Turbine Design Manual

AXIAL TURBINE DESIGN MANUAL

CHAPTER 4

PART 2


Dr K W RAMSDENDIRECTOR GAS TURBINE TECHNOLOGY PROGRAMMESDEPARTMENT OF POWER AND PROPULSIONSCHOOL OF ENGINEERINGCRANFIELD UNIVERSITYCRANFIELD, BEDFORDMK43 0AL

DISCLAIMER

SCHOOL OF ENGINEERINGDEPARTMENT OF POWER AND PROPULSION

These notes have been prepared by Cranfield University for the personal useof course delegates. Accordingly, they may not be communicated to a thirdparty without the express permission of the author.

The notes are intended to support the course in which they are to bepresented as defined by the lecture programme. However the content maybe more comprehensive than the presentations they are supporting. Inaddition, the notes may cover topics which are not presented in thepresentations.

Some of the data contained in the notes may have been obtained from publicliterature. However, in such cases, the corresponding manufacturers ororiginators are in no way responsible for the accuracy of such material.

All the information provided has been judged in good faith as appropriate forthe course. However, Cranfield University accepts no liability resulting fromthe use of such information.


SUMMARY

This document facilitates the aerodynamic design of both a low and high pressureturbine allowing the user to work step by step through the calculation procedure.

The turbines are matched to a two spool compressor having an overall pressure ratioof 16.

One of two alternative turbine entry temperatures may be chosen, namely, 1250K or1650K representative of industrial and aeronautical technology, respectively.

The HP turbine RPM is chosen at 15000 whilst that of the LP is estimated by limitingthe LP compressor stage one rotor tip relative Mach number to 1.15.

In both cases, the turbines have a mean diameter of 0.45m.

The inlet Mach number to the HP turbine is 0.30 and the corresponding axial velocityis maintained constant throughout.

A critical assessment is carried out in terms of likely performance and, whereappropriate, suggestions made for modifications taking into account the prescribedapplication.

The results calculated by the user can be directely compared with the valuesappended.


CONTENTS

PAGE

BACKGROUND NOTES

NOTATION AND UNITS 1

1.0 INTRODUCTION 2ATWO SHAFT ARRANGEMENT 2B

2.0 SPECIFICATION

2.1 THE COMPRESSOR SYSTEM 3

2.2 THE HP TURBINE SYSTEM 4

3.0 HP TURBINE DESIGN CONSTRAINTS 5

4.0 HP TURBINE ANNULUS DIAGRAM 5

5.0 HP TURBINE DESIGN TABULATION

5.1 OVERALL SPECIFICATION 6

5.2 INLET ANNULUS GEOMETRY 6

5.3 EFFICIENCY PREDICTION 6

5.4 OUTLET ANNULUS GEOMETRY 7

6.0 HP TURBINE FREE VORTEX DESIGN

6.1A DESIGN TABULATION - TET = 1250K 8A

6.1B VELOCITY TRIANGLES - TET = 1250K 8B



7.0 HP TURBINE DESIGN ASSESSMENT

7.1A DESIGN SUMMARY - TET = 1250K 10A

7.1B RECOMMENDATIONS - TET = 1250K 10B



8.1B RECOMMENDATIONS TET = 1650 K 11B

(CONTINUED)

AXIAL TURBINE DESIGN MANUALCONTENTS ( CONTINUED )

PAGE

9.0 LOW PRESSURE TURBINE DESIGN

9.1 LP COMPRESSOR SPECIFICATION 12

9.2 LP COMPRESSOR DESIGN CONSTRAINTS 12

9.3 ESTIMATION OF LP COMPRESSOR ( LP TURBINE ) RPM 13

10.0 LP TURBINE OVERALL DESIGN

10.1 OVERALL SPECIFICATION 14

10.2 HP TURBINE EXIT ANNULUS GEOMOETRY 14

10.3 INTER-TURBINE ANNULUS GEOMETRY ESTIMATION 1510.4 LP TURBINE EFFICIENCY PREDICTION 16

10.5 LP TURBINE OUTLET ANNULUS GEOMETRY 17

11.0 LP TURBINE FREE VORTEX DESIGN


11.1B VELOCITY TRIANGLES - TET =1250K 18B



12.0 LP TURBINE DESIGN ASSESMENT





( CONTINUED)

AXIAL TURBINE DESIGN MANUALCONTENTS (CONTINUED)

ANNEXES

ANNEX A

PAGE

SUMMARY OF CONTENTS A1

A 1.O HP TURBINE DESIGN TABULATION

A 1.1 OVERALL SPECIFICATION A2

A 1.2 INLET ANNULUS GEOMETRY A2

A 1.3 EFFICIENCY PREDICTION A2

A 1.4 OUTLET ANNULUS GEOMETRY A3

A 2.0 HP TURBINE FREE VORTEX DESIGN

A 2.11 DESIGN TABULATION - TET = 1250K A4A

A 2.1B VELOCITY TRIANGLES-TET = 1250K A4B

A 2.2A DESIGN TABULATION - TET = 1650K A5A

A 2.2B VELOCITY TRIANGLES- TET = 1650K A5B

A 3.0 HP TURBINE DESIGN ASSESSMENT

A3.1A DESIGN SUMMARY - TET = 1250K A6A

A 3.1B DESIGN SUMMARY - TET 1650K A6B

ANNEX B

B 1.0 GUIDNACE NOTES FOR CALCULATIONS B1

ANNEX C

GAMMA = 1.40 C1 AND C2



(CONTINUED)

AXIAL TURBINE DESIGN MANUALCONTENTS (CONTINUED)

ANNEXES

ANNEX D

PAGE

D 1.0 SMITH'S EFFICIENCY CORRELATION D1

ANNEX E

E1.0 LOW PRESSURE TURBINE DESIGN TABULATION

E1.1 ESTIMATION OF LP COMPRESSOR (LP TURBINE) RPM E1

E1.2 LP TURBINE INLET ANNULUS GEOMETRY E2

E1.3 LP TURBINE EFFICIENCY PREDICTION E2

E1.4 LP TURBINE OUTLET ANNULUS GEOMETRY E3

E2.0 LOW PRESSURE TURBINE FREE VORTEX DESIGN

E2.1A DESIGN TABULATION - TET = 1250K E4A

E2.1B DESIGN TABULATION - TET = 1650K E4B

E3.0 LOW PRESSURE TURBINE FREE VORTEX DESIGN

E3.1A DESIGN TABULATION - TET = 1250K E5A

E3.1B DESIGN TABULATION - TET = 1650K E5B

E4.0 LOW PRESSURE TURBINE DESIGN ASSESSMENT

E4.1A DESIGN SUMMARY - TET = 1250K E6A

E4.1B DESIGN SUMMARY - TET = 1650K E6B

ANNEX F

F1.0 INTER-TURBINE ANNULUS GEOMETRY ESTIMATION F1

AXIAL TURBINE DESIGN MANUAL-1-

NOTATION AND UNITS

SYMBOLS UNITS

A Cross sectional area m2Cp Specific heat at constant pressure Joules / kg.KD Diameter mh Annulus height mH Stagnation enthalpy Joules / kgM Mach numberN Revs per minute min. -1p Static pressure n/m2P Stagnation pressure n/m2q Mass flow function (WT /Ap ) 1/( Joules kg/K )Q Mass flow function (WT /AP ) 1/( Joules kg/K )R Gas constant Joules/kg.KRc Compressor pressure ratioRov Overall pressure ratiot Static temperature KT Stagnation temperature KU Blade speed m/secV Velocity m/secW Mass flow kg/sec Gas angle degrees Ratio of specific heats Change in: Work done factor

ABBREVIATIONS SUFFICES

BMH Blade mid height a Axialisent Isentropic efficiency ann Annuluspoly Polytropic efficiency in Stage inletFAR Fuel air ratio mean At mid heightHP High pressure out outletLP Low pressure R (or H) At the root (or hub)NGV Nozzle guide vane T At the tip or casingstoi. Stoichiometric w Whirl directionTET Turbine entry temperature 0 Nozzle outlet (abs)

1 Rotor inlet (rel)2 Rotor outlet (rel)3 Rotor outlet (abs)

AXIAL TURBINE DESIGN MANUAL-2A-

1.0 INTRODUCTION

This Document facilitates the aerodynamic design of both a low and high pressure turbineallowing the user to work step by step through the calculation procedure.

The turbines are matched to a two spool compressor having an overall pressure ratio of 16.

One of two alternative turbine entry temperatures may be chosen, namely 1250K or 1650K,representative of industrial and aeronautical technology, respectively.

The HP turbine RPM is chosen at 15000 whilst that of the LP is estimated by limiting the LPcompressor (stage one) rotor tip relative Mach number to 1.15.

In both cases, the turbines have a mean diameter of 0.45m.

The inlet Mach number to the HP turbine is 0.3 and the corresponding axial volocity ismaintained constant throughout.

A critical assessment is carried out in terms of likely performance and where appropriate,suggestions made for improvements taking into account the prescribed application.

The results estimated by the user may be compared with values appended.

The following design constraints are imposed :-

Constant axial velocityConstant mean diameter = 0.45mRPM = 1500050% reaction at blade mid heightFree vortex flow distributionAxial HP inlet flow with a Mach number of 0.3Straight sided annulus walls

AXIAL TURBINE DESIGN MANUAL2B

LPC HPC HPT LPT

TWO SHAFT TURBOJET (OR TURBOFAN CORE ENGINE)

FIGURE 1


SPECIFICATION


2.0 SPECIFICATION

2.1 THE COMPRESSOR SYSTEM.

The compressor system has the following specification :

Inlet temperature (T1) 300

Inlet pressure (P1 ) 101325

Overall pressure ratio (Rov) 16.0

LP pressure ratio (Rc) 3.56

HP pressure ratio (Rc) 4.494

HP RPM (Nhp) 15000

Polytropic efficiency (poly) ( both spools ) 0.90

Mass flow (W) 40.0

With these data and the formulae below, the following can be calculated :

LP COMPRESSOR HP COMPRESSOR

Pressure ratio 3.560 4.494

isent0.882 0.879

Inlet temperature 300 449

Temperature rise T 149 274

Outlet temperature 449 723

Power = W. Cp. T(megawatts)

5.99 11.03

NOTE :1R

1R

poly

1

c

1

cisent

1RT

T1-

cisent

1

and1

RCp

where: = 1.4 and R = 287 ie, Cp = 1005


2.0 SPECIFICATION2.2 THE HP TURBINE SYSTEMThe hp turbine is required to supply only the hp compressor power since it is assumed thatthere are no mechanical losses.The turbine mass flow is the compressor flow plus the fuel flow. The latter is obtained bycalculating the fuel flow and hence the fuel/air ratio (FAR) required to raise the compressoroutlet temperature to the specified TET. This is calculated based on an enthalpy balance. Thecorresponding values of FAR are shown in the table below assuming a combustor efficiencyof 100%.

The mean specific heat is calculated from values of Cp for both air as well as for thecombustion products. See for example Walsh and Fletcher.

Cp air = ao + a1 X+ a2X2 + a3X3 + a4X4...

Where X = (T/1000)

Cp kerosene = Cp f= bo + b1 X+ b2X2 + b3X3 + b4X4...

Cp comb_gas = Cp air+(FAR/(1+FAR))* Cp fR=287.05-0.0099FAR+1e-7(FAR2)

A0 0.992313 B0 -0.71887A1 0.236688 B1 8.747481A2 -1.852150 B2 -15.8632A3 6.083152 B3 17.2541A4 -8.89393 B4 -10.2338A5 7.097112 B5 3.081778A6 -3.23473 B6 -0.36111A7 0.794571 B7 -0.00392A8 -0.08187 A8 -0.71887

Based on a similar, but slightly different, approach the following values are used here:

Compressor outlet temperature (K) 723 723

Turbine entry temperature (K) 1250 1650

Combustor temperature rise (K) 526.7 927

Fuel / Air Ratio (FAR) 0.0159 0.0289

Mass Flow (air +fuel) (Kg/s) 40.64 41.16

HP Turbine Power (megawatts)(To drive hp compressor)

11.03 11.03

Mean specific heat - Cp (joules/Kg.K) 1184 1275.5

Inlet stagnation pressure - Pin (n/m2)(Assumes 5% Combustor pressure loss)

1540140 1540140

Ratio of specific heats, = 1/(1-R/Cp) 1.32 1.29

NOTE: GAS CONSTANT - R = 287 joules/Kg K


HP TURBINE DESIGN


3.0 HP TURBINE DESIGN CONSTRAINTS.

The following design constraints are imposed :-

Axial inlet flow with a Mach number of 0.3Constant axial velocityConstant mean diameterRPM = 1500050% reaction at blade mid heightFree vortex flow distributionStraight sided annulus wallsConstant mean diameter = 0.45m

The assumption of constant axial velocity would require an iteration on NGV exit gas angle, o, so that mass flow continuity is satisfied.The annulus area distribution would then be an automatic outcome of the calculations.For simplicity, however, it is assumed that the annulus is straight sided (see the diagrambelow). This introduces only a small error.Additionally, it is assumed that the exit plane of the NGV is half way along the annulus. Thisimplies that the axial chord of the NGV is greater than that of the rotor which allows areasonable spacing between the blade rows.

4.0 HP TURBINE ANNULUS DIAGRAM.

The following general annulus configuration is used :-

AXIS

h outh in

L / 2

L

NGV BLADE

D mean


5.0 HP TURBINE DESIGN TABULATION.

5.1 OVERALL SPECIFICATION.

TET 1250 1650

Mass flow W (Kg / s) 40.64 41.16

Power (megawatts) 11.03 11.03

Specific Heat Cp (and ) 1184 (1.32) 1275.7 (1.290)

5.2 INLET ANNULUS GEOMETRY.

P = 16 x 101325 x 0.95

Inlet Mach Number 0.30 0.30

Q = W.T / A.P(See Tables - ANNEX C )A = W.T / Q.P

h = A / (.Dmean)

Dtip = Dmean + h

Dhub = Dmean - h

Hub/Tip Ratio = Dhub / Dtip

5.3 EFFICIENCY PREDICTION - (MEAN HEIGHT)

Temperature Drop T = Power / W.Cp

Umean = U = RPM. Dmean / 60

H/U2 = CpT /U2Va / Tin( for Min = 0.3, See ANNEX C - use appropiate )Va

Va / U

isent (Smith's Chart value minus 2 %)(See Annex D)

NOTE : SEE PAGE A2 FOR SOLUTIONS


5.0 HP TURBINE DESIGN TABULATION ( CONT. )

5.4 OUTLET ANNULUS GEOMETRY.

TET 1250 1650

Va

T3 = Tin - T

Work done factor 0.98 0.98

Vw = (H/U2) . U/

Vw3 = (Vw-Umean) /2(50 % Reaction)

3 = tan-1 (Vw3/Va)

V3 = Va/Cos3

V3/T3

M3 (See ANNEX C, use appropiate )

Q3 (See ANNEX C)

R = (1-T/ (isent. Tin)) /(-1)

P3 = Pin x Rov (See note below)

A3 = W.T3 / P3.Q3

Aann = A3 / Cos3

h = Aann / ( Dmean)

Dtip = Dmean + h

Dhub = Dmean - h

Hub/Tip Ratio = Dhub/Dtip

NOTE: P3 = Pout (In the direction of V3)

SEE PAGE A3 FOR SOLUTIONS


6.0 HP TURBINE-FREE VORTEX DESIGN

6.1A DESIGN TABULATION - TET = 1250K

ROOT BMH TIP

D (NGV exit) = (Din + Dout) /2

D (Rotor exit) (See Table 5.4 - page 7)

Va (Constant radially)

Vw3mean (See Table 5.4 - Page 7)

Vwomean = (Vw-Vw3) mean(See Table 5.4)Vwo = Vwomean x Dmean/D(D at NGV exit)

o = tan-1 (Vwo / Va)

Vw3 = Vw3mean . Dmean/D(D at rotor exit)

3 = tan-1 (Vw3 / Va)

U (For exit velocity triangles)= Umean . D/Dmean (D at rotor exit)

Vo = Va / Coso

Nozzle Acceleration, Vo / Vin (= Vo / Va)

V1 = (Va2+(Vwo-U)2)

1 = Cos-1 (Va / V1)

V2 = (Va2+(U+Vw3)2)

2 = Cos-1 (Va / V2)

Rotor Acceleration, V2 / V1

NOTE : SEE PAGE A4A FOR SOLUTIONS

AXIAL TURBINE DESIGN MANUAL-8B-

6.0 HP TURBINE-FREE VORTEX DESIGN (CONT)

6.1B VELOCITY TRIANGLES - TET = 1250 K

From the data provided on Page A4A, draw below the velocity triangles appropriate to thestage at Root, Blade Mid Height and Tip.

NOTE: USE A SCALE OF 1cm = 100m/s

TIP

BMH

ROOT

NOTE: SEE PAGE A4B FOR SOLUTIONS


6.0 HP TURBINE-FREE VORTEX DESIGN


ROOT BMH TIP

D (NGV exit) = (Din+Dout)/2

D (rotor exit) (See Table 5.4 - page7)

Va (Constant radially)

Vw3mean (See Table 5.4 - page7)

Vwomean = (Vw-Vw3)mean(See Table 5.4)

Vwo = Vwomean xDmean/D(D at NGV exit)o = tan-1 (Vwo/Va)

Vw3 = Vw3mean x Dmean/D(D at rotor exit)

3 = tan-1 (Vw3/Va)

U (For exit velocity triangles)= Umean x D/Dmean (D at rotor exit)

Vo = Va/Coso

Nozzle Acceleration, Vo/Vin = Vo/Va

V1 = (Va2+(Vwo-U)2)

1 = Cos-1 (Va/V1)

V2 = (Va2+(U+Vw3)2)

2 = Cos-1 (Va/V2)

Rotor Acceleration, V2/V1

NOTE : SEE PAGE A5A FOR SOLUTIONS


6.0 HP TURBINE-FREE VORTEX DESIGN (CONT)

6.2b VELOCITY TRIANGLES - TET = 1650K

From the data provided on Page A5A, draw below the velocity triangles appropriate to thestage at Root, Blade Mid Height and Tip.


TIP

BMH

ROOT



7.0 HP TURBINE DESIGN ASSESSMENT.

7.1A DESIGN SUMMARY - TET = 1250K

NOTE: See ANNEX B for method of calculation.

AT BLADE MID HEIGHT NGV EXIT BLADE EXIT

Static temperature

Speed of sound

Absolute Mach number

Axial Mach number

DATA FROM PAGE A4AHUB TO CASING ROOT BMH TIP

NGV Exit Gas Angle o

Nozzle Deflection, o+in

Rotor Deflection, 1+2

Nozzle Acceleration Vo / Vin

Rotor Acceleration V2 / V1

Exit swirl, 3

Reaction

STAGE OVERALL DATA

Inlet hub/tip ratio(See Page A2)Outlet hub/tip ratio(See Page A3)

NOTE: SEE PAGE A6A FOR SOLUTIONS



7.1B RECOMMENDATIONS - TET = 1250 K

(SEE PAGE A6A for data)

(A) ARE THE AXIAL MACH NUMBERS OK ?

(B) IS THE NGV LEAVING GAS ANGLE ACCEPTABLE ?

(C) IS THE ROTOR EXIT SWIRL ACCEPTABLE ?

(D) ARE THE GAS DEFLECTIONS OK ?

(E) IS THE ROTOR ROOT ACCELERATION OK ?

(F) IS THE NGV TIP ACCELERATION OK ?

(G) IS THE INLET HUB/TIP RATIO OK ?


8.0 HP TURBINE DESIGN ASSESSMENT.




Static temperature

Speed of sound


Axial Mach number

DATA FROM PAGE A5AHUB TO CASING ROOT BMH TIP

NGV Exit Gas Angle o

Nozzle Deflection o+in

Rotor Deflection 1+2

Nozzle Acceleration Vo / Vin

Rotor Acceleration V2 / V1

Exit Swirl 3

Reaction

STAGE OVERALLDATA

Inlet hub/tip ratio(See Page A2)Outlet hub/tip ratio(See Page A3)





(SEE Page A6B for data)




(D) ARE THE GAS DEFLECTIONS OK?





LP TURBINE DESIGN


9.0 LOW PRESSURE TURBINE DESIGN

9.1 LOW PRESSURE COMPRESSOR SPECIFICATION

The low pressure compressor has the following specification (See Page 3)

Inlet temperature Tin 300Inlet pressure Pin 101325Mass flow W 40

Polytropic efficiency poly 0.90Isentropic efficiency isent 0.88Compressor power 5.99 megawatts

9.2 LOW PRESSURE COMPRESSOR DESIGN CONSTRAINTS

The following design assumptions are made:-

Axial inlet flow (no inlet guide vanes)

Inlet axial Mach number Ma = 0.5

Rotor tip relative Mach number M1 = 1.15

Mean diameter Dmean = 0.45

The compressor RPM is limited to that value corresponding to a maximum rotor relative tipMach number of 1.15. Accordingly, the following velocity triangle applies at the tip of the firststage rotor:-

M

U tip

Ma = 0.51 = 1.15


9.3 ESTIMATION OF LP COMPRESSOR (LP TURBINE) RPM

The following tabulation gives the sequence of calculations to estimate blade tip speed andRPM.(See also velocity triangle at the rotor tip shown on page 12).

Ma 0.5

Va /Tin ( See ANNEX C, for = 1.4 )

Va

Qin = W.Tin / Pin.Ain

Ain

hin = Ain/( .Dmean )Dtip = Dmean + hin

Dhub = Dmean - hin

Hub/Tip Ratio = Dhub / Dtip

Tin/tin (See ANNEX C, for = 1.4)

t in

V1 = M1 ( R tin )

Utip = (V12 - Va2)

RPM = 60.Utip/( Dtip )

NOTE: SEE PAGE E1 FOR SOLUTIONS


10.0 LP TURBINE OVERALL DESIGN

10.1 OVERALL SPECIFICATION.

LP TET 1021 1440

Mass flow 40.64 41.16

Power (megawatts) 5.99 5.99

Specific heat, Cp (and ) 1184 (1.32) 1275.7 (1.290)

RPM 10980 10980

Blade mid height reaction 50% 50%

10.2 HP TURBINE EXIT ANNULUS GEOMETRY

(SEE PAGE A3)

TET 1250 1650

Dmean 0.45 0.45

Dtip = Dmean + h 0.529 0.524

Dhub = Dmean - h 0.371 0.376

h = (Dtip-Dhub)/2 0.079 0.074

A = .Dmean.h 0.112 0.105

Hub/Tip Ratio = Dhub / Dtip 0.702 0.718

Va 205.1 233.0

Vw out mean 215.4 210.5


10.3 INTER-TURBINE ANNULUS GEOMETRY ESTIMATION

The factors concerning selection of inter-turbine axial space and annulus flare angle areconsidered in ANNEX F. Accordingly, an annulus flare of 300 ( included angle ) is selectedwith an axial space of 0.00635m. This is an example estimate for a closely spaced bladerows. For your own designs select spacings based on the values of local upstream chord asdiscussed in the lectures (e.g. St0.25Cax) The lp inlet annulus area is then estimated using the hp exit values of Table 10.2 and theinter-turbine data in table 10.3 below.The inter-turbine geometry is shown diagramatically below :-

y

y

15

0.00635

D mean

AXIS

HP EXIT LP INLET

o

TABLE 10.3 LP TURBINE INLET ANNULUS GEOMETRY

LP TET. 1021 1440

LP Turbine inlet pressure ( See Table A1.4 ) 583713 768530

Dmean 0.45 0.45

Dtip = Dtip (hp exit) + 2y ( See ANNEX F )

Dhub = Dhub (hp exit) - 2y

h = (Dtip- Dhub)/2

A = .Dmean . h

Hub / Tip Ratio = Dhub / Dtip

Va = Va(hp exit) x h(hp exit) / h(lp entry)

Vw in (mean) (As for HP exit) 215.4 210.5

NOTE : SEE PAGE E2 FOR SOLUTIONS


10.4 LP TURBINE EFFICIENCY PREDICTION

(SINGLE STAGE AT MID HEIGHT)

LP TET 1021 1440

Temperature Drop = Power / (W.Cp)

Blade Speed, Umean = U = RPM. . D / 60

H/U2 = CpT / U2 (Single Stage)

Va (See Table 10.3 - Page 15)

Va / U

isent (Smith's Chart Value minus 2 %)


THE ABOVE EFFICIENCY PREDICTION IS VALID FOR A SINGLE STAGE TURBINE.

THE DESIGNER CAN NOW SELECT A SINGLE OR TWO STAGE DESIGN.

For the low TET ( industrial ) case, a two stage design would probably be preferred to give ahigh overall efficiency in favour of low weight. If then, the work is split equally, each stagewould have a H/U2 of 1.1015 and an efficiency of of approximately 91.5% (see Smith's Chart- ANNEX D ).It is probable that an equal work split would be chosen since both stages would discharge atnear axial leaving velocity.

IMPORTANT NOTE

THE PRELIMINARY DESIGN NOW CONTINUES ASSUMING A SINGLE STAGELP TURBINE IS FEASIBLE FOR BOTH TET CASES CONSIDERED.

THIS DECISION IS REVIEWED ON COMPLETION OF THE PRELIMINARY DESIGN


10.5 LP TURBINE OUTLET ANNULUS GEOMETRY.

LP TET 1021 1440

Va

T3 = Tin - T

Work Done Factor 0.97 0.97

Vw = (H/U2) . U/

Vw = (Vw - Umean )/2( 50% Reaction )

3 = tan -1 (Vw3/Va)

V3 = Va / Cos3

V3/T3

M3 (See ANNEX C, use Appropriate )

Q3 ( See Tables-ANNEX C )

Pressure Ratio R = ( 1 - T/ ( isent Tin )) / (-1)

P3 = Pin x R (See note below)

A3 = W T3 / P3 Q3

Aann = A3 / Cos3

h = Aann / ( Dmean)

Dtip = Dmean + h

Dhub = Dmean - h

Hub / Tip Ratio = Dhub/Dtip

NOTE : P3 = Pout ( In the direction of V3 )



11.0 LP TURBINE-FREE VOTEX DESIGN


ROOT BMH TIP

D (NGV Exit) = (Din + Dout)/2

D (Rotor exit) (See Table 10.5 - Page 17 or Page E3)

Va (Table 10.3, Constant Radially)

Vw3mean (See Table 10.5 Page 17 or Page E3)

Vwomean = (Vw - Vw3)mean(See Table 10.5 Page 17 or Page E3)

Vwo = Vwomean x Dmean / D(D at NGV exit)

0 = tan -1 (Vw0/Va)

Vw3 = Vw3mean x Dmean / D(D at Rotor exit)

3 = tan -1 (Vw3/Va)

U for exit velocity triangles = Umean x D/Dmean(D at Rotor exit, Umean Table 10.4)

V0 = Va / Cos 0

in = tan -1 (Vw3hp. out / Valpin)(Vw3hp. out - Table 6.1A, Page 8A)

Vin = Valpin / Cos in)

Nozzle Acceleration = V0/Vin

V1 = (Va2+(Vwo-U)2)

1 = Cos -1 (Va/V1)

V2 = (Va2+(U+Vw3)2)

2 = Cos -1 (Va/V2)

Rotor Acceleration = V2/V1

NOTE : SEE PAGE E4A FOR SOLUTIONS


11.0 LOW PRESSURE TURBINE - FREE VORTEX DESIGN

11.1B VELOCITY TRIANGLES - TET = 1250 K

(MID HEIGHT REACTION = 50%)

From the data provided in Page E4A, draw below the velocity triangles appropriate to thestage at Root, Blade Mid Height and Tip.


TIP

BMH

ROOT

NOTE: SEE PAGE E4B FOR SOLUTIONS


11.0 LP TURBINE-FREE VORTEX DESIGN11.2A DESIGN TABULATION - TET = 1650K

ROOT BMH TIP

D (NGV exit) = (Din + Dout)/2

D (Rotor exit) (See Table 10.5 - Page 17 or Page E3)

Va (Table 10.3, Constant Radially)

Vw3mean (See Table 10.5 - Page 17 or Page E3)

Vwomean = (Vw - Vw3)mean(See Table 10.5 - Page 17 or Page E3)

Vwo = Vwomean x Dmean / D(D at NGV exit)0 = tan -1 (Vw0/Va)

Vw3 = Vw3mean x Dmean/D(D at Rotor exit)3 = tan -1 (Vw3/Va)

U (for exit velocity triangles) = Umean x D/Dmean(D at Rotor exit, Umean Table 10.4)V0 = Va / Cos0

in = tan -1 (Vw3hp. out / Valp.in)(Vw3hp out - Table 6.2A, Page 9A)

Vin = Valp. in /Cos in)

Nozzle Acceleration. V0/Vin

V1 = (Va2+[Vwo-U]2)

1 = Cos -1 (Va/V1)

V2 = (Va2+[U+Vw3]2)

2 = Cos -1 (Va/V2)

Rotor Acceleration. V2/V1

NOTE : SEE PAGE E5A FOR SOLUTIONS


11.0 LOW PRESSURE TURBINE - FREE VORTEX DESIGN11.2B VELOCITY TRIANGLES - TET = 1650 K

(MID HEIGHT REACTION = 50%)

From the data provided on Page E5A, draw below the velocity triangles appropriate to thestage at root, blade mid height and tip.

USE A SCALE OF 1cm = 100m/s

TIP

BMH

ROOT

NOTE : SEE PAGE E5B FOR SOLUTIONS


12.0 LP TURBINE DESIGN ASSESSMENT.

12.1A DESIGN SUMMARY - TET = 1250 K



Static temperature

Speed of sound


Axial Mach number

DATA FROM PAGE E4AHUB TO CASING ROOT BMH TIP

in

NGV Exit Gas Angle 0

Nozzle Deflection 0+in


Nozzle Accel. Vo/Vin

Rotor Accel. V2/V1

Exit swirl 3

Reaction

STAGE OVERALL DATA

Inlet hub/tip ratio

Outlet hub/tip ratio

NOTE: SEE PAGE E6A FOR SOLUTIONS


12.0 LP TURBINE DESIGN ASSESSMENT


(SEE PAGE E6A - DESIGN SUMMARY)







(G) IS THE INLET HUB / TIP RATIO OK ?


12.0 LP TURBINE DESIGN ASSESSMENT.


NOTE : see ANNEX B for method of calculation.


Static temperature

Speed of sound


Axial Mach Number

DATA FROM PAGE E6BHUB TO CASING ROOT BMH TIP

in

NGV Exit Gas Angle 0

Nozzle Deflection 0+in


Nozzle Acceleration V0/Vin

Rotor Acceleration V2/V1

Exit Swirl 3

Reaction

STAGE OVERALL DATA

Inlet hub/tip ratio

Outlet hub/tip ratio

NOTE : SEE PAGE E6B FOR SOLUTIONS


12.0 LP TURBINE DESIGN ASSESSMENT


(SEE PAGE E6B- DESIGN SUMMARY)



(C) IS THE ROTOR EXIT ACCEPTABLE ?






ANNEX A

HP TURBINE DESIGN RESULTS

AXIAL TURBINE DESIGN MANUAL-A1-

APPENDICES.

SUMMARY OF CONTENTS

ANNEX A

Presents the results of the high pressure turbine design.Design tabulations and velocity triangles are included for free vortex flow distribution.A critical assessment of the alternative designs is included.

ANNEX B

Presents additional guidance notes for calculations.

ANNEX C

Contains tables for the compressible flow of air for the three appropriate values of .

ANNEX D

Smith's Efficiency Prediction.

ANNEX E

Presents the results of the low pressure turbine design.Design tabulations and velocity triangles are included for free vortex flow distribution.A critical assessment of the alternative designs is included.

ANNEX F

Contains guidance notes for inter-turbine annulus area estimation.


ANNEX B

GUIDANCE NOTES FOR CALCULATIONS

AXIAL TURBINE DESIGN MANUAL-B1 and B2-

ANNEX B

B 1.0 GUIDANCE NOTES FOR CALCULATIONS.

These notes will assist in the calculations for tables 7.1A, 7.1B, (HP) and 12.1A, 12.1B (LP) ofthe turbine design assessment.

VV V

V

Vw Vw

V1

0 2

3

30

Vw

a

The above diagram shows the velocity triangles for a stage. The following calculationprocedures are recommended:-

AXIAL MACH NUMBER AT NGV EXIT, Ma

Ma = Va / ( R to )

Where to = To - (Vo2 / 2Cp) NOTE: To = Tin

and from the geometry of the velocity triangles above:-

Vo2 = Va2 + Vwo2

AXIAL MACH NUMBER AT ROTOR EXIT, Ma

Ma = Va / ( R tout)

Where: tout = t3 = T3 - (V32 / 2 Cp) NOTE: T3 = Tin - TStage

and from the geometry of the velocity triangles above:-

V32 = Vw32 + Va2

ABSOLUTE MACH NUMBER AT NGV EXIT, Mo

Mo = Vo / ( R to)

Where: to = To - (Vo2 / 2Cp) NOTE: (To = Tin and Vo as above)


-B3 and B4-

ABSOLUTE MACH NUMBER AT ROTOR EXIT, M3

M3 from Table 5.4 (HP Turbine)from Table 10.5(LP Turbine)

NGV ACCELERATION, Vo / Vin

Vo as aboveVin = Va at inlet to the HP turbine.Vin = V3 hp exit at inlet to the LP turbine.

ROTOR ACCELERATION, V2 / V1

Where from the velocity triangles above:-

V2 = Va / Cos2V1 = Va / Cos1

DEFLECTIONS:

Rotor deflection = 1 +2 Where:

VaVwU

tan 312

and:

VaUVwtan 011

NGV deflection = o + in Where: in = 0 for HP turbineand: in = 3 hp exit for LP turbine

STAGE REACTION.

stage

rotor

stage

rotor

Tt

Hh

00

Reaction,


ANNEX C

COMPRESSIBLE FLOW TABLES

GAMMA = 1.40 PAGE C1 AND C2




ANNEX D

EFFICIENCY CORRELATION

AXIAL TURBINE DESIGN MANUAL-D1-

ANNEX D

D1.0 EFFICIENCY CORRELATION

(SINGLE STAGE TURBINES)

REFERENCE: SMITH S F., "A SIMPLE CORRELATION OF TURBINE EFFICIENCY"(Journal of The Royal Aeronautical Society. 69 (1969) 467)


ANNEX F

INTER - TURBINE ANNULUS GEOMETRY ESTIMATION

AXIAL TURBINE DESIGN MANUALF1

ANNEX F

F1.0 INTER-TURBINE ANNULUS GEOMETRY ESTIMATION

This note explains the calculations necessary to complete Table 10.3, page 15.

TURBINE OVERALL ANNULUS GEOMETRY

AX IS

HPNO ZZLE

HPBLADE

LPNO ZZLE

LPBLA DE

X

A finite distance, x, is required between the HP exit and LP entry. The value of x is, typically, approximately25% of the previous blade row axial chord or 1/4 inch. (whichever is larger).The value of annulus flare angle, , usually limited to 30o (included), will depend on the magnitude of axialchords chosen for each of the blade rows.In any event, inter-turbine annulus flare will result in a reduction in the axial velocity between HP turbine exitand LP turbine inlet.The whirl component of velocity, Vw3, at HP exit will, however, remain unchanged in the inter-turbine spacesince angular momentum will be conserved.Since blading considerations are not covered in this design study, the axial distance, x, is assumed to be 1/4inch. (0.000635m) and annulus flare angle is taken to be 30o (included).If the annulus height increase between HP exit and LP inlet is 2y, the reduction of axial velocity can beestimated, as follows:-

y = 0.00635 tan (/2)

h lp entry = h hp exit + 2yWhere:- h hp exit is the annulus height at hp exit.

(See Table 5.4 page 7 or Table A1.4 page A3)Va lp inlet = Va hp outlet. hhp exit / h lp inlet

NOTE: Vw3hp exit = VWin lp inlet

1Dr. David MacManus , Dr. Ken Ramsden, Dr. Anthony JacksonGas Turbine Technology ProgrammesDEPARTMENT OF POWER AND PROPULSIONSCHOOL OF ENGINEERINGCRANFIELD UNIVERSITY

CHAPTER 4

AXIAL TURBINE

DESIGN AND PERFORMANCE

Presentation slides v2013-v1.1

1

Turbines - General Bibliography1. Japikse, D., Introduction to turbomachinery, Oxford University Press, 1997.2. Cohen, H., Rogers, G., and Saravanamuttoo, H., Gas turbine theory, Longman Scientific and

Technical, 3rd Edition, 1987.3. The jet engine, Rolls-Royce plc, 5th Edition, 1996.4. Cumpsty, N., Jet propulsion, Cambridge University Press, 1997.5. Dixon, S., Fluid mechanics and thermodynamics of turbomachinery, Butterworth-Heinemann, 4th

Edition, 1998.6. Turton, R., Principals of turbomachinery, E.&F.N. Spon, 1984.7. Lakshminarayana, B., Fluid dynamics and heat transfer of turbomachinery, John Wiley and Sons,

1996.8. Van Wylen, G., Sonntag, R., Fundamentals of classical thermodynamics, John Wiley and Sons,

1985.9. Wilson, D., Korakianitis, T., The design of high-efficiency turbomachinery and gas turbines, 2nd

Edition, Prentice Hall, 1998.11. Mattingley, J., et al.Aircraft engine design, AIAA education Series, 1987.12. Kerrebrock, J., Aircraft engines and gas turbines, MIT Press, 1992.13. Oates, G., Aerothermodynamics of aircraft engine components, AIAA education Series, 1985.14. Aungier, R., Turbine aerodynamics, ASME Press, New York, 200615. Sieverding, C., Secondary and tip-clearance flows in axial turbines, Von Karman Institute, LS1997-116. Arts, T., Turbine blade tip design and tip clearance treatment, Von Karman Institute, LS2004-217. Booth, T., Tip clearance effects in axial turbo-machines , Von Karman Institute, LS1985-518. Sunden, B., Xie, G., Gas Turbine Blade Tip Heat Transfer and Cooling: A Literature Survey, Heat Transfer

Engineering, 31:7, 527-554, 2010. 2

2DISCLAIMERSCHOOL OF ENGINEERING

DEPARTMENT OF POWER AND PROPULSION

These notes/slides have been prepared by Cranfield University or its agents for thepersonal use of course attendees. Accordingly, they may not be communicated toa third party without the express permission of the author.

The notes/slides are intended to support the course in which they are to bepresented as defined by the lecture programme. However the content may bemore comprehensive than the presentations they are supporting. In addition, thenotes may cover topics which are not included in the presentations.

Some of the data contained in the notes/slides may have been obtained from publicliterature. However, in such cases, the corresponding manufacturers or originatorsare in no way responsible for the accuracy of such material.

All the information provided has been judged in good faith as appropriate for thecourse. However, Cranfield University accepts no liability resulting from the use ofsuch information.

3

Turbine aerodynamics - programme

Part A: Turbine aerodynamics

Introduction to aero design Arrangements, architectures, characteristics Work Frame of reference and parameters Introduction to turbine aerodynamic features Introduction to turbine aerodynamic design Turbine annulus design Turbine stage aerodynamics Loading, flow, coefficient, specific work and reaction Designing for high power

4

3Turbine aerodynamics - programme

Turbine efficiency Turbine blading Three-dimensional aerodynamics Streamline curvature and secondary flows Unsteady aerodynamics Introduction to cooling

Part B: Axial turbine design exercise

HP and LP designs Specification, constraints Effect of TET Design summary , assessment and recommendations

5

Preliminary design

6

4Gas turbine applications

This image cannot currently be displayed.

Industrial Power generationSiemens 340 megawatts (MW) SGT5-8000H gas turbine.

Marinee.g. MT30marinized version ofan aero GT. 40MWrange

Oil and gas

7

http://www.siemens.co.in/

Rolls-royce.com

7

Gas turbine applicationsPropulsion

8

airbus.com

Boeing.com

Lockheed.com8

5Turbine design drivers

Preliminary design stage considerations How much do you need to know..and when?

What is the application? Propulsion or power Civil Military Short duration? Disposable?

How does this affect the design approach ? Time to market Market size and duration Preliminary design fidelity Evolution or revolution

9

Turbine design drivers

What are the design aspects for consideration ? Specific fuel consumption (and/or block fuel burn)

Temperature Pressure BPR Component efficiency

Emissions

Weight

Size Embedded configurations (civil or military)

Life10

6Turbine design drivers

Reliability Risk/benefit trade off E.g. tip gap, TBC, cooling strategy, stress margins

Noise Turbine noise Effect of LPC noise on turbine design

Time to manufacture Robustness

Change in operations Change in future processes

Growth potential Cost

Manufacture Ownership Replacement parts Power/thrust supply (risk ownership) Maintanence

11

Turbine design disciplines

Aerodynamics

Cooling and thermal management

Mechanical design

Stress

Lifing

Costs

Weights

Manufacturing

Logistics

Purchasing

12

7Possible output from a turbine preliminary design

Number of stages

Work split for multi-stage turbines

Aerodynamic conditions

Annulus shape and dimensions

Blade and vane aspect ratio

Blade and vane space/chord ratio

Blade and vane airfoil numbers

Radial work distribution

Inter-row axial spacing

13

Design process and considerations

Stage 0Preliminary evaluations

Stage 1Preliminary design

Stage 2Full concept definition

Stage 3Product realisation

Stage 4Development andproduction

Stage 5In service

Stage 6Disposal

Main focus forturbine aerodynamicdesign work

2,3 and 4Daerodynamicdesign

1D, 2D and maybe 3Daerodynamic design

1D and maybe 2Daerodynamic design

14

8The importance of preliminary design

Jones 2002

Knowledge ofthe design

15

16

Basic turbine performance

9

activity)(moleculartpCW

(kinetic)2

2W.V

COMPRESSOR INLET TURBINE INLET

TEMPERATURE K 300 1600

SOUND SPEED m/s 350 780

MACH NUMBER 0.5 0.5

VELOCITY m/s 175 390

FUNDAMENTAL PERFORMANCE PARAMETERS

ENERGY

TEMPERATURE t , T (static molecular; total plus kinetic)

PRESSURE p , P (static - molecular bombardment; total - adds kinetic term)

POWER W Cp T (total energy change per second; molecular plus kinetic)

SPEED OF SOUND Rta (sound transmitted by molecular collision)

MACH NUMBERaVM (better to use than velocity)

EXAMPLE:

17

18

COMPRESSORPOWER

TURBINEPOWERCOMBUSTOR

ENERGY INPUT

USEFUL POWER

ENERGY

ENTROPY

P2

P1

= Turbine Power Compressor Power

THERMALEFFICIENCY InputEnergyCombustion

PowerUseful

USEFUL POWER AND THERMAL EFFICIENCY

10

19

DESIGNERS SOLUTIONS FOR HIGHEST USEFUL POWER

DESIGN FOR HIGH TURBINE INLET TEMPERATURE

Red MINUS blue (PT-PC)equals output power

Largest whenHighest pressure ratioand orHighest TET

T

S

PT

PC

20

T

s

EFFICIENCY OF GAS TURBINE ENGINES

IDEALCOMPRESSORWORK

ACTUALCOMPRESSORWORK

COMBUSTORENERGYINPUT

IDEALTURBINEWORK

ACTUALTURBINEWORK

1

2

3

44

2

P1

P2

Compressor Isentropic Efficiency

)TT()T'T(

c12

12

W.Cp.(T2-T1) = idealcompressor workW.Cp.(T2-T1) = actualcompressor work

)'TT()TT(

T43

43

W.Cp.(T3 - T4) = actual turbine workW.Cp.(T3 T4) = ideal turbine work

Turbine Isentropic Efficiency

)TT()TT(

THERMAL23

141

Thermal Efficiency =(Useful Work/CombustorEnergy Input)

Where:Useful work = turbine work - compressor work= W.Cp.(T3 -T4) - W.Cp.(T2-T1)Combustor Energy Input = W.Cp.(T3 - T2)

11

Basic arrangements

21

22

Engine architectures and gas pathThis image cannot currently be displayed.

Images from Rolls Royce 22

12

23

Single spool axial flow turbojet

Images from Rolls Royce

Engine architectures and gas path

23

24

Engine architectures and gas pathThis image cannot currently be displayed.

Images from Rolls Royce 24

13

25

Idealised gas path conditions

This image cannot currently be displayed.

Images from Rolls Royce

TEMPERATURE

VELOCITY

PRESSURE

25

IMAGE COURTESY ROLLS ROYCE

GAS GENERATOR TURBINES

POWER TURBINE

26

14

TRENT AERO ENGINE IMAGE COURTESY OF ROLLS-ROYCE

TURBINES

27

Rolls Royce T900

Specifications:BPR 8OPR 41Stages 1LPC, 8IPC, 6HPC,

1HPT, 1IPT, 5 LPTFan diameter 116 inchesThrust 76,500lbAircraft A380

A MILITARY LOW BYPASS RATIO TURBOFAN

Specifications:BPR 0.4OPR 25Stages 3LPC, 5HPC

1HPT, 1LPTFan diameter 29 inchesThrust 20,000lbAircraft Typhoon

IMAGE COURTESY ROLLS ROYCE

EJ200

28

15

Turbine designs

29

Shrouded HPturbine

Unshrouded HP turbine

HIGH BYPASS RATIO TURBOFANS

IMAGE COURTESY ROLLS ROYCE 30

16

HIGH BYPASS RATIO TURBOFANS

IMAGE COURTESY ROLLS ROYCE 31

T800

~GE90

TURBINE TECHNOLOGY IMPROVEMENTS HISTORY

1950 NOW

TIP SPEED m/s 250 350 +

STAGETEMPERATUREDROP, K

150 250 +

EXPANSIONRATIO

2 2.5 +

STAGEPOLYTROPICEFFICIENCY %

86 92 +

TURBINE ENTRYTEMPERATURE K

1200K 1800K +

32

17

TERMINOLOGYFUEL / AIR RATIO FARSTOICHIOMETRIC ALL OXYGEN USED

(COMPLETE COMBUSTION)OUTLET TEMPERATURE PROFILE TTQ

PRESSURE LOSS FACTOR 2V21P

COMBUSTOR GAS FLOW FEATURESLINER

FLAME TUBE DILUTION HOLES(BURNER)

SWIRLERFUEL SPRAY NOZZLE

PRIMARYZONE

SECONDARYZONE

SECONDARY AIR

LINER

TURBINE NEEDS GOODTEMPERATURE TRAVERSE QUALITY

33

Combustor exit profile

He 2004 He 2004

Povey 2009T/Tmean

34

18

35

Conventional multi-stage turbine

U1 U2

U2

U1

U1

Relative

Absolute

Typical conventional arrangement

Vanes turn and accelerate flow for next blade row.

Controlled work split between the HP and IP systems

36

Contra-rotation multi-stage turbine

U1

U2

U1

U1

U2

RelativeAbsolute

Reversal of the HP shaft rotation relative to the IP (LP) shaftIP NGV required to get the correct flow angle and velocity into the IP rotorReduced turning on and reduced secondary flows on the IP NGVIncreased IP NGV efficiencyControlled work split between HP and IP.

19

37

Statorless contra-rotation multi-stage turbine

U1

U2

U1

U1

U2

Relative IP

Absolute

Relative HP

IP NGV is removed.Reduced length, weight, costEliminated IP NGV lossClosely coupled HP-IP rotorscan result in unsteadyinteractions -> reducedefficiency and possiblevibration.

The inlet conditions to the IP rotor are limited by the exit conditions from the HP rotor. i.e. theabsence of the IP NGV means that the flow cannot be pre-conditioned as in a conventionalarrangement. The HP rotor exit swirl is limited by the HP rotor turning and the whirl velocity islimited by the rotor exit Mach number.A consequence of this is that the work split is uneven. The HP stage typically has a much higherwork level than the IP (LP).

Eulers work equation

38

20

Steady Flow Energy Equation

For each kilogram of fluid entering the controlvolume at position 1, the total energy is:

Similarly at point 2: Q is the heat addition (positive into the system)

and W is the work (positive when done by thefluid)

The energy balance equation then becomes:

z1z2

h1,, V1 h2,, V2

Q

W

SystemgzVhEtot 1

2111 2

gzVhEtot 22

222 2

gzVhgzVhWQ 12112222 22

This is known as the Steady Flow Energy Equation.

For an axial turbomachine it reduces to:

For an ideal gas h = Cpt and the total enthalpy is Also recall,

22200 VtCTCH pp

2

2

211

,1

thatRemember.2

1

MtT

aVMRtaandRC

tCV

tT

pp

00201222211 22 TCHHVhVhW p

39

Compressible Form of Bernoullis Equation

If there is no heat transfer to or from the gas the flow is ADIABATIC. Henceconservation of energy tells us that the Total Energy (usually called the TotalEnthalpy) is conserved i.e. ho = constant.

Considering a perfect gas:p = RT Equation of Stateh= specific enthalpy= CpT Calorifically perfect gasho=specific total enthalpy = CpT0

The specific* enthalpy is defined as h = e + P/ and the specific internal energye = CvT.

*The word specific means per unit mass flow and is often omitted.

40

21

Compressible Form of Bernoullis Equation (continued)

The energy equation for an adiabatic, steady flow is given by:

Therefore:

PressureEnergy

InternalEnergy

KineticEnergy all per unit mass flow

22

22

2

22

21

1

11

VpeVpe

Recall that specific enthalpy is defined as h =e+p = e+p/ ( is specificvolume).

enthalpy)(totaltan 02

22

21

1 22htconsVhVh

For a calorifically perfect gas h=CpT and similarly h0 =CpT0

e)temperaturtotalis(tan 002

22

21

1 22TTCtconsVTCVTC ppp

T1 0

2

0

2

22T

TCVTCVTC

ppp Eqn 1.7

41

Compressible Form of Bernoullis Equation (continued)

Recalling: ,

2

20

211 M

aa

TTo

So far the ONLY assumptions have been a Perfect gas and ADIABATIC FLOW.If the flow is also ISENTROPIC (i.e. the entropy is constant no shock present andoutside viscous layers like the boundary layer) then:

p = k=RT and hence

RTV

aVM

22202

112

112

MRT

RTMTC

VT

p

1T

1

RCp and 0222

0 21 RTVaa

121ooo M2

11TT

pp

42

22

A-A

x

r

x

q

Vx

Vq

Rotation W

Rotor

Streamtube

r2

r1

Centreline

A-A

Figure 1.1


43

One of the most fundamental aspects of turbomachinery aerodynamics is the processof work input (compressors) and the work extraction (turbines) processes. The samemodel is adopted for both compressors and turbines as outlined below.

The work extraction and addition process is performed by rotation. It is the rotatingcomponents that transfer work. The fixed components, or stators, are not explicityinvolved.

Figure 1.1 shows the flow field through a generic rotor passage for an axial-typemachine but including a change in mean radius. Consider the flow along a streamtubethat enters at radius r1 and exits at radius r2.

The shaft is rotating with an angular velocity W (rad/s) and is producing a torque T. Torque is the rate of change of angular momentum and if the massflow is steady, then

the change in angular momentum in a time Dt is give by:


)( 2211

VrVrmT

rVtmT

tmrVT

Rotation

Rotor

Streamtube

r2

r1

Centreline

A-A

Rotation

Rotor

Streamtube

r2

r1

Centreline

A-A

44

23

Eulers work equation The rate of change of angular momentum equals the torque:

Power is defined as

Work per unit mass of flow therefore is:

Rotor blade speed at radius r is defined as U=Wr

Therefore.

This is known as Eulers work equation.

It applies to all types of turbomachines. It shows that all transfer of work processes(either in or out) are reflected in a change in angular momentum via a rotating blade row.This is principally done using the pressure forces which act in the circumerential directionupon rows of rotating aerofoils.

Recall:

22112211

VrVrmVrVrtmT

2211 VrVrmTP

2211/, VrVrmPWWork k

2211 VUVUWk

45

UVTCWTCmP

pk

p

0

0

ork,Specific wPower,

Frame of reference

46

24

U

NGV

ROTOR

TURBINE STAGE

Turbine stage aerodynamics

47

Frame of reference

For an axial machine the following co-ordinate system is defined:

x is axial

r is radial

q is circumferential

x

Rotation W

q

Vx

Vr

Vq

r

Please note:

This nomenclature is for this section onlywhich applies to compressors and turbinesalike. Subsequent sections use individualnotation for turbines based on axial stationnumbers. 48

25

Frame of reference The absolute and relative frame of reference velocities are therefore (please note the changes in nomenclature from this section)

Both axial and radial velocities are independent of frame of reference i.e. Vx=Wx and Vr =Wr. For the tangential velocities: Vq= Wq+Wr = Wq+U

Notice that Vq and Wq are positive in the direction of rotation. U is Bladespeed.

Absolute Relative

Vx Axial velocity Wx

Vr Radial velocity Wr

VqCircumferential velocity(tangential, whirl or swirl

velocity)Wq

Total velocity222VVVV rx

222WWWW rx

49

Frame of reference An important concept is the distinction

between absolute and relative framesof reference. For the rotor shown, theinlet stationary frame velocity is V. Ithas two components and an absoluteswirl angle of a1. By subtracting theblade speed term, U, the relativevelocity vector is obtained.

This is the effective velocity seen by therotor. A similar analysis at the exit planetransforms from the relative to absoluteframe of reference. Conventionalturbomachinery notation uses positivevelocities and angles in the direction ofrotation.

Blade speed = Wr, where W is rotational speed and r is the local radius. Axial velocity is independent of frame of reference and relative whirl velocity is obtained

from Wq= Vq-U For example, from a given inlet absolute velocity, flow angle and blade speed, all other

vectors can be determined.

xq

Rotors

Relativewhirl velocity Wq

Absolutewhirl velocity Vq

Axialvelocity Vx = Wx

a1

50

Blade speed U

26

Frame of reference

a1

51

b1 a1 b1

Relativevelocity W

b1

a1

Effect of NGV exit angle (fixed Va)

Effect of blade speed (fixed Va) Effect of NGV exit velocity

Blade speed U

Static, stagnation and relative properties

Following on from the absolute and relative velocities there are also the equivalentrelative and absolute stagnation (or total) properties.

For example, for an incompressible flow, the absolute total pressure is:

However, in the rotating frame of reference, the total pressure seen by the rotor is:

Static quantities are unchanged by frame of reference. Stagnation properties are dependent on the frame of reference. For compressible flows:

221

0 VpP

221

0 WpP REL _

referenceofframeRelative2

referenceofframeAbsolute2

100

2

0

100

2

0

TT

PPand

CWTT

TT

PPand

CVTT

relrel

prel

p

52

27

Energy equation and rotating blade rows

For a rotor the Euler work equation applies:

For a compressor work is done on the fluid (Wk is negative) so stagnationenthalpy rises (h02 > h01).

For a turbine work is done by the fluid (Wk is positive) so stagnation enthalpydecreases.

By rearranging this equation:

Which states that h0-UVq is constant across a rotor blade row. This quantity isreferred to a ROTHAPLY and is denoted by I.

0201 hhWk

02012211

2211

hhVUVUW

VUVUW

k

k

22021101 VUhVUh

22021101 VUhVUhI

53

Rothalpy and Frame of Reference

Rothalpy in the absolute frame of reference is defined as :

Looking at the change of reference frame:

Therefore rothalpy in the rotating frame is given by:

UVVhUVHI o 2

21

222

222

2222

2222

2

2

UUVWV

UUWWV

UWWWV

VVVV

rx

rx

22

21

21 UWhI

UWVWVWV rrxx ,,

54

28

Rothalpy and Frame of Reference Total enthalpy in absolute frame (absolute total enthalpy):

Total enthalpy in relative frame of reference (relative total enthalpy):

Rothalpy can be expressed as:

20 2

1Vhh

20

0

21UhI

UVhI

rel

Rothalpy along a streamline is conserved across any blade row eithermoving or stationary. It applies along an arbitrary streamline for anadiabatic flow and in the absence of gravity and it is invariant. For axialmachines with no change in radius the U2 term cancels and changes inrelative stagnation enthalpy and rothalpy are the same.

20 2

1 Whh rel

55

Rotary stagnation temperature

20

0

21UhI

UVhI

rel

Rothalpy along a streamline is conserved across any blade row

Where T0 is the rotary stagnation temperature.

prel

pp

pppp

CrTT

rWC

tCIT

CU

CW

CH

CIT

2

21

22

22

00

2220

220

0

0

00

TCI

TC

p

p

Rothalpy,H,EnthalpyTotal

pppp CrVT

CUV

CH

CIT

0

00

Relative

Absolute

For axial machines with constant radius the changes in relative stagnation temperatureand rotary stagnation temperature are the same.

56

29

Change of Frame of Reference

Relative Stagnationp0rel, Torel

What a rotor mounted probe sees

Rotary Stagnationp0w, Tow

Equivalent of stagnation in a rotor

Stagnation Statep0, To

What a stationary probe sees

100

2

0 2

TT

pp

CVTT

p

100

2

0 2

TT

pp

CWTT

rr

pr

Static Statep, T

what the gas sees

1

0

0

0

0

22

00 2

TT

pp

CVWTT

rr

pr

100

222

0 2

TT

pp

CrWTT

p

1

0

0

0

0

22

00 2

rr

pr

TT

pp

CrTT

1

0

0

0

0

00

TT

pp

CrVTT

p

57

I Rothalpy = CpT0wM. Rose - 1998

Frame of Reference - notes

Rothalpy, I = CpT0w, is conserved along a streamline. For isentropic flow the rotary stagnation pressure, p0w, is also conserved

along a streamline. For an adiabatic rotor and with a thermally perfect gas the rotary stagnation

temperature is constant. This is true even for a change in radius, viscosityand effects of friction. If the flow is also reversible, then the rotary stagnationpressure (Pow) is also constant.

All relationships between the different states are isentropic compressible flow.

Nomenclature (for this section only) SubscriptsI Rothalpy = CpT0w r relative state

P pressure w rotary state

r radius 0 stagnation state

T temperature q whirl component

V absolute velocity

w rotational speed

W relative velocity

58

30

Frame of Reference

Relative total pressure is defined as

Absolute and relative Mach numbers:

100

TT

pp rr

120

20

211

211

MPP

MTT

120

20

211

211

relr

relr

MP

P

MT

T

Absolute Relative

59

Introduction to turbines

60

31

Turbine Aerodynamics

Introduction:The design of a turbine system requires the carefulintegration of a range of technologies includingaerodynamics, cooling, materials, sealing, transmissionsetc.. It is a complicated task, but still at the heart of thedesign is the aerodynamics of the turbomachinery whichtends to drive the system requirements and push thelimitations of the other technologies.

The detailed flow field inside a turbine is extremelycomplicated where there are shock waves, unsteadyfeatures, secondary flows, interactions, rotating flows,wakes, tip leakage vortices, cooling air, annulus leakageetc. However, a very simplified analysis based on steadyconditions along a (2-D) mean line flow path provides areasonable insight into the fundamental workings of theturbine. This approach is frequently used by industry asa preliminary design method.

Shrouded HP Turbine bladeIMAGE COURTESY OF ROLLS-ROYCE 61

The High Pressure (HP) turbine of a modern aero engine can produce in the order of49,000 HP (36.5MW) at take-off.

One turbine rotor blade produces in the order of 700 HP which is the power output ofabout 9 Ford Fiestas.

The peak gas temperature in the HP turbine is in the order of 400 degrees hotter thanthe melting point of the blade material.

The tip speed of the HP rotor is over 1000 mph.

HP Turbine Trivia

LPT

IPTHPT

Combustor

IMAGE COURTESY OF ROLLS-ROYCE62

32

Harsh environment &a demanding job:

Peak gas temperature 2000K

Melting temperature ~1400K

Cooling air ~15% flow @ 900K

Shrouded High Pressure Turbine

Metal Temp DT strong effecton blade life

Blade experiences > 65000g

Life required for a civil aeroengine6 years @14hrs/day


High Pressure Turbine

HPT stage coolingHPT blade cooling arrangements


33

65

Turbine Aerodynamic Features

Snap shot of a predicted HP turbine flow field

EntropyStatic Pressure

66 66

34

Turbine blade aerodynamic features

6767

Turbine Aerodynamic FeaturesTransonic HPT aerodynamics

Mach Number

Richardson (2009)

Schlieren

M2_is = 1.2

6868

35

69

Turbine aerodynamics

DLR Turbine cascade flow:

Increasing Mach number

visualization of densitygradients:

pressure waves, von Karmanvortices, wakes and shocks

70

Turbine aerodynamics

MEX0.85 MEX 0.98

MEX 1.2 MEX 1.5

36

Turbine Aerodynamic Aspects

HP TurbineHGV, Re = 1.5E6Rotor, Re = 6.0E5

LP TurbineStage 1NGV, Re = 4.0E5Rotor, Re =2.0E5

IP TurbineHGV, Re = 1.2E6Rotor, Re = 2.6E5

HP NGVTurbulent Flow from LEPrimarily Due to Film Cooling

HP RotorTurbulent Flow from LEPrimarily Due to Film Cooling,Strong Wake and Potential Interaction

IP NGVComplex 3D Flowwith Transition

IP RotorUnsteady, Strong Wake andPotential Interactionwith Transition

LP Vane/BladesUnsteady TransitionalSeparation Bubbles,Becalmed Regions, etc

Primary gas path turbine flow regimes

LP TurbineStage 5NGV, Re = 1.0E5Rotor, Re = 1.4E5 71

M. Taylor 2003

Turbine overtip leakage(section 4.7.7)

72

37

Tip clearance and leakage

Tip clearance is the distance between the tip of a rotating airfoil and stationary part.

Fluid leakage occurs over the blade tip due to the pressure difference

Overtip Leakage Loss

Clearance x Exchange Rate

Clearance Gap: Mechanical designof turbine and control of casing androtor thermal transients

Exchange Rate: Predominantlyinfluenced by choice of blade tip stylee.g. Shrouded, shroudless

Arts 2004-273


Flow over a Shroudless blade

Arts VKI LS2004-274

38


3-Dimentional Flow Features in a Axial -Turbine Rotor Passage

Arts VKI LS2004-275

76

Impact of overtip leakage:

Reduction in massflow through the blade passage

Reduction in work done by the fluid on the blade

Flow ejecting from tip gap mixes with passage flow

Heat transfer effects e.g. Tip Burnout, blade damage.


The main factors influencing the tip leakage loss are the following

Clearance gap size

Design style

The pressure difference between the pressure and suction surface.

39


How to Minimise losses at a given clearance level

Reduce the section lift at the tip through selection of the velocity diagrams

Reduce the pressure drop across the blade (reaction, overall blade loading)

Increase the blade height in the gas path (for a given tip clearance)

Impede leakage across tip (Viscous Mechanism)

77

Tip clearance and leakageEffect of tip clearance on the efficiency ofsingle stage shroudless turbines

For a shroudless stage : Tip size equal to 1% of blade span cause 2% dropin stage efficiency. ( Hourmouziadis and Albrecht 1987)

Arts VKI LS2004-278

40


Tip clearance exchange rate for different turbine reactions as a function of gap-to-blade height ratio.

Booth VKI_LS1985-579


Blade tip styles: Shrouded and Shroud

+ Measurable gain in stage efficiency

+ Improved fatigue strength

- Difficulty to cool the shrouded area

- Larger cooling flow budget

- Higher blade and disk centrifugalforces/stresses

-cost increase particularly forinternally cooled blades

Shrouded blade

Arts VKI LS2004-280

41

Shrouded Blade geometry


Arts VKI LS2004-2

Fences

Fins

81

Ratio of clearance area to throat area ( Ac/Ath)


Comparison of OTL loss exchange rates for shrouded and unshrouded HPTurbines

Arts VKI LS2004-282

42


Over tip leakage heat transfer effects

Leakage flow entering the main stream on suction side also causes largeincreases of heat transfer near the tip

High heat transfer rates near the pressure edge of the tip are related toreattachment of the flow separation

The acceleration of leakage flow into the clearance gap and thinning of boundarylayer enhances the heat transfer on the airfoil pressure surface

High heat transfer rates on the blade tip, Cause Tip Burnout

83

Blade damage in the tip region

Distress to HP Rotor Tip after in service operation

Sunden and Xie, 2010

Tip clearance Heat Transfer Effects - blade

84

43

Introduction to turbine design

85

86

4.1 INTRODUCTION TO TURBINE DESIGNThe design of axial flow turbines is a complex compromise

between the conflicting requirements:

o aerodynamicso thermodynamicso mechanical integrityo materials technology

This is especially true for aircraft engines with:stringent demands for:

o low weighto high strengtho extended life.

CHAPTER 4 PART 1 PAGE 4.01

44

4.2 THE COMPROMISES BETWEEN AERODYNAMIC, COOLING ANDMECHANICAL REQUIREMENTS

Any preliminary design procedure must include an estimation of at least the following:

o Number of stageso Annulus shape and dimensions (hub, mean or tip diameter)o Blade and vane aspect ratioo Blade and N.G.V space/chord ratioso Profiles of nozzle guide vanes and rotor bladeso Axial spacing between blade rowso Work split for multi-stage turbineso Radial distribution of work

PRELIMINARY DESIGN


87

To meet these requirements the turbine design team has to take accountseveral factors, for example:

o Blade centrifugal stress levels

o Disc centrifugal stress levels

o Maximum installation diameter

o N.G.V and blade cooling requirements

o Overall weight limitations


88

45

MECHANICAL INTEGRITY LIMITATIONS TO TURBINE POWER

Blade shapeSimple for manufacture - complex for good aerodynamics

Stress Blade centrifugal stress proportional to A x N2For a given shaft speed this sets the upper annulus area limitDepends on material and component: range 20-50x106 rpm2m2Disk stress gives a limit on rim speed ~ 400m/s

Rpm (N) Chosen to match the compressor needs

A Keep as small as possible to also reduce weight

One approach is to put the blades at highest diameter. This reduces blade height for agiven AN2

However:This also increases the blade speed and turbine power increases with U

The blade mass reduces and the blade cooling requirement reduces

NB: Hub tip ratio not greater than 0.9 for low overtip leakage loss89

4.3 TURBINE DESIGN SPECIFICATION

4.3.1 TURBINE DESIGN CRITERIA

The overall cycle calculations undertaken within the performancedepartment will lead to a specification for the turbine component as follows:

o W Mass flowo P3 Turbine inlet pressureo T3 Turbine entry temperatureo Power Requiremento Pressure ratio split


90

46

Turbine Design Aspects Successfully turbine design requires close co-operation between the aerodynamic,

cooling, mechanical, stress and design disciplines. Final designs usually demand acertain amount of compromise between aerodynamics and mechanical constraints:

Parameter Aerodynamic objectives Mechanical objectives

No. of stages Large: to reduce loading and Machnumbers

Small: Reduce weight, length &cost

Meandiameter

Large: to give high blade speed, lowloading, high efficiency

Small: reduce weight and costMinimise blade and disc stresses

Annulus area Large: enough for optimum Va/U Small: blade stresses are proportionalto Area x rpm2

Rotor andNGV aspectratios

High: reduce wetted area, secondarylosses and heat load

Low: to mimimize deflections andvibration. Must enable cooling.

1

47

THE PROCESS OF EXPANSION

93

Static pressure Total pressure

Mach number

Turbine annulus design

94

48

4.5 TURBINE ANNULUS DIAGRAMS4.5.1 CHOICE OF ANNULUS DIAGRAM

CHAPTER 4 PART 1PAGES 4.04 4.06

95

General arrangement of HP and IP turbines

A RISING LINE ANNULUS DIAGRAM

Figure 4.03Typical HP/LPAnnulus Geometry


DISCDISC

49

97

HP-IP-LP turbine arrangement

Aeroengine

Aggressive turbine ducts

Marn Graz (2008)

100

50

o constant Va

o falling Va

o rising Va

4.5.2 CHOICE OF AXIAL VELOCITY DISTRIBUTION

Figure 4.04

CHAPTER 4 PART 1 PAGE 4.06 4.07101

CHOICE OF Vax DISTRIBUTION

CHAPTER PART 1 PAGE 4.07

DESIGN FOR RISING Va - HP TURBINES

Compared with constant Va, the outcomes of this choice are:

o higher blade friction losseso lower efficiency

but:o lower blade heighto lower stress for a given RPMo lower rim load (AN2) for given RPMo less cooling air requirement for cooled stages.

102

51

DESIGN FOR RISING Va - LP TURBINES


o higher blade friction losses, lower efficiencyo higher exhaust losses through higher Vao longer exhaust diffuser

But:o lower exit blade height and masso lower rim load (AN2) for given RPMo lower blade stress for a given RPMo less cooling air requirement (if cooled)





DESIGN FOR FALLING Va - HP TURBINES


o lower blade friction losseso higher efficiency

But:o higher blade height and higher masso higher stress for a given RPMo higher rim load (AN2) for given RPMo more cooling air requirement for cooled stages.

104

52

DESIGN FOR FALLING Va - LP TURBINES


o lower blade friction losses, higher efficiencyo lower exhaust losses through lower Va outo shorter exhaust diffuser

But:o higher exit blade height and increased masso higher rim load (AN2) for given RPMo higher blade stress for a given RPM



105



PRELIMINARY DESIGN CHOICE

At the preliminary design stage:

o details of blades and vanes are unknown

o therefore assume constant axial velocitythroughout the turbine.

106

53

Turbine stage aerodynamics

Velocity trianglesStage loadingFlow CoefficientReaction

107

Turbine Stage Aerodynamics

The turbine stage is typically able to turn the flow more than in a compressorstage. This is because the flow is exposed to a favourable pressure gradient.

The flow is expanding and the pressure is reducing across the stage. The axialMach number is kept reasonably constant through the turbomachinery at around0.4 0.5. Consequently the annulus area increases through the turbine toaccommodate the change in density as the flow expands.

The general purpose of expansion through a blade row is to increase the velocityand therefore have a reduction in the cross-sectional area.

The expansion from the combustion region to the atmosphere is accomplishedthrough a number of separate turbine stages. This enables the Mach numbers tobe controlled as well as facilitating the incorporation of multiple shafts for thebenefit of the compressor system.

Each blade row, either stationary or rotating, turns the flow and usually acceleratesit in its own frame of reference. The continuing changing of frame of reference iswhat enables the Mach numbers to be controlled.

108

54


ABSOLUTE GAS CONDITIONS - STATION REFERENCES

IN 0 3

THE CONSTANT MEAN DIAMETER TURBINE STAGE

MEANSTREAMLINE

BLADE

NGV

AXISr

AA

109

CHAPTER 4 PART 1 PAGE 4.09 to 4.12

THE CONSTANT MEAN DIAMETER VELOCITY TRIANGLESV in V a

N G V

V w in

V 0V a

UV 1

V 3V 2

R O TO R

U

V a

V w 3

V w 0

U

THERMODYNAMICS

E STAGE = CP (T O T 3) = H

Specific power

= U (Vw0 - Vw3)

FINALLY H = U V w

HU

= VwU2

bladeabsrel UVV

110

Power = rate of workCirc. force on the rotor per unit mass= rate of change of momentum = Vw

Work = Force x distance= Vw x distance

Power per unit mass= Vw x distance / time= Vw x U

55

COMBINED VELOCITY TRIANGLES

V0

V3V1

V

Vw

U

NGV

ROTOR

Vw0 Vw 3

Va

VIN

2ao a3a1a2

111

CONSTANT V a

CONSTANT U

UVw=

UH2

LOADING

STAGE LOADING COEFFICIENT. It is a measure of theenergy exchange, per unit massflow, for a given blade speed.High stage loading implies a large static pressure drop. It islimited by the aerodynamics of the blade rows to efficientlydeliver the required expansion.


FLOW COEFFICIENT =

The parameter is referred to as the flowcoefficient. It is a measure of turbine massflow at agiven rotor speed.

UVa

VaU


112

CONSTANT Va and U


212

302

tantan

tantan

UV

UV

UH

UV

UV

UH

aw

aw

ROTOR

21

30

tantantantan

aw

aw

VVVV

NGV

23

10

10

tantan

tantan

tantan

a

a

aa

VUVU

VVUa

w

VV 0

0tan

a

w

VV 1

1tan

10 -U ww VV

56


For the case where there is no change in radius across the rotor the velocity triangles can beplaced on a common base of blade speed, U:

The specific stage work output isthe product of the base vector, U,and the apex vector, DVw.

The stage loading is the ratio ofthe apex, DVw, to the base, U.

The flow coefficient is the ratio ofthe side vector, Va, to the base, U.

These types of velocity trianglesare routinely used in the designprocess to graphically representthe turbine aerodynamics.

113

Some Turbine Design Parameters

Specific Work

Stage Reaction (more on this later!)

TTCP

03o1

32

T-Tt-t

TU

TN & Engine & TurbineSemi-dimensional Speeds

Introduce these parameters

2P

2 TU

TTC

UH

Stage Loading

Flow CoefficientUVA

2UH

114

57

Typical turbine stage loadings are:

HP Turbine 1.5-2.0

IP Turbine 1.5-2.0

LP Turbine 2.0-3.0

High stage loading leads to higher turning and a modest increase in Mach Number,however there is more work per stage which can lead to fewer stages.

Low stage loading leads to lower turning and a modest decrease in Mach Number,however you are not getting the best out of the turbine.

Turbine Stage Loading

Low Stage Loading High Stage Loading

NGV ROTOR NGV

ROTOR

Vw

Va = constant

115

Turbine Flow Coefficient

Same mean radius and blade speed

NGV RotorNGV Rotor

Low Va/U High Va/U

NGVROTOR

Vw = constant

116

58

Turbine Flow Coefficient Reduced flow coefficient, Va/U, leads to reduced Mach Numbers, increased exit

angles and turning in both the vane and rotor, and a larger annulus height. This willresult in reduced aerofoil cord and/or numbers off (reduced trailing edge loss) toachieve the required work (sail area) and reduced cost.

In addition the aspect ratio of the aerofoils will be increased, resulting in reducedsecondary loss. However, the turbine is larger and heavier and the blade stress willbe increased.

As the hub diameter will be reduced, there is the potential for reduced leakage lossdue to the reduced area of the seals. At the casing the overall result depends on twoopposing effects, as the area of the seals is increased there is the potential forincreased leakage, however, assuming the tip gap is fixed, the tip gap to height ratioof the rotor will be reduced, providing the potential for reduced tip leakage flow perunit area.

Due to the civil aircraft markets desire to minimise the aircraft's fuel consumption andmaximise profits, a civil engine design is primary driven on the requirement tominimise the specific fuel consumption (SFC), i.e., maximum the efficiency. However,although a low Va/U design can result in reduced cost, the corresponding increase inweight and size has to be balanced in order to achieve the optimum design for aparticular airframe and mission requirement.

Typical values : Va/U = 0.4 - 0.6117

4.6.9 TURBINE STAGE REACTION

Turbine stage reaction is formally defined as the ratio of static enthalpy change acrossthe rotor to the total enthalpy drop across the stage:

A simplified definition of reaction for explanatory purposes is:stage

rotor

pp


stage

rotor

stage

rotor

Tt

Hh

Reaction,

118

31

32

HHHH

For a repeating stage where V1= V3 then

59

Turbine Reaction

Zero Reaction (Impulse) Turbine: No overall static pressure drop acrossthe rotor. Constant flow area across the rotor passage. Work is done purelyby the change in tangential momentum only with turning up to 150.

V1= V2

Large suction and pressure surface diffusions, Flow separation leading to increased loss, enhanced heat transfer at re-

attachment points. Very sensitive to inlet conditions. Diffusion on suction surface limits amount of available lift, i.e., low lift

coefficient leads to high number of aerofoils and/or blade chord,

Large surfacediffusions.Possibility ofseparatedflows.

Mn

Cax

Inlet Exit

V 0V 3

V 1V 2

NGV ROTOR

RelativeAbsolute

119

4.6.9 CHOICE OF STAGE REACTION


ZERO REACTION (IMPULSE ROTOR)

No overall static pressure change across rotor.o rotor relative velocities are equalo low stage leaving gas angleso Large PS and SS surface diffusion limits the lift coefficiento Potential for flow separation - > inc. loss, heat transfer hot spots

In practice:

o ensure V2 / V1 > 1.15

o good for power turbines(most of the available stage inlet energy can be converted into shaftpower)

o high total to static efficiency

V 0V 3

V 1V 2

NGVROTOR

120

60


100% REACTION

No overall static pressure change across nozzle.

o NGV velocities are equalo No acceleration across the stator (ensure V0 = V3 )o high stage leaving gas angleso High bearing loadso Increased over tip leakageo high rotor Mach Numbers

In practice:

o ensure V0 / V3 > 1.15o only the tip conditions

of free vortex turbines are of high reaction

V0V1

V3

V2


NGVROTOR

121


50% REACTION

o The power is achieved partly through momentum change, partlythrough pressure change

o 2D loss (Mach number)2, therefore from the velocity triangles you mightexpect that minimum loss will occur when the triangles are symmetrical(V0=V2)

o Delivers a good balance between peak Mach numbers, diffusion coefficients,over-tip leakage reduction and bearing loads.

In practice:

o popular for gas generator turbinessince high kinetic energy flow remainsfor subsequent stage(s)

o Relative to a high reaction, it has reduced inlet Mach number and angle atrotor inlet. Offset by increased NGV exit angle to deliver the same work.


V0

V1V3

V2

.

122

61



.

123

Mn

Inlet MnReduced

Exit MnIncreased

Cax

Reactionblading shape

Impulseblading shape

Turbine reaction summary For a given stage loading and flow coefficient, the shape of the velocity triangles

reflects the turbine reaction.

U

0% Reaction (Impulse) 100% Reaction

50% Reaction

In all cases, UDV,and Va/U are thesame.

DVw

V 0V 3

V 1V 2

U

V0V1

V3

V2

NGV ROTOR

DVw

DVw

124

62

REACTION

V0

V1V3

V2

.

125

stage

rotor

stage

rotor

Tt

Hh

00

Reaction,

stageoutstagein

rotoroutrotorin

HHHh

For a repeating stage where V NGV out= V NGV in then

ao

a3

a1

a2

U

wV

outinoutin

0out0in0stage

HHHH

HHH

22

22outin VV

122 TanTan

UVa

23

10

10

tantan

tantan

tantan

a

a

aa

VUVU

VVUa

w

VV 0

0tan

a

w

VV 1

1tan

10 -U ww VV

REACTION

V0

V1V3

V2

.

126

ao

a3

a1

a2

U

2/Vw

122 TanTan

UVa

2/Vw

a

a

w

VV 2

2tan a

w

VV 1

1tan

21w Tan-TanV aV

12

1211w

TanTan2

a

TanTanTan2

Tan2Va

a

aa

a

V

VVV

UaTanTan

UVa 122

1221

ww VVU

Vw1 Vw2

63

50% REACTION

V0

V1V3

V2

.

127

ao

a3

a1

a2

U

wV 122 TanTan

UVa

1225.0if TanTan

UVa

23

10

tantan

tantan

a

a

VUVU

1012 TanTanTanTanVU

a

02

2312 TanTanTanTanVU

a

31

Symmetric stage vel. triangles

223UVV ww

The effects of increasing turbine reaction:

Small changes in reaction is typically achieved by opening up the NGVthroat area and closing down rotor throat area. This then results in thefollowing changes:

Reduced area contraction and velocity ratio overNGV.

Reduced NGV exit Mach number.but increasedlift coefficient (NGV).

Reduced rotor inlet Mach number leading tonegative incidence onto the rotor.

Increased RELATIVE total temperature at inlet torotor

Increased Dp across rotor. So tip leakageincreases.

Increased rotor exit gas tangential whirl. Increased rotor exit Mach numberbut

decreased lift coefficient (Rotor). Increased back surface deflection on rotor.

NGV leading edge skew increased throat area

128

64

Turbine design for high power

129

4.6.7 STAGE DESIGN FOR HIGHEST POWER

TURBINE POWER IS LIMITED BY:

O Aerodynamic factors

o Thermodynamic (cooling) factors

o Mechanical integrity factors

IN GENERAL

POWER = W . U . V W


AERODYNAMIC LIMITATIONS:-Gas turningMach number (losses)Loading (H/U2)

MECHANICAL INTEGRITY LIMITATIONS:-Radial stressBlade speedMaterial properties

130

65

4.6.7 INCREASE STAGE POWER BY INCREASING FLOW

CONSTANT=P*ATWIN

ININ

HIGHEST FLOW WHEN NOZZLE GUIDE VANES ARE CHOKED

when M throat = 1

For specified TIN, PIN and A*

POWER = W . U . V W


In general the turbine designer is not free to change the massflow. It isinherently tied to the overall cycle and performance through thrust, BPR, TET,OPR etc. This effectively sets Va.A.

131

O REDUCE NUMBER OF N G Vs

O COOLING AIR REQUIRED IS REDUCED

but O N G Vs move apart and reduces overlapand effectiveness

GOOD VALUE OF S/C0.7 (see later)

O NGV aerodynamic loading increases and theaerodynamics get more challenging.

INCREASE STAGE POWER BY INCREASING NGV THROAT AREA

POWER = W . U . V W

CONSTANT=P*ATWIN

ININ

132

66

ENGINE UP-RATING TO HIGHER POWER

TURBINE DESIGN FOR HIGHEST POWER

o Increase pressure ratio add zero compressor stage

SINCE:CONSTANT=

P*ATWIN

ININ

o Increase nozzle throat area toaccommodate for choked flow

Best to increase TET

and pressure ratio together FIXED TET

INCREASED TETT

S133

4.6.7 INCREASE STAGE POWER BY INCREASING V w

For a given W and U this can be achieved in two ways:

Increase Vw0 i.e. 0

Increase Vw3 i.e. 3


POWER = W . U . V W

134

67

4.6.7 INCREASE DESIGN POWER BY INCREASING 0

V0

V3V1

V2

U

INCREASED 0


For cooled stages:

trailing edge of the high 0 NGV needs to be thinner for the sameboundary layer wake thickness.

difficult to engineer trailing edge cooling passages into the profile.

Avoid excessive wall scrubbing in high Mach number flows

typically, the limit occurs when 0 = 70 - 72

135

4.6.7 INCREASE DESIGN POWER BY INCREASING 3


For cooled stages:

o for the final stages of an LP turbine outlet swirl into jet pipeis high increase gas path and jet pipe loss.

o reheat gutters (if fitted) difficult to align with the flow

if 3 > 15.

V0

V3V1

V2

U

INCREASED 3

136

68

V0

V3V1

V2

U

INCREASED U

4.6.7 INCREASE DESIGNPOWER BY INCREASING U


o If RPM is fixed by the device the turbine is drivingtherefore increase U only by increasing the turbine diameter

o Otherwise stresses increase ( AN2 )

but o annulus height reduced for a given massflow will requireresult less cooling air since blades are radially shorter.

and o increased blade speed, means 0 and 3 fall relieving bothcooling problems (high 0) and downstream loss (high 3)

POWER = W . U . V W

137

138

A simple overall turbine aero design sequence (1/2)

Requirements from cycleinlet and outlet p and tmass flow inpower required e.g. to drive compressorrotational speed, n, e.g. from compressor

choose mean diametercalculate mean blade speed; check < 350m/scalculate loading h/u2

calculate number of stages;h/u2

69

139

A simple overall turbine aero design sequence (2/2)

select axial velocity at inlet (= outlet velocity?)calculate inlet area

start sketching annulus shapedoes it fit therest of the engine?Iterate design choices to give best annulus shape

select reactioncalculate velocity triangles at mean radius

select radial equilibrium typecalculate tip and root velocity trianglescheck limits reaction, turning

choose aspect ratios

calculate blade and vane numbers

proceed to blade shape design if required

Turbine efficiency

140

70

T

Pout

Pin

ACTUALTURBINE

WORKOUTPUT

Tin = TET

Tout

Tout

IDEALTURBINE

W

Turbine Design Manual

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