Development of a Very High Pressure Ratio Single Stage Centrifugal Compressor

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International Review on Modelling and Simulations (I.RE.MO.S.), Vol. xx, n. x

June 2008

Manuscript received and revised May 2008, accepted June 2008 Copyright © 200 8 Praise Worthy Prize S.r.l. - All rightsreserved

Development of a Very High Pressure Ratio Single Stage CentrifugalCompressor

Valeriu Dragan 1, Ion Malael 2, Bogdan Gherman 3

Abstract – The current paper refers to the preliminary design of a high pressure single stagecentrifugal compressor for use in a novel jet engine architecture. Computational Fluid Dynamicsmethods are used to determine flow patterns and increase design efficiency as well as managetradeoffs. A finalized pre-design geometry is presented and discussed in detail. Further work willinvolve tailoring the compressor and the rest of the engine flow path to better integrate inachieving peak performance. Copyright © 2009 Praise Worthy Prize S.r.l. - All rights reserved.

Keywords : Centrifugal compressor, High pressure ratio, CFD, k-omega SST, Tangential Pulse Detonation Engine

I. Introduction

The purpose of this paper is to present the details of asingle stage 14:1 centrifugal compressor which is to beused in a novel Pulse Detonation Engine (PDE)architecture.

Although the goal is to obtain a 6:1 static to total pressure ratio, the total to total performance parameterswill also be discussed since they offer betterrepresentation and correlation to existing designs.

Current state of the art examples of very high pressure ratio single stage centrifugal compressors arescarce in the open literature, Refs [1, 2]. However turbomachinery designers are currently exploring the practicalaspects of the implementation of such stages.

Since this is merely a pre-design stage, we will onlyfocus on the aerodynamics of the centrifugal rotor.

Traditional pre-design methods, especially the linearmodels Refs [3, 4] involve specifying a total-to-total

pressure ratio as a design parameter and a diffusionfactor or relative Mach number ratio. In our case a blendof the two had to be implemented as a singular design

parameter in the in-house design code in order to designfor the static outlet pressure.

Since the engine architecture implies that the entireengine is in rotating motion - hence there are no large

parts in relative motion, the use of a vaned, stationarydiffuser is excluded from the compressor design. Also,since the rotor casing is linked to the burning chamberassembly, it makes sense that the compressor rotor beshrouded, avoiding therefore the tip clearance leakagelosses - which can be significant Refs[5-7].

Due to the fact that the minimal detonation cell sizeis higher than the outlet height of the centrifugalcompressor rotor, an expansion rotating plenum is

envisioned.

In the expansion plenum a diffusion process willoccur leading to a significant static pressure recoverywhich will increase the static to total pressure ratio andefficiency. Another aspect linked to the design of the

plenum is the natural de-swirling of the fluid if the plenum expands radially inward, rather than outward -which will help the integration of the compressor withthe engine assembly. The specific problems andenvisioned solutions for the plenum crossover, size andslope distribution are however, beyond the scope of this

paper.

II. The 3D CFD Compressor Simulation

At this stage, the compressor design is tested in athorough manner, using advanced CFD methods,

particularly the RANS k-omega SST with curvature androtation compensation model and structured grid aroundthe rotor geometry.

Since the SST model used is a blend of two turbulencemodels Ref [8], both the standard k-epsilon Ref [9] andWilcox's k-omega Ref [10] have been used. The k-epsilon has been re-expressed by Menter into k-omegaformulation, in order to make the two models blend,using a blending function, F 1. In doing so, the overallresults are less influenced by the user specified inletvalue of omega but make full use of the superior

boundary layer modeling of the Wilcox model - whichdoes not use wall functions, as opposed to k-epsilon.

Therefore, the standard k-epsilon model is re-expressed:

( ) +

=

+2

+ − ′ (1)

( ) + = +

2 +

2 + 2 −22 , (2)

whereas the Wilcox model reads:



Valeriu Dragan, Ion Malael, Bogdan Gherman

Copyright © 200 8 Praise Worthy Prize S.r.l. - All rights reserved International Review on Modelling and Simulations, Vol. x, N. x

( ) +

=

+1

+ − ′ (3)

( ) + = +

1 +

1 −12 .

(4)

In addition to the blending of the two above models,the SST turbulence model used also the followingformulation for the eddy-viscosity, =

1

max ( 1 , 2 ) where = / , S is an invariant measure

of the strain rate and F 2 is a second blending functionintroduced by Menter [11].

Also, due to the particular problems implied by therotating domain and the high blade loading - associatedwith a high relavite curvature betwen the blade and thenatural streamline path-, a correction for curvature androtation, proposed by Spalart and Shur [12] andimplemented in Ansys CFX.

The mesh in all cases is based on a blocking structurewhich maintains a boundary layer type discretizationnear the airfoils and the hub and shroud surfaces. Thiseases the control over orthogonality, aspect ratio as wellas growth ratio (which was chosen ~1.15:1) and y+(chosen to be ~1, as per the general recommendations fork-omega RANS models).

Initially, the cases were ran with total inlet pressure – static outlet pressure boundary conditions, in order tospeed up convergence; the result file (*.res) was thenused for the initialization of the much sounder(physically wise) total inlet pressure-outlet mass flow

boundary conditions.

Using the turbo-macros available in Ansys CFX, theglobal parameters of the rotors were deduced andsynthesized in histograms. Since the requirements of thecompressor rotor are atypical, i.e. high static to total

pressure ratio in one stage, multiple approaches weretried before settling on the final functional typologywhich was then refined in order to obtain the parametersin admissible margins of loss. It must be stated that theefficiency considered is the static to total isentropic and

polytropic efficiencies, which – from physics – cannotexceed 50% (under the assumption that the total to totalisentropic and polytropic efficiency is around 80%).

Three configurations were considered, as presented in

the previous deliverable, as follows:1. Rotor – plenum with a relatively (for the currentcontext) low total to total pressure ratio (8:1) design

point.2. Rotor with low outlet Mach number – in order to

directly recover the dynamic pressure3. Rotor with medium outlet Mach number and high

pressure ratio design point.

II.1. The Rotor – Plenum configuration

Working under the assumption that an expansion plenum will fulfill the same role as a collector (or

volute), the flow from the rotor was redirected through a

90° annulus into a rotating plenum (which rotates at thesame rate as the rotor itself).

The CFD simulations carried out were preceded bythroughflow analysis in order to insure the correct

pressure recovery of the assembly. After a number ofruns, the conclusion was that the radius required by the

bend in order to avoid flow separation (and unsteadyfluctuations which may impair the operation of the rotor)will have to be larger than the initial throughflowcalculations predicted.

Fig. 1. The plenum rotor configuration geometry

Note that the apparent angle of flow in meridional plane is exaggerated due to the 90° bend of the plenum

It appears that the concept of recovering thedynamic pressure through the use of a plenum leads tohigh total pressure losses due to flow separation at the

plenum bend. This concept has been abandoned for thefurther design stages.

TABLE ITHE ROTOR BASIC GEOMETRIC AND THERMODYNAMIC DESIGN POINT

PARAMETERS

Parameter Value

Number of blades 14 Main + 14 Splitter blades

Backsweep angle 0° Relative velocity

ratio(before plenum)

0.5

Diameter 210 [mm] Blade height 5.47 [mm] Leading edge

inclination 19°

Blade thickness hub 2 [mm] Blade thickness

shroud 2 [mm]

Axial length 0.15





Fig. 2 The meridional velocity vector plot

a.

b.Fig.3 The absolute velocity flow field at (a.) 20% of blade height (b.)

80% of blade height.

TABLE IITHE MASS AVERAGED PERFORMANCES OF THE ROTOR

Quantity Inlet Outlet RatioTemperature 285.12 [K] 492.544 [K] 1.73

Total Temperature 301.402 [K] 590.327 [K] 1.96 Pressure 83618.1 [Pa] 322823 [Pa] 3.86

Total Pressure 101287 [Pa] 611720 [Pa] 6.03Temperature 285.12 [K] 492.544 [K] 1.73

TABLE IIITHE POWER CONSUMPTION AND EFFICIENCY OF THE ROTOR

Quantity Value

Total-to-static isen.efficiency 0.408516Total-to-static poly.

efficiency 0.491583 Power (all blades) 580504 [W]

II.2. The Rotor with low outlet Mach numberconfiguration

Another approach was to reduce the outlet Machnumber in order to decrease the minimal curvature radiusof the plenum hub. Also, because the outlet velocity isalready small, there is less dynamic pressure to berecovered – hence the static pressure of the outlet flow isalready near the values required by the project. In orderto minimize the workload on the parts downstream(namely the combustor) the beta (axial) outlet angle wasset to 30° (backsweep) this makes the rotor prone tounstable operation (surge as well as stall) due to thelowering of the pressure gradient on the upper side of the

blades (which leads to flow separation pockets near thetrailing edge). As the CFD results presented below show,the backsweep angle of the blades does little to insure theflow angle once the air is clear of the blades. This is aclear indication that the slip factor is highly dependent onthe angular velocity of the rotor (in addition to number of

blades, backsweep and the diameter ratio). Because therecirculation vortices also move upstream (against thecentrifugal force), they consume a part of the shaft power

proportionate with their mass and temperature gradient.Increasing the number of splitters may be an option,

however, at this point, the next step considered was to better correlate the backsweep angle with the flow angle,in order to obtain higher efficiencies and better flows.

TABLE IVTHE ROTOR BASIC GEOMETRIC AND THERMODYNAMIC DESIGN POINT

PARAMETERS

Parameter Value

Number of blades 14 Main + 14 Splitter blades

Backsweep angle 30° Relative velocity ratio

(before plenum) 0.25

Diameter 231 [mm] Blade height 14.73 [mm]

Leading edge inclination 19° Blade thickness hub 3 [mm]

Blade thickness shroud 1.5 [mm]





Fig. 4 The rotor geometry

Fig. 5 The relative velocity plot for a meridional plane surface

As seen above, the relative outlet velocity, the onethat matters in this instance, since the combustors arealso rotating), is around 80 m/s. This means that the bulkof the total pressure given by the rotor is static.

a.

b.Fig. 6 The absolute velocity flow field at (a.) 20% of blade height (b.)

50% of blade height.

From Figure 6 b it can easily be seen that the flowseparates early (at ~ 60% of the chord, measured fromthe leading edge). This generates high losses in the rotorefficiency as well as a low slip factor. In turn, the lowslip factor leads to an outlet flow angle which is nolonger close to 30° - as initially desired – thereforedenying the purpose of having a blade with low

backsweep. A known solution for increasing the slipfactor is to increase the number of blades or splitter rows.However, due to the high angular velocity of the rotor aswell as the high blade loadings, the blades will have to bethicker than the typical 1.5 mm, making the increase innumber of blades difficult due to flow choking.

The global results from this simulation are listed below. It needs to be pointed out that neither theefficiency nor the desired pressure ratio were achieved,mainly due to the large recirculation vortices formed onthe suction sides of the blades.

TABLE VTHE MASS AVERAGED PERFORMANCES OF THE ROTOR

Quantity Inlet Outlet RatioTemperature 284.186 [K] 534.737 [K] 1.88Total Temperature 301.052 [K] 682.415 [K] 2.27

Pressure 83755.7 [Pa] 470482 [Pa] 5.62

Total Pressure 101287 [Pa] 1.14175e6 [Pa] 11.27Temperature 284.186 [K] 534.737 [K] 1.88

TABLE VITHE POWER CONSUMPTION AND EFFICIENCY OF THE ROTOR

Quantity ValueTotal-to-static isen.

efficiency 0.432265Total-to-static poly.

efficiency 0.534027 Power (all blades) 651.4 [kW]





II.3. Rotor with medium outlet Mach number and high pressure ratio design point

Lastly, a highly backswept blade rotor was tested,tailored to have a static to total pressure ratio of 6.4:1 anda total to total pressure ratio above 10:1. This step wastaken due in part to the high pressure losses expected atthe combustor inlet.

A series of modifications were employed in order toreduce the recirculation zone, by increasing the

backsweep angle of the shroud airfoil.

TABLE VII THE ROTOR BASIC GEOMETRIC AND THERMODYNAMIC DESIGN POINT

PARAMETERS

Parameter Value

Number of blades 14 M + 14 s Backsweep angle 65°

Relative velocity ratio(before plenum)

0.45

Diameter 251 [mm] Blade height 8.27 [mm]

Leading edge inclination 0° Blade thickness hub 3 [mm]

Blade thickness shroud 3 [mm]

Fig. 7 The axonometric view of the rotor

a

b

cFig. 8 The mesh used a) leading edge detail, b) trailing edge detail c)overall view

Fig. 9 The relative velocity plot for a meridional plane surface

Fig.10 The absolute velocity flow field at 20% of blade height





Fig.11 The absolute velocity flow field at 80% of blade height

TABLE VIITHE MASS AVERAGED PERFORMANCES OF THE ROTOR

Quantity Inlet Outlet RatioTemperature 290.162 [K] 584.4 [K] 2.01Total Temperature 301.03 [K] 722.487 [K] 2.41

Pressure 90126 [Pa] 678078 [Pa] 7.52Total Pressure 101287 [Pa] 1425910 [Pa] 14.1Temperature 290.162 [K] 584.4 [K] 2.01

TABLE VITHE POWER CONSUMPTION AND EFFICIENCY OF THE ROTOR

Quantity ValueTotal-to-total isen.

efficiency 0.801631Total-to-static isen.

efficiency 0.512363Total-to-total poly.

efficiency 0.859711Total-to-static poly.

efficiency 0.618054 Power 705.5 [kW]

An argument can be made in favor of the use of alinear design method, based on the slip factor paradigm,rather than a method based on the jet-wake concept, suchas the TEIS [13-14] model. This is because the flowfield, as seen in Figs.10-12, consists largely of the jetregion, minimizing the impact of a more elaboratemethodology that factors in the losses associated with thewake region.

Fig.12 - 3D streamlines of the flow inside the compressor

Various slip factor models have been proposed in theliterature [15-17], each having its advantages anddisadvantages in terms of range and accuracy. The slipfactor correlation in our case consists of an algorithmwhich considers four slip consecrated factors andanalyzes the trend of the results, iteratively pruning the

results that are farthest from the average.The resulting flow coefficient is much higher than the

typical charts presented by Casey and Robinson [18] orCasey and Marty [19].

_ . .. .

2

m T E

T E

C

U

(5)

. . 0.6057T E

where

_ . .m T E C is the aria averaged meridional throughflow

velocity at the trailing edge

2

U is the peripheral wheel speed

However, the correlations with the polytropicefficiency seem not applicable in this case, possibly dueto the local turbo machinery Mach number, Eq.2, whichis quite high in some portions of the outlet, as can beinferred from the velocity plot in Fig.12 as well as fromthe Relative Mach number at the trailing edge depicted inFig.13.

2_ . .

0

T E

t

air

V M

k R T

(6)

where

2_ . .T E V is the absolute air velocity at the trailing edge

0T is the temperature at the rotor inlet.

Note that this is not an actual Mach number, but ratheran abstract concept used in turbo-machinery design.

Fig.13 - Relative Mach number distribution at the outlet

From Fig.12 it can be seen that the apparentrecirculation region seen at the tip of the blade is actuallya 3-dimensional vortex with the axis oriented on thethroughflow direction. This explains why the rotor

blockage is not high, as well as the fact that the rotordiffuses the flow in an efficient manner.

Another argument in favor of the efficient diffusion is





the entropy distribution seen in Fig.14.

Fig.14 - Entropy distribution at the outlet

III. Conclusions and Further Work

The main goal of the paper was to provide acentrifugal rotor design and its CFD simulation resultswhich can achieve a static to total pressure ratio of atleast 6:1 for a mass flow of around 1.7 kg/sec. Variousconfigurations were tested and summery judged beforesettling on the final type of rotor. The chosen rotor hasthe characteristics described in section 2.c, where themesh and typical CFD results are also presented. Due tothe high speed of the rotor and the high pressure ratiodesign point, the only viable option was to have a highly

backswept bladed rotor as opposed to a straight radialone. The latter was dismissed earlier in the study (seesection 2.b.) because the slip factor was too low, whichmeant that the efficiency of the rotor was too low (due to

the recirculation zone formed on the blades) and that thefluid angle would also be high – which denies the

purpose of having no backsweep for the blades.Therefore, a highly backswept rotor was designed,

reaching the required specifications, namely the static tototal pressure ratio of 6.3:1 at a 1.72 kg/sec mass flow.Due to the fact that the whole TIDE assembly is rotatingat the same speed, only the static to total efficiencieswere listed, as they are the most relevant – howeversmall they may seem. It must be pointed out that both thetotal to total pressure ratio as well as efficiencies aresignificantly higher than the ones usable for the TIDE

configuration.Further work will include the design and CFD testingof the downstream diffusion plenum and also a CFDoptimization design study for the rotor-plenum assembly,with the primary goal of optimizing the static-to-totalefficiency.

Acknowledgements

The research presented in this paper is the result of theProject "Tangential Impulse Detonation Engine" TIDE,financed by the European Commission, Grant agreementno: 335091

References[1] Colin Osbosne, P. W. Runstadler, Jr., and W. Dodd Stacy,

Aerodynamic and mechanical design of an 8:1 pressure ratiocentrifugal compressor,NASA CR-134782 , April 1975.

[2] William 1. McAnUf, 10:1 Pressure ratio single stage centrifugal

compressor program, , USAAMRDL Technical Report 74-15,April 1974.

[3] David Japikse, Nicholas C. Baines, Introduction toTurbomachinery, ISBN-13: 978-0933283107,Concepts ETI 1997.

[4] David Japiske, Centrifugal Compressor Design and Performance,ISBN-13: 978-0933283039,Concepts ETI 1996.

[5] S.M. Swamy, V. Pandurangadu, Effect of tip clearence on performance of a centrifugal compressor, IJRET: InternationalJournal of Research in Engineering and Technology eISSN: 2319-1163,Volume: 02 Issue: 09 | Sep-2013 . H.

[6] N. Sitaram and S. M. Swamy, Performance Improvement of aCentrifugal Compressor by Passive Means, International Journalof Rotating Machinery Volume 2012,http://dx.doi.org/10.1155/2012/727259.

[7] Hark-Jin Eum, Young-Seok Kang, Shin-Hyoung Kang, Tipclearance effect on through-flow and performance of a

centrifugal compressor, KSME International Journal, June 2004,Volume 18, Issue 6, pp 979-989 .[8] Menter, F.R., “Multiscale model for turbulent flows”, In 24th

Fluid Dynamics Conference. American Institute of Aeronauticsand Astronautics, 1993.

[9] **Ansys CFX User Guide, 2.2.2.1. The k-epsilon Model inANSYS CFX, retreived 2015

[10] Wilcox, D.C., “Multiscale model for turbulent flows”, In AIAA24th Aerospace Sciences Meeting. American Institute ofAeronautics and Astronautics, 1986.

[11] Menter, F.R., “Two -equation eddy-viscosity turbulence modelsfor engineering applications”, AIAA -Journal., 32(8), pp. 1598 -1605, 1994.

[12] Spalart, P.R., and Shur, M. “On the sensitization of turbulencemodels to rotation and curvature”, Aerospace Sci. Tech., 1(5), pp.297-302, 1997.

[13]

Sungho Yoon, Je Hyun Baek, A sensitivity analysis ofcentrifugal compressors’ empirical models, KSME InternationalJournal September 2001, Volume 15, Issue 9, pp 1292-1301.

[14] Robert John Pelton, One-Dimensional Radial FlowTurbomachinery Performance Modeling, Department ofMechanical Engineering Brigham Young University December2007.

[15] Abraham Frenk, A slip factor calculation in centrifugal impellers based on linear cascade data, Becker Turbo System Engineering(2005).

[16] Alfred F. Stahler, The Slip Factor of a Radial Bladed CentrifugalCompressor, J. Eng. Gas Turbines Power 87(2), 181-188 (Apr 01,1965) (8 pages) doi:10.1115/1.3678159.

[17] F. J. Wiesner, A Review of Slip Factors for Centrifugal Impellers,J. Eng. Gas Turbines Power 89(4), 558-566 (Oct 01, 1967) (9

pages) doi:10.1115/1.3616734.[18] Casey M.V., Robinson C.J. (2006), “A guide to turbocharger

compressor characteristics”, in Dieselmotorentechnik”, 10thSymposium, 30-31 March, 2006, Ostfildern, Ed. M. Bargende, ,TAE Esslingen, ISBN 3-924813-65-5.

[19] Casey, M.V., and Marty, F., (1985), "Centrifugal compressors - performance at design and off-design conditions", Proceedings ofthe Institute of Refrigeration, Vol. 82, 1985-1986, pages 71-80.

Authors’ information 1 NRDI Gas Turbines Comoti, Buchares, Romania. Obtained his Ph.D.title from the Aerospace Engineering Faculty of the PolitehnicaUniversity of Bucharest in 2012 and has since been a scientificresearcher with the CFD department of the Comoti National Institute.His research includes the Coanda effect, turbomachinery design andoptimization as well as theoretical and applied physics andmathematics.





2 NRDI Gas Turbines Comoti, Buchares, Romania. Obtained his Ph.D.title from the Aerospace Engineering Faculty of the PolitehnicaUniversity of Bucharest in 2013. His scientific researcher activitywithin the CFD department of the Comoti National Institute spans for 6years. His research includes wind turbine design and development,CFD simulations on screw compressors, flow control methods andturbomachinery design.

3

NRDI Gas Turbines Comoti, Buchares, Romania. Obtained his Ph.D.title from the Aerospace Engineering Faculty of the PolitehnicaUniversity of Bucharest in 2013 and has since been a the head of theCFD department of the Comoti National Institute. His research includesthermo-acoustics, combustion and turbomachinery design.

Development of a Very High Pressure Ratio Single Stage Centrifugal Compressor

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