Turbine Design Manual

AXIAL TURBINE DESIGN MANUAL

CHAPTER 4 PART 2


Dr K W RAMSDEN DIRECTOR – GAS TURBINE TECHNOLOGY PROGRAMMES DEPARTMENT DEPAR TMENT OF POWER AND PROPULSION PROPULSION SCHOOL OF ENGINEERING CRANFIELD UNIVERSITY CRANFIELD, BEDFORD MK43 0AL

DISCLAIMER SCHOOL OF ENGINEERING DEPARTMENT OF POWER AND PROPULSION

These notes have been prepared by Cranfield University for the personal use of course delegates. delegates. Accordingl Accordingly, y, they may not be communicated communicated to a third party without without the express permission permission of the author. The notes are intended to support the course in which they are to be presented presented as defined by the lecture programme. programme. However However the content may be more comprehensiv comprehensive e than the presentation presentations s they are supporting. supporting. In addition, the notes may cover topics which are not presented in the presentations. Some of the data contained in the notes may have been obtained from public literature. literature. However, However, in such cases, the corresponding corresponding manufacturers manufacturers or originators are in no way responsible for the accuracy of such material. All the information provided has been judged in good faith as appropriate for the course. However, However, Cranfield Cranfield University University accepts no liability liability resulting resulting from the use of such information.


SUMMARY

This document facilitates the aerodynamic design of both a low and high pressure turbine 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 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 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 velocity is maintained constant throughout. A critical assessment is carried out in terms of likely performance and, where appropriate, suggestions made for modifications taking into account the prescribed application. The The resu result lts s calc calcul ulat ated ed by the the user user can can be dire direct ctel ely y comp compar ared ed with with the the valu values es appended.


CONTENTS

PAGE

BACKGROUND NOTES NOTATION AND UNITS

1

1.0

INTRODUCTION TWO SHAFT ARRANGEMENT

2A 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

6.2A


9A

6.2B


9B

7.0

HP TURBINE DESIGN ASSESSMENT

7.1A

DESIGN SUMMARY - TET = 1250K

10A

7.1B

RECOMMENDATIONS - TET = 1250K

10B

8.0


8.1A


11A

8.1B

RECOMMENDATIONS TET = 1650 K

11B (CONTINUED)


CONTENTS ( 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


14

10.2

HP TURBINE EXIT ANNULUS GEOMOETRY

14

10.3 10.4

INTER-TURBINE ANNULUS GEOMETRY ESTIMATION LP TURBINE EFFICIENCY PREDICTION

15 16

10.5

LP TURBINE OUTLET ANNULUS GEOMETRY

17

11.0

LP TURBINE FREE VORTEX DESIGN

11.1A


18A

11.1B

VELOCITY TRIANGLES - TET =1250K

18B

11.2A


19A

11.2B


19B

12.0

LP TURBINE DESIGN ASSESMENT

12.1A


20A

12.1B


20B

12.2A


21A

12.2B


21B

( CONTINUED)


CONTENTS (CONTINUED) ANNEXES ANNEX A

PAGE SUMMARY OF CONTENTS

A1

A 1.O

HP TURBINE DESIGN TABULATION

A 1.1


A2

A 1.2

INLET ANNULUS GEOMET RY

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


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

GAMMA = 1.32

C3 AND C4

GAMMA = 1.29

C5 AND C6

(CONTINUED)


CONTENTS (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


-1-

NOTATION AND UNITS

SYMBOLS

A Cp D h H M N p P q Q R Rc Rov t T U V W

 

 

UNITS m2 Joules / kg.K m m Joules / kg

Cross sectional area Specific heat at constant pressure Diameter Annulus height Stagnation enthalpy Mach number Revs per minute Static pressure Stagnation pressure Mass flow function (W T /Ap ) Mass flow function (W T /AP ) Gas constant Compressor pressure ratio Overall pressure ratio Static temperature Stagnation temperature Blade speed Velocity Mass flow Gas angle Ratio of specific heats

min. -1 n/m 2 n/m2 1/( Joules kg/K ) 1/( Joules kg/K ) Joules/kg.K

K K m/sec m/sec kg/sec degrees

Change in: Work done factor

ABBREVIATIONS

SUFFICES

BMH

Blade mid height

a

Axial

 isent 

Isentropic efficiency

ann

Annulus

Polytropic efficiency Fuel air ratio High pressure Low pressure Nozzle guide vane Stoichiometric Turbine entry temperature

in Stage inlet mean At mid height out outlet R (or H) At the root (or hub) T At the tip or casing w Whirl direction 0 Nozzle outlet (abs) 1 Rotor inlet (rel) 2 Rotor outlet (rel) 3 Rotor outlet (abs)

poly FAR HP LP NGV stoi. TET


-2A-

1.0 INTRODUCTION

This Document facilitates the aerodynamic design of both a low and high pressure turbine 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 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 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 0.3 and the corresponding axial volocity is maintained 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 velocity Constant mean diameter = 0.45m RPM = 15000 50% reaction at blade mid height Free vortex flow distribution Axial HP inlet flow with a Mach number of 0.3 Straight sided annulus walls


2B

LPC

HPC

FIGURE 1 TWO SHAFT TURBOJET (OR TURBOFAN CORE ENGINE)

HPT

LPT


SPECIFICATION


-3-

2.0 SPECIFICATION 2.1 THE COMPRESSOR SYSTEM. The compressor system has the following specification :

Inlet temperature

(T1)

Inlet pressure

(P1 )

101325

Overall pressure ratio

(Rov)

16.0

LP pressure ratio

(Rc)

3.56

HP pressure ratio

(Rc)

4.494

(Nhp)

15000

HP RPM

300

(poly)

Polytropic efficiency Mass flow

( both spools )

(W)

0.90 40.0

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

LP COMPRESSOR

HP COMPRESSOR

Pressure ratio

3.560

4.494

isent

0.882

0.879

300

449

149

274

Outlet temperature

449

723

Power = W. Cp.  T (megawatts)

5.99

11.03

Inlet temperature Temperature rise

T

γ 1

isent 

NOTE :

and

Cp 

R  1

Rc

γ

 1

 1

Rc poly

1

where:

 = 1.4

T  and R = 287

T1

isent

 -1   R c   1   ie,

Cp = 1005


-42.0 SPECIFICATION 2.2 THE HP TURBINE SYSTEM The hp turbine is required to supply only the hp compressor power since it is assumed that there are no mechanical losses. The turbine mass flow is the compressor flow plus the fuel flow. The latter is obtained by calculating the fuel flow and hence the fuel/air ratio (FAR) required to raise the compressor outlet temperature to the specified TET. This is calculated based on an enthalpy balance. The corresponding values of FAR are shown in the table below assuming a combustor efficiency of 100%. The mean specific heat is calculated from values of Cp for both air as well as for the combustion 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 f 2 R=287.05-0.0099FAR+1e-7(FAR ) A0 A1 A2 A3 A4 A5 A6 A7 A8

0.992313

0.236688

-1.852150

6.083152

-8.89393

7.097112

-3.23473

0.794571

-0.08187

B0 B1 B2 B3 B4 B5 B6 B7 A8

-0.71887

8.747481

-15.8632

17.2541

-10.2338

3.081778

-0.36111

-0.00392

-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

(megawatts)

11.03

11.03

(joules/Kg.K)

1184

1275.5

(n/m )

1540140

1540140

1.32

1.29

HP Turbine Power (To drive hp compressor) Mean specific heat - Cp Inlet stagnation pressure - Pin (Assumes 5% Combustor pressure loss)

Ratio of specific heats,

 = 1/(1-R/Cp)

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


HP TURBINE DESIGN


-53.0 HP TURBINE DESIGN CONSTRAINTS.

The following design constraints are imposed :Axial inlet flow with a Mach number of 0.3 Constant axial velocity Constant mean diameter RPM = 15000 50% reaction at blade mid height Free vortex flow distribution Straight sided annulus walls Constant 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 diagram below). This introduces only a small error. Additionally, it is assumed that the exit plane of the NGV is half way along the annulus. This implies that the axial chord of the NGV is greater than that of the rotor which allows a reasonable spacing between the blade rows. 4.0 HP TURBINE ANNULUS DIAGRAM. The following general annulus configuration is used :-

h in

NGV

BLADE

h out

L/2 L

D mean

AXIS


-65.0 HP TURBINE DESIGN TABULATION. 5.1 OVERALL SPECIFICATION.

Mass flow

TET

1250

1650

W (Kg / s)

40.64

41.16

11.03

11.03

1184 (1.32)

1275.7 (1.290)

Power

(megawatts)



Specific Heat Cp (and )

5.2 INLET ANNULUS GEOMETRY. P = 16 x 101325 x 0.95 Inlet Mach Number

0.30 = W.T / A.P

Q (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 Umean = U

H/U2 Va / Tin

T = Power / W.Cp = RPM.

 Dmean / 60

= CpT /U2

( 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

0.30


-7-

5.0 HP TURBINE DESIGN TABULATION ( CONT. )

5.4 OUTLET ANNULUS GEOMETRY.

TET

1250

1650

0.98

0.98

Va = Tin -  T

T3 Work done factor



Vw

= (H/U2) . U/

Vw3

= (Vw-Umean) /2 (50 % Reaction)

3

= tan-1 (Vw3/Va)

V3

= Va/Cos3

V3/T3 (See ANNEX C, use appropiate  )

M3 Q3

(See ANNEX C)

R

= (1-T/ (isent. Tin)) /( -1)

P3

= Pin x Rov (See note below) = W. T3 / P3.Q3

A3

= A3 / Cos3

Aann



h

= Aann / ( Dmean)

Dtip

= Dmean + h

Dhub

= Dmean - h

Hub/Tip Ratio

NOTE:

= Dhub/Dtip

P3 = Pout (In the direction of V3) SEE PAGE A3 FOR SOLUTIONS


-8A6.0 HP TURBINE-FREE VORTEX DESIGN 6.1A DESIGN TABULATION - TET = 1250K

ROOT D (NGV exit)

= (Din + Dout) /2

D (Rotor exit)

(See Table 5.4 - page 7)

Va Vw3mean Vwomean (See Table 5.4)

BMH

(Constant radially) (See Table 5.4 - Page 7) = (Vw-Vw3) mean

Vwo = Vwomean x Dmean/D (D at NGV exit) = tan- (Vwo / Va) o Vw3 (D at rotor exit)

= Vw3mean . Dmean/D

3

= tan- (Vw3 / Va)

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

= Va / Coso

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

TIP


-8B6.0 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 the stage at Root, Blade Mid Height and Tip. NOTE: USE A SCALE OF 1cm = 100m/s

TIP

BMH

ROOT

NOTE: SEE PAGE A4B FOR SOLUTIONS


-9A6.0 HP TURBINE-FREE VORTEX DESIGN 6.2A DESIGN TABULATION - TET = 1650K

ROOT D (NGV exit) D (rotor exit)

= (Din+Dout)/2 (See Table 5.4 - page7)

Va

(Constant radially)

Vw3mean 7)

(See Table 5.4 - page

Vwomean (See Table 5.4)

= (Vw-Vw3)mean

Vwo Dmean/D (D at NGV exit)

= Vwomean x

o

= tan-1 (Vwo/Va)

Vw3 (D at rotor exit)



3

= Vw3mean x Dmean/D = tan-1 (Vw3/Va)

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

= Va/Coso

Nozzle Acceleration, Vo/Vin

= Vo/Va

V1

= (Va +(Vwo-U) )



= Cos-1 (Va/V1)

1

V2

= (Va +(U+Vw3) )



= Cos-1 (Va/V2)

2

Rotor Acceleration, V2/V1

NOTE : SEE PAGE A5A FOR SOLUTIONS

BMH

TIP


-9B-

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 the stage at Root, Blade Mid Height and Tip. NOTE: USE A SCALE OF 1cm = 100m/s

TIP

BMH

ROOT



-10A-

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 A4A ROOT

HUB TO CASING NGV Exit Gas Angle

o

Nozzle Deflection,

o+in

Rotor Deflection,

 +

Nozzle Acceleration

Vo / Vin

1

Rotor Acceleration

BMH

2

V2 / V1

3

Exit swirl, Reaction

STAGE OVERALL

DATA

Inlet hub/tip ratio (See Page A2) Outlet hub/tip ratio (See Page A3) NOTE: SEE PAGE A6A FOR SOLUTIONS

TIP


-10B7.0 HP TURBINE DESIGN ASSESSMENT 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 ?


-11A8.0 HP TURBINE DESIGN ASSESSMENT. 8.1A DESIGN SUMMARY - TET = 1650K NOTE: See ANNEX B for method of calculation.

AT BLADE MID HEIGHT

NGV EXIT

BLADE EXIT


DATA FROM PAGE A5A ROOT

HUB TO CASING NGV Exit Gas Angle

o

Nozzle Deflection

o+in

Rotor Deflection

1+2

Nozzle Acceleration

Vo / Vin

Rotor Acceleration

V2 / V1

Exit Swirl

BMH

3

Reaction

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


TIP


-11B8.0 HP TURBINE DESIGN ASSESSMENT 8.1B RECOMMENDATIONS - TET = 1650 K (SEE Page A6B for data)



(C) IS THE ROTOR EXIT SWIRL ACCEPTABLE ?

(D) ARE THE GAS DEFLECTIONS OK?





LP TURBINE DESIGN


-129.0 LOW PRESSURE TURBINE DESIGN

9.1 LOW PRESSURE COMPRESSOR SPECIFICATION

The low pressure compressor has the following specification (See Page 3) Inlet temperature Inlet pressure Mass flow

Tin Pin W

Polytropic efficiency Isentropic efficiency Compressor power

poly isent

300 101325 40

0.90

0.88 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 tip Mach number of 1.15. Accordingly, the following velocity triangle applies at the tip of the first stage rotor:-

M = 1.15 1

Ma = 0.5

U tip


-13-

9.3 ESTIMATION OF LP COMPRESSOR (LP TURBINE) RPM The following tabulation gives the sequence of calculations to estimate blade tip speed and RPM. (See also velocity triangle at the rotor tip shown on page 12).

Ma Va /Tin

0.5 ( See ANNEX C, for  = 1.4 )

Va Qin

= W.Tin / Pin.Ain

Ain

.Dmean )

hin

= Ain/(

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

= (V1 - Va )

RPM

= 60.Utip/(

Dtip )

NOTE: SEE PAGE E1 FOR SOLUTIONS


-14-

10.0 LP TURBINE OVERALL DESIGN 10.1 OVERALL SPECIFICATION.

LP TET Mass flow Power

(megawatts)

Specific heat, Cp

(and )

RPM Blade mid height reaction

1021

1440

40.64

41.16

5.99

5.99

1184 (1.32)

1275.7 (1.290)

10980

10980

50%

50%

10.2 HP TURBINE EXIT ANNULUS GEOMETRY (SEE PAGE A3) TET Dmean

1250

1650

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

0.702

0.718

Va

205.1

233.0

Vw out mean

215.4

210.5

Hub/Tip Ratio

= Dhub / Dtip


-1510.3 INTER-TURBINE ANNULUS GEOMETRY ESTIMATION The factors concerning selection of inter-turbine axial space and annulus flare angle are considered in ANNEX F. Accordingly, an annulus flare of 30 0 ( included angle ) is selected with an axial space of 0.00635m. This is an example estimate for a closely spaced blade rows. For your own designs select spacings based on the values of local upstream chord as discussed in the lectures (e.g. St≈0.25Cax) The lp inlet annulus area is then estimated using the hp exit values of Table 10.2 and the inter-turbine data in table 10.3 below. The inter-turbine geometry is shown diagramatically below :-

HP EXIT

LP INLET

y 0.00635

15

o

y D mean AXIS

TABLE 10.3 LP TURBINE INLET ANNULUS GEOMETRY LP TET. LP Turbine inlet pressure

( See Table A1.4 )

Dmean Dtip

= Dhub (hp exit) - 2y

h

= (Dtip- Dhub)/2

Hub / Tip Ratio Va Vw in (mean)

1440

583713

768530

0.45

0.45

215.4

210.5

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

Dhub

A

1021

= .Dmean . h = Dhub / Dtip = Va(hp exit) x h(hp exit) / h(lp entry) (As for HP exit)

NOTE : SEE PAGE E2 FOR SOLUTIONS


-16-

10.4 LP TURBINE EFFICIENCY PREDICTION (SINGLE STAGE AT MID HEIGHT)

LP TET Temperature Drop Blade Speed, Umean = U

H/U2 Va

1021

1440

= Power / (W.Cp) = RPM.

 . D / 60

= CpT / U2 (Single Stage) (See Table 10.3 - Page 15)

Va / U

isent

(Smith's Chart Value minus 2 %)

NOTE : SEE PAGE E2 FOR SOLUTIONS

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 a high overall efficiency in favour of low weight. If then, the work is split equally, each stage would 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 at near axial leaving velocity.

IMPORTANT NOTE THE PRELIMINARY DESIGN NOW CONTINUES ASSUMING A SINGLE STAGE LP TURBINE IS FEASIBLE FOR BOTH TET CASES CONSIDERED. THIS DECISION IS REVIEWED ON COMPLETION OF T HE PRELIMINARY DESIGN


-17-

10.5 LP TURBINE OUTLET ANNULUS GEOMETRY.

LP TET

1021

1440

0.97

0.97

Va = Tin - T

T3 Work Done Factor



Vw

= (H/U2) . U/

Vw

= (Vw - Umean )/2

( 50% Reaction )

3

= tan -1 (Vw3/Va)

V3

= Va / Cos3

V3/T3 M3 Q3 Pressure Ratio

(See ANNEX C, use Appropriate  ) ( See Tables-ANNEX C ) R = ( 1 -  T/ ( isent Tin ))  / (-1)

P3

= Pin x R (See note below)

A3

= W  T3 / P3 Q 3

Aann

= A3 / Cos3



h

= Aann / ( Dmean)

Dtip

= Dmean + h

Dhub

= Dmean - h

Hub / Tip Ratio

= Dhub/Dtip

NOTE : P3 = Pout ( In the direction of V3 ) NOTE : SEE PAGE E3 FOR SOLUTIONS


-18A-

11.0 LP TURBINE-FREE VOTEX DESIGN 11.1A DESIGN TABULATION - TET = 1250K

ROOT D (NGV Exit) D (Rotor exit)

= (Din + Dout)/2 (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) = tan -1 (Vw0/Va)

0 Vw3

(D at Rotor exit)

3

= Vw3mean x Dmean / D = tan -1 (Vw3/Va)

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

in Vin Nozzle Acceleration

= Va / Cos 0 = tan - (Vw3hp. out / Valpin) (Vw3hp. out - Table 6.1A, Page 8A) = Valpin / Cos in) = V0/Vin

V1

= (Va +(Vwo-U) )

1

= Cos -1 (Va/V1)

V2

= (Va +(U+Vw3) )

2

= Cos -1 (Va/V2)

Rotor Acceleration

= V2/V1

NOTE : SEE PAGE E4A FOR SOLUTIONS

BMH

TIP


-18B11.0 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 the stage at Root, Blade Mid Height and Tip. NOTE: USE A SCALE OF 1cm = 100m/s

TIP

BMH

ROOT

NOTE: SEE PAGE E4B FOR SOLUTIONS


-19A11.0 LP TURBINE-FREE VORTEX DESIGN 11.2A DESIGN TABULATION - TET = 1650K

ROOT D (NGV exit) D (Rotor exit)

= (Din + Dout)/2 (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) = Vwomean x Dmean / D

Vwo (D at NGV exit)

= tan - (Vw0/Va)

0 Vw3 (D at Rotor exit)

= Vw3mean x Dmean/D = tan -1 (Vw3/Va)

3

U (for exit velocity triangles) = Umean x D/Dmean (D at Rotor exit, Umean Table 10.4) V0 = Va / Cos0 = tan - (Vw3hp. out / Valp.in) (Vw3hp out - Table 6.2A, Page 9A)

in

= Valp. in /Cos in)

Vin Nozzle Acceleration. V0/Vin V1

= (Va2+[Vwo-U]2)

1

= Cos -1 (Va/V1)

V2

= (Va2+[U+Vw3]2)

2

= Cos - (Va/V2)

Rotor Acceleration. V2/V1

NOTE : SEE PAGE E5A FOR SOLUTIONS

BMH

TIP


-19B11.0 LOW PRESSURE TURBINE - FREE VORTEX DESIGN 11.2B VELOCITY TRIANGLES - TET = 1650 K (MID HEIGHT REACTION = 50%) From the data provided on Page E5A, draw below the velocity triangles appropriate to the stage at root, blade mid height and tip. USE A SCALE OF 1cm = 100m/s

TIP

BMH

ROOT

NOTE : SEE PAGE E5B FOR SOLUTIONS


-20A12.0 LP TURBINE DESIGN ASSESSMENT. 12.1A DESIGN SUMMARY - TET = 1250 K NOTE: See ANNEX B for method of calculation. AT BLADE MID HEIGHT

NGV EXIT

BLADE EXIT


HUB TO CASING

DATA FROM PAGE E4A ROOT

BMH

in 0

NGV Exit Gas Angle Nozzle Deflection

0+in

Rotor Deflection

1+2

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

TIP


-20B12.0 LP TURBINE DESIGN ASSESSMENT 12.1B RECOMMENDATIONS - TET = 1250 K (SEE PAGE E6A - DESIGN SUMMARY)

(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 ?


-21A12.0 LP TURBINE DESIGN ASSESSMENT. 12.2A DESIGN SUMMARY - TET = 1650K 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

HUB TO CASING

DATA FROM PAGE E6B ROOT



in

NGV Exit Gas Angle

0

Nozzle Deflection

0+in

Rotor Deflection

1+2

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

BMH

TIP


-21B-

12.0 LP TURBINE DESIGN ASSESSMENT 12.2B RECOMMENDATIONS - TET = 1650 K (SEE PAGE E6B- DESIGN SUMMARY)



(C) IS THE ROTOR EXIT ACCEPTABLE ?

(D) ARE THE GAS DEFLECTIONS OK ?





ANNEX A

HP TURBINE DESIGN RESULTS


-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


-B1 and B2ANNEX 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) of the turbine design assessment.

 Vw V 0

V 2

V 1

V 3 Vw 0

V a

Vw 3

The above diagram shows the velocity triangles for a stage. The following calculation procedures 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: T = Tin -  T 3 Stage

and from the geometry of the velocity triangles above:V32 = Vw32 + Va2 ABSOLUTE MACH NUMBER AT NGV EXIT, M o 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, M 3 M3

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

NGV ACCELERATION, Vo / Vin Vo as above Vin = Va at inlet to the HP turbine. Vin = V3 hp exit at inlet to the LP turbine. ROTOR ACCELERATION, V 2 / V1 Where from the velocity triangles above:V2 = Va / Cos 2 V1 = Va / Cos 1 DEFLECTIONS: Rotor deflection = 1 + 2

Where: and:

NGV deflection = o + in

 U  Vw 3   2  tan 1    Va   Vw0  U  1  tan 1    Va 

in = 0 Where: in = 3 hp exit and:

STAGE REACTION.

Reaction,





hrotor t rotor   H 0 stage T 0 stage

for HP turbine for LP turbine


ANNEX C

COMPRESSIBLE FLOW TABLES GAMMA = 1.40

PAGE C1 AND C2

GAMMA = 1.32

PAGE C3 AND C4

GAMMA = 1.29

PAGE C5 AND C6

C1

C2

C3

C4

C5

C6


ANNEX D

EFFICIENCY CORRELATION


-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


F1 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



HP NOZZLE

HP BLADE

LP NOZZLE

LP BLADE

 X

A X IS

A finite distance, x, is required between the HP exit and LP entry. The value of x is, typically, approximately 25% of the previous blade row axial chord or 1/4 inch. (whichever is larger). The value of annulus flare angle, , usually limited to 30 o (included), will depend on the magnitude of axial chords 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 exit and LP turbine inlet. The whirl component of velocity, Vw3, at HP exit will, however, remain unchanged in the inter-turbine space since angular momentum will be conserved. Since blading considerations are not covered in this design study, the axial distance, x, is assumed to be 1/4 inch. (0.000635m) and annulus flare angle is taken to be 30 o (included). If the annulus height increase between HP exit and LP inlet is 2y, the reduction of axial velocity can be estimated, as follows:y = 0.00635 tan (/2) h lp entry = h hp exit + 2y Where:-

h hp exit is the annulus height at hp exit. (See Table 5.4 page 7 or Table A1.4 page A3)

NOTE:

Va lp inlet = Va hp outlet. h hp exit / h lp inlet Vw3hp exit = VWin lp inlet

CHAPTER 4 AXIAL TURBINE DESIGN AND PERFORMANCE Presentation slides v2013-v1.1

Dr. David MacManus , Dr. Ken Ramsden, Dr. Anthony Jackson Gas Turbine Technology P rogrammes DEPARTMENT OF POWER AND PROPULSION SCHOOL OF ENGINEERING CRANFIELD UNIVERSITY

1

Turbines - General Bibliography 1. Japikse, D., “Introduction to turbomachinery”, Oxford University Press, 1997. 2. Cohen, H., Rogers, G., and Saravanamuttoo, H., “Gas turbine theory”, Longman Scientific and Technical, 3 rd Edition, 1987. 3. “The jet engine”, Rolls-Royce plc, 5 th Edition, 1996. 4. Cumpsty, N., “Jet propulsion”, Cambridge University Press, 1997. 5. Dixon, S., ”Fluid mechanics and thermodynamics of turbomachinery”, Butterworth-Heinemann, 4 th 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”, 2 nd 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, 2006 15. Sieverding, C., “ Secondary and tip-clearance flows in axial turbines”, Von Karman Institute, LS1997-1 16. Arts, T., “Turbine blade tip design and tip clearance treatment”, Von Karman Institute, LS2004-2 17. Booth, T., “Tip clearance effects in axial turbo-machines “, Von Karman Institute, LS1985-5 18. Sunden, B., Xie, G., “Gas Turbine Blade Tip Heat Transfer and Cooling: A Literature Survey”, Heat Transfer Engineering, 31:7, 527-554, 2010. 2

1

DISCLAIMER SCHOOL OF ENGINEERING DEPARTMENT OF POWER AND PROPULSION These notes/slides have been prepared by Cranfield University or its agents for the personal use of course attendees. Accordingly, they may not be communicated to a third party without the express permission of the author. The notes/slides are intended to support the course in which they are to be presented as defined by the lecture programme. However the content may be more comprehensive than the presentations they are supporting. In addition, the notes may cover topics which are not included in the presentations. Some of the data contained in the notes/slides may have been obtained from public literature. However, in such cases, the corresponding manufacturers or originators are in no way responsible for the accuracy of such material. All the information provided has been judged in good faith as appropriate for the course. However, Cranfield University accepts no liability resulting from the use of such 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

2

Turbine 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

3

Gas turbine applications Industrial Power generation Siemens 340 megawatts (MW) SGT58000H gas turbine.

This image cannot currently be displayed.

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

Oil and gas

Rolls-royce.com

Marine e.g. MT30 marinized version of an aero GT. 40MW range 7

Gas turbine applications Propulsion

Boeing.com

airbus.com

Lockheed.com

8

4

Turbine design drivers •

Prelim Prelimina inary ry design design stage stage consid considera eratio tions ns • How much much do do you need need to know… know…..an ..and d when when? ?

•

What What is the the appl applic icati ation on? ? • Prop Propul ulsi sion on or powe power r • Civil • Military • Short Short durati duration? on? Dispos Disposabl able? e?

•

How does does this this affect affect the design design approa approach ch ? • Time Time to mark market et • Mark Market et size size and and dura durati tion on • Prel Prelim imin inar ary y desi design gn fidel fidelity ity • Evol Evolut utio ion n or revo revolu lutio tion n

9


What are the design design aspect aspects s for for consid considera eration tion ? •

Specif Specific ic fuel fuel consump consumptio tion n (and (and/or /or block block fuel fuel burn) burn) • Temp Tempe erature • Pressure • BPR • Compo Compone nent nt effic efficie ienc ncy y

•

Emissions

•

Weight

•

Size •

•

Embedde Embedded d config configura uratio tions ns (civil (civil or milita military ry))

Life

10

5


Reli Reliab abiility lity • •

•

Noise • •

• •

Turbi urbine ne nois noise e Effe Effect ct of LPC LPC noi noise se on turb turbine ine design design

Time Time to manu manufa fact ctur ure e Robustness • •

• •

Risk Risk/b /bene enefit fit trad trade e off off E.g. E.g. tip tip gap, TBC, TBC, coolin cooling g strateg strategy, y, stress stress margins margins

Chan Change ge in oper operat atio ions ns Chan Change ge in futu future re proc proces esse ses s

Grow Growth th pote potent ntia iall Cost • • • • •

Manuf anufac actu turre Ownership Repl Replac acem emen entt part parts s Power/ Power/thr thrust ust supply supply (risk (risk owners ownership) hip) Maint aintan anen enc ce 11

Turbine design disciplines •

Aero Aerody dyna nami mics cs

•

Cooli Cooling ng and therma thermall manage managemen mentt

•

Mech Mechan anic ical al desi design gn

•

Stress

•

Lifing

•

Costs

•

Weights

•

Manuf anufac actu turi ring ng

•

Logis gistics

•

Purcha rchasi sin ng 12

6

Possible output from a turbine preliminary design •

Numb Number er of stag stages es

•

Work split split for multimulti-sta stage ge turbin turbines es

•

Aerod Aerodyna ynamic mic condit condition ions s

•

Annul Annulus us shape shape and dimen dimensio sions ns

•

Blad Blade e and and vane vane aspe aspect ct rati ratio o

•

Blade Blade and vane vane space/ space/cho chord rd ratio ratio

•

Blade Blade and vane vane airfoi airfoill numbe numbers rs

•

Radia Radiall work work distri distribut bution ion

•

Inte Interr-ro row w axia axiall spac spacin ing g

13

Design process and considerations 1D and maybe 2D aerodynamic design

Stage 0 Preliminary evaluations Stage 1 Preliminary design

1D, 2D and maybe maybe 3D aerodynamic design

Stage 2 Full concept definition

Main focus for turbine aerodynamic design work

2,3 and 4D aerodynamic design

Stage 3 Product realisation Stage 4 Developmen Developmentt and production Stage 5 In service Stage 6 Disposal

14

7

The importance of preliminary design

Knowledge of the design

Jones 2002 15

Basic turbine performance

16

8

FUNDAMENTAL PERFORMANCE PARAMETERS       

ENERGY

W.V 2 2 W

C t p

(kinetic) (molecular

activity)

TEMPERATURE

t , T

(static – molecular; total –plus kinetic)

PRESSURE

p , P

(static - molecular bombardment; total - adds kinetic term)

POW ER

W Cp ΔT

(total energy change per second; molecular plus kinetic)

SPEED OF SOUND MACH NUMBER

a

 M

Rt V a

(sound transmitted by molecular collision) (better to use than velocity)

EXAMPLE:

TEMPERATURE K

COMPRESSOR INLET

TURBINEINLET

300

1600

SOUND SPEED m/s

350

780

MACH NUMBER

0.5

0.5

VELOCITY m/s

175

390

17

USEFUL POWER AND THERMAL EFFICIENCY

P2

ENERGY

TURBINE POWER

COMBUSTOR ENERGY INPUT

USEFUL POWER

= Turbine Power – Compressor Power

COMPRESSOR POWER

P1 THERMAL EFFICIENCY



Useful Power Combustion Energy Input

ENTROPY

18

9

DESIGNER’S SOLUTIONS FOR HIGHEST USEFUL POWER DESIGN FOR HIGH TURBINE INLET TEMPERATURE

Red MINUS blue (PT-PC) equals output power T Largest when Highest pressure ratio and or Highest TET

PT

PC

S 19

EFFICIENCY OF GAS TURBINE ENGINES Compressor Isentropic Efficiency

3

T

c



( T ' 2  T1 ) ( T2  T1 )

COMBUSTOR ENERGY INPUT P2

W.Cp.(T’ 2-T1) = ideal compressor work W.Cp.(T2-T1) = actual compressor work

2 ACTUAL TURBINE WORK

2’ ACTUAL COMPRESSOR WORK

Turbine Isentropic Efficiency

4

 T4 )  (T3  T ' 4 ) (T3

T

IDEAL TURBINE WORK

IDEAL COMPRESSOR WORK

W.Cp.(T3 - T 4) = actual turbine work W.Cp.(T3 –T’4) = ideal turbine work

P1

4’

1

s Thermal Efficiency = (Useful W ork/Combustor Energy Input)

THERMAL

1

(T4 (T3

T1 ) T2 )

Where: Useful work = turbine work - compressor work = W.Cp.(T3 -T4) - W.Cp.(T 2-T1) Combustor Energy Input = W.Cp.(T 3 - T 2)

20

10

Basic arrangements

21

Engine architectures and gas path This image cannot currently be displayed.

Images from Rolls Royce

22

11

Engine architectures and gas path Single spool axial flow turbojet

Images from Rolls Royce23

Engine architectures and gas path This image cannot currently be displayed.

Images from RollsRoyce

24

12

Idealised gas path conditions This image cannot currently be displayed.

PRESSURE

TEMPERATURE

VELOCITY Images from RollsRoyce 25

GAS GENERATOR TURBINES POWER TURBINE

IMAGE COURTESY ROLLS ROYCE

26

13

TRENT AERO ENGINE – IMAGE COURTESY OF ROLLS-ROYCE

Rolls Royce T900 TURBINES

Specifications: BPR

8

OPR

41

Stages

1LPC, 8IPC, 6HPC, 1HPT, 1IPT, 5 LPT

Fan diameter

116 inches

Thrust

76,500lb

Aircraft

A380

27

A MILITARY LOW BYPASS RATIO TURBOFAN

EJ200

IMAGE COURTESY ROLLS ROYCE Specifications: BPR

0.4

OPR

25

Stages

3LPC, 5HPC 1HPT, 1LPT

Fan diameter

29 inches

Thrust

20,000lb

Aircraft

Typhoon 28

14

Turbine designs Shrouded HP turbine Unshrouded HP turbine

29

HIGH BYPASS RATIO TURBOFANS


30

15

HIGH BYPASS RATIO TURBOFANS

T800

~GE90


31

TURBINE TECHNOLOGY IMPROVEMENTS HISTORY 1950

NOW

TIP SPEED m/s

250

350 +

STAGE TEMPERATURE DROP, K

150

250 +

EXPANSION RATIO

2

2.5 +

STAGE POLYTROPIC EFFICIENCY %

86

92 +

TURBINE ENTRY TEMPERATURE K

1200K

1800K +

32

16

COMBUSTOR GAS FLOW FEATURES LINER

SWIRLER FUEL SPRAY NOZZLE SECONDARY AIR

PRIMARY ZONE

SECONDARY ZONE

LINER FLAME TUBE (BURNER)

DILUTION HOLES

TERMINOLOGY FUEL / AIR RATIO STOICHIOMETRIC

FAR ALL OXYGEN USED (COMPLETE COMBUSTION) TTQ

OUTLET TEMPERATURE PROFILE PRESSURE LOSS FACTOR

P

1 2 V 2

TURBINE NEEDS GOOD TEMPERATURE TRAVERSE QUALITY 33

Combustor exit profile

Povey 2009

He 2004

T/Tmean

He 2004

34

17

Conventional multi-stage turbine

U1

U1

U2

U1

U2

Typical conventional arrangement

Relative

Vanes turn and accelerate flow for next blade row.

Absolute Controlled work split between the HP and IP systems

35

Contra-rotation multi-stage turbine

U1

U1

U1 U2 U2 Relative Absolute

Reversal of the HP shaft rotation relative to the IP (LP) shaft IP NGV required to get the correct flow angle and velocity into the IP rotor Reduced turning on and reduced secondary flows on the IP NGV Increased IP NGV efficiency Controlled work split between HP and IP.

36

18

Statorless contra-rotation multi-stage turbine Relative HP Relative IP

U1

U1

Absolute

U2

IP NGV is removed. Reduced length, weight, cost Eliminated IP NGV loss Closely coupled HP-IP rotors can result in unsteady interactions -> reduced efficiency and possible vibration.

U1 U2

The inlet conditions to the IP rotor are limited by the exit conditions from the HP rotor. i.e. the absence of the IP NGV means that the flow cannot be pre-conditioned as in a conventional arrangement. The HP rotor exit swirl is limited by the HP rotor turning and the whirl velocity is limited by the rotor exit Mach number. A consequence of this is that the work split is uneven. The HP stage typically has a much higher work level than the IP (LP). 37

Euler’s work equation

38

19

Steady Flow Energy Equation •

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

Q

E tot 1  h1  V 2  z 1g 2 1

E tot 2

h1,, V1

 h2  V 2  z 2 g

•

Similarly at point 2:

•

Q is the heat addition (positive into the system) and W is the work (positive when done by the fluid)

•

h2,, V2

System

2 2

z1

z2

W

Q  W  h2  V 22 2  z 2 g   h1  V 12 2  z 1g 

The energy balance equation then becomes:

This is known as the Steady Flow Energy Equation.



•

For an axial turbomachine it reduces to: W  h1

• •

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

 1  1

V 2 2tC p   1

2

.

Remember that

 V 12 2  h2  V 22 2  H 01  H 02  C pT 0 H 0 C p



 C pT 0  C pt  V 22 2  R   1

and a   Rt , M 

V a

M 2 39

Compressible Form of Bernoulli’s Equation If there is no heat transfer to or from the gas the flow is ADIABATIC. Hence conservation of energy tells us that the Total Energy (usually called the Total Enthalpy ) is conserved i.e. ho = constant.

Considering a perfect gas: p = ρRT h= specific enthalpy= CpT ho=specific total enthalpy = CpT0

Equation of State Calorifically perfect gas

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

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

40

20

Compressible Form of Bernoulli’s Equation (continued) The energy equation for an adiabatic, steady flow is given by:

Internal Energy

p1  1



e1

2



Pressure Energy

V 1 2

 e2 

p 2  2



V 2 2

2

Kinetic Energy

all per unit mass flow ( is specific

Recall that specific enthalpy is defined as h =e+p = e+p/

volume). Therefore:

h1 

V 1

2

 h2 

2

V 2

2

 cons tan t  h0 (total enthalpy)

2

For a calorifically perfect gas h=CpT and similarly h 0 =CpT0 2

C pT 1  C pT 

V 1

 C pT 2 

2

V 2 2

V 2

 C pT 0

2

2

 cons tan t  C pT 0 (T 0 is total temperatur e)



1

V 2 2C pT



T 0

Eqn 1.7

T

41

Compressible Form of Bernoulli’s Equation (continued) Recalling: C p





 R   1

T 0 T

M 

,

 1

V a



V  RT

and

a02

 a2 

  1 2 V 2

  RT 0

  1 2 V 2 M 2 RT   1  1  1 M 2C pT 2 RT 2 2

 a     1 2    0   1  M  T  a  2  

T o

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 and outside viscous layers like the boundary layer) then: p = k =RT and hence 





T    1       1 M2    1   o     o   1  p 2  T      

po

42

21

Euler’s work equation A-A

A-A

Streamtube

Vq r 2 Vx

r 1 Rotor Centreline Rotation W

r

q

x

x Figure 1.1

43

Euler’s work equation •

•

•

• •

One of the most fundamental aspects of turbomachinery aerodynamics is the process of work input (compressors) and the work extraction (turbines) processes. The same model is adopted for both compressors and turbines as outlined below. The work extraction and addition process is performed by rotation. It is the rotating components that transfer work. The fixed components, or stators, are not explicity involved. Figure 1.1 shows the flow field through a generic rotor passage for an axial-type machine but including a change in mean radius. Consider the flow along a streamtube that enters at radius r 1 and exits at radius r 2. 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 D t is give by: A-A

T  mrV 

t

Streamtube

m rV  t  (r V  r V ) T  m 1  1 2  2 T 

r 2 r 1 Rotor Centreline Rotation  44

22

Euler’s work equation •

The rate of change of angular momentum equals the torque:

T 

 m

r 1V  1  r 2V  2   m r 1V  1  r 2V  2 

 t

•

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 Euler’s 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 direction upon rows of rotating aerofoils.

•

Recall:

  r V  r V  P  T   m 1  1 2  2

W k

  r V  r V  Work , W k  P / m 1  1 2  2

 U V  U V 1

 1

2

 2

 C T Power, P  m p 0

Specific w ork, W k

 C pT 0  UV   45

Frame of reference

46

23

Turbine stage aerodynamics

NGV

ROTOR

U

TURBINE STAGE

47

Frame of reference •

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

x is axial

Vr

r is radial

V

Vq

q is circumferential

x

x

r q

Please note:

Rotation W

This nomenclature is for this section only which applies to compressors and turbines alike. Subsequent sections use individual notation for turbines based on axial station numbers. 48

24


The absolute and relative frame of reference velocities are therefore

•

(please note the changes in nomenclature from this section) Absolute

Relative

Vx

Axial velocity

Wx

Vr

Radial velocity

W r

Vq

Circumferential velocity (tangential, whirl or swirl velocity)

Wq

V  V x 2  V r 2  V  2

Total velocity

W  W x 2  W r 2

 W  2

•

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

•

Notice that Vq and Wq are positive in the direction of rotation. U is Blade speed. 49


An important concept is the distinction between absolute and relative frames of reference. For the rotor shown, the inlet stationary frame velocity is V. It has two components and an absolute swirl angle of a1. By subtracting the blade speed term, U, the relative velocity vector is obtained.

•

This is the effective velocity seen by the rotor. A similar analysis at the exit plane transforms from the relative to absolute frame of reference. Conventional turbomachinery notation uses positive velocities and angles in the direction of rotation.

q

x a1

Axial velocity V x = W x

Absolute whirl velocity Vq

Relative whirl velocity W q

Blade speed U Rotors

•

Blade speed = W r, 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 W q= Vq-U

•

For example, from a given inlet absolute velocity, flow angle and blade speed, all other vectors can be determined. 50

25

Frame of reference

a1

b1

a1

Blade speed U

b1

Effect of NGV exit angle (fixed Va)

a1

b1

Relative velocity W

Effect of NGV exit velocity

Effect of blade speed (fixed Va)

51

Static, stagnation and relative properties •

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

•

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

P 0 •

 p  21  V 2

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

P 0 _ REL

 p  12  W 2

•

Static quantities are unchanged by frame of reference.

•

Stagnation properties are dependent on the frame of reference.

•

For compressible flows: T 0

 T 

T 0rel

V 2 2C p

 T 

W 2 2C p



and

 T   1  0 P  T 

P 0

Absolute frame of reference 

and

 T   1   0 rel  P  T 

P 0 rel

Relative frame of reference 52

26

Energy equation and rotating blade rows •

For a rotor the Euler work equation applies:

W k

W k

 U V  U V

W k

 U V  U V  h  h

1

1

 1

 1

2

2

h h 01

02

 2

 2

01

02

•

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

•

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

•

By rearranging this equation:

•

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

h01  U 1V  1

I  h01  U 1V  1

 h  U V 02

2

 2

 h02  U 2V  2 53

Rothalpy and Frame of Reference •

Rothalpy in the absolute frame of reference is defined as :

I  H o •

1

 UV   h  V 2  UV  2

Looking at the change of reference frame:

V 2

 V x 2  V r 2  V  2

 W  W  W   U  V 2  W 2  2UW   U 2 2

V

V 2 •

2 x

2

2 r

V x  W x

, V r

 W r , V   W   U

 W 2  2UV   U 2

Therefore rothalpy in the rotating frame is given by:

1 1 I  h  W 2  U 2 2 2 54

27

Rothalpy and Frame of Reference •

Total enthalpy in absolute frame (absolute total enthalpy ):

h0 •

1 2

 h  V 2

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

1 2 h0 rel  h  W 2 •

Rothalpy can be expressed as:

I  h0

 UV  1 2 U 2

I  h0 rel 

•

Rothalpy along a streamline is conserved across any blade row either moving or stationary. It applies along an arbitrary streamline for an adiabatic flow and in the absence of gravity and it is invariant. For axial machines with no change in radius the U2 term cancels and changes in relative stagnation enthalpy and rothalpy are the same. 55

Rotary stagnation temperature Rothalpy along a streamline is conserved across any blade row

 C pT 0

Total Enthalpy , H0

I  h0

 UV 

I  h0 rel 

Rothalpy, I  C pT 0

1 2

U 2

Where T0 is the rotary stagnation temperature. T 0 

I C p



H 0 C p

T 0 

I C p

 t 

T 0  T 0 rel 

T 0



I C p





W 2 2C p

1 2C p

U 2 2C p



W

2

  2r 2 

Relative

 2 r 2 2C p

H 0 C p



UV  C p

 T 0 

 rV 

Absolute

C p

For axial machines with constant radius the changes in relative stagnation temperature and rotary stagnation temperature are the same. 56

28

Change of Frame of Reference “What a stationary probe sees” T 0 r

Stagnation State p0, To

 T 0 

T 0

p0 p0

C p

 T    0   T 0 



 T 

V 2 2C p

 T   0 p  T 

p0



W

 T    0 r  p0  T 0 

p0 r

T 0

 rV 

 T 0 

2

“What a rotor mounted probe sees”

 V 2 

2C p 

Relative Stagnation p0rel, Torel

 1

T 0 r  T 

“what the gas sees”

 1

W 2 2C p

T     0r  p  T 

p0 r

Static State p, T



 1

T 0

 1

T 0  T p0 p



W

2

  r 2

2

 T 0 r 

 2 r 2

2C p

 T    0  p0 r  T 0 r 

p0





 1

2C p

T     0   T 



 1

I Rothalpy = CpT0w

Rotary Stagnation p0w, Tow

M. Rose - 1998

“Equivalent of stagnation in a rotor” 57

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, viscosity and effects of friction. If the flow is also reversible, then the rotary stagnation pressure (Pow) is also constant.

•

All relationships between the different states are isentropic compressible flow. Nomenclature (for this section only)

Subscripts

I 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

29

Frame of Reference •

Relative total pressure is defined as

•

Absolute and relative Mach numbers:

T 0 T

 1

  1 2 M 2

  1 2  M    1  P  2 

P 0

Absolute

T 0 r T 

 1

P 0 r P

 1

p0 r  T    0 r  p  T 



 1

  1 2 M rel 2

  1 2  M rel    1  2  



 1

Relative

59

Introduction to turbines

60

30

Turbine Aerodynamics Introduction: The design of a turbine system requires the careful integration of a range of technologies including aerodynamics, cooling, materials, sealing, transmissions etc.. It is a complicated task, but still at the heart of the design is the aerodynamics of the turbomachinery which tends to drive the system requirements and push the limitations of the other technologies. The detailed flow field inside a turbine is extremely complicated where there are shock waves, unsteady features, secondary flows, interactions, rotating flows, wakes, tip leakage vortices, cooling air, annulus leakage etc. However, a very simplified analysis based on steady conditions along a (2-D) mean line flow path provides a reasonable insight into the fundamental workings of the turbine. This approach is frequently used by industry as a preliminary design method.

Shrouded HP Turbine blade

IMAGE COURTESY OF ROLLS-ROYCE

61

HP Turbine Trivia • The High Pressure (HP) turbine of a modern aero engine can produce in the order of 49,000 HP (36.5MW) at take-off. • One turbine rotor blade produces in the order of 700 HP which is the power output of about 9 Ford Fiestas. • The peak gas temperature in the HP turbine is in the order of 400 degrees hotter than the melting point of the blade material. • The tip speed of the HP rotor is over 1000 mph. LPT IPT HPT

Combustor

62


31

Shrouded High Pressure Turbine

Harsh environment & a demanding job:

Metal Temp D T strong effect on blade life

Peak gas temperature 2000K

Blade experiences > 65000g

Melting temperature ~1400K

Life required for a civil aero engine 6 years @14hrs/day

Cooling air ~15% flow @ 900K

63


High Pressure Turbine

HPT blade cooling arrangements HPT stage cooling IMAGE COURTESY OF ROLLS-ROYCE

64

32

65

Turbine Aerodynamic Features Snap shot of a predicted HP turbine flow field Static Pressure

Entropy

66

66

33

Turbine blade aerodynamic features

67 67

Turbine Aerodynamic Features Transonic HPT aerodynamics

M2 _is = 1.2

Schlieren

Mach Number Richardson (2009)

68 68

34

Turbine aerodynamics

DLR Turbine cascade flow: Increasing Mach number visualization of density gradients: pressure waves, von Karman vortices, wakes and shocks 69

Turbine aerodynamics

MEX0.85

MEX  1.2

MEX  0.98

MEX  1.5

70

35

Turbine Aerodynamic Aspects •

Primary gas path turbine flow regimes

HP Rotor Turbulent Flow from LE Primarily Due to Film Cooling, Strong Wake and Potential Interaction

IP NGV Complex 3D Flow with Transition

IP Rotor Unsteady, Strong Wake and Potential Interaction with Transition

LP Vane/Blades Unsteady Transitional Separation Bubbles, Becalmed Regions, etc

HP NGV Turbulent Flow from LE Primarily Due to Film Cooling

M. Taylor 2003

HP Turbine HGV, Re = 1.5E6 Rotor, Re = 6.0E5

IP Turbine HGV, Re = 1.2E6 Rotor, Re = 2.6E5

LP Turbine Stage 1 NGV, Re = 4.0E5 Rotor, Re =2.0E5

LP Turbine Stage 5 NGV, Re = 1.0E5 Rotor, Re = 1.4E5

71

Turbine overtip leakage (section 4.7.7)

72

36

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 design of turbine and control of casing and rotor thermal transients Exchange Rate: Predominantly influenced by choice of blade tip style e.g. Shrouded, shroudless 73 Arts – 2004-2

Tip clearance and leakage Flow over a “Shroudless blade”

74 Arts – VKI LS2004-2

37

Tip clearance and leakage

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


Tip clearance and leakage 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.

76

38

Tip clearance and leakage 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 leakage Effect of tip clearance on the efficiency of single stage shroudless turbines

For a shroudless stage : Tip size equal to 1% of blade span cause 2% drop in stage efficiency. ( Hourmouziadis and Albrecht 1987) 78 Arts – VKI LS2004-2

39


Tip clearance exchange rate for different turbine reactions as a function of gapto-blade height ratio. 79 Booth – VKI_LS1985-5


Shrouded blade + Measurable gain in stage efficiency + Improved fatigue strength - Difficulty to cool the shrouded area - Larger cooling flow budget - Higher blade and disk centrifugal forces/stresses -cost increase particularly for internally cooled blades

Blade tip styles: Shrouded and Shroud


40


Fences

Fins

Shrouded Blade geometry



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

Comparison of OTL loss exchange rates for shrouded and unshrouded HP Turbines


41

Tip clearance and leakage Over tip leakage heat transfer effects High heat transfer rates on the blade tip, Cause Tip Burnout

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

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

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

83

Tip clearance Heat Transfer Effects - blade Blade damage in the tip region

Distress to HP Rotor Tip after in service operation

Sunden and Xie, 2010 84

42

Introduction to turbine design

85

4.1 INTRODUCTION INTRODUC TION TO TURBINE DESIGN The design of axial flow turbines is a complex compromise between the conflicting requirements:

o o o o

aerodynamics thermodynamics mechanical int nte egrity materials te tec chnol olo ogy

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

o o o

low weight high strength extended life. CHAPTER 4 PART 1 PAGE 4.01 86

43

4.2

THE COMPRO COMPROMISES MISES BETWEEN BETWEEN AERODYN AERODYNAMIC AMIC,, COOLING COOLING AND MECHANICAL REQUIREMENTS PRELIMINARY DESIGN

Any preliminary design procedure must include an estimation e stimation of at least the fo llowing: o o o o o o o o

Number of stages Annul Annulus us shap shape e and and dime dimens nsio ions ns (hub, (hub, mean mean or tip diame diamete ter) r) Blade lade and and vane ane aspe aspec ct rati ratio o Blad Blade e and and N.G N.G.V spac space/ e/ch chor ord d rati ratios os Prof Profile iles s of nozz nozzle le guide guide vane vanes s and and rotor rotor blade blades s Axia Axiall spac spacin ing g betw betwee een n blad blade e row rows Work Work ‘spl ‘split it’’ for for mult multii-st stag age e turb turbin ines es Radia adiall dist distri ribu buti tion on of work ork

CHAPTER 4 PART 1 PAGE 4.01 87

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

Blad Blade e cent centri rifu fuga gall stre stress ss lev levels els

o

Disc Disc cent centri rifu fuga gall stre stress ss lev levels els

o

Maxim aximum um inst instal alla lati tion on diam diamet eter er

o

N.G N.G.V and and blad blade e cool coolin ing g requ requir irem emen ents ts

o

Overal eralll weigh eightt limi limita tati tion ons s

CHAPTER 4 PART PART 1 PAGE 4.02 88

44

MECHANICAL INTEGRITY LIMITATIONS TO TURBINE POWER Blade shape Simple for for manufacture manufacture - complex complex for good aerodyna aerodynamics mics Stress

Blade centrifugal centrifugal stress proportional proportional to A x N2 For a given shaft speed this sets the upper annulus area limit Depends on material and component: range 20-50x106 rpm2m2 Disk stress 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 a given given 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 ratio not greate greaterr than 0.9 for low overti overtip p leakage leakage loss loss

4.3

TURBIN TURBINE E DESIG DESIGN N SPECIF SPECIFICA ICATIO TION N

4.3.1 4.3.1

TURBIN TURBINE E DESIG DESIGN N CRITE CRITERIA RIA

89

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

W P3 T3

Mass flow Turbine Turbine inlet pressure Turbine Turbine entry temperature Power Requirement Pressure ratio split

CHAPTER 4 PART 1 PAGE 4.03

90

45

Turbine Design Aspects •

Successfully turbine design requires close co-operation between the aerodynamic, cooling, mechanical, stress and design disciplines. Final designs usually demand a certain amount of compromise between aerodynamics and mechanical constraints:

P arameter

Aerodynamic objectives

M echanical objectives

No. of stages

Large: to reduce loading and Mach numbers

Small: Reduce weight, length &cost

Mean diameter

Large: to give high blade speed, low loading, high efficiency

Small: reduce weight and Minimise blade and disc stresses

Annulus area

Large: enough for optimum Va/U

Small: blade stresses are proportional to Area x rpm2

Rotor NGV ratios

High: reduce wetted area, secondary losses and heat load

Low: to mimimize deflections vibration. Must enable cooling.

Optimized for best performance.

Sufficient cross sectional area for cooling passages. Large enough LE, TE and wedge angles for manufacturing, stress and cooling requirements

and aspect

cost

and

1
Rotor and NGV Profiles

91

4.4

THE PROCESS OF EXPANSION

A IN

VIN A out < A in V o ut > V in p OUT < p IN VOUT

VOUT DESIGN CRITERIA o o o o o

A OUT

1.15

IN

FLOW TOACCELERATE AS FARAS POSSIBLE TURNING LIMITED TO 130 0 CAN DRIVE 5 STAGES OF COMPRESSOR WITH ONE TURBINE STAGE HIGHEST TEMPERATUREAT LEADING AND TRAILING EDGES MASS FLOW LIMITED BY CHOKING


92

46

THE PROCESS OF EXPANSION

Static pressure

Total pressure

Mach number

93

Turbine annulus design

94

47

4.5

TURBINE ANNULUS DIAGRAMS

4.5.1

CHOICE OF ANNULUS DIAGRAM

CHAPTER 4 PART 1 PAGES 4.04 – 4.06 95

General arrangement of HP and IP turbines A RISING LINE ANNULUS DIAGRAM

Figure 4.03 Typical HP/LP Annulus Geometry

DISC

DISC


96

48

HP-IP-LP turbine arrangement Aeroengine

97

Aggressive turbine ducts Marn – Graz (2008)

100

49

4.5.2

CHOICE OF AXIAL VELOCITY DISTRIBUTION

o

constant Va

o

falling Va

o

rising Va

Figure 4.04

CHAPTER 4 PART 1 PAGE 4.06 – 4.07

101

CHOICE OF Vax DISTRIBUTION

DESIGN FOR RISING Va

-

HP TURBINES

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

higher blade friction losses lower efficiency

o o o o

lower blade height lower stress for a given RPM lower rim load (AN2) for given RPM less cooling air requirement for cooled stages.

but:

CHAPTER PART 1 PAGE 4.07 102

50


DESIGN FOR RISING Va - LP TURBINES Compared with constant Va, the outcomes of this choice are: o o o

higher blade friction losses, lower efficiency higher exhaust losses through higher Va longer exhaust diffuser

o o o o

lower exit blade height and mass lower rim load (AN2) for given RPM lower blade stress for a given RPM less cooling air requirement (if cooled)

But:


CHOICE OF Vax DISTRIBUTION DESIGN FOR FALLING Va

-

HP TURBINES

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

lower blade friction losses higher efficiency

o o o o

higher blade height and higher mass higher stress for a given RPM higher rim load (AN2) for given RPM more cooling air requirement for cooled stages.

But:


51

CHOICE CHOICE OF Vax DISTRIBUTION

DESIGN FOR FALLING Va Va - LP LP TURBINES Compared with constant Va, the outcomes of this choice are: o o o

lower lower blade blade fric fricti tion on losse losses, s, highe higherr effi effici cienc ency y lower lower exhau exhaust st loss losses es thro throug ugh h lowe lowerr Va out out shor shorte terr exha exhaus ustt diff diffus user er

o o o

higher higher exit exit blade blade heigh heightt and incre increas ased ed mass mass higher rim load (AN2) for given RPM high higher er blad blade e stre stress ss for for a give given n RPM RPM

But:

CHAPTER 4 PART 1 PAGE PAGE 4.07 105


PRELIMINARY PRELIMINARY DESIGN CHOICE At the preliminary design stage: o

deta detail ils s of blad blades es and and vane vanes s are are unkn unknow own n

o

ther therefo efore re assu assume me cons consta tant nt axia axiall velo veloci city ty throughout the turbine.


52

Turbine stage aerodynamics •Velocity triangles •Stage loading •Flow Coefficient •Reaction

107

Turbine Stage Aerodynamics •

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

•

The flow is expanding expanding and the pressure pressure is reducing reducing across across the stage. stage. The The axial Mach number is kept reasonably constant through the turbomachinery at around 0.4 – 0.5. Consequently the annulus area increases through the turbine to accommodate the change in density as the flow expands.

•

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

•

The expansion expansion from from the combus combustion tion region region to the atmospher atmosphere e is accomplis accomplished hed through a number of separate turbine stages. This enables the Mach numbers to be controlled as well as facilitating the incorporation of multiple shafts for the benefit of the compressor system.

•

Each blade blade row, row, either stationary stationary or rotating, rotating, turns turns the flow and usually usually accelerates accelerates it in its own frame of reference. reference. The continuing changing changing of frame of reference reference is what enables the Mach numbers to be controlled. 108

53

THE CONSTANT MEAN DIAMETER TURBINE STAGE ABSOLUTE GAS CONDITIONS - STATION REFERENCES IN

0

3

BLADE NGV

MEAN STREAMLINE

A A

r

AXIS


V in Va

Vw

THE CONSTANT CONSTANT MEAN DIAMETER VELOCITY TRIANGLES THERMODYNAMICS

in

E STAGE = CP (T O – T 3 ) =

H

NG V

Power = rate of work Circ. force on the rotor per unit mass = rate of change of momentum = ΔVw 

Work = Force x distance = ΔVw x distance Power per unit mass = ΔVw x distance / time = ΔVw x U

V0 Va

V1

Specific power

U

= U (Vw0 - Vw 3)

Vw0

ROTOR





V rel  V abs

U



 U blade

FINALLY

H V2

U

 V3

U

2

=

H= U Vw

Vw U

Va V w3

CHAPTER 4 PART 1 PAGE PAGE 4.09 to 4.12110

54

COMBINED VELOCITY TRIANGLES CONSTANT

Va

CONSTANT

U

V

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

IN

H

LOADING

U2

=

Vw U

NGV ΔVw

V U

V0

a1

V

V2

ao

Vw

a3

V 3

U

1

a2

Vw 3

0

Va

a The param eter is referred to as the flow coefficient . It is a measure of turbine massflow at a given rotor speed.

Va U

FLOW COEFFICIENT =

ROTOR


111

COMBINED VELOCITY TRIANGLES NGV

ROTOR

CONSTANT Va and U

V w  V a tan  0  tan  3  V w  V a tan  1  tan  2   H V w V a   tan  0  tan  3  2 U  H tan  0



tan  1 

V w0 V a V w1 V a

U  V w0 - V w1

U 2



U V w U



U V a U

tan  1  tan  2 

U  V a tan  0  V a tan  1  U V a U V a

 tan  0  tan  1   tan  3  tan  2  CHAPTER 4 PART 1 PAGE 4.13

112

55

COMBINED VELOCITY TRIANGLES For the case where there is no change in radius across the rotor the velocity triangles can be placed on a common base of blade speed, U: •

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

•

The stage loading is the ratio of the apex, D Vw, to the base, U.

•

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

•

These types of velocity triangles are routinely used in the design process to graphically represent the turbine aerodynamics.

113

Some Turbine Design Parameters Introduce these parameters

 H

Stage Loading

U 2

V A U

Flow Coefficient

C P  T T

N T

&

U T

t2 - t3 To1 - T03

Specific Work

H U2



CP T T

 U     T 

2

Engine & Turbine Semi-dimensional Speeds Stage Reaction (more on this later!)

114

56

Turbine Stage Loading •

• •

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, ROTOR however you are not getting the best out of the turbine.

NGV

ROTOR

Δ Vw

NGV

Va = constant Low Stage Loading

High Stage Loading

115

Turbine Flow Coefficient NGV

Rotor NGV

Rotor

Same mean radius and blade speed

Δ Vw = constant NGV ROTOR

Low Va /U

High Va /U

116

57

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 will result in reduced aerofoil cord and/or numbers off (reduced trailing edge loss) to achieve the required work (sail area) and reduced cost.

•

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

•

As the hub diameter will be reduced, there is the potential for reduced leakage loss due to the reduced area of the seals. At the casing the overall result depends on two opposing effects, as the area of the seals is increased there is the potential for increased leakage, however, assuming the tip gap is fixed, the tip gap to height ratio of the rotor will be reduced, providing the potential for reduced tip leakage flow per unit area.

•

Due to the civil aircraft markets desire to minimise the aircraft's fuel consumption and maximise profits, a civil engine design is primary driven on the requirement to minimise 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 in weight and size has to be balanced in order to achieve the optimum design for a particular airframe and mission requirement.

•

Typical values : Va/U = 0.4 - 0.6 117

4.6.9

TURBINE STAGE REACTION

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

Reaction,  

hrotor t  rotor H stage T stage

A simplified definition of reaction for explanatory purposes is:

For a repeating stage where V1= V3 then

 

 

 protor  pstage

H 2  H 3 H 1  H 3


58

Turbine Reaction •

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

NGV

ROTOR

V0 V2 V1

Large surface diffusions. Possibility of separated flows.

V3 Mn

Inlet

Exit

Relative Absolute

V1= V2

Cax

•

Large suction and pressure surface diffusions,

•

Flow separation leading to increased loss, enhanced heat transfer at reattachment 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,

4.6.9

119

CHOICE OF STAGE REACTION ZERO REACTION (IMPULSE ROTOR)

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

In practice:

ROTOR

V0

NGV

V2 V1

o

ensure V2 / V 1 > 1.15

o

good for power turbines (most of the available stage inlet energy can be converted into shaft power) high total to static efficiency

o

V3


120

59

4.6.9

CHOICE OF STAGE REACTION 100% REACTION

No overall static pressure change across nozzle. o o o o o o

NGV velocities are equal No acceleration across the stator (ensure V0 = V3 ) high stage leaving gas angles High bearing loads NGV Increased over tip leakage high rotor Mach Numbers V0 V2 V1

ROTOR

V3 In practice: o o

ensure V0 / V 3 > 1.15 only the tip conditions of free vortex turbines are of high reaction CHAPTER 4 PART 1 PAGE 4.20

121

4.6.9

CHOICE OF STAGE REACTION 50% REACTION

o o

o

.

The power is achieved partly through momentum change, partly through pressure change 2D loss (Mach number )2, therefore from the velocity triangles you might expect that minimum loss will occur when the triangles are symmetrical (V0=V2) Delivers a good balance between peak Mach numbers, diffusion coefficients, over-tip leakage reduction and bearing loads.

In practice: o

o

popular for gas generator turbines since high kinetic energy flow remains for subsequent stage(s)

V0 V2 V1 V3

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


122

60

4.6.9

CHOICE OF STAGE REACTION

Impulse blading shape

Reaction blading shape .

Mn

Exit Mn Increased

Inlet Mn Reduced

Cax


123

Turbine reaction summary •

For a given stage loading and flow coefficient, the shape of the velocity triangles reflects the turbine reaction. 0% Reaction (Impulse)

100% Reaction

NGV

DVw

ROTOR

DVw

V0 V2 V1

V3

V0

V2

V1 V3

U DVw

•

In all cases, UDV, and Va/U are the same.

50% Reaction

U

124

61

REACTION

Vw

Reaction, .  

V0

ao V1

a1

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

a2

V2

H0stage  H0in  H0out 

V3

a3

 Hin 

U



tan  0 tan  1



V w0

 

U  V a tan  0  V a tan  1 

V a V w1

U V a

V a

U

U  V w0 - V w1

V a

hrotor t  rotor H 0stage T 0stage

  

 tan  0  tan  1 

V in 2

2

2

 Hout 

V out 2

 Hin  Hout

hrotorin  H rotorout H stagein  H stageout

V a

Tan 2  Tan 1 

2U

 tan  3  tan  2 

125

REACTION

Vw / 2

Vw / 2

.

  

V0

ao

a2

V2 V1

a1

tan  2

V3

a3

Vw

a

2 V a 2



V w 2

tan  1 

V a

V w1 V a

Vw2

Vw1

a

2U

Tan 2  Tan 1 

Vw  V a Tan  1 - Tan  2 

U

a

V a

 V a Tan  1 

V a 2

Tan  1  Tan  2   V a Tan  1

Tan  2  Tan  1    

V a 2U

Tan 2  Tan 1  

a U

  

1 2U

V

w2

 V w1  126

62

50% REACTION

Vw

  

V0

ao

a2

V2 V1

a1

V a 2U

.Tan 2

if   0.5  

V a 2U U

V3

V a

a3

U V a

U

U V a

  Tan 2  Tan 1   Tan 0  Tan 1 



V a

  Tan 2  Tan 1   Tan 3  Tan 2 

Tan 2  Tan 1   tan  0  tan  1   tan  3  tan  2 

Symmetric stage vel. triangles

  2   0 U

 Tan 1 

V w3



V w 2



U 2

  1   3 127

The effects of increasing turbine reaction: Small changes in reaction is typically achieved by opening up the NGV throat area and closing down rotor throat area. This then results in the following changes: – Reduced area contraction and velocity ratio over NGV. – Reduced NGV exit Mach number….but increased lift coefficient (NGV). – Reduced rotor inlet Mach number leading to negative incidence onto the rotor. – Increased RELATIVE total temperature at inlet to rotor – Increased Dp across rotor. So tip leakage increases. – Increased rotor exit gas tangential whirl. – Increased rotor exit Mach number…but decreased lift coefficient (Rotor). – Increased back surface deflection on rotor.

NGV leading edge skew – incre ased throat are a

128

63

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

AERODYNAMIC LIMITATIONS:Gas turning Mach number (losses) Loading (ΔH/U2) MECHANICAL INTEGRITY LIMITATIONS:Radial stress Blade speed Material properties IN GENERAL

POWER = W . U .  V W CHAPTER 4 PART 1 PAGE 4.15

130

64

4.6.7

INCREASE STAGE POWER BY INCREASING FLOW POWER = W . U .  V W

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

For specified T IN, PIN and A* HIGHEST FLOW WHEN NOZZLE GUIDE VANES ARE CHOKED

W IN TIN A * PIN

= CONSTANT

when M throat = 1


POWER = W . U .  V W

INCREASE STAGE POWER BY INCREASING NGV THROAT AREA W IN TIN A * PIN

but

= CONSTANT

O

REDUCE NUMBER OF N G V’s

O

COOLING AIR REQUIRED IS REDUCED

O

N G V’s move apart and reduces overlap and effectiveness GOOD VALUE OF S/C≈0.7 (see later)

O

NGV aerodynamic loading increases and the aerodynamics get more challenging. 132

65

TURBINE DESIGN FOR HIGHEST POWER ENGINE UP-RATING TO HIGHER POWER SINCE:

o

WIN TIN = CONSTANT A * PIN

Increase pressure ratio – add zero compressor stage T

Best to increase TET

INCREASED TET

and pressure ratio together

o

FIXED TET

Increase nozzle throat area to accommodate for choked flow S 133

4.6.7

INCREASE STAGE POWER BY INCREASING V w POWER = W . U .  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


66

4.6.7

INCREASE DESIGN POWER BY INCREASING

V0

0

V2

V1

V3 U

INCREASED

0

For cooled stages: • trailing edge of the high 0 NGV needs to be thinner for the same boundary 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 CHAPTER 4 PART 1 PAGE 4.16

135

4.6.7

INCREASE DESIGN POWER BY INCREASING

V0

3

V2 V3

V1 U

INCREASED

For cooled stages:

3

o

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

o

reheat gutters (if fitted) difficult to align with the flow if 3 > 15. CHAPTER 4 PART 1 PAGE 4.17

136

67

POWER = W . U .  V W V0

4.6.7 INCREASE DESIGN POWER BY INCREASING U

V2

V3

V1 U

INCREASED U

o

If RPM is fixed by the device the turbine is driving therefore increase U only by increasing the turbine diameter

o

Otherwise stresses increase (   AN2 )

but

o

annulus height reduced for a given massflow will require result less cooling air since blades are radially shorter.

and

o

increased blade speed, means 0 and 3 fall relieving both cooling problems (high 0) and downstream loss (high 3) CHAPTER 4 PART 1 PAGE 4.17

137

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

Requirements from cycle inlet and outlet p and t mass flow in power required e.g. to drive compressor rotational speed, n, e.g. from compressor



choose mean diameter calculate mean blade speed; check < 350m/s calculate loading δh/u2 calculate number of stages; δh/u2 <2.5 per stage δh/u2 <1.8 for last lp stage



select best outlet va /u from smith chart calculate exit va and area Check AN2 limits



select outlet hub/tip ratio (>0.5)

……continued

138

68

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

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



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



select reaction calculate velocity triangles at mean radius



select radial equilibrium type calculate tip and root velocity triangles check limits – reaction, turning



choose aspect ratios



calculate blade and vane numbers



proceed to blade shape design if required 139

Turbine efficiency

140

69

4.7

4.7.1

AXIAL TURBINE EFFICIENCY

ISENTROPIC EFFICIENCY DEFINITION

t

(Tin

Tout )

(Tin

T ' out )

Tin =TET

T

Tout

Pin

ACTUAL TURBINE WORK OUTPUT

t

IDEAL TURBINE WORK OUTPUT

T’out

T'out

Pout

Tin

( T) T 'out Tin (1 ) Tin

 P    out   Pin 

 1 

ENTROPY S


141

Turbine loss mechanisms Secondary flows Unsteady interactions

Overtip leakage

Endwall scrubbing

Shock losses

NGV

Rotor

Profile losses

Trailing edge losses Cooling air mixing

Disk windage

142

70

4.7.2

TURBINE LOSS MECHANISMS

MECHANISM Profile loss:

CAUSE boundary layer growth over blade surfaces

Annulus loss:

turning of the boundary layer on the end walls, with associated flow separation

Secondary loss:

interaction of end wall and profile boundary layers

Tip clearance

tip leakage of flow from pressure to suction surface

Shock loss:

supersonic flow over back surfaces

Cooling loss:

mixing of discharged cooling air with main flow.

Trailing edge loss:

wake growth due to increased trailing edge thickness CHAPTER 4 PART 1 PAGE 4.24 143

Turbine losses 3 Approximate efficiency loss breakdown

st 2

1

0 Secondary

Trail in g Edge

Profile

Over Tip Leakage

Win dage

Wetted Area

Annulus & Stacking

144

71

Turbine efficiency •

A common approach for preliminary design purposes is to use an efficiency correlation chart to examine the effects of flow coefficient (Va/U) and stage loading ( DH/U2) on he expected turbine efficiency.

•

The data was assembled from over 70 cold-flow rig tests where the reaction varied from 20-60% with blade aspect ratios of about 3-4. The effect of tip leakage has been removed and the efficiencies are therefore higher than achievable in practice.

•

Overall, the chart shows a clear ridge of peak efficiency as well as the benefits of keeping the flow coefficient and loading as low as possible.

•

Mach numbers were predominately sub and transonic. Therefore the data will only include modest effects of shock losses.

ΔH/U2

Va/U

145

From Japikse – Introduction to turbomachinery.

Ideal turbine stage characteristic We have seen that the specific work of a turbine stage is given by:  H = U Vw And therefore the loading and turning are related as

H V W  2 U

U

V w  V w 0  V w 3  V w 0  V w 2  U   V w 0  V w 2   U V w  V a Tan 0  Tan 2   U

NGV ΔVw

H V w V a   Tan 0  Tan 2   1 2 U

U

U

V0

a1

V

V2

ao

1

U Vw

Since O and 2 remain substantially constant away from design. This is affected by deviation from the exit metal angle which is generally small.

0

a2

a3

Va

V 3 Vw 3

ROTOR

146

72

Ideal turbine stage characteristic H V w V a   Tan 0  Tan 2   1 2 U

U

U

the characteristic for a stage is a straight line with slope (tan O - tan 2)

e.g. O = -2 = 60 Vw = 2U

H U2





0

2

A 2.0 U

1.0

B

Vw = U

 Va



0

2

U

U 147

Turbine characteristics Japikse

•

This figure shows how the rotor inlet (a1) and exit (a2) relative flow angles can be superimposed on the efficiency map.

•

This example is for a 50% reaction turbine.

•

Highest loading occurs when the inlet relative whirl angle (a1) is about +40 combined with a relative exit whirl angle (a2) of between -60  and -70. This gives a rotor turning of up to 110.

•

For a 50% reaction turbine the ridge of maximum efficiency is along the line where rotor exit relative angle is about 62.

ΔH/U2

a1 a2 Va/U

148

73

STAGE DESIGN FOR BEST EFFICIENCY A

FIGURE 4.11 B

C

HP TURBINES

SMITH’S EFFICIENCY CHART LP TURBINES

LINE OF BEST EFFICIENCY

 H   2  = 6.5  U 

 Va    - 2.9  U 

CHAPTER 4 PART 1 PAGE 4.27 – 4.28

149

STAGE DESIGN FOR BEST EFFICIENCY BEST EFFICIENCY – HIGH PRESSURE TURBINES Line B shown on Figure 4.11 can represent a design target for HP turbines and can be described in terms of the following: ΔH/U2 = 8.3 Va/U – 2.78 or

η IS = 0.98

– 0.048 . ΔH/U2

(corrected by 2% for over-tip leakage) BEST EFFICIENCY – LOW PRESSURE TURBINES Line C shown on Figure 4.11 can represent a design target for LP turbines and can be described in terms of the following: ΔH/U2 = 2.84 Va/U – 0.96 or

η IS = 0.98 – 0.058* ΔH/U2 (corrected by 2% for over-tip leakage) CHAPTER 4 PART 1 PAGE 4.27 – 4.28

150

74

Turbine Characteristics •

•

The turbine characteristics are usually plotted in terms of semidimensional parameters. Pressure ratio: P 02/P01 which is usually expressed as a specific work:

Design point

 stage

N T

C p T T 01

m T 01

N

AP 01

T

•

Corrected flow (capacity):

•

Corrected speed:

•

Once the NGV is choked, the turbine capacity does not increase further with increasing specific work.

•

 60%

N T

 100%

 80%

N T 1

Beyond the design point and with increasing work, the turbine efficiency drops sharply as it begins to encounter limiting output.

m T 01 AP 01

N T N T N T

 100%

 80%

Choking point

 60%

Turbine ch’ics - choked NGV

C p T T 01

151

Introduction to turbine loss models

152

75

Loss Mechanisms in Axial Turbines The geometric description of the flow regions includes many parameters having different length scales. Associated with the blade profile are

Associated with the flow path are

• Radial distribution of stagger angle, • Stagger angle • Camber and thickness, • Blade camber • Lean, twist, sweep, skew & flare • Chord • Aspect ratio • Blade spacing • Hub/tip ratio • Maximum thickness • Tip clearance • Thickness distribution • Endwall curvature • Leading and trailing edge radius • Surface roughness and cooling hole • Flow path area change • Axial spacing between blade rows distribution • Radial distribution of cooling holes. The flow contains various complex features which depend on the details of the design • Three-dimensionality and vortical flows • Shock waves • Large pressure gradients in all directions • Shock wave-boundary layer interaction • Interacting boundary layers and wakes • Rotation and heat transfer • Curvature 153

Axial Turbine cascade loss

Turbine cascade loss data– total pressure loss Reaction and impulse blading Reaction blades have an overall flow acceleration Reaction blade – better performance over wider incidence Relatively constant exit angle

154

76

Turbine loss correlation There are many correlations published to provide estimates of turbine blade row loss. The aim is to provide a method of estimating the turbine row and stage efficiency during the design stage. Despite the advances in computational methods, these types of techniques are still heavily relied upon to provide efficiency estimates. These preliminary estimates can have a notable effect of the overall design strategy. These models can include aspects of total pressure loss such as: Profile loss Trailing edges Tip leakage Secondary flows Annulus loss Disk windage

Some take into account: Reynolds number effects Mach number range Design point Off-design – effect of incidence

The example is a simple model is Soderberg’s (1949!): Easy to use within ~3% for turbine efficiency Design point 155

Soderberg (1949) Loss Model Correlation aims takes into account profile loss and secondary flow loss. The effect of tip leakage can be added for rotors separately. The correlation parameters are: Blade aspect ratio (H/Cx) Thickness to chord ratio (tmax/l) Space chord ratio (s/Cx) Reynolds number (Re) The loss parameter is based on the incompressible energy loss coefficient: V 2  V 2   2is 2 2 V 2is If Zweifel’s criteria for s/cx is adopted (discussed later) , then Soderberg proposed a Nominal loss coefficient :  *

   0.04  0.06    100 

2

where 

  1   2

This applies for an aspect ratio H/Cx of 3, tmax/l =0.2 and Re = 105 156

77

Soderberg’s Loss Model     *  0.04  0.06   100 

= Thickness-to-chord-ratio



Dixon, S. L. 2005

2

for t max /l  0.2

  1   2

(Fluid Deflection Angle)

Aspect ratio H/Cx of 3, and Re = 105 157

Soderberg’s Loss Model For aspect ratios other than 3 (but still at a Reynolds number of 105), the correlation is extended based on the nomina l loss coefficient, ς*:

 1   * 0.993  0.021 c x / H  nozzles 1   1  1   * 0.975  0.075 c x / H  rotors 1   1

158

78

Soderberg’s Loss Model For different Reynolds number a further modification can then be made.

Re 

Where  2 and V 2 are density and

 2V 2Dh

Dh

velocity at the row exit, and Dh is



the hydraulic diameter at the throat



2HsCos 2  4 A flow  Perimeter H  sCos 2 

s

H

PS

SS

o Trailing edge

 105    2   1  Re  

s

o  sCos 2 α2

0.25

159

Turbine blading • • •

Aspect ratio Pitch spacing Blade shape

160

79

ASPECT RATIO

ASPECT RATIO, (AR) = h / c

SPAN OR HEIGHT, h

Aspect ratio determined by: EFFICIENCY VIBRATIONS ROBUSTNESS COOLING No. OF BLADES COST MANUFACTURING For preliminary design purposes, select initial AR from blades of similar span (see correlations)

CHORD AT MID SPAN, c

161

Turbine blade aspect ratio

The stator and rotor aspect ratios can be considered individually if necessary.

Dt

Rotor:

ARr = Hr /Cxr

Stator:

ARs = Hs/Cxs

Based on a range of turbine designs and engines some guidelines can be established for both ARr and ARs.

Sagerser et al, NASA

Dh

162

80

Turbine blade aspect ratio - rotors

Sagerseret al, NASA

≈

+

௛ ௧

LPT: HPT, IPT:

A 13.4 10.5

B -11.8 -10.0

163

Turbine blade aspect ratio - stators

Sagerseret al, NASA

≈

+

௛ ௧

LPT: HPT, IPT:

A 11.0 6.5

B -10.9 -6.0

164

81

Turbine blade aspect ratio - stators LPT5 AR_S≈7.6 AR_R≈4.6

LPT1 AR_S≈2.4 AR_R≈6.4 HPT AR_S≈1.4 AR_R≈2.3

IPT AR_S≈0.7 AR_R≈4.5

Sagerseret al, NASA

165

Turbine blade aspect ratio - rotors LP HP LP1

IP LP5

HP Sagerseret al, NASA

166

82

Turbine blade aspect ratio - stators LP5

LP HP

LP1 HP

IP

Sagerseret al, NASA

167

Axial chord and spacing

Once the aspect ratio is selected then the blade axial chord is set for a given annulus height: AR= H/C x Dt

This enables the inter-row spacing to be set. Based on the average inter-row gap and the average axial chord the following relationship is considered: ்

Sagerser et al, NASA

Dh

≈

௧

௫

Where at is found to range from 0.2 to 1.0. A typical value within a stage is ~0.25.

Sagerseret al, NASA

168

83

Space/chord ratio and number of blades

“SPACE”, s, = DISTANCE BETWEEN BLADES

CHORD, c CAN BE AXIAL OR ACTUAL

Space/chord ratio= s/c Once the blade height, aspect ratio and chord have been determined, the blade pitch spacing, and hence the number of blades, can be estimated. There are correlations which propose the optimum spacing based on the aerodynamic and loss characteristics

OPTIMUM s/c FROM ZWEIFFEL COEFFICIENT OR OTHER METHODS 169

SPACE/CHORD RATIO – ZWEIFFEL COEFFICIENT METHOD CAX Lift = mass flow x change in whirl velocity

P1

p2

= W. ΔVW = ρ . V A . S . ΔVW Ideal lift = (P1 – p2) . C AX Define CL = lift / ideal lift

V1

= [ρ . V A . ΔVW . (S/C AX)] / (P1 – p2)

V2

170

84

SPACE/CHORD RATIO – ZWEIFFEL COEFFICIENT METHOD P 0

Po loss =ΔPo / (0.5.ρ. V2) Minimum at CL ~ 0.8

Separation losses

Loss Skin-friction losses Minimum loss

cx s

CL CL = LIFT / IDEAL LIFT = [ρ . V A. ΔVW . (S/C AX)] / (P1 – p2) 171

Turbine optimum space/chord ratio (alternative to Zweiffel method)

172

85

Blade numbers

௦

Dh

Dt ௥

௥

௦

N=

௛

+

௧

/ The blade number selection also depends on the vibration characteristics. Typically the .rotor and stator numbers are selected to avoid common multiple of blades as this can give rise to resonance and HCF.

AR selection => h/c h is known therefore c is obtained Space/chord ratio criteria => s/c c is known therefore s is obtained.

173

2D turbine blade shape Basic simple circular arc form Curvature change on the suction surface near the throat.

Leading edge circle or elipse

if turning (or deflection) is very high, a separation bubble is initiated just upstream of the throat.

R2 CURVATURE CHANGE POINT

R1 R3

THROAT

TRAILING EDGE – CIRCLE IF UNCOOLED

This usually re-attaches just downstream of the throat. The flow separation will cause a small penalty in the aerodynamic efficiency and usually limits application to turning not greater than 90. Separated flow causes very high local heat transfer coefficients

174

86

2D turbine blade shape Multiple circular arc form

A more complex geometrical profile used multiple circular arcs This improves the aerodynamics by introducing an additional radius of curvature into both the pressure and suction surfaces. This delays flow separation to allow application to cooled blades with turning angles not exceeding around 110o.

175

Turbine Design Lift Distribution

Mach number

Avoid LE spikes

Offload the nose Design for incidence variation Accommodate skew

Avoid excessive local Mn peak Minimise local SS diffusion to avoid separation

Smooth distributions

Maximize area Minimise local PS diffusion to avoid separation

Cax

176

87

Prescribed velocity distributions (PVD) Simple profile shapes are too crude for advanced turbine designs where the aerodynamic performance is crucial and the flow turning is expected to be high. An inverse design method is more commonly used. This specifies a required velocity (or lift) distribution and a geometry shape is generated. This is referred to a a Prescribed Velocity Distribution (PVD) method. The process typically is based on a simplified version of the Navier-Stokes equations with a boundary layer correction. Whilst almost all cooled blades and vanes are of PVD design today, the corresponding base profile shapes are more complex and require more sophisticated and costly manufacturing techniques. 177

4.8.2

BASE PROFILE SHAPE

VELOCITY DISTRIBUTIONS

Figure 4.15 TYPICAL TURBINE BASE PROFILE VELOCITY DISTRIBUTIONS


88

Turbine NGV and Lift Characteristics [From Oates]

179

Turbine Rotor and Lift Characteristics [From Oates]

Poor aerodynamic features 180

89

PVD 2D Blade design output Lift Coefficient Limited by Peak Mn. Full Lift Distribution – Aerofoil Numbers Chosen For Cost and Forced Response.

Large Leading Edge Circle Size – Stagnation Point Control and TBC.

Large Leading Edge Wedge Angle to Satisfy Cooling Geometry Requirements. Large Trailing Edge WedgeAngle Leads to Reduced Pressure Surface Lift.

Taylor, 20 06

181

Three dimensional aspects

182

90

Radial Equilibrium •

This expression relating pressure gradient to velocity and radius has many implications for turbomachinery aerodynamics. In particular in helping to understand the internal flow pressure gradients and the generation of secondary flows.

•

For example.

2  p   V r 

A swirling annular flow. p++ p--

NGV Rotor

p++

Flow

p-Static pressure distribution

p-p++

Meridional view

Endview 183

Streamline curvature and secondary flows •

The pressure gradients created along a curved streamline can have a profound effect on the aerodynamics of the turbomachinery components. The creation of secondary flows is frequently due to this mechanism and occurs in both stationary and rotating frames of reference. Secondary flows will be discussed in more detail in a later section. Flow going through a blade row:

p++ Path of fluid

p+ Pressure gradient

Radius of curvature r of streamline, r p

F 

F p- -

p+

Velocity, V

2  p   V r r

Centripetal force on fluid, F

p184

91

Streamline curvature and secondary flows Boundary layer going around a bend • Boundary layer velocity profile p++

Centripetal force on fluid, F p-

• Low velocities at the wall

p+

Pressure gradient

• Pressure gradient is applied by freestream fluid above the boundary layer is primarily maintained throughout the boundary layer.

p+ p- Velocity,V

F 

p-

2  p   V r • The lower the velocity => the smaller r the radius of curvature

• To maintain the pressure gradient the lower velocities follow a tighter bend. High pressure

• Boundary layer streamlines - viewed from above • The boundary layer is describes as being skewed or over-turned. • The resulting flow-field is called secondary flow .

Low pressure

185

Streamline curvature

p   p

Vq Va dr

p   p

p   p

2

as

Vr

2 Vs

p r s

r dq

Meridional plane (x-r)

Circumferential plane (r- ) •

The mass of the fluid element is rrdqdr.

•

The centripetal accelerations are

2 V local  plane

r local  plane See Saravanamuttoo etc al 186

92

Streamline curvature •

Centripetal force due to circumferential flow (F1) is: 2

V  rd  dr  r

•

The radial component of the centripetal force associated with flow along the curved streamline (F 2) is: F 2

•



mV s2 r s

cos  s

 (  rd  dr )

V s

2

r s

cos  s

Radial component of the force required to linearly accelerate the flow along the streamline (F3) is: F 3

•

m

dV s

Total inertia force, Fi, is: F i

dt

sin  s

 (  rd  dr )

dV s dt

sin s

V 2 V 2  dV   rd  dr    s cos  s  s sin s  r s dt  r  See Saravanamuttoo etc al

187

Streamline Equilibrium •

The total pressure force is: F P  ( p   p )r  dr d   prd   2( p   p )dr d  2

•

2

By combining with the expression for the inertial forces and neglecting all terms above 1 st order the following equation is obtained: 1 dp  dr



V 

2

r



V s

2

r s

cos  s



dV s dt

sin  s

•

This is the complete radial equilibrium equation.

•

For many cases, r s is so large and a s so small that the last two terms can neglected and the equation reduces to the familiar simple radial equilibrium expression. 1 dp  dr



V 

2

r

See Saravanamuttoo etc al

188

93

Vortex Energy Equation •

The simple radial equilibrium expression is frequently applied to the flows across an individual blade row and to examine the effect of radius.

•

Stagnation enthalpy, h0, at any radius, r, for a given absolute velocity, V, is:

V 2 h0  h  2

 h  21 (V a2  V r 2  V  2 )

•

However, Vr , is usually neglected and:

•

The variation of enthalpy with radius is:

h0

 h  12 (V a2  V  2 )



dV dh  V a a dr dr

dh0 dr

dh dr

Recall, Tds = dh –dp/r, and

•

Neglecting second-order terms and filling back into Eqn (A):

dh0 dr

 T



dV  dr

(A)

ds dT 1 dp 1 d  dp  ds   2 dr dr  dr  dr

•

 T

 V

ds 1 dp dV   V a a dr  dr dr

 V



dV  dr See Saravanamuttoo etc al

189

Vortex Energy Equation •

The simple radial equilibrium expression is used for the second term on the RHS: 2

dh0 dr

•

 T

ds V   dr r

dV a dr

 V



dV  dr

And the radial entropy gradient is also frequently neglected to give the vortex energy equation:

dh0 dr

•

 V a



V  2 r

 V a

dV a dr

 V



dV  dr

Neglecting the viscous loss terms, a frequently used design criteria is the condition of constant specific work as a function of radius. This means that the radial distribution of h0 will not change relative to the inlet conditions through the machine. Therefore:

dh0 dr

0

V  2 r

 V a

dV a dr

 V



dV  dr See Saravanamuttoo etc al

190

94

Free Vortex Equation •

A further simplification can be made by assuming that the radial distribution of axial velocity axial is kept constant so that:

dV a dr

0

V  2 r

 V a

V 



dV 



dV  V 

r dr r

dV a dr

 V



dV  dr

0

dr

•

Which when integrated gives: Vr = constant

•

This is known as the free vortex condition.

•

Therefore, the three conditions of (1) constant specific work (2) constant axial velocity and (3) free vortex variation of whirl velocity, satisfy the radial equilibrium equation. This is frequently taken as a preliminary design starting point See Saravanamuttoo etc al

191

Free vortex design It should be borne in mind that the enthalpy gradient downstream of the rotor is constant so that the enthalpy drop through the turbine is constant at all radii. This typically results in very twisted blades with a large variation in reactions from hub to tip. The extent of this also then depends on the hub-tip ratio.

 K const / r U  K const r

V 

As far as velocity triangles are concerned the following results:Very high root turning, low root reaction, high root loading

V  _ hub

The image part with relationship ID rId12 was not found in the file.

V  _ tip

V 0

V 1

V 0

V 1 U hub

V 0

V 1 U mid

U tip

192

95

Vortex design It is not necessary to use a free vortex flow and other options can be selected. Vortex flow choices can also be selected to still meet the radial equilibrium condition. For example, a constant nozzle angle could be considered:  0  constant Through the vortex flow equation this then results in:

V  r sin

2

 2

 constant

Other NGV exit angle distributions can also be considered as well as other design objectives such as constant massflow distributions or constant loading DH 2 U

These aspects can be used to control the blade reaction, local turning and secondary flows,

193 Japikse

Three dimensional flow fields

IP NGV exit flow Contours of absolute total pressure

194

96

Turbine secondary flows 3

4

PS

SS

SS

PS 4

2

5 3 2

PS

5

SS

1 LE

1

PS

SS

195

Three-dimensional considerations: Turbine Nozzle Guide Vane

Before test This image cannot currently be displayed.

Painted oil-dyes

Highly skewed boundary layers

Separation lines

196

97

3D design considerations

197


Harrison 1992 198

98


199 Giminez 2011


Suction side

Pressure side

200 Giminez 2011

99


201 Giminez 2011


202 Giminez 2011

100

3D design considerations Loss coefficient

SKE

203 Giminez 2011

Turbine stage aerodynamics Unsteady stage calculation Snapshot from transient CFD prediction

contours of density gradient

contours of entropy 204

101

Unsteady Turbine Flow Features HWA traverse plane

Modulation of tip leakage 1 NGV pitch

Rotor wake

Overtip leakage

Secondary flow

Rotor mainstream

1 rotor pitch Instantaneous plot of absolute velocity

205

Unsteady Turbine Flow Features Viscous wake

Wake total pressure deficit

NGV wake impingement and migration Shock Systems

Potential field

Variation in static pressure field

TE and suction surface shocks • Strong static pressure pulse • High frequency content • Impact of shock position and shock movement 206

102

Turbine cooling introduction

207

Turbine cooling if TET > 1250k cooling needed; modern TETs >1800k Typically at stagnation points on the blade surface; leading edge T = 1.05 Tgas trailing edge T = 1.20 T gas Cooling Methods: air cooling – convection, impingement, films, pedestals, ribs sophisticated materials – nickel alloys thermal barrier coatings modern manufacturing methods lost wax casting (including single crystal) internal ceramic cores laser drilling 208

103

Turbine cooling typical cooling air needs Blade row

% of core air

source

1st NGV (hp) 1st rotor (hp)

10 % 5%

HPC delivery HPC delivery

2nd NGV 2nd rotor

2% 3%

HPC delivery mid HPC

other

(sealing)

1 to 2 % mid compression

Flow quantities related to TET and to combustor exit temperature profile Essential to seal hub gaps between rotors and stators with air to keep discs cool Combustor-Turbine interface is very important 209

Turbine cooling air system

Rolls Royce

210

104

TYPICAL ENGINE SECONDARY SECONDARY AIR SYSTEM

211


Turbine Entry Temperature

1800

F119

Cooled turbine blades

Uncooled turbine blades

1700 1600

EJ200 F404 RB199

1500

SC Cast

s c i m a r e C

Spey

1400 1300

Conway DS Cast

1200 1100

Dart

1000

Derwent

Avon 3

Equiaxed Cast

Wrought Wr ought Alloys

1950 1950 1955 1955 1960 1960 1965 1965 1970 1970 1975 1975 1980 1980 1985 1985 1990 1990 212

105

TURBINE COOLING PROGRESS Cooling Flow for an Ideal Isothermal Blade/ Cooling Flow ofActual Blade

 

T gas _ rel  T blade T gas _ rel  T coolairinl et

m* =

mc C p hg Sg l

213

COMPARISON OF COOLING METHOD

214

106

NGV cooling – courtesy of Rolls-Royce

215


HP TURBINE BLADE COOLING

216


107

Turbine blade cooling – courtesy of Rolls-Royce

217 IMAGE COURTESY ROLLS ROYCE

Bibliography 1. Japikse, D., “Introduction to turbomachinery”, Oxford University Press, 1997. 2. Cohen, H., Rogers, G., and Saravanamuttoo, H., “Gas turbine theory”, Longman Scientific and Technical, 3 rd Edition, 1987. 3. “The jet engine”, Rolls-Royce plc, 5 th Edition, 1996. 4. Cumpsty, N., “Jet propulsion”, Cambridge University Press, 1997. 5. Dixon, S., ”Fluid mechanics and thermodynamics of turbomachinery”, Butterworth-Heinemann, 4 th 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”, 2 nd Edition, Prentice Hall, 1998. 11. Mattingley, J., et al.”Aircraft engine design”, AIAA education Series, 1987. 12. Hünecke, K., “Jet Engines”, Airlife, 1997. 13. Kerrebrock, J., “Aircraft engines and gas turbines”, MIT Press, 1992. 14. Oates, G., “Aerothermodynamics of aircraft engine components”, AIAA education Series, 1985.

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Turbine Design Manual

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