/

/

!

/

/

/

NASA-CR-174646 •

NASA

R84AEB379

p..

National Aeronautics and m

m

Space Administration m

P-,l

EXTENDED PARAMETRIC REPRESENTATION OF "

COMPRESSOR FANS AND TURBINES =

Volume II- PART User's Manual

_lrq

O'.._

\

t

FINAL REPORT _ = = _.

HZ,"¢ LJ

_2u

March 1984 r_ ,_ _ _ .._

_ _rl_ 0

Dy 0 _-_

General Electric Company _ m _ =

Aircraft Engine Business Group z _., _

.. Advanced Technology Programs _ ,_

Cincinnati, Ohio 45215 _u__o .. _-. •

•:3" _ ,.._ :=:) O_

FOR _ o o _

_. )-.i ;:>

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION "- <

I E-_ "_:_ _

LEWIS RESEARCH CENTER _ _ _ _ o

21000 BROOKPARK ROAD _J _ r_ t o"} l;_, =_ I

CLEVELAND, OHIO 44135 < r_ _ ,<,

1'% _..... ___\

CT} , _ ":- -'_

I

Contract

NAS3-23055

ENERAL ELECTRI C Advanced Aircraft Technology Engine Business Programs Group Deparlment

Cincinnati, Ohio 45215

,aR_GI_',!AL PAGE IS

,gF POOR QUALITY

1. Repot! No I 2. Government Acc*u_on No.

I

NASA CR-174646

4. Totle _ _bt,ll¢

Extended Parametric Representation of Compressors F.aqs

and Turbines Vol. II - P_RT I!SEP.'sManual(Haran_trlc Turbine)

?. A_Thot Isl

G.L. Converse

g. Pro'form, rig OfpnizatiO#l NIm4 lind Addto14

General Electric Company

Aircraft Engine Business Group

Cincinnati, Ohio 45215

12. S(=ons_'mgAgoftcyNlmomdAd¢lrlm

National Aeronautics and Space Administration

Washinoton, D.C. 20546

3. Reclp_lnl'$ C,Illilog No,

S. Report Olte

March 1984

6. Performlr$90rg_mzat_on C_}owe

8. Porformtt_ Otpnlzlt*on Repot! No

P,84AE B3 79

10. Wm'k Un, t No.

11 Co.trier or Gtlnt No.

NAS3-23055

13. Type of RoDort _O PIp'lOCI Cov_lKI

Contract Reoort

Auoust 1982 - October 1983

14. _lor,ngA0emcvCoOe

15 Sup_lmontwy NOI_

Project Manaoer, James W. Gauntner, Aerospace Enqineer, NASA

Lewis Research Center, Cleveland, Ohio

16, A_,strecl

A turbine modeinq technique has been developed which will anable the user to obtain consistent and

rapid off-design performance from design point input. This technique is apDlicable to both axial

and radial flow turbine with flow sizes ranging from about one pound per second to several hundred

Pounds per second. The axial flow turbines may or may not include variable qeometry in the first

staoe nozzle. A user-specified option will also permit the calculation of desion point cooling flow

levels and correspondino changes in efficiency for the axial flow turbines. The modeling technioue

has been incorporated into a time-sharing program in order to facilitate its use. Because this report contains a description of the input output data, values of typical inputs, and example cases,

it is suitable as a user's manual. This report is the second of a three volume set. The titles of

the three volumes are as follows:

(I) Volume I

(2) Volu_e II

(3) Volume Ill

CMGEN USER's Manual (Parametric Compressor Generator)

PART USER's Manual (Parametric Turbine)

MODFAN USER's Manual (Parametric Modulating Flow Fan)

17. Key Worm (SuilgmtoelbV Aulh_ls|l

Parametric Turbines

Off-Design Performance

Axial and Radial Flow

19. Security O=uif. 10f t_t _Wt|

Unclassified

18. DilU,_,o_ Statement

20. Security Unclassified Cl4u, f. (of th*s Pe9o) 22. I_,ce"

NASA-C-168(Rev 10-75)

TABLE OF CONTENTS

Section Page

1.0 INTRODUCTION

2.0

3.0

PROGRAM STRUCTURE

PROGRAM INPUTS

5

4.0 PROGRAM OUTPUTS 16

5.0 PROGRAM DIAGNOSTICS 17

6.0 EXAMPLE CASES 19

7.0 ANALYTICAL BACKGROUND

7.1 Turbine Map Representation

7.2 Turbine Flow Model

7.3 Turbine Loss Model

7.4 Comparison of Radial Turbine Test

Results with Program Output

32

32

32

37

43

LIST OF SYMBOLS 49

REFERENCES 50

PRECEDING PAGE BLANK NOT FILMED

iii

LIST OF ILLUSTRATIONS

Figure

.

,

3.

4.

5.

6.

,

,

9.

i0.

ii.

Flow Chart Showing Flow of Control in Parametric

Turbine Program.

Input to First Example Case.

Input to Second Example Case.

Turbine Flow Representation.

Turbine Efficiency Representation.

Comparison of Measured and Calculated Values of Inlet

Turbine Flow Function.

Comparison of Measured and Calculated Values of

Total-to-Total Efficiency.

Radial Turbine Performance Map.

Radial Turbine Swirl Map.

Radial Turbine Flow Comparison.

Radial Turbine Efficiency Comparison.

Page

9

ii

33

35

38

42

45

46

47

48

r;rr - ,r_p

pF, ECEDING PAGE P,I,ANK NOT i ..........
LIST OF TABLES

Table Page

le Summary of Turbine Design Point Data

II. Summary of Variable Geometry Turbines

Included on Data Base

III. Default Settings for Variables in Namelist

"INPUT"

IV. Variable Settings to Trigger Default Calculation of Some Design Point Input

14

V, Default Settings for Variables in Namelist

"INPUT i"

14

VI. Design Point Data - INFLOW Radial Turbine 44

vi

i_i • .'.
1.0 INTRODUCTION

The NASA Lewis Research Center employs a general computer program (Reference I)

for calculating the thermodynamic performance of jet propulsion engines. To calculate off-deslgn engine performance, the user must input component maps. These maps

define the characteristics of the various components over their full range of

operating conditions.

For advanced propulsion systems these characteristics are not generally known.

Furthermore, the typical user of the program is not sufficiently knowledgeable and/or

cannot afford the time to do an extensive design analysis of the component in question.

Instead he usually scales some available map.

The objective of the study is an improved method of representing the turbine

component when performing calculations of off-deslgn performance for advanced airbreathing Jet engines. This method, which is a computer program called PART, is compatible in both form and format with the cycle program of Reference i and the example

map representation of Reference 2.

The current program is a follow-on to NASA Contract NAS3-21999. Under the

original contract an axial flow turbine model for large flow size machines was developed. Under the current contract, the model was extended to include both small

axial flow turbines (i.e., flow sizes down to about I pps), and small fixed geometry

uncooled radial flow turbines.

Because this report contains a description of the input-output data, values of

typical inputs, and sample cases, it is suitable as a user's manual. A brief

description of the engineering analysis used to generate the program is given near

the end of the report.

The program uses turbine design point data as input to generate off-design

values of turbine flow-function and total-to-total efficiency over a range of

pressure ratios and speeds specified by the user. A user-specified option will also

permit calculating design point cooling flows for the axial flow machines, and the

corresponding change in turbine efficiency. The cooling flow subroutine, developed at

the Lewis Research Center, is described in Reference 3.
ORZGiNAL PAGE iS

OF POOR QUALITY

Table I. Sugary of Turbine Design Po_ut Data.

No. Data Base NRme* No. of Stages

I HPTI-I

2 H_TI-2

3 HPTI-3

4 HPT2-4

5 HPT2-5

6 HPT3-6

7 LPTI-I

8 LPT1-2

9 LPT2-3

I0 LPT2-4

II LPT4-5

12 LPT4-6

13 L_T6-7

14 PT3-1

15 AT3-1

16 AT3-2

17 AT3-3

18 AT4-4

19 VATI-1

20 VAT I-2

21 VATI-3

22 VATI-4P

23 VAT I-4X

24 VAT2-SP

2.5 VAT2-SX

1

1

1

2

2

3

1

1

2

2

4

6

3

3

3

3

4

1

1

1

1

I

2

2

IZ-IQ.'D **

0.0596

0.0705

0.0335

0.0670

0.0787

O. 0810

O. 0220

0.0_25

0.0571

O. 065

O. 066.5

0.0709

0.0814

0. 0800

0.0590

0.078.5

O. 063.5

0.0499

O. 044

O. 060

0.0238

0.0328

0.0328

0.0636

0.0636

*HPT - High Pressure Turbine

LPT - Low Pressure Turbine

PT - Power Turbine

AT - Air Turbine Test Rig

VAT - Variable Area Turbine

TFF_*

14.6

16.4

88.5

17.3

32.4

45.5

45.0

45.0

58.5

60.4

106.0

134.4

104.9

210.0

_o

43.16

38.8.5

99.0

60.0

290.0

61.8

61.8

61.8

61.8

** Symbols defined in Table III.
Table II. Sumzar7 of Varisble Gecme:r 7 Turbines

Included on Data Base.

Turb ine

I_o. De s iguac ion

VAT1-1

VATI-2

VATI-3

VATI-4P

VATI-&X

VAT2-SP

VAT2-SZ

NO. Of

St: age s

First Stage l_zzle _ea Ibtcios

Z

50.0 62.5 75.0

71.0 86.0 100.0

76.0 84.0 92.0

70.0 100.0 130.0

70.0 100.0 130.0

70.0 100.0 130.0

100.0

87..5 100.0

109.0 120.0

100.0 108.0 116.0
The Aircraft Engine Group of the General Electric Company has a turbine

data base consisting of 25 turbines having design point turbine flow functions

ranging from about 14 to 290. The number of stages for each of these turbines

together with the approximate design point values of specific work output divided

by inlet total temperature (DHQTD) and flow function (TFFD) are summarized in

Table i. The last sevel turbines shown in the table are varlable-geometry turbines.

Table II shows the set of first stage nozzle area ratios for each of the seven

variable-geometry turbines. Five of these variable-geometry turbines were generated

by turbine design and off-design computer programs similar, if not identical, to

that described in Reference 4. Two of the turbines shown in Table II were generated

from air turbine test carried out by the Lewis Research Center. The results of

these tests are given in References 5 to 8. The Table II designation of the NASA

test turbines have been given a trailing X. The analytical prediction of the performance of these turbines obtained from Reference 9 has been a trailing P.

All of the turbines in data base discussed above are of the large axial-flow

type. In order to obtain data for small axial-flow turbines and radial flow turbines

the open literature was used. References 13 thru 17 give the references used for

small axial flow turbines. References 18 thru 24 give those for radial turbines.

4
2.0 PRO(;RAM STRUCTLr_E

Aflov chart shoving the flov of control in the ICASA parametri: turbine

program is shown in Figure 1. After the input has been read and processed,

the program carries out a simple pitch line analysis starting rich the last

stage of the turbine. The analysis starts at the exit of the turbine stage

(in order to avoid iteration) and calculates the bucket and nozzle flow

angles. This stage geometry is then used to generate the stage flow and loss

characteristics using the analytically based correlations developed during

the progr am . Successive stages are then calculated until the first stage is

reached. The first stage characteristics are then [enerated, and the stages

stacked for each value of the first s_age turbine nozzle area specified. 1f

the turbine is cooled, then the procedure given in Referen:e 3 is used to

calculate both the cooling flow requirements, and the cool_ed turbine efficiency. Finally, the output i.s processed to obtain a turbine map representation compatible with the cycle deck of _efereuce 1.
I CALC. EXIT I

CONDITIONS

N-I STAGE

ORIGINAL P_o,wE _'m

OF POOR QUALi'FY

CALC. s2

FOR NEAT

AREA KATIO

SETN. i i

CALC. COOLING FLOWS &

E.':FICIENCY SCALAR

Figure i. Flow Chart Showln8 Flow of Contro2 in Parametric

Turbine Program.

6
3.0 PROGRAM Z_PUT$

OF POO:: !" ..,_ ,-.

All of the PART inputs are of the free.field £or_at (NAHELIST) type, and

begin in column two. There is no specified, order to the inputs. The program

initially lists the contents of the lqAHELIST INP. L'_ together with the default

settings of all the input variables. The user may then change as many of the

inputs as desired. The program then echoes the updated l_L_r_--LIST. If none of

the inputs are changed, the progra_ will execute the f_rst example cue and

the user can inspect the output. The input variables together with the default settings for a turbine are stnmuarized in Table III.

The first six input variables in Table III are used to control the n,_ber

and values of speed, pressure ratio, and nozzle area ratios (transformed into

nozzle angle) to be written on the output giles. For example, in the input to

the first example case shown in Figure 2, all o£ the corrected speed and pressure ratio arrays are used by the program, but only the first three positions

in the area ratio array, l_ote that speeds and pressure ratios are entered in

increasing value, but that area ratio| are entered in decreasing value (this

is so that the nozzle angles will be written in increasing order ou the output

file). Speeds less than 10X should not be used. The input to the second example case sho_'n in Figure 3 illustrates the use of the first six variables

to limit the size of the output files.

Some of the design point inputs will be calculated internally by the prc,-

grEn, if the user inputs the correct valoe to trigger the calculation. This

subset of inputs together with the required settings are sum,-arized in Table

IV. An input value equal to or less than zero will trigger all of the calculations with the exception of exit swirl angle, here a value greater than 90

degrees eust be input (180 degrees is recom,=ended).

A mini,,_ set of design point input would consist of NSTG and DEOTD.

The values o_ TFFD and Y.NRTD could be input as 100.0 and the resulting values

of TFFD interpreted as percent. The user could then use the settings in Table

IV to trigger prosra= calculations o_ the re_a_ning design point in fo_at ion.

The use of the progr _m to calculate the number og stages will frequently result in a single-stage turbine, s_nce the only upper l_it on turbine radius

is the limiting value o_ ri_ speed. This is not usually sufficiently restrictive to require the use of additional stages.

If the user wishes the progr_ to calculate the value o_ design Point

cooling _low, and the corresponding decrease in turbine efficiency, the JCOCL

switch in the NAHZLIST _NPUT should be set to 1. The progr_ will then list

the contents of the _HEI.IST I_UT1 together with the default settings of all

the variables. The user may then change as many of the inputs as desired.

Since the degault eetti_s of the _LIST II_PUT ere for _n uncooIed turbine,

these inputs (namely, TTII_, FTIN) rust be changed in order to successfully

calculate cooling flows. The input variables gor NA_LIST II_UT1 together

with their default settings are summarized in Table %'. The input to the

second example case sho_ in Figure 3 illustrates the proper format for a

cooled three-stage turbine.
Table Ill.

ORIGINAL PA,_ ;_

OF POOR QUALITY

Default Settings for Yariibles in Name|iat "Input."

IqSPDS

.PR

_l(i)

bAR

ARM

NSTC

JCOOL

DH_ro

ETATTD

TFFD

XNRTD

FSID

ANGSRX

X_qZXD

TTIN

PTIN

F_qGD

ETAN

R3QR2

RHQRT3

Units.

None

None

None

lions

None

None

None

None

Btu/lbm "B

None

Ibm "R 112

aecapsl

rpm/'aZ/2

Rose

Degrees

None

" R

p, ia

None

None

None

None

e_ault

al ue S

(Axial TurbSn(

IOZ to I50Z

20

I.I to 6.6

3

1.3, 1.0, 0.7

I

0

0.03278

0.923

62.98

15.7

0.373

518.67

14. 696

0.0

.94

1.0

• 733

Demcript ion

Number of Speed Lines Desired

The Array o[ Percent Corrected Speeds (Hax of 15)

Number of Pressure Ratios Desired

The Array of Pressure Ratios (Haw o[ 20)

Number of First StaLe Nozzle Area Ratios

Array of Nozzle Area Ratios (Max of 6)

Number of Turbine Stages (Max of 6)

Coolin8 Flow Switch (O-Uncooled; I-Cooled)

Specific Mork Output Divided by Inlet Temperature

Turbine Total-to-Total E[ficienc 7

T.rbinp. Inlet Flay Function, i.e.,

(TrP - wT,_-tlPt)

Turbine Corrected Speed (XNRT - N/_-)

AvataRs Turbine pitch line loading, i.e.,

PSID - (DHQT/[ 2(U/,_-tt)2/go J ]/NSTG

Exit Pitch Line Svlrl A._gle (Positive _en Opposite

to Direction of Notation)

Exit Fitch Line Axial Hach Number

Turbine Inlet Total Temperature

Turbine Inlet Total Pressure

Turbine Inlet Fuel-Air Ratio

Nozzle Efficiency (Ratio of Exit Actual to ideal

Itlnet_. c Energy)

Pitch Line Radius Ratio (Rotor Exit to Inlet)

Radius Ratio at Rotor Exlt (First Guess)

8
OF' P,._,.,,., Q(J/_LJ"EY

m,..=.,= .... "'''''PARAMETRIC TURBINE ='mmmCmmmmmm'=mmmm

P=A'R*T

AXIAL OR RADIAL TURBINE? l-RADIAL. 8 OR CR=AXIAL

=B

DESCRIPTION OF INPUT VARIABLES IN PART PROGRAM

(NAMLLISl INPUt)

U_ITS;TTIN-DEG R,PTIN.P$1A,W-PPS,H=BTUILBM,N_RPM

MAP RANGE_ARRAY VALUES MUST BE IN ASCENDING ORDER)

N_PDS -15 NO OF SPEEDLINES _E_IkED(MAX-I5)

APCNC ARRAY OF PERCENT CORRECTED SPEEDS

NPR =2_ NO OF PRESSURE RATIOS DESIRED(I, LAX=ZB)

APR ARRAY OF PRESSURE RATIOS

NAN "6 NO OF NOZZLE AREA RATIOS(MAX=6)

ANN ARNAY OF FIHST STAGE NOZZLE AREA RATIOS

NSTG "6 NO OF TUkBINE STAGES(I'_X-6t

INTEGER SWITCHES

JCOOC o_ COOLING FLOW SW|TCH(_-UNCOOLED,IsCOOLEDI

DESIGN POINT VA. UES OF:

DHQTD 5PECLFIC WORK OuTPuT DIVIDED BY TTIN

ETAIT_ TUR_IN[ TOTAL-TO-TOTAL EFFICIENCY

TrFD TuHBII_L INLET FLOW FUNCTION

{TFF-W=_RI(TTIN)/PTIN)

KNRTD TU_INc COkRECIEO $PEEO(N/SORT(TTINII

PSI_ AVERAGE IURBINE PITCH LINE LOADING

PSJB-DHQT/(Z*(U/SURI'tTTIN)''ZIGJ))INSTG

ANG_WX EXI_ PI]C. LINE SWIRL ANGLE(tCOUNT-ROT)

xMZKD EXIT PITCH LINE AXIAL MACH NUMBER

TTIN TUR_Ih£ IHLET TOTAL TEMPERATUXE

PTIN TUR_IhE [NLEI _,J_AL PKE_SRUE

FA_G_ TUA_INr INLET FUEL-AIR RAI|O

ETAN NOZ_LL EFFtRATIO ACTUAL TO iDEAL EXiT KE)

GEOMETRY SPECIFICATIONS:

W3U_Z PITChLINL RAD RATIO(ROTOR EXIT T_ INLET)

RnQR13 kAOlU_ KATIO AT ROTOR EXIT(FIRST _UES$)

NAMELIST INPUT

N_PbS - 15,

APCNC (I} _

13 13_._, 14_._, Ib_._#B,

NPR = _.

APK (I) =

I I.I_#@. 1.2_@d, 1.4_g_,

4B.BBBB,

BB.BB#Bo

IZB.BBB_,

1.6BBB,

2.ZBBB,

3.BBB#,

Figure 2. Input to First Example Case
A3

17

NAR

AEN

1

5

!

NSTG -

DHQTD -

TFFD -

PSIO -

ANGSWXPT|N •

E]AN "

R_b_T3-

END NAMELIST

4.4DMJ, 4,ZBUg,

m 3t

(|)-

e

i.Z49_, 1,144ff,

1, 0COOL - m,

B.B327BB, ETATTD•

6_.gB_BB_, XNRTO •

_.B5IIU_, XHZXD -

14.b9_, FARGD -

_.94_B, R3ORZ -

B.733J_.

INPUT

J

5

g

13

NPR

APK

!

5

9

13

17

NAR

ARN

!

5

]

NSTG "

TFFD -

PSID -

ANGSWXPT|N -

[TAN •

R_URT3=

END NA_ELI$T

[NT[A CnANu/$ TO NAHELIST INPUT

-$INPUT$

NAMLLIST iNPuT

N_PD_ - IS,

APCNC 1l)-

5_._,

l.l_d,

1.7_,

2.4_B_,

3.Z8_,

(1}-

1.3_, t._d_,

|.349_ 1.1440,

1, aCOOL " 8,

_._3Z78B

_2.98ad_

14.Gg0_U_

_.944_U_

#.733_g

INPUT

NASA OUTPUT ON IFC=I_,I6 •

B.7BBI, 8Q •

I.IIIB,

1.923BOB,

i.373BBB,

518.669996,

28.g_. 3B.BBBB, 48.Jgge,

I.ZB_, |.4BgB, 1.68BB,

Z.6##_, Z.BSB#, 3.e#eS,

3.4B_a, 3,6_8#, 3.8_0,

4.Z#_B, 4.4B#B, 4.5BBB,

i/. 7BO',O, Ill. ,

1.B_B, I.IBBB.

ETATTD• B.923BBE

XNRTO = 193.5ZB#B_

XHZXD • B.373BBB

TTIN - 518.669990

K3QRZ - I.ESBBBB

lO

Figure 2 - (Continued) Input to First Example Case
OF 2 ....

P*A*R*T

AXIAL OR RADIAL TURBINE? I-RADIAL, • OR CR-AXIAL

-8

DESCRIPTION OF INPUT VARIABLES IN PART PROGRAM

(NAMELIST INPUT)

UNITS:TTIN-DEG R,PTIN=PSIA,W-PPS,HeBTU/LBM,N-RPM

MAP RANGE(ARRAY VALUES MUST BE IN ASCENDING ORDER)

NSPDS •IS NO OF SPEEDLINES DESIRED(HAX-IS)

APCNC ARRAY OF PERCENT CORRECTED SPEEDS

NPR =2B NO OF PRESSURE RATIOS DESIRED(MAR-Z•)

APR ARRAY OF PRESSURE RATIOS

NAB =6 . NO OF NOZZLE AREA RATIOS(MAX-6)

ARM ARRAY OF FIRST STAGE NOZZLE AREA RATIOS

NSTG -6 NO OF TURBINE STAGESIMAX-6)

INTEGER SWITCHES

OCOOL -B COOLING FLOW SWITCH(I-UNCOOLED,IaCOOLED)

DESIGN POINT VALUES OFI

DHGTD SPECIFIC WORK OUTPUT DIVIDED BY TTIN

[TATTD TURBINE TOTAL-TO-TOTAL EFFICIENCY

TFFD TURBINE INLET FLOW FUNCTION

(TFF=W*SQRT(TTIN)IPTIN)

XNRTD TURBINE CORRECTED SPEED(N/SORTITTIN))

PSID AVERAGE TURBINE PITCH LINE LOADING

PSID.DHQTI(Z*(U/SQRT(TTIN)eeZIGO))/NSTG

ANGSWX EXIT PITCH LINE SWIRL ANGLE_*COUNT-ROT)

XMZXD EXIT PITCH LINE AXIAL MACH NUMBER

TTIN TURBINE INLET TOTAL TEMPERATURE

PTIN TURBINE INLET TOTAL PRESSRUE

FARGD TURBINE INLET FUEL-AIR RATIO

ETAN NOZZLE EFF(RATIO ACTUAL TO IDEAL EXIT KE)

GEOMETRY SPECIFICATIONS:

R3ORZ PITCHLINE RAD RATIO{ROTOR EXIT TO INLET)

RHQRT3 RADIUS RATIO AT ROTOR EXIT(FIRST GUESS)

NAMELIST INPUT

NSPDS " IS,

APCNC (I)"

] I•olllf, ZB.ImBB, 3m. BBB8.

6 SB.#_B8. 68.1Bg8. 7J,_BBS,

9 9J.IBBB, IIn. JBBB, IIB.BBBB,

13 138.BEBB. I4B./BBB, 15E.BBBB.

NPR • 2B,

APR If)"

I l.l•gg, 1.2•g•, 1.4BBS,

S 1.7Riff, 1.B888, Z.BB_J,

9 Z.4•BB, Z.E88m, Z.8BJI,

4B.JBBB,

88.8SB8,

IZI.SBBB,

1.6BBB,

Z.Zg_B,

3.lBsg,

F_gure 3. Input to Second Example Case

II
ORIGINAL PAGE iS

OF POOR QUALITY

13 3.ZJJJ,

17 4.81mJ.

MAR = 3,

ANN (1l5 B.

1 1,249J_

NSTG • 1.

DH_TD •

TFFD -

PSID •

AN_S_X•

PTIN -

ETAN •

RHORT3-

END NAMELIST

ENT[R CHANGES

mS|NPUT

1.Emil,

8. o

1.144H,

4COOL •

#.D3Z78J.

62.BBJJSl,

i. B51188.

15,ZJ_##B,

14.696_8J,

9.g4d888,

B.733388.

INPUT

_t

ETATTD"

XNRTD •

XMZXD •

TTIN •

FARGD •

R3ORZ •

TO NAMELIST INPUT

•NSPDS'6,

-APCNC=Z_._4D. o64.,d_..Imm.,128..

-NPR-S,

=APR-Z._,2,S,3.J,3.S,3.B,

-MAR=|,

-ARN=I.J.

•NSTG'3,

"OCOOL'I,

=DHOTD'i.1635,

•TFFD-SB.B3,

•XNRTD'4J.IB,

-PSID-I.6,

•ETATTD-B.886,

-ANGSWX'Z.9,

-XMZXD-8.4|,

•TTIN•Z58_.,

-PIIN-S9.8,

-FARGU-B.JZ,

-$

1.9Z3mlJ,

|93.S2_BBi,

J.3738JI,

SIS.66999B,

4.

l.mlBDBB_

DESCRIPTION OF INPUT VARIABLES IN PART PROGRAM

(NANELIST INPUTIi

KINDOFuAN ORDERED COMBINATION OF DIGITS REPRESENTING

THE COOLING CONFIGURATION OF THE TURBINE

TC-TOTAL TEMPERATURE OF THE COOLING FLOW

FARCX=FUEL-A|R RATIO OF THE COOLING FLOW

YEAR-FIRST YEAR OF SERVICE FOR SIATOR VANE MATERIAL

YEAR B-FIRST YEAR OF SERVICE FOR ROTOR BLADE HATEKIAL

ELiFE=DES|RED LIFE OF TURBINE AIRFOIL

NAMELIST INPUTI

_INDOF-, 11J_2E,

TC = 584.JB_B8H, FARCX • B.

VE_R = IgBB., YEARB - |g84.,

ELIFE = I.IB_BS_E _S,

END NAMEL|ST INPUTI

ENTER CHANGES TO NAMELIST INPUTI

mSINPUTI

•K|NDOF-864_,

•TC-78_..

-$

NAMELIST INPUT

NSPOS • 6,

APCNC ¢I)"

12

Figure 3 - (Continued) Input to Second Example Case
ORIGINAL PP,GE f_

OF POOR QUALITY

5 IJO.JSBS, 12m. SEB_,

9 9E.BfBE, IBS.B_BB,

13 13_.IBIB, 148.BBBS,

NPR - S,

APR (l)"

] 2.#SBS, 2.S88R,

S 3.BBfS. I.SBBB,

9 2.4JSB, 2.68SB,

13 3.298g. 3.48_B,

17 4.#EEB, 4.2JBg,

NAR = 1,

ARN (I)"

1 1.1818, l.mSBJ,

S l. , B. ,

| |.249E, 1.144#,

NSTG • 3, 3COOL " 1,

DHOTD - /.1635#1, ETATTDTFFD - S8.S3JBBJ, XNRTD -

PSID - • I.SESBBB, XHZXD -

ANGSWX- 2.g#BSEE, TTIN e

PTIN - S9.BBSBEB, FARGO -

ETAN - I,gdEEBB, R3QR2 =

RHQRT3- E.?333EB,

END NAHELIST INPUT

PCBLED" 8.86478 PCNCH- I.EZJB| EFF4*

NASA OUTPUT ON ]FC-IS,|6 &

71.mBBB. 8B.mBJB,

lIB.SBS_. IZB.JBB8,

ISB.SBSBo

].IRBB, 3.SBI8,

:.mBBB, 2.21BB,

2.8_Bg, 3.SBB_,

3.68Be, 3.8B_8,

4.4BBB, 4.6EBEo

E.?BIB, B. ,

I.EEE8, l.EJ88,

#.886BIB

4ff.188Bg8

i.dIBBBB

ZSSB.SJBBSB

#.I2B_BB

I.#EJSEE

1.8835 PRN" 3.297

Figure 3. - (Continued) Input to Second Example Case

13
ORIG;j_,_L PAOE I_

OF POOR QUALITY

Table IV. Variable Settings to Tr_gger Default Calculation

of Some Design Point Input.

Variable

I/area Setting Act ion Taken

NSTG O. 0

ETATTD

PSID

ANGS_ ,

_wl2.XD

0.0

0.0

180.0

0.0

Progrm Calculates Nmnber of Stages

(Not Rec_euded)

Progr_ Calculates Design Po_.nt Efficiency

Design Point Loading Set to 0.9

Y.xit Swirl Angle Calculated From Zero Hub

Re act ion

Sets Exit Axial Math Number to 0.5

Table V. Default Settings for Variables in l_.nelist "Inputl"

Vat iab le De fault

Name Ih_ics Value Description

KIRDOF None 86_00000

TC

FARCX

Ye ar

Ye ar B

ELIFE

• R

hr8

"/00.0

0.0

1980

1980

I0,000

An Ordered Combination of D_gics

Represent ink the Cooling Configuration of the Turbine

Total Temperature of the Cooling

F1 ow

Fuel-A_.r l_t_o of the Cooling Flow

First Year of Serwice for Stator

Vane Material

First Year of Service for Kotor

Blade Material

Desired L_fe of Turbine Airfoil

14
The _nteger variable KINDOF represents the cooling configuraticn of the

turbine. Each blade row starting with the first stage stator is assigned an

integer value characterizing the type of cooling employed as follows:

0

1

2

3

4

5

6

7

8

9

_cooled

Convec t ion coo 1 ins

Convect ion with coating

Advanced convect ion

Fil" with convection (75= trailing edge injection)

Film with convection (50Z trailing edge injection)

Film with convection (25Z trailing edge injection)

Transpiration with convection (25% trailing edge inject'ion)

Full coverage film

Transpiration

For exmnple, the 86A00000 configuration has the first "three blade rows

cooled and the remaining five rows tmcooled (a four-stage turbine). For a

detailed description of the cooling flow calculetio_ and the various cooling

flow coufigurat_ons, the reader should consult Reference 3.

15
4.0 PROGRAM OUTPUTS

The basic output from the program consists of two tables. These tables

show the turbine efficiency and turbine flow function variations for each of the

first stage nozzle area ratios, pressure ratios, and percent corrected speeds

specified in the input. The input values of area ratio are converted to first

stage nozzle angles before being printed out. The output tables for the first

example case are shown on pages 22 through 27. The table structure is compatible

with NASA cycle deck requirements given in Reference 2 (pages 23 and 24).

The output tables can be visualized as three dimensional, composed of a

series of planes with each plane assigned a value of nozzle angle, BETA. Then in

each BETA plane, the dependent variable (ordinate axis) is a function of pressure

ratio, PR, and corrected speed, rpm. The dependent variables are respectively

turbine corrected flow, W, and total-to-total efficiency, ETA.

For example, in the output table on page 30 the forty-five lines of the

dependent variable correspond to the fifteen values of corrected speed, where each

speed occupies three lines. And the twenty values of the dependent variable in

each three line group correspond to the twenty values of pressure ratio.

In addition to these two tables, there is a terminal listing summarizing

the resultsof the cooling flow calculation, if this option was used. The value

of the total cooling flow, PCBLED, is printed out together with the cooling flow

for the first stage nozzle alone, PCNCH. The new cooled turbine efficiency value,

EFF4, is given together with the new value of the total-to-total pressure ratio

across the turbine, PRN. An example of this printout is shown on page 13 in the

second example case. With the flows, shaft work, and turbine pressure ratio known,

the user can calculate the new cooled turbine efficiency, ETATTD, using the bookkeeping procedure compatible with the cycle deck representation to be employed.

A cycle deck efficiency scalar could then be used or, if desired, the program could

be rerun on the uncooled branch using the new design point efficiency value as an

input.

16
5.0 PROGRAM DIAGNOSTICS

The PART computer program contains error printouts to aid the user in

trouble shooting his input. A listing of the error messages and their meanings

are given below.

i. LIMITING VALUE OF UTIP=I800.0, CALCULATED VALUE OF UTIP=

This warning message is printed out if the calculated tip speed of a

radial turbine exceeds 1800 fps.

2. LIMITING VALUE OF UHUB=I600.0, CALCULATED VALUE OF UHUB=

This warning message is printed out only if the calculated rim speed

exceeds the recommended value (this is a disk stress warning).

3. LIMITING VALUE OF ANS=42.0E9, CALCULATED VALUE OF ANS=

This warning message is printed out if the product of the exit annulus

area and the rpm squared exceeds the recor_nended value (this is a centrifugal

stress limit on the rotor blading).

4. QUIRE CTR ERROR--(CALLING LINE=,I5,)

There are eight iterations in the program. Seven of the iterations are

balanced using the Method of False Position. This method is contained in the subroutine QIREXX. A maximum of 25 passes is allowed for any single iteration to

balance. If the iteration does not balance within the specified tolerance, the

error message will appear with the number of the offending iteration in the I5

Format field.

Normally, the occurrence of such an error will not cause a problem.

However, in the case of QIRE loop number five which calculates the turbine

efficiency for the specified input values of pressure ratio and corrected speed,

an additional message indicating the convergence error is printed out. This message

has the form:

DHQT= ,ERR= ,PQP=

where the blanks contain the current values of specific enthalpy change divided

by inlet total temperature, the convergence error in pressure ratio, and the

17

pressure ratio at which the error occurred.
The user should inspect the error to see if the degree of convergence is

satisfactory, if not, it may be necessary to restrict the range of input speeds

and/or pressure ratios requested. The individual QIRE loops together with the

calling routines and type of iteration are as follows:

QIRE CALLING

LOOP ROUTINES C_fENTS

i INLETX

2 VELRAT

3 CHOKEX

4 ROT CKX

5 PRTEFF

6 FSTACK

7 CHOKEX

Calculates individual stage efficiencies from the input

value of overall turbine efficiency (NSTG>I).

Obtains the axial velocity ratio across the rotor.

Solves for the value of nozzle Mach number when the

rotor chokes.

Solves for exit annulus choke location given the

location of rotor choke.

Calculates efficiency for input values of speed and

pressure ratio.

Solves for the "polytropic" exponent for a multistage

turbine.

Solves for the value of the nozzle overexpanded Mach

number after nozzle choke and before rotor choke.

There is one iteration in the program balanced by the Newton-Raphson Method. A maximum of 25 passes is allowed for convergence. If an error occurs the program will

print out the warning message

ZERO DERIVATIVE IN NEW RAP LNCALL = I i0

The value i will appear in the Ii0 field since this is the first Newton-Raphson loop.

NEWTONRAPHSON CALLING

LOOP ROUTINE

i CHOKEX

COMMENTS

Calculates the value of UQATI at the speed where both

the nozzle and the rotor are choked.

18
6.0 EXAMPLE CASES

Two example cases are given in order to illustrate the use of the program.

The first case utilizes the default settings to generate the output for a singlestage, uncooled, variable-geometry turbine. The second case is a single stage radial

turbine.

A complete record of the two terminal sessions including a listing of the

output tables is given on the following pages. The program inputs and outputs have

been discussed previously in Sections 3.0 and 4.0.

19
mREMOVE CLEARFIL[S

tOLD /NASAPT/NASAPART

_eFRN

I05Bi 1B/2_/83 |l.lZZ

OF POOR QUAL;%"_

tet---------t-at-OPARAMETRIC TURBINEW-t-t-u-t-mmatR_we

ptAaR'T

AXIAL OR RADIAL TURBINE? I-RADIAL, B OR CA-AXIAL

-J

DESCRIPTION OF INPUT VARIABLES IN PART PROGRAM

(NAMELIST INPUT}

UNITS:TTIN=DEG R,PTIN'PSIA,W-PPS,H-BTU/LBM,N-RPM

MAP RANGE(ARRAY VALUES MUST BE |N ASCENDING ORDER]

NSPDS -15 NO OF SPEEDLINES DESIRED(MAX-If)

APCNC ARRAY OF PERCENT CORRECTED SPEEDS

NPR =Zm NO OF PRESSURE RATIOS DESIRED(NAX=2B)

APR ARRAY OF PRESSURE RATIOS

NAR -6 NO OF NOZZLE AREA RATIOS(MAX-6)

ARN ARRAY OF FIRST STAGE NOZZLE AREA RATIOS

NSTG "6 NO OF TURBINE STAGES(MAX-6)

INTEGER SWITCHES

OCOOL -B COOLING FLOW SVITCNIB-UNCOOLED,I=COOLED)

DESIGN POINT VALUES OF:

DHQTD SPECIFIC YORK OUTPUT DIVIDED BY TTIN

ETATTD TURBINE TOTAL-TO-TOTAL EFFICIENCY

TFFD TURBINE INLET FLOW FUNCTION

(TFF-U'SORT(TTIN)/PTIN)

' XNRTD TURfiINE CORRECTED SPEED(N/SQRT(TTIN))

PSID AVERAGE TURBINE PITCH LINE LOADING

PSI_-DHQT/(2"(U/SORT(TTIN)''2/G_))/NSTG

ANGSWX EXIT PITCH LINE SWIRL ANGLE(_COUNT-ROT)

WMZXD EXIT PITCH LINE AXIAL MACH NUMBER

TTIN TURBINE INLET TOTAL TEMPERATURE

PTIN TURBINE INLET TOTAL PRESSURE

FARGD TURBINE INLET FUEL-AIR RATIO

ETAN NOZZLE EFF(RATIO ACTUAL TO IDEAL EXIT KE)

GEOMETRY SPECIFICATIONS:

R3ORZ PITCHLINE RAD RATIO(ROTOR EXIT TO INLET)

RHQRT3 RADIUS RATIO AT ROTOR EXIT(FIRST GUESS)

NAMELIST INPUT

NSPDS - i5,

APCNC (I) =

I Ig.B_, 2_.8_B, 3B.BBB_, 4B.BBBB,

5 5S._BBa, 6_.Ba_, 7B.BBgg, BB,BBBg,

9 9B.Bg_, IBg. Bg_g, |18.BBBB, IZB.BBBB,

13 13_.Sg2_, 14B.BBBg, 152.gBSB,

NPR " 2g.

APR (I)-

5 1.7BBB, I.B_Bg, 2.BBBB, Z.ZBBB,

9 Z.4BBB, 2.68B8, 2.BBBB, 3.B#BB,

2O
13 3.2B,g_.

17 4. JBB_I,

NAR i, 3,

ARN ( I )-

1 L . 3Bgg.

5 g. .

! | .Z49_,

NSTG = I,

DHQTD "

TFFD =

PSID "

ANGSWX"

PTZN "

ETAN =

RNQRT3-

END NAMELIST

3.4Bgg, 3.5888o 3.8888,

4.ZB_g, 4.4888° 4.6888,

l.Bggg,

1.L44_,

JCOOL = B,

g.B3Z78B,

62.98_Bg,

B.8511_B,

15.2BgB_2,

14.696_B_,

B.94_2_B.

B.733388.

INPUT

L

1

5

9

13

NPR

APR

!

5

9

13

17

NAR

ARN

1

5

1

NSTG "

DHQTD "

TFFD =

PSID =

ANGSWX=

PT|N =

ETAN =

RHQRT3=

ENTER CHANGES TO NAMELIST INPUT

=$1NPUT$

NAMEL]ST INPUT

NSPDS - 15,

APCNC (I)=

IB.BBBB.

5B.BSBB,

9#.888g.

13g.BB#_.

- 28.

(IJ=

l.lBB_.

3.288_.

4.888_,

• 3t

(I)"

1.3B8g, 1.8g_8.

g. , _. ,

1.2498. 1.144_,

1. aCOOL • Bo

8.B32788,

6_.988_88,

8.851188,

15.ZSBEgB,

14.69688_o

8.9488BB,

8.733388,

END NAMEL1ST [NPUT

NASA OUTFUT ON IFC=15,16 &

ETATTDXNRTD =

XMZXD -

TTIN =

FARGD=

R3QRZ "

8.788g, B. ,

i.BBBg, I.BBBg,

B.923888,

193.528888,

B.37388B,

518.669998,

8.

1.888_88_

28.BBBg, 3B.8BBg, 48.8888,

68.88_g, 78.8888, 88.8888,

I82.88gg, IIB.8888° 128.B88g,

14B.SBBg, 158.8888,

L.ZBg8, 1.4888, 1.6Bgg,

1.8B_B, 2.B88g° Z.ZBB_,

2.58_g, Z.88Bg, 3.8B8g,

3.48B_, 3.6B88° 3.888B.

4.Z_88, 4.488B, 4.688g,

ETATTDXNRTD =

XMZXD •

TTIN "

FARGO =

R3QRZ •

B.7BBB, 8. ,

1.8888o I.BBBgo

8.9238£B,

193.SZggBgo

8.373888,

518.669998,

8. o

I.J88BBg,

21
269 BETA 3

RPM 15

RPM 15

RPHI5

PR 20

PR 20

PR 20

EFF 20

EFF 20

EFF 20

EFF 20

-EFF 20

EFF 20

EFF 20

EFF 20

EFF' 20

EFF 20

EFF 20

EFF 20

EFF. 20

EFF 20

EFF 20

EFF " 20

EFF 20

EFF 20

EFF 20

EFF 20

EFF 20

EFF 20

EFF 20

-EFF---'2o

EFF 20

EFF 20

EFF 20

EFF-- 20

EFF RO

EFF 20

I EFF 20

EFF 20

EFF 20

EFF 20

EFF 20

EFF 20

EFF 20

EFF 20

EFF 20

-EFF - 20

EFF 20

EFF 20

EFF 20

-EFF 2O

RPM 15

RPM ! 5

RPM 15

PR ZO

PR 20

PR 20

EFF 20

LFF 20

£FF 20

TURB 1NE

61.

I0.

60.

-" 150.

1.10

2.20

3.60

0.511

O. 231

O, 193

O. 765

O. 424

0.371

O. 877

O. 560

O. 506

0.912

0.891

O. 580

O. 901

O. 7.%0

O. 626

O. 860

O. 767

O, 662

O. 799

0.811

0,688

0,718

O. 825

O, 705

O. 622

O, 831

0.716

O. 507

O, 833

O. 722

O. 385

O. 830

O. 724

0. 253

O. 824

O, 723

O. 106

0.815

O. 721

0,0

O. 804

0.715

0.0

O, 791

O. 709

10.

80.

150.

1.10

2.20

3,60

O. 442

O. 190

O. 158

OF POOR Q_J.!_::,L!:,_'

EFFICIENCY VS. PR, RPM0 AND BETA

66. 75.

20. 30. 40.

90. I00. 110.

50.

120.

60.

130.

1.20 1.40 1.60 1.70

2.40 2.60 2.60 3.00

3.80 4.00 4.20 4.40

0.405 0.321 0,282 0.269

0.222 0.215 0.209 0.204

0.190 0.108 0.186 0,164

0.655 0.550 0.497 0,479

'0.412 0.401 0.393 0,386

0.367 0.363 0.360 0,'357

0.601 0.708 0.655

0.567 0.557 t 0.546

0,499 0.493 "0.487

0.879 0.811 0.765

0.667 0.648 0.632

0.570 0.561 0.553

0.914 0,874 0.835

0.725 0.705 0.685

0.617 0.608 0.600

0.920 0.910 0.878

0,762 0.739 0.719

0.652 0.643 0.635

0.905 0.925 0.902

0.765 0.762 0.743

0.678 0,669 0,661

0.875 0.925 0.912

0.799 0.778 0.759

0.695 0.686 0.678

0.833 0.915 0.911

0.807 0.786 0.768

0.706 0.697 0.669

0.761 0.895 0.903

0.6T'O 0,790 0.773

0.712 0.703 0.695

0.719 " 0.868 0.688

0.609 0.790 0.774

0.714' 0.706 0.698

0.649 0.634 0.868

0.804 0.786 0.771

0.714 0.706 0.698

0.571 0.79A 0.844

0.797 "0,780 0,766

0.712 0.704 0.696

0.486 0.750 0.616

0.788 0.772 0.'_58

0,707 0.700 0.693

0.394 0.701 0.784

0.777 0.762 0.749

0.701 0.694 0.687

20. 30. 40.

90. 100. il0.

1,20 1.40 1.60

2.40 2.60 2.80

3.60 4.00 4.20

0.344 0.269 0.235

0,_63 0,176 0.171

0.155 0.153 0.161

I

1,80

3.2O

4.60

70.

140.

2. O0

3.40

0.258 0.242

0.200 0.196

0.182

0.464 0.441

0.380 0.375

0.354

0.637 0.622 0.598

0,634 0.524 0.515

0,482 0.476

0.748 0.733 0.711

0.619 0.604 0.591

0.545 0.538

01820 ' 0.808 0.780

0.667 0.652 0.639

0.592 0,585

0.866 0.852 0.818

0.702 0.687 ' 0.672F-'-

0.626 0.622

0,892 0.877 0.841

0,726 0.712 0.699

0,654 0.647

0,903 0.868 0.853

0.743 0.728 0.716

0.670 0.663

' 0.905 0.691 0.859

0,753 0.739 0.727

0,681 0.674

0,899 0.888 0.858

_.758 0.'744 0/732

0,687 0.680

0.889 0.879 0.853

0.759 0.746 0.734

0.690 0.683

0.872 0.866 0.845

0.757 0.745 0.734

0.691 0.684

' 05852 0.850 0.633

0.752 0.741 0.730

0,689 0.603

0,827 0.831 0.819

0.748 0.735 0.725

0,686 0.680

0,799 0.809 0.602

0,737 0.727 0.717

' 0.681 0.675

50, 60. 70.

120. 130. 140.

1,70 1,80 - 2.00

3.00 3.20 3.40

4,40 4.60

0.223 0.214 0.200

0.1'67 • 0.'1_4' 0.160

0,149 0.146

22
EFF 20 0.695 0.578

EFF 20 0.352 0.340

EFF 20 0.299 0.295

EFF 20 0.8300 731

EFF 20' r0:488 0.474

(FF 20 0.424 0.419

EFF 20 0.893 0.827

(FF 20 0.600 0.565

-(FF 20 0.534 0.524

EFF 20 0.912 0.864

EFF 20 0.691 0.676

EFF 20 0.633 0.630

EFF 20 0:900 0.911

(FF 20 0.760 0.745

(FF 20 0.702 0.696

EFF 20 0.867 0.919

EFF 20 0.811"' 0.799

EFF 20 0.746 0.739

(FF 20 0.817 0.910

(FF 20 0.848 0.836

0_776 0.769

EFF 20 0.783 0.890

(FF 20 0.874 0.861

EFF 20 0.796 0.788

[FF 20 0.676 0.8_g

EFF 20 0.890 0.877

£FF 20 0.609 0.801

EFF 20 0.589 0.820

[FF''20 0.899 0.866

EFF 20 0.817 0.809

EFF 20 0.486 0.774

£FF 20 0.802 0.889

"LrFF 20 0:821 0.8_3

EFF 20 0.379 0.721

EFF 20 0.902 0.889

£FF 20 0.822 0.813

[F_'ZO 0:265' 0.6_1

£FF 20 0.897 0.866

EFF 20 0.820 0.812

EFF 20 0.141 0.596

[FF -20 0.891 0.880

(FF 20 0.816 0.808

RPM 15 I0. 20.

RPM 15 80. 90.

-I_PH "IB 1_0,

PR 20 1.10 1.20

PR 20 2.20 2.40

PR 20 3.60 3.80

[FF 20 0.372 0.287

EFF 20 0.156 0.149

EFF 20 0.128 0.126

EFF 20 0.602 0.491

-_FP 20 0:290 D.Z/S

EFF 20 0.243 0.239

EFF 20 0.739 0.634

EFF 20 0.403 0.390

"_ ZO 0.344 0.339

EFF 20 0.816 0.732

EFF 20 0.500 0.484

EFF 20 0.432 0.427

LPP ZO 0.8_MI O,7UU

[FF 200 S60 0.664 I

0.474

0.330

0.291

0.626

0.462

0.415

0.736

0.573

0.527

0.614

0.663

0.626

0.866

0.735

0.690

0,900

0.789

0.733

0.918

0.825

0.752"

0.925

0.850

0.781

0,922

0.865

0.794

0.912

0.874

0.801

0.895

0.878

0.80_

0.873

0.878

0.806

0.845

0.675

0.804

0.613

O, 870

O. 801

30.

I00.

• 1.40

2.60

4.00

o.zz2

0.144

0.125

0.397

0.270

0.236

0.532

0.378

0.33:

O. 635

0.472

0.423

0.713

0.551

0.422 0.405

0.321 0.314

0,286 0.285

0.569 0.549

0.451 0.443

0.411 0.408

0.682 0.662

0.563 0.554

0.524 0.522

0.766 0.749

0.652 0.646

0.623 0.619

0.828 0.813

0.727 0.721

0.685 0.680

0._72 0.859

0.780 0.772

0.727 0,722

0,901 0.892

0.816 0.604

0.756 0.750

0.918 0.913

0.838 0.826

0.775 0.769

0.926 0.924

0.852 0.839

0.767 0.781

0.927 0.928

0.860' '0.847

0.794 0.788

0.921 0.926

0.864 0.651

0.798 0.791

0.910 0.919

0.864 0.852

0.799 0.792

0.895 0.907

0.861 0.849

0.797 0,791

0.875 0,891

0.857' 0.845

0.794 0.786

40. 50.

110. 120.

0.390 0.369

0.308 0.303

0.282

0.533 0.507

0.436 0.430

0.405

0.646 0.620

0.540 0.540

0.520

0.733 0.709

0.641 0.637

0.615

0.800 0,778

0.715 0.709

O. 675

O, 649 0. 828

O. 763 O. 754

0.717

0.884 0.864

0.794 0.785

0.744

0.906 0.689

0.815 0.805

0.763

0.919 0.90_

0.828 0.618

0.775

0.925 0.913

' 0.836 0.826

0.782

0.925 0.916

0.840 0.630

0.785

0.921 0.915

0.840 0.831

0.786

0.912 0.909

0.838 0.829

0.785

0.900 0.900

0.834 0.82_

0.782

60. 70.

130. 140.

1,60

2.8o

4.20

o.193

o.14o

o.123

o.351

0.263

0.233

0.478

0.369

0.331

O. 560

0.461

0.418

O. 861

0.540

I

1.70 1.80 2.00

3.00 3.20 3.40

4.40 4.60

0.184 0.176 0.1U4

0.136 0.133 0,131

0.122 0.120

0.335 0.323 0.304

0.256 0.251 0.247'

0.231 0.228

0.460 0.445 0.421

0.361 0.355 0.349

0.328" 0.325

0.561 0.545 0.519

0,452 0.445 0,438

0,415 0.411

0.642 0.6"26 0.600

0,531 0.523 0.516

23
OF POOR QUALiT-/

EFF 20 0.510 0.505 0.500

EFF 20 0.665 0.837 0.770

EFF 20 0.647 0.631 0.619

EFF 20 0.576 0.573 0.568

EFF 20 ' r0.656 0.859 0.812

EFF 20 0.702 0.688 0.676

£FF 20 0.637 0.63! 0.626

EFF 20 0.837 0.868 0.64!

'EFF 20 0.747 0.734 0.723

EFF 20 0.686 0.66t 0,677

EFF 20 0.804 0.666 0.660

EFF 20 0.784 0,773 0.763

'[FF ZO O._Zg 0.7Z4 ' 0.720

EFF 20 0.762 0.656 0.670

EFF 20 0.813 0.603 0.794

EFF 20 0.765 0.760 0.757

"EFF ZO 0.712 " 0_639 01874

EFF 20 0.836 0.828 0.820

EFF 20 0.794 0.790 0.78g

EFF 20 0.655 0.816 0.872

0.853 0,847 "" 0.841

EFF 20 0.818 0.816 0.613

EFF 20 0.590 0.786 0.666

EFF 20 0.666 0.861 0.656

[FF 20 0,838 ' 0.036 0.634

£FF 20 0.519 0.755 0.855

EFF 20 0.675 0,871 0.668

EFF 20 0.654 0.652 0.850

EFF ZO 0.437 0.Tla 0,840

EFF 20 0.680 0.678 0.676

EFF 20 0,866 0.864 0,863

EOT

0.495 0,491 0,488

0.724 0,706 0.691 0.666

0.608 0.593 0,59! 0.584

0.563 0.559 0._55

0.772 0.756 0.742 0.719

0.666 0.657 0,649 0.643

0.622 0.618 0.614

0.609 0.795 0.783 0.763

' 0.714 0.706 ' 0.690 0_692

0.673 0.669 0.666

0.835 0.824 0.614 0.798

0.754 0.746 0.740 0.734

0.716 ' ' 0.713 0.710

0,654 0.846 0.836 0.625

0,767 0.780 0,774 0.769

• 0,753 0.751 0.748

' 0.867 0.860 0.855 " 0.645

0.814 0.806 0.603 0,798

n 785 0.763 0.780

0.873 0.870 0.667 0.660

0,835 0,830 0.826 0.822

0.611 0.809 0.807

0,875 0.875 0,874 0.671

0.852 0.64g 0.644 0.841

0.632 0.830 0,628

0.873 0.675 0.677 0.677

0.865 0.861 0.858 0.656

0,849 0.847 0.841

0,666 0.633 0,876 0,880

0,874 0,871 0,869 0,867

0.862 0.857 0.851

I I

24
270

BETA 3

RPM 15

RPH 15

RPM 15

PR 20

PR 20

PR 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

-TFF-_o

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

RPM 15

RPM 15

RPP! 15

PR 20

PR 20

PR 20

TFF 20

TFF 20

TFF _0

TURBINE FLOW FUNCTION VS, PR,

61. 68. 7,_.

I O. 20, 30.

BO. 90. 100.

-" 150.

1.10 1.20 1 .40

2.20 2.40 2.60

3.60 3.80 4 O0

68. 255 ' 82. 286 83.415

83.415 83.415 83.415

83.415 63.415 83.415

57.320 75.666 81 . 115

61.115 81. 115 61, 115

81 • !!5 01 , 115 61 . 115

49. 673 68. 861 79. 254

79. 254 79.2_4 79. 254

79. 264 ' 79,254 79,25"4

44.944 63. 159 77.026

77. 742 77. 742 77. 742

77. 742 77. 742 77. 742

42.231 ' 58.647 74. 137

76.517 76.517 76.517

76.517 76.517 76.517

40.912 55.833 71 .302

75,550 75. 550 76. 550

75. 550 75,550 75. 550

40.566 53.859 68.612

74. 769 74, 769 74. 769

74 • 769 74 . 769 74 • 769

40. 864 62. 736 66. 666

74. 192 74.192 74. 192

74. 192 74. 192 74. 192

41 . 636 62.26;7 65.45'6

73. 760 73. 760 73. 780

73. 760 73, 780 73. 780

42.717 52. 303 64.521

73.619 73.5'1"9 73.519

73.519 73.519 73.519

44 • 132 52. 746 64 . 009

73. 396 73. 396 73. 396

73,39"G 73. 396 ' 73. 39]5

45. 774 53. 515 63. 875

73. 375 73. 400 73. 400

73. 400 73. 400 73. 400

47. 558 54. 551 54.06_3

73. 422 73. 520 73. 520

73. 520 73. 520 73. 520

49. 830 55. 792 64 . 526

73. 573 73. 741 73. 746

73. 746 73. 746 73. 746

52.666 67.218 65.223

73. 842 74 • 046 74 . 070

74 • 070 74. 070 74. 070

I0, 20. 30,

8,0. 90, 100,

150.

1 . 10 1 . ZO 1 .40

2.20 2.40 2.60

3.60 3.60 4. O0

46. 554 59. 744 66.417

66. 427 56. 427 ' 56.427

86. 427 66. 427 66. 427

ii

RPM, AND BETA

40.

110,

50,

120,

60.

130.

1.50

2.60

4.20

83.415

83.415

83.416

61.115

01.115

81.115

79.254

79.254

79.254

77.742

77.742

77.742

76,517

76.517

76.517

75,480

75.5_0

75.550

74.095

74.769

74.769

72,650

74.192

74.192

71.369

73.760

73.780

70.363

73,_19

73.319

69.668

73.396

73.396

69,282

73.400

73.400

69.184

73.520

73._20

69,345

73. 746

73.746

69.734

74.070

74.070

40,

!10.

1.60

2.80

4,20

66.427

56.427

66.427

1.70

3.00

4.40

83.415

83.415

83.415

81.115

91.115

81.1'15

79.254

79.254

79 ' 254

77,742

77. 742

77. 742

76.517

76.517

76.517

75._50

75.550

75,_50

74.751

74,769

74.769

73.802

74.192

74.192

72,796

73.780

73.780

71.930

73._19

73.519

71.'297

73.396

73.396

70.695

73.400

73.400

70.743

73.520

73.520

70.826

73,746

73.746

71,123

74.070

• 74".070

50,

120,

1.70

3.00

4,40

66,4_7

66.427

66.427

i

1.00

3.20

4,60

63.415

83.415

83.415

81.115

' 81,115

81.115

79.254

79,254

79_.254

77. 742

77. 742

77. 742

76.517

76.517

76,517

75.550

75.550

7_.550

74.769

74.769

• 74.769

74,179

74,192

74.192

73.497

73.780

73,760

72.814

73_519

73.519

72.268

73.396

73.396

71.919

73.400

73.400

71'.788

73.520

73.520

71.873

73.746

73,746

72.157

74.070

74.070

60.

130.

1.00

3.20

4.60

66.427

86.427

66.427

70.

140,

2.00

3.40

' 83,415 '

63.416

81.115

81.115

79.254

79.254

77.742

77.742

76.517

76.517

75.550

75,550

74. 769

74. 769

74. ! 92

74. 192

73,780

73,780

73.490

73.519

73.2O5

73.396

73.005

73.400

72.943

73.520

73.037

73.746 "

73,287

74,070

70.

140,

2.00

3.40

66.427

66.427

25
OF POOR (_UALFF'{

TFF

TFF

TFF

TFF

--_;-F F

TFF

TFF

TFF

TFF'

TFF

TFF

TFF

TFF

TFF

TFF

TFF

' TFF

TFF

TFF

TFF

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

2O

20

20

20

20

41.255 55.777

66.427 66.427

66.427 66.427

37.670 52.242

-_6.427 66.427

66.427 66.427

35.530 49.451

66.427 66.4?7

66.427 66.427

34.501 47.430

66.427 66.427

68.427 66.427

34.272 '46.110

68.427 86.427

66.427 66.427

34.596 45.357

68,387 66.387

66.387 66.387

35.099 44.793

65.919 65.919

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

RPH 15

RPM 15

'RPlq 15

65.919 65.919

35.654 44,574

65.400 65.400

65.400 65.400

36.817 ' 44.668"

64.918 64.918

64,918 64,918

37.966 45.050

6,4.514 647535

64.535 64,535

36.203 45.636

64.114 64.217

64.217 64.217

40,599 46.414

63,799 63.996

64.000 64.000

42,086 47.339

63.576 83.834

63.863 63.863

43.622 48.382

63.455 63.739

63799 63.799

I0. 20.

80. 90.

160.

65.717 66

66.427 66

66.427 66

64.290 66

66.427 66

66.427 66

62.558 66

66.427 66

66.427 66

60.852

66.427

66.427

59,33"I

66.427

66.427

58.072

66.387

66.387

56.74 7

65 91 9

65.919

55.687

65.400

65.400

54,935

64.918

64.918

54.503

64._35

64.535

54.319

64.217

64.217

64.379

64.000

64.000

54.635

63.863

63.863

55.057

63.799

63.799

30.

tO0.

427

427

427

427

427

427

_78

427

427

65 694

66 427

66 427

64.877

66.427

68,427

63.971

66.387

66.387

62.716

65.919

85.919

61.549

65._00

65.400

60.578

64.918

64.918

59.865

64.535

64.535

69.365

64.217

64.217

59.096

64._00

64.000

59To2o

63.863

63.863

59.113

63,799

63.799

40.

110.

66.427

66.427

66.427

66.427

66.427

66.427

66.427

66.427

66.427

60.427

66 427

66,

66.

66.

66.

427

427

427

427

66,427

66.427

66.427

66.427

66.427

66,427

66.427

66.427

66.374

66.427

66.427

66.007

66.427

66.427

65.408

66.387

66.387

64.335

65.919

65.919

63.255

65.400

65,400

62,303

64.918

64.918

61.563

64.535

64.635

61.005

64.217

64.217

60.659

64,000

64.000

_o, 494

63.863

63.863

60.491

63,799

63.799

50.

120.

66.427

66,427

66.427

66,427

66,415

66,427

66.427

66.160

66.387

66.367

65.320

65.919

65_919

64.365

65.400

65.400

63.470

64.918

64.918

62.744

64.535

64.535

62.172

64.217

64_217

61.793

64,000

64.000

611583"

63.863

63.863

61.527

63.799

63.799

60.

130.

66.427

66.427

66.427

66.427

66,387

66.387

65.919

85.919

65.330

65.400

64,666

64_916

64.070

64.535

63.553

64.217

63,175

64.000

'62.929

63.863

62.812

63.799

70.

140.

PR

PR

PR

TFF

TFF

TFF

TFF

" TFF

TFF

TFF

TFF

TFF

TFF

TFF

TFF

' TFF

TFF

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

20

1.10 1.20 " 1.40 1.60 1.70 1.80 2.00

2.20 2.40 2,60 2.80 3.00 3.20 3.40

3.60 3.80 4.00 4.20 4.40 4.60

31.843 40._36 46.229 ' 46.499 46.499 46.4_9 ' 46,499

46.499 46.499 46.4_9 46.499 46.409 46.499 46.499

46,499 46,499 46.499 46.499 46.499 46.499

28,946 38,494 45.552 46,499 46.499 46.499 46.499

46.499 46.499 46.499 46"_-,499 46.499 46-499 ' 46.499

46.499 46.499 46.499 46.499 46.499 46.499

27.234 36.733 44.688 46.490 46.499 46.499 46.499

46.499 46,499 46,4_9 46.499 46.499 46.499 46.499

46.499 46._99 46,499 46_499 46.499 46.499

26.354 35.425 43.814 46.317 46.499 46.499 46.499

46.499 46.499 46,499 46.499 46.499 46,499 46.499

46.499 46.499 46.499 46.499 46,499 46.499

Z6.111 34.574 ' 43.034 46.'015 ' 46.451 461"_99 46,499

46.499 46.499 46,499 46.499 46.499 46.499 46,499

I I

26
TFF 20 46,499 46.499 46.499 46,499 46.499 46.499

TFF 20 26,350 34.136 42.408 45+672 46.294 46.497 46,499

TFF 20 46+499 46.499 4C.499 46,499 46.490 46.499 46,499

TFF 20 46,d99 46.499 46.499 46,499 46.499 46.499

"TFF 20 26,936 34.033 41.960 45,349 46.097 46,441 46+499

TFF 20 46,499 46.499 46,499 46,499 46.499 46.499 46,499

TFF 20 46,499 46.499 46.499 46,499 46.499 46.499

TFF 20 27,769 34.210 41.689 45,080 45.9_4 46.344 46,499

TFF 20 46,499 46:'499 46.499 '46,499 46.499 46.499 46.499

TFF 20 46,499 46.499 46.499 46,499 46.499 46.499

TFF 20 28,776 34.603 41.580 44,891 45.746 46.243 46,499

TFF 20 46,499 46,499 46.499 46,499 46.499 46.499 46,499

TFF '20 46,499 46.499 46.499 46,499 46.499 46.499

TFF 20 29,900 35.163 41,615 44,764 45.637 46,162 46,499

TFF 20 46,499 46.499 46.499 46,499 46.499 46.499 46,499

TFF 20 46,499 46,499 46.499 . 46,499 46.499 46.499

'_FF 20 31,101 " 35,646 41.770 44,754 ' 45.582 46,109 46,498

TFF 20 46,499 46.499 46.499 46,499 46.499 46.499 46,499

TFF 20 46 499 46.499 46.499 46,499 46.499 46,499

TFF 20 32,345 36,617 42.022 44,795 45.579 46,089 46,493

46_499 " 46.499 46,499 "'46,499 46.499 " 46.499" '46_499

TFF 20 46,499 46,499 46,499 46,499 46,499 46.499

¥FF 20 33,607 37.446 42.350 44,695 45,623 46.101 46,491

TFF 20 46,499 46.499 46.499 46,499 46,499 46.499 46,499

TFF 20 46,499 46.499 46.499 48,499 46.499 ' 46.499

TFF 20 34,868 38.310 42.732 45.042 45.703 46,138 46,492

TFF 20 46,499 46.499 46.499 46.499 46,499 46,499 46,499

TFF 20 46+499 46,499 46.499 46,499 46.499 46.499

TFF 20 36_091 39+167 43.1_I '4_,222 45.811 46.196 46,496

TFF 20 46.499 46.499 46.499 46,499" 46.499 46,499 46,499

TFF 20 46,499 46,499 46.499 46,499 46,499 46.499

EOT

J

I i II I r ....

27
"REMOVECLEARFILES

"OLD INASAPT/NASAPART

UFRN

BOB62 1_/28183 IB.ZOZ

ORiGt_',_AL ..........

OF POOR QUALtT:_;'

*'''=''''''''*''''PARAMETRIC TURBINE ='=='*'=='='''¢''"

P=A'R'T

AXIAL OR RADIAL TURBINE? |-RADIAL, B OR CR=AXIAL

-1

DESCRIPTION OF INPUT VARIABLES IN PART PROGRAM

(NAMELIST INPUT)

UNITS:TTIN=DEG R,PTIN=PSIA,W=PPS,H-BTU/LBM,N-RPM

MAP RANGE(ARRAY VALUES MUST BE IN ASCENDING ORDER)

NSPDS =15 NO OF SPEEDLINES DESIRED(MAX-IS)

APCNC ARRAY OF PERCENT CORRECTED SPEEDS

NPR "2_ NO OF PRESSURE RATIOS DESIRED(MAX-2B)

APR ARRAY OF PRESSURE RATIOS

NAR -6 NO OF NOZZLE AREA RATIOS(MAX'6)

ARN ARRAY OF FIRST STAGE NOZZLE AREA RATIOS

NSTG =6 NO OF TURBINE STAGES(MAX=6)

INTEGER SWITCHES

OCOOL =B COOLING FLOV SWITCH(B=UNCOOLED,I-COOLED)

DESIGN POINT VALUES OF:

DHOT_ SPECIFIC WORK OUTPUT DIVIDED BY TTIN

ETATTD TURBINE TOTAL-TO-TOTAL EFFICIENCY

TFFD TURBINE INLET FLOW FUNCTION

(TFF-_'SORT(TTIN)/PTIN)

XNRTD TURBINE CORRECTED SPEED(N/SQRT(TTIN))

PSID AVERAGE TURBINE PITCH LINE LOADING

PSID-DHQT/(Z'(U/SORT(TTIN_'*3/G_}_/NSTG

ANGSWX EXIT PITCH LINE SWIRL ANGLE(-COUNT-ROT)

XMZXU EXIT PITCH LINE AXIAL MACH NUMBER

TTIN TURBINE INLET TOTAL TEMPERATURE

PTIN TURBINE INLET TOTAL PRESSRUE

FARGD TURBINE INLET FUEL-AIR RATIO

ETAN NOZZLE EFF(RATIO ACTUAL TO IDEAL EXIT KE)

GEOMETRY SPECIFICATIONS:

R3QR2 PITCIILINE RAD RATIO(ROTOR EXIT TO INLET)

RHORT3 RADIUS RATIO AT ROTOR EXIT(FIRST GUESS)

NAMELIST INPUT

NSPDS = IS,

APCNC (I) =

1 IB.gBBB, 2g.g_Dg, 3B.BBB_, 4B.BBBg,

9 9g.Bg_, Ig_.g_g, IIB.B_, IZJ.BBBB,

13 13g.BgBg, I4_._B_, 15g._g_,

NPR • ZB,

APR (I)-

1 I.IB_B, 1.2B_g, 1.4_g, 1.6B_,

5 I.TBff_, I.BB_, 2.B_g_, Z.ZeBB,

9 Z.4BB_, Z.EB_B, 2.BBBB, 3.BB_g,

28
13

17

NAR

ARN

!

5

I

NSTG -

DHQTD =

TFFD =

PSID -

AN_SWXPTIN -

ETAN =

RHQRT3-

END NAHELIST

3.2B_, 3.4gBg,

4._gBS, 4.2B_B,

m ],

(I)=

l.gBg_, g. ,

t i

B.3398. 1.144g.

1, 0COOL " B,

B.B4933B,

8.3395_,

B.4871_B,

B.

37.93D_EB,

INPUT

ETATTD=

XNRTD -

XHZXD •

TTIN -

FARGD=

R3QR2 •

ENTER CHANGES TO NAHEL[ST INPUT

-$1NPUT$

NAHELIST

NSPDS " 15,

APCNC (II=

I

5

9

13

NPR

APR

1

5

9

13

17

NAR

ARN

1

5

1

NSTG •

DHQTD •

TFFD -

PSID -

ANGSWX =

PTJN =

ETAN "

RHQRT3=

INPUT

IB.BBBg,

5B.BBBB,

13g.BBgS,

= 28,

(I)=

l.lBgg,

1.7B_,

2.4B_.

3.ZB_B,

m |l

(I)-

].BBBg,

m.

g.33gB,

1,

END NAHELIST

2B.BBBS,

6B,HBSB,

IBB.BB_8,

14_.BB08,

1.238B•

2.688g,

3.4B88,

4.ZHBB,

8, |

1.144g,

3COOL = B,

B.B4933B,

B 3395BB,

8 4871B#,

B t

37 93ggg#,

B 94_BBB,

B ZgBBBg,

INPUT

NASA OUTPUT ON IFC=15,16 &

3.6BBB,

4.4BBB,

B.868BBB,

ITIS.BBBBBB,

B.Z2BBBB°

85B.BBBB_B,

B.ZgIBBB,

3B.BBBB,

7B.BS#B,

IIB.BS_B,

ISB.BBSB,

4B.BBBB,

8B.BB##,

12B.BBBB,

1.4BBB,

Z.BBgB.

3.6BBB,

4.4BBg,

|.6EBB•

2.2BBB,

3.BBBB,

3.SBBB,

4.6#BB,

8° !

I.BBBB, I.BBBB,

ETATTD=

XNRTD =

XNZXD =

TTIN •

FARGO •

k3QRZ =

B.SGSBBB,

1716.BBBBBB,

B.22BB##,

85B.B_BBBB,

B.291BBB,

29
ORIGIr_AL D_

OF POOR Q _._. C_;

269

BETA I

RPM 15

RPM 15

TURBINE EFFICIENCY VS. PR, RPM, AND BETA

50.

10. 20. 30. 40.

80. 90. 100. 110.

60. 60. 70.

120. 130. 140.

RPN

PR

PR

PR

EFF

EFF

EFF

EFF

15

2O

20

20

2O

20

20

20

150.

1.10 1.20 1.40 1.80

2.20 2.40 2.60 2.80

3.60 3.80 4.00 4.20

0.354 0.262 0.197 _.169

0.134 0.128 0.123 0.119

0.109 0.107 O.IOS 0.104

0.644 0.496 0.380 . 0,328

0.26Z 0.2_1 0.242 ' 0._34

0.214 0.211 0.207 0.205

0.82_ 0.667 0.545 0.47_

0.384 0.368 0.3_5 , 0.344

0.31_ 0.310 0.306 0.302

0.831 0.817 0.684 0.806

0.497 0.477 0.461 0.448

0.412 0.405 0.399 0.394

[FF'

EFF

EFF

EFF

"EF_-

EFF

EFF

EFF

20

20

20

20

20

20

20

2O

EFF 20

(FF 20

EFF 20

[FF 20

EFF 20

EFF 20

EFF 20

[FF 20

EFF 20

[FF 20

EFF 20

EFF "20

£FF 20

EFF 20

EFF 2O

EF_ ZO

EFF 20

EFF 20

EFF 20

"-E'FF 20

EFF 20

EFF 20

EFF 20

[FF 20

EFF 20

EFF 20

EFF 20

[FF 20

EFF 20

EFF 20

EFF 20

EFF 20

EQT

l ,

O. 461 O. 86] 0"790 O. 717

O. 600 O. 577 O. 559 O. 544

O. 502 O. 4194 O. 487 O. 441

O. 0 O. 772 O. 853 O. 802

O. 1591 0. 857 0. 647 0. 631

O. 585 O. 576 0.669 O. 562

O. 0 O. 445 O. 660 O. 856

O. 766 O. 744 O. 724 O. 708

0. 660 O. 601 D.'6dZ O. 63_

O. 0 O. 0 O. 786 O. 868

O. 825 O. 806 O. 788 O. 773

0.724 0.715 0.706 0.699

010 O. 0 0.'_91 O. 825

O. 862 O. 850 O. 837 O. 824

O. 778 O. 770 O. 761 O. 754

0.0 0.0 O, 12t 0.705

0. 674 0 '. 873 0. 967 0. 867

O. 821 O. 614 O. 807 O. 800

0.0 0.0 0 0 0.462

O. 854 O. 870 O. 874 O. 872

O. 8.%1 0." 84_ O. 839 0. 834

0.0 0.0 0.0 0.0

O. 792 O. 833 O. 85_ O. 864

O. 865 O. 862 O. 858 O. 8,'55

0.0 0.0 0"0 0.0

O. 670 O. 753 " O. 800 O. 828

O. 860 O. 861 O. 861 O. 860

0.0 0.0 0.0 0.0

0_-4_2 0.60I O. 59G ' 0.7_1

O. 834 O. 840 O. 645 O. 648

0.0 0.0 0.0 0.0

0.037 0.353 0.517 0.615

0. 770 0.79_ 0. 806 0._81

1.70 1.80 2.00

3.00 3.20 3.40

4.40 4.60

0.160 0.152 0.142

0.116 0.113 0.111

0.102 0.101

0.311 0.298 0.277

0.228 0.223 0.218

0.202 0.200

0.452 0.433 0.405

0.335 0.328 0.32I

0.298 0.294

0.579 0.657 0.522

0.437 0.427 0.419

0.389 0.385

0.689 0.666 0.628

0.631 0.620 0.610

0.476 0.471

0.778 0.756 0.720

0.617 ' 0.60_ 0._94

0.656 0.650

0.641 0.824 0.793

0.693 0.681 0.670

0.528 0.621

0.870 0.664 0.9n5

0.769 0.746 0.736

0.691 0.685

0.867 0.870 0.872

0.811 0.799 0.786

0,747 0.741

0.786 0.629 0.865

0.848 0.838 0.830

0,794 0.788

0.631 0.725 0.817

0.868 0.663 0.867

0.829 '0.824

0.330 0.522 0.709

0.868 0.869 0.867

0.851 0.847

0.0 0.122 0._10

0.843 0.6_3 0.868

0.869 0.867

0.0 0.0 0.132

0.786 0.809 0'.824

0.850 0.851

0.0 0.0 0.0

0.681 0.727 0.757

0.821 ' 0.826

3O
"j/

270

BETA 1

RPH 15

RPH 15

TURBINE

50.

10.

80.

FLOW FUNCTION VS. PR,

20. 30.

90. 100.

RPH, AND BETA

40. 50. 60. 70.

110. 120. 130, 140.

RPH 15

PR 20

PR 20

PR 20

TFF 2O

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

-"TF'F'- 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

TFF 20

EOT

150.

1,10 1.20 1,40

2.20 2.40 2.60

3.60 3,80 4.00

0.217 0.278 0.327

0.339 0.339 0.339

0.339 0.339 0.339

0.204 0.271 0,324

0.339 0.339 0.339

0.339 0.339 0.329

0.182 0.259 0.319

0.339 0.339 0.339

0.339 0.339 0,339

0,147 0.241 0.312

0.339 0.339 0.339

0.339 0.339 0.339

0.085 0.215 0.302

0,339 0,339 0.339

0,339 0,339 0.339

0,026 0,175 0,287

0,339 0.339 0.339

0.339 0.339 0.339

0.030 0,107 0.264

0.339 0.339 0.339

0.339 0.339 0.339

0.035 0.035 0.230

0.339 0.339 0.339

0.339 0.339 0,339

0.039 0.039 • 0,176

0.338 0.339 0.339

0.339 0.339 0.339

0.043 0.043 0,070

0.334 0.339 0.339

0.359 0.339 0.339

0.047 0.047 0.047

0.323 0.334 0.338

0.339 0.339 0,339

0.052 0.052 0.052

0.303 0.322 0.332

0.339 0.339 0.339

0.056 0.056 0,056

0.268 0.300 _.318

0.339 0,339 0.339

0.060 0.060 0.060

0.204 0.258 0.2_0

0.338 0.339 0,339

0,065 0.065 0.065

0.076 0.181 0.239

0.329 0.334 0.337

1.60 1.70 1.80 2.00

2.80 3.00 3.20 3.40

4.20 4,40 4.60

0 339 0,339 0.339 0.339

0 339 0.339 0,339 0.339

0 339 0.339 0.339

0 338 0.339 0 339 0,339

0 339 0.339 0 339 0,339

0 339 0.339 0 339

0 337 0.339 0 339 0.339

0 339 0.3R9 0 339 0.339

0 339

0 339 0.339

0 339 0.339

0 339

0,337 0 339

0.339 0 339

0,339 0 339

0.333 0 338

0.339 0 339

0.339 0 339

0.326 0 334

0.339 0 339

0,339 0 339

0.316 0 326

0.339 0 339

0.339 0 339

0'.298 0 314

0.339 0 339

0.339 0 339

0.269 0 293 0.321

0.339 0.339 0.339

0.339 0.339

0.223 0.259 0.301

0.339 0.339 0.339

0.339 0,339

0.141 0,201 0.268

0.339 0,339 0.339

0.339 0.339

0,0_6 0.090 0.211

0.335 0.338 0.339

0,339 0.339

0.060 0,060 0,100

0.323 0.331 0.335

0,339 0.339

0.065 0.065 0,065

0,297 0,313 0.323

0.339 0.339

0.339

0.335

0,339

0.339

0.331

0.339

0.339

0.325

O.339

0.339

0.314

0.339

0.339

0,299

0.339

0,339

0.274

0.339

0.339

0.234

0.339

0.339

0.168

0.339

0.339

0.052

0,337

0,339

0.056

0.329

0.339

0.060

0.310

0.339

0.065

0,274

0.338

0.339

0,339

0.339

0.339

0.339

0.339

0.339

0.339

0.339

0.339

0.337

0.339

0.332

0.339

31
ORIGINAL PAGE _S

OF POOR QUALI_f

7.0 ANALYTICAL BACKGROUND

The following section has been written in order to give the user a general idea of the type of turbine representation used in the progr= and the

approach used in the derivation of the equations. Details of the derivations together with sample calculations may be found in the Monthly Progress

Reports (e.g., References 10, 11, and 12).

7.1 TURBZ_TE MAP REPRESEntATION

Typically, cycle deck entry to a turbine map is through corrected speed,

N/SQRT(T), and actual energy, Dll/_, with turbine flow function, W_SQRT(T)/P,

and total-to-total efficiency being output. Total-to-total pressure ratio is

sometimes used instead of actual energy as the seco_ map _ntry.

The discussion of the turbine map representation can be conveniently

subdivided in:o two parts: the flow and the effi:iency.

The flow model is illustrated by the three sketches shown in Figure 4.

The two curves on the top in the figure are used to generate the flow representation on the bottom. Sketch 4-1 shows the turbine stage characterist_c

(i.e., a plot of turbine loading against flow coefficient). Sketch /,-2 shows

the dependence of the maximum value of the turbine flow function on corrected

speed. With the corrected speed and DH/T known, the stage loading can be

calculated, and the flow coefficieut obtained from Sketch A-1. Ouce the flow

is choked (i.e.. the choked branch of the stage characteristic), the flow

coefficient remains constant for that speed. Sketch 4-2 is next used to obtain the maxim,era value of the turbine flow function at the corrected speed of

interest. The value of the turbine flow function is then calculated. The

equations used are as follows:

• (vs/z)/[2(v/_)2/soJ]

cl_ = ($1Cos a2)IC_IA t)

.

32
Chokecl-_. b.

0.5

-0.5

0 0.5 1.0

F1ov Coeff, _ I Cz/U

4-1 Stage Characte_£s_ic

Corre=ted Speed, N/v_"

&-3 Flov Fu_c:io_ Contours

Figure 4. Turbine Flov Representation.

33
vheTe

ORIGINAL PAGE IS

OF POOR QUALITY

DE 'T " turbine s*.ase specific en*.halpy drop divided by ir.le', total

te=persture, _tu/lbw R

E/SQRT(T) " corre=te_ speed, R_M/SQRT(E)

C

• pi_ch line radios, ft

• velocity, ft/sec

= speed of sound at inlet total te=pera_ure, f=/se=

= i_let turbine flo_ function, lb=/sec*SQ_T( R)/psis

Cos(= 2) - nozzle exit ankle ..

The value of Cos(= 2) is obtained frcB the design point _r, forna:ion as

is the value of the pitch line radius.

The efficiency =odel is illustrated by the five sketches shown i_ Fi=ure

5. The f_rst three curves in =he figure are used to generate the last _.'o

sketches. ._e "backbone" of the turbine _,_ shorn in Sketch 5-_ is the locus

of _he peak eff_cienc_ at each value of DR/T. Th_s locus is obtained fro=

Sketch 5-1, which shc_s turbine pltch line loading along the map "backbone"

as = fu_¢ticm of DE/T. The "backbone" efficienc_es are obta_ned fro= Sketch

5-2. This sketch g_ves the "backbone" loss (defined as the d_fference be-

_ee_ the ides1 =md actual values ©f D_/T) as 8 f_c_ton of DE/;. _th =he

"bsckbo=e" loa_=_ a=d eff_c_e_cies k_ot_ at each DE/_, Ske:ch 5-3 is used to

evslu=te the "off-backbcme" loss and to obta_ the efficiency at sm_ value

of corrected speed. When the =urbane "off-backbone" loss is plotted w_th the

coordinates shc.._ in Sketch 5-3, the resultlnE curves are =early linear at

a_y _an DE/_. These five curves, _hree m_ivariate and t_a_ b_variste, ere

sufficient to define _he turbine _.p. Rote that as sbov_ _ Sketch _-5, the

desl_ point does not genera!IT fall on the '_ackbone" but is sepers_ed fro=

_t b7 a "s:a_d-off" distance vhich is calculated fro= desiL_ pclnt _nforv.mfinn.

_ne analytical basis for =he five correlating ¢urves is dis:ussed _n the

follovin= sections.

7 . 2 T_..'_I_IR_ T!..OV MODEL

"The turbine stage characteristic serves as the basis for model i_q_ the

turbine flow. An ana!T_¢al expression for the s_age characteristic of s

turbine can be obtained by using =he continuity, energy, and angular

momentu_ equations, together w_th a number of relationships from the pitch

line vector diagram. In deriving this equation, it is assu_ed that the pitch

line flow angles at nozzle and bucket exit are invariant, and that the axial

velocity ratio across the bucket is constant.

34
Q

o

C_ ....

i ii

=

e=

Actual ]_nerL_" , D_/T

5-1 Backbone Loading

_,,4 t _

I

-1(_/_Bk_1) l(_/_Bk.1 ) [1 Corrected Speed, N//T

5-3 loss Tuncclon 5-_ 3ackboue Locus

"I""

i=_"+

Corrected Speed, S/_/T

$-5 Efficiency Ccnncours

YLsure 5. Turbine Eff_cLency Representation.

35
...... _ .... --- ---_ --L

ORIGINAL PAGE IS

OF POOR QUALITY

This later a_-s=:ytlor, _e reasonable for incc_ress_._le or Io_" M_cb num.,beT (_ 0.:5)

flows. It sho_'d b_ e_-_haE!zed, however, that the f:na _. co=relations h_ve n_ su:h

reset _.ctions.

The sta_ characteristic for a sln£1e-sta_ tur_.:_t _th :be abov_ as-_'.--y:_ns

ca._ be wrltten in the fc._-.

%_ere

%

_2 =

_3 "

R =

= DEI(2U /goJ), Turbine stage Loa_ins

= Meridic_al velocity co..-_o_ent

- Cz2/_2, _low coefficient

Nozzle exit flc_- an_le

Bucket exit flow angle

Turbine Pitch Line Radius

|

Selectin_ • :el•fence point _8 assu_Ln& _hat

C• 2 _ ts_ _3 " s consts_t,

this equa:_may be v_Itten as

;%

(2)

$6

1re: SmCb=iLe_ flo_, the refe:e_ce l_,_t (ib_cste_ b_ t_e s.bscri_ _, v_s

selecze_ •: _he des_|t_ print on the :u_i_e _p. For chek_4 f;c_, the re_e_-

_r_ce _¢i=: vie selec_e_ at the critical 1_i_: (su_sCril_t [;MY) on tl_e tm'l_ne

map. The ¢r_tica_ pci:'.t is l_>ce:ec_ •t the value of D_,'Ta_ t_e refe_e,,ce

spee_ (e.8., lO_:) v_ere _¢sle r,b©kin| firs: o:c,_s. Y=_ J _S_/_le-sec_s_tr.

tur_i_e, the _n|le 12 il cll©u}i_e4 fra_ the _:pu: tl_Ue of u=ttle _ea ra_.

L . . (3)

Toe _ilocity r•t_o, ClOt, for • lpei.ut 8: • stle:_e_ speed is dete_slne_

by calc_Iet_| • pseu£©a_es st shah the _b u_er is &80_ tO _)_I_

(i.e., at the u_ turbine flov fraction [or the: •pee_). T_,_s _se_._sTa•

is i|ll/_e_ t_ be cons:ant f©. _hat epee_. T_t Kate. u_r._e: (_eloc_t_ r_L_)

at _n_ _int on the spee_ line is then c•lculete_ fr_ the uo.al fie.. fern,crier,

• eq.stions. J_ definition, tt_t pseudo•tea _sr_es v_t_, spee_ ie direct I_¢_r"

t_on to the ns:t;-_.n turb_._e flov f_mct_n _•r_.oti©n with speed. Tr,is setho_
OF PO©i:_ QL:AL_'Y

of calculating the flow coefficient yes found to give better results than

the _. obtained using the first stage nozzle throat area for all speeds. For

the case in which the first stage nozzle is choked, the tvo procedures are

identical.

TTpically, the calculated and measured values of velocity ratio are

vithin about 6_, viCh the larger errors occurring at the higher _.ach numbers.

The predicted value of the normalized flow coefficient intercept (ac DP./T=0)

are vichin about .SZ of experimentally derived values. These errors combine

co yield flov errors on the order of 5Z for nominal ares maps (i.e., nozzle

are• ra_.ios equal to 1). Slightly higher values may occur for ocher scacor

sect ings.

A typical comparison becveen measured and calculated v•Iues o£ the curbine flov function is shorn in Figure 6. This figure is for Cesc turbine

u,,mber 25 in Table 1. The maxim,m error shorn on this figzJre is about 2.&Z

and occurs ac the lover end of the test dace. This type of plot was used in

obtaining the error esti_naces given above.

7.3 TUI_IN_ LOSS MODEL

There ere four key seeps in the development of the equations governing

the turbine off-design loss model. These |Ceps are

. The development of an equation giving the turbine total-to-total

efficiency ac a general point in terms of nozzle and bucket efficiencies coupled vich a semiempirical loss term due to the depar-

• Cure of the rotor inci6ence angle from the opChn,_.

The trensfor=ation of the semiempirical incidence angle loss law

so as to elhninate the explicit occurrence of the incidence angle

by introducing the stage loading.

. The differentiation of the resulting efficiency expression in

order co obtain the locus of peak efficiencies.- This peak efficiency ridge chert becomes the "backbone" of the map.

The substitution of the peak efficiency relationships back into

the general efficiency equation in order Co obtain an expression

for the "off-backbone" loss.

The development of the efficiency expression proceeds from the (h,s)

diagrm for adiabatic flov through • cvo-d/_ensior_l turbine stage as shown

_n the folloving sketch.

3?
ORIGINAL PAG_ |_J

OF POOR QUALITY

63

62

61

l-.

3 60

_" 59

58

57

55

0.02 0.03 0.04 0.05 0.06 0.07

AcCual E_erEy, DHQT

O VAT2-SX (AR = 1.0)

Q Calculated Values

s/,'_" = Is3.5

(100_ Corrected Speed)

l I

0.08

Figure 6. Comparison of Measured and Calculated Values of Inlet

Turbine Flow Function.

38
i

b

mL-.- i

b=

_tropy, $

Enthalpy-Ent_opy Diagr_ for a Turbine Stage

Using the station =,,tubers shorn _ the abc_e sketch, the definition of

turbi=e total-to-total effic_ency ,_,y be vritten in the form:

By definition, the nozzle efficiency is equal to the ratio of the actuel

nozzle exit kinetic energy to the ideal nozzle exit kinetic energy. A similar

definition in terms of relative velocities holds for the bucket efficiency.

For off-design calculations at any incidence angle (i), an additional loss

term must be included, i.e.,

,,-,,.-(,-k)_. (,-oo.,,.,)_ c_)

v_ere

- nozzle efficiency

T1B - bucket efficiency

W2 - bucket inlet relative velocity

W3 - bucket exit relative velocity

39
OF POOR QUALI+Ff

The semiempirical incidence angle loss law is based on the assumption that

the kinetic energy of the component of velocity normal to the optimum incidence

angle is lost. This is a fairly standard assumption (see, for example, Reference 4).

Powers other than 2 are frequently used on the cosine.

Before introducing the incidence angle loss term into the efficiency expression,

it was transfored into the following expression

The stage characteristic was then used to substitute for flow coefficient in

terms of stage loading. The substitution of this results into the expression for

efficiency yielded, after simplifying, the following results.

(7)

u --, - +- IL-';

6- (8)

(9)

The temperature ratios in Equations 8 and 9 are of order one as is the bucket

axial velocity ratio. If these ratios together with the blade row efficlencies and

exit flow angles are assumed to remain constant then Equation 7 can be differentiated,

and thepeak efficiency point located.

_,_ = (_r_ _A _ q°e (lO)

L > (11)

Note that if the nozzle and bucket efficiencies equal unity in Equation (9),

then A=0.0. Then there is no loss other than incidence and Spk = Sop as

expected.

40
ly substituting Equations I0 and Ii into Equation 7, the following expression for "off-backbone" loss can be obtained.

Spk "_ " *pk (_A + B) - I1: (12)

Equacionm I0, 11, and 12 give the location of the peak efficiency, the

magnitude of the peak efficiency, and the variation Lu efficiency as we move

sway from the peak.

These equations represent the stage loss characteristic of • turbine.

The design point inforlation _s used to obtain the initial v•lues of A and B

as _II as the values of the blade roy efficiencies and metal angles. The

loss equations are then applied at incremental values of DHQT st•reins at

zero to obtain the turbine egficieucies. Approximate retationships are used

for temper•cure and velocity ratios to obtain new values of A and B got each

T_pically, the calculated values of the loss slopes and those obtained

from air turbine test data are _[¢h_n about _ for corrected speeds v_th_n

plus or minus 20_ of the des_.$n point value. The val_es of the "backbone

ef£iciencies" |•her•ted by the above equ•cions do not include either l_eynold's

Number effects or the severe rotor exit losses encountered near exit annulus

choke. In order to account _or these effects, the loss along the peak e_iciency rids• _a• _mpiricslly modified usin_ the results of the NASA air

turbine tests. Althoush relatively _ood correlation existed between the

d_gferent test turbines at lo_ values of DItQT, the drop in eggic_e_-y in the

ne_shborh.ood of exit annulus choke _as so severe th•t correlation _•s dt_icult. For this reason, variations in efficiency on the order o_ _ can be

obtained _n this region.

A comparison between measured and calculated values of the turbine cot alto-tots1 efficiency is shown _n F_gure 7. This figure _s for test turbine

number 25 in Table I. The saxi_,_ error shown on this fisure is about 0.8_.

This type of plot _as used in obtaining the error estimates _iven above.

41
0.96

W,J

W,*

q

4_

o

p=

!

0

4g

!

ig

0

w_

w,

[-

0.94

0.92

i

0.90

0.88

0.86----

O. 86

0.82

0.02

,/

0.03

•- 0.8%

i •

i

l

O VAT2-SX (AR = 1.0)

D Calculated Values

N/,/_" = 193.5

(lOOZ Corrected Speed)

O. 04 O. 05 O. 06 O. 07 O. 08

Actual Energy, DI_QT

Figure 7. Comparison of Measured and Calculated Values of Total-to-Total

Efficiency.

42
7.4 Comparison of Radial Turbine Test Results and Program Output

A comparison was made between the program output and the "SOLAR" radial

turbine described in Reference 20. The key design point parameters are summarized

in Table IV. These values are used as the default settings for radial turbines as

shown in the second example in Section 6.

The performance map is shown in Figure 8. The exit annulus choke curve forms

the physical limit of the map. The portion of the map above this limit line represents a mathematical extension of the map which is necessary for cycle deck

iteration purposes. The predicted swirl map is shown in Figure 9. The predicted

equivalent weight flows are compared with the test data in Figure i0. The solid lines

are the predicted values. In Figure II the total-to-statlc efficiency is compared

with the so-called blade to jet speed ratio. This parameter is the ratio of the inlet wheel speed to the velocity calculated by expanding the flow isentropically

through the inlet total to exit static pressure ratio. This is the usual manner of

presenting radlal-turblne efficiency data. The solid lines are the predicted values.

The sharp breaks in the lines are due to interpolation. Values of DH/TA at intervals

of 0.005 were used to read the map efflciencles and flows from Figure 8. The breaks

are due to missing the peak efficiency at a given speed. A smaller interval could not

be used due to size limitations on the program.

In general the comparison is quite good, and is probably within the accuracy

that the data could be read from the relatively small curve given in Reference 20.

43
ORIGINAL PAGE IS

OF POOR QUALITY

TABLE VI.

...., .....

Design Point Data - INFLOW Radial Turbine

NSTG

_CR2

T1

P1

P1/PS3

i;1

DECTD

EIATTD

PSID

Trn)

]MZXD

ANGS"_

VZ3C2 (i)

ANGS2

SOLAR (REF. 20)

Rotor Dia. - &.75"

II I I I

1

0.291

0.200

2.375-in

8500R

37.9 psia

2.53

0.433 pp$

0.0_93

(_.868

O.AS?

O. 3395

1718.0

0.22

0.0

0.:33

-1. S°

44
Exic Annulus Choke

: l

SOLAR-RADIAL

r _-_ - - -

(.

TURBINE

I

320

PLTOO I

Figure 8. Radial Turbine Performance Map.

45
ORIGINAL PAGC i.S

OF POOR QUALII','

_i_"

d_

C_

_D

Z

cg,

I

...1

Z

...1

0"I

SN I RL M_P

i

r

• I

Figure 9. Radial Turbine Swirl Map.

46
OH i C _ _ '_:_

T

PCNC

120

lO0

8O

60

::k! ....

r- 1

08/Lg/B3

10 .b46

I

!

lI:

I I

l

Figure i0. Radial Turbine Flow Comparison.

d7
ORIGINAL PAGE I9

OF POOR QUALITY

I

PCNC I

120 I

I00

A

0

0

0

l

T

2B .3b

r

• i

r

"i--÷ "

..... k....

t i

t _"

.$2. .60 .bB .76

BLAOE-JET SPEEO RAT[O

(Solar 4.75-in. Dla. Radial Turbine)

Figure ii. Radial Turbine Efficiency Comparison.

d8
L!_T OF $.vM._LS

A,a

),b

C

¢p

8o

h

t

J

P

KI

S

T

U

W

o

I

At]

e

¢

_n|tant|

Conltant i

Veloc ity, fp8

Conic&hi Pressure Specific I;eat. B:u/lb_'R

D_ensio_l Constant, 32.17 ft lb_/lbf sec 2

Z:ChaI py, )t u/lbm

Incidence Angle (i = |2 - e2o_), degrees

l_cha,_cal Vquivalenc of Beat, 778.16 ft. lbf/Btu

Spe ed, rl:_

PTessure L p.sia

P.adiua, ft

Gas Coust_.t, 53. 35 ft lbf/lb='R

_t_opy, Btu/lbm'R

Absolute T,_persture, " It

Wheel Speed, fpl

itelat_.ve Veloc;-ty, fps

Angle of Absolute Velocity _i_h Ax_aI, degrees

/mile of i_lstive Velocity Vector rich Axial, degrees

Drop in Total EnthalpT, Btu/lbm

i_t_o of Specific Beats

Znthalpy _s, Coeff_.cit_t

Fluid Density, llm/ft 3

ILttio or Total Taperature _o Sc_dard Te=perature

q,_urbine Stale Ix>ading [V " AS/CI_32/IoJ)]

lrlem Coefeictent (* " Cz/U)

Zfficten_y

Subscripts

1

2

3

)

d

0

op

pk

Tr

S

g

Nozzle Inlet

it_tor Inlet

i_tor Exit

ltucket

Design Point Val_e

lk:zzle

St qnat ion

Opt tn--

Peak

Tot al-to-Toc al

Isen_ropic

tx in1

49
L)RLGII'_AL PAGE IS

OF POOR QUALITY

ItEFE_NCES

,

e

_e

Go

e

*

e

Fishbach, Laurence R., and Caddy, M_chael J., "b'NEP: The Navy-_ASA

Enl£ne Progr_," RASA _q X-71857, 1975.

Fishbach, Laurence H., "Zonfig and Rekonfig - Two Interactive PreProcessing Programs to the NAVY/NASA Engine Program (_EP " NASA

_.T_'_.-_2636,May 1981.

I0.

Geun_ner, James W, "A1|orit_ for Celculatin$ Turbine COoI_._ Flow and

the Resultin$ Decrease in Turbine Ef£iclency," RASA _M81453, Feb.,

1980.

11.

Flatg, I.E., "Analytical Procedure and Compu:tr Progr-- for Decenaining

the Off-Desig_ Perfor1|ance of AxialoFlov Turbines, " I_ASA CR-710, March

1966 (bE 167FPD29A, August 1967).

12.

Whitney, Warren J., Szanca, Edward M., Sider, krmar8, and Monroe,

Daniel [., "Cold-Air I_vestigac_on of • Turbine for High-Te_npera=ure

Application. lit - Overall Stage Perforaance," IIASA Tlq D-_389, 1968.

Whitney, Warren J., Sch_, Barold, and khni._, Yr_k P., "Cold-Air

Ynvestigaticn of s Turbine for Rish-Tempere_ure Application. IV -

Two-Stage Turbine Ferforsaoce."

Schtm, Warold J., Moffitt, Thomas P., and Behning, Frank P, "£ffecl: of

Variable Stator Area on Performance of a Single-Stage Turbine Suitable

for Air Cooling. 1%1 - Turbine Perforaance With 130-Percent Design

S_ator Area," RASA TM X-1663. 1968.

Schun, Eerold J., Seance, Edward M., and Pruet, Herman W., Jr., "Effect:

of Variable S_etor Area on Performance of a Single-Stage Turbine Suitable for Air Cool,rig. V_ - Turbine Performance W_tb 70-Percent Design

Starer Area," NASA 2_J X-1697, 1968.

Ylagg, _.!_., "Analysts of Overall and Internal Performance of Variable

_eome:ry One- and _ac-Sca_e Axial-Flow Turbines," RASA CR-SA_A9 (GE 166

FPD259), 1966.

Converse, G.L., "TurbLne Modeling TechnLques to Co,erase Off-Deslgn

Performance Data for _o_h Single and _lci|tage Axial F:ov Turbines,"

November Monthly Progress Report, General Electric, R?gAEG59_-2,

l_ov e_ber, 1979.

Converse, G.L., "Turbine Modeling Techniques to Generate Off-Design

Performance Da_e for ]k_Ch Single and Multistage Axial Flow Turb£nes,"

December Honthl 7 Progress Report, General Electric, R79AEG598-3,

December, 1979.

Converse, G.L., "Turbine Modeling TechnLques co Generate O_f-Desiwn

Performance Data for Ik_th Single and _ltistage Axial Flow Turbines,"

February Monthly Progress Report, General _lec_r_¢, R79AEG598-5,

February, 1980.

5O
REFERENCES- (CONTINUED)

Small Axial Flow Turbine

13. Schlegel, J.C.; Liu, H.C.; Waterman, W.F., "Reduction of End-Wall Effects

in a Small, Low-Aspect-Ratlo Turbine by Radial Work Redistribution",

Journal of Engineering for Power, Trans. ASME, Series A, January 1976.

14. Stewart, W.L., "A Study of Axlal-Flow Turbine Efficiency Characteristics in

Terms of Velocity Diagram Parameters, ASME Paper No. 610-WA-37, 1961.

15. Holeski, D.E.; Steward, W.L.; "Study of NASA and NACA Single-Stage Axial

Flow Turbine Performance as Related to Reynolds Number and Geometry,"

Journal of Engineering for Power, Trans ASME, July 1964.

16. Wong, R.Y.; Nusbaum, W.J.; "Air-Performance Evaluation of a 4.0-1nch-MeanDiameter Single-Stage Turbine at Various Inlet Pressures From 0.14 to 1.88

Atmosphere and Corresponding Reynolds Numbers from 2500 to 50,000", NASA

TND-1315,1962.

17. Ohlsson, G.O.; "Low Aspect Ratio Turbines", Journal of Engineering for Power

Trans. ASME, Series a, Vol. 86, 1964, pp. 13-17.

Radia_ Flow Turbines

18. Lane, J.M., "Cooled Radial In-Flow Turbine for Low Specific Speeds and Low

Velocity Factors", Paper presented at the Gas Turbine Conference and Products

Show, ASME, March 9-12, 1981.

19. Rohlik, H.E.: Kofshey, M.G.: "Recent Radial Turbine Research at the NASA Lewis

Research Center", ASME 72-GT-42, 1972.

20. Rogers, Colin, "Efficiency and Performance Characteristics of Radial Turbines",

SAE Paper 660754, 1966.

21. Futral, Samuel M.; Wasserbauer, Charles A.; "Off-Design Performance Prediction

with Experimental Verification For a Radial-Inflow Turbine: NASA TND-2621, 1965.

22. Rizika, J.W., et.al., "The Design and Performance Analysis of Radial in Flow

Turbines", in 2 volumes, NREC Report No. 1067-1, 1067-2, Northern Research and

Engineering Corporation, Cambridge, Massachusetts, 1964.

51
REFERENCES - (CONTINUED)

23. Wood, Homer J.: "Current Technology of Radial-Inflow Turbines for Compressible Fluids", Journal of Engineering for Power, Trans. ASME, Series

A, Vol. 85, 1963.

24. Knoernschild, E.M.: "The Radial Turbine for Low Specific Speeds and Low

Velocity Factors", Journal of Engineering for Power, Trans. ASME, Series

A, Vol. 83, 1961.

52
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