted Performance for a SupersonicCompressor Stagerdquo ASME Paper GT2006-90409 2006

[7] J A Han H M Yan J J Zhong P Sun and Y Yu ldquoNumericalresearch of two-dimensional flow-path in ram-rotorrdquo Journal ofAerospace Power vol 23 no 6 pp 1054ndash1060 2008

[8] J A Han J J Zhong H M Yan P Sun and Y Yu ldquoNumericalresearch of three dimensional flow-path in a ram-rotorrdquo Journalof Aerospace Power vol 24 no 5 pp 1079ndash1088 2009

[9] L Yang J J Zhong and J A Han ldquoNumerical research of theram-rotor with different geometric parametersrdquo ASME PaperGT2011-46051 2011

[10] S P Lawlor and P Baldwin ldquoConceptual design of a supersonicCO2compressorrdquo ASME Paper GT2005-68349 2005

[11] Ramgen Power Systems Inc Gas Turbine Engine Shock WaveBased Ramgen Engine httpwwwramgencomapps ASCEbreakthroughhtm

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of