NASA Contractor Report 175066

Characterization of Real Gas Properties

for Space Shuttle Main Engine Fuel

Turbine and Performance Calculations

(NASA-CR-175066) CHARACTERIZATION OF REAL N86-27418

GAS PEOPEETIES FOE SPACE SHUTTLE MAIN ENGINE

FUEL TURBINE AND PEBFOBMANCE CALCULATIONS

Final Report {Sverdrup Technology, Inc.), Unclas

97 p BC A05/MF AQ 1 CSCL 21H G3/20 43234

Gary J. Harloff

Sverdrup Technology, Inc.

Lewis Research Center

Cleveland, Ohio

June 1986

Prepared for

Lewis Research Center

Under Contract NAS 3-24105

NASA

National Aeronautics and

• Space Administration
TABLE OF CONTENTS

Page

SUMMARY 1

INTRODUCTION 1

NOMENCLATURE 2

THERMODYNAMIC PROPERTIES 3

MIXING RULE 3

H2 THERMODYNAMIC AND TRANSPORT PROPERTIES ..... . 5

H20 THERMODYNAMIC AND TRANSPORT PROPERTIES 5

H2/H20 THERMODYNAMIC AND TRANSPORT PROPERTIES 5

AIR THERMODYNAMIC AND TRANSPORT PROPERTIES ... 7

MIXTURE PROPERTIES ........ . 7

AIR EQUIVALENT CONDITIONS 8

SSME FUEL TURBINE PERFORMANCE CALCULATION . 9

SUMMARY OF RESULTS ....... . 9

REFERENCES 10
CHARACTERIZATION OF REAL GAS PROPERTIES FOR SPACE SHUTTLE MAIN ENGINE

FUEL TURBINE AND PERFORMANCE CALCULATIONS

Gary J. Harloff

Sverdrup Technology, Inc.

Lewis Research Center

Cleveland, Ohio 44135

SUMMARY

Real thermodynamVc and transport properties of hydrogen, steam, the SSME

mixture, and air are developed. The SSME mixture properties are needed for

the analysis of the space shuttle main engine fuel turbine. The mixture conditions for the gases, except air, are presented graphically over a temperature

range from 800 to 1200 K, and a pressure range from 1 to 500 atm. A1r properties are given over a temperature range of 320 to 500 K, which are within the

bounds of the thermodynamics programs used, 1n order to provide mixture data

which 1s more easily checked (than H2/H20) . The real gas property varlatlon of the SSME mixture 1s quantified.

Polynomial expressions, needed for future computer analysis, for viscosity,

Prandtl number, and thermal conductivity are given for the H2/H20 SSME fuel

turbine mixture at a pressure of 305 atm over a range of temperatures from

950 to 1140 K. These conditions are representative of the SSME turbine

operation.

Performance calculations are presented for the space shuttle main engine

(SSME) fuel turbine. The calculations use the air equivalent concept. Progress

towards obtaining the capability to evaluate the performance of the SSME fuel

turbine, with the H2/H20 mixture, 1s described.

INTRODUCTION

The SSME fuel turbopump operates with a mixture of H2 and H20 at about

330 atm and 1105 K. These conditions are such that actual gas dynamic measurements 1n the turbine are difficult to obtain. One computational tool at NASA

Lewis for analyzing turbomachlnery 1s the combined computer programs of Katsanls

and McNally (refs. 1 to 4). The program accepts constant thermodynamlc and

transport gas property data for each blade row. A current limitation of the

analysis 1s that the boundary layer program (ref. 2) requires the temperature

dependence of the transport properties to be Input as a polynomial function.

The program has thus far been limited to air properties.

The goals of the present study were:

(1) Determine the H2/H20 mixture thermodynamlc and transport

properties variation

(2) Calculate the air equivalent performance
(3) Curve fit the variation of y, Cp, and Pr with temperature at the

appropriate pressure

(4) Calculate the H2/H20 mixture performance accounting for property

varatlons from blade row to blade row

(5) Modify the Katsanls and McNally computer programs to account for real

gas effects.

The first three goals are addressed herein.

NOMENCLATURE

2cact

2 2

CId/Cact

CP

Cv

H,h

k

M

n

Pr

Rld/Ract

Rp

R

S

T

W/Wcr

Z

sound speed

actual sound speed squared, c

Ideal/actual sound speed squared

specific heat at constant pressure, J/g-K

specific heat at constant volume, J/g-K

enthalpy, J/g

thermal conductivity, J/cm-s-K

molecular weight

mole fraction

Prandtl number

total pressure, atm

pressure, atm

Ideal/actual gas constant ratio

total pressure ratio

gas constant

entropy, J/g-K

sea level temperature

total temperature, K

temperature, K

relative velocity/relative velocity at sonic condition

compressibility
(3p/3p)j

(ap/3T)p

B

Y

5

n

X

v

<j>1j

partial derivative of pressure with respect to density at constant

temperature, atm-cc/g

partial derivative of pressure with respect to temperature at

constant density, atm/K

relative flow angle, deg

ratio of specific heats

degrees of freedom

efficiency

transport property

molecular viscosity, g/cm-s

density, g/cc

mixture property

THERMODYNAMIC PROPERTIES

Real gas properties for H2 and H20 at elevated temperature and pressure are reported by Hendrlcks et al. (refs. 5 and 6), Goldberg and Haferd

(ref. 7), and McCarty (ref. 8). All of the literature reviewed for hydrogen

and steam present empirical relationships; theoretical relationships apparently

do not exist. In contrast, a good theoretical real gas basis exists for air,

see for example HUsenrath and Klein (ref. 9). Perfect gas properties are

available for hydrogen, Svehla (ref. 10) or the JANNAF tables (ref. 11). The

JANNAF tables do cover real gas properties for ^0. Raznjevlc (ref. 12)

presents a comprehensive collection of thermodynamlc properties.

The Roder (ref. 13) 1975 parahydrogen report covers temperatures from the

triple point to 700 K for pressures up to 3000 atm. The valid range of temperature and pressure for the NASA computer programs GASP (ref. 5) and WASP

(ref. 6) are given 1n table I. 'GASP' and 'WASP' stand for gas properties and

water and steam properties respectively. The temperature of Interest, 1100 K,

1s higher than the limit of 1000 K, but the programs are believed to be appropriate for the current study. The computer programs GASP and WASP were modified such that mixture properties could be easily calculated.

MIXING RULE

It was assumed that the gas components occupy the entire space at the

mixture temperature and pressure. For each gas, the mass dependent properties

were divided by molecular weight and, except for viscosity and conductivity,

the mass Independent properties were mole fraction weighted, e.g.,

Hm = nh =
Sm = ns =

m

nm1x =

Pm1x =

where the overbar represents mole basis properties. The other properties are:

where

__ s

c

 =

•**• Z + T

P x- -,p

C

"

 CV

 = 2 /3£\

WT

z

T

and

z" W\ H /mixture

The GASP and WASP computer programs compute the partial derivatives ap/3T|p

and ap/ap|y. Other partial derivatives are obtained by Maxwell's equations.
For viscosity, and thermal conductivity, the mixing rule of W1lke

(ref. 14) was used. The mixing rule 1s:

where \] 1s either viscosity or thermal conductivity of gas 1.

H2 THERMODYNAMIC AND TRANSPORT PROPERTIES

Thermodynamlc and transport properties for H2 are presented 1n figures 1

to 20 for a range of temperatures from 800 to 1200 K and pressures from 1 to

500 atm. The real to perfect sound speed squared ratio varies from 1.0 to

1.13, the perfect to real gas constant ratio varies from 1.0 to 1.027, and

compressibility varies from 1.0 to 1.13. The enthalpy and entropy are not

zero at their respective reference temperatures e.g., 298 and 0 K due to the

empirical nature of GASP and WASP. The shift 1s not Important 1n the use of

the enthalpy and entropy as only differences are of Interest. The quantities

of Cp/R and CV/R approach their theoretical limits of (?'+ 2)/2 = 3.5

and |/2 = 2.5 where 5 = 5 1s the molecular degrees of freedom.

H20 THERMODYNAMIC AND TRANSPORT PROPERTIES

Thermodynamlc and transport properties for H20 are presented 1n figures 21

to 40 for a range of temperatures from 800 to 1200 K and pressures from 1 to

500 atm. The real to perfect sound speed squared ratio varies from 0.65 to

1.0, the perfect to real gas constant ratio varies from 1.0 to 7.4, and compressibility varies from 0.61 to 1.0. As previously mentioned the enthalpy

and entropy are not zero at their respective reference temperatures. The

quantities of Cp/R and CV/R approach their theoretical limits of

U + 2)/2 = 4.5 and 5/2 = 3.5 where 5 = 7 1s the molecular degrees of

freedom.

.H2/H20 THERMODYNAMIC AND TRANSPORT PROPERTIES

Thermodynamlc and transport properties for H2/H20 are presented 1n figures 41 to 60 for a range of temperatures from 800 to 1200 K and pressures from

1 to 500 atm. The H2 and H20 mole functions of 0.8687 and 0.1313 were

determined by a computational analysis of the combustion process (ref. 15).
The real to perfect sound speed squared ratio varies from 1.0 to 1.19, the

perfect to real gas constant ratio varies from 1.0 to 1.39, and compressibility

varies from 1.0 to 1.075. Again, the enthalpy and entropy are not zero at

their respective reference temperatures. The ratios of Cp/R and CV/R

approach their theoretical limits of U + 2)/2 = 3.5 and 1/2 = 2.5 where

5 = 5 1s the molecular degrees of freedom.

The boundary layer code requires that y, Pr, and k be known polynomlnals 1n temperature. Obtaining these polynomials removes the limitation of

using air equivalent conditions. Thus, these transport properties for the

hydrogen/steam mixture were fit using polynomial relationships for future

turbine performance use. The polynomials were Initially assumed to be up to

4th order 1n the temperature to sea level temperature ratio (T/Tsi) as the

boundary layer computer program (ref. 2) needs this form. The pressure 1s for

305 atm and temperatures vary from 950 to 1140 K. The functional dependence

of the transport properties on T/Tsi follows:

molecular viscosity

yj.T\ » 0.2171 + 0.17677

y(Tsl)

Prandtl number

Pr = 0.62366 - 0.015834 £r-\ - 0.61071E-04 (~

VsU \V

thermal conductivity

k(T

= 1.1879 + 0.032504

where:

T 288.16 K,

y(T ,) = 0.3345E-03, ~

k(Tsl) . 0.19E-02 ~

An obvious problem with this approach 1s that the transport properties are a

strong function of pressure which 1s not accounted for by this form of the

equations.

For eventual use 1n TSONIC (ref. 1), MERIOL (ref. 3), and BLAYER (ref. 2)

the options to account for real gas effects 1n the thermodynamic and transport

properties Include: (1) using GASP and WASP and calling these subroutines as

needed, or (2) curve fitting these data as functions of T and P and calling

the empirical representation of the computer programs. The forms of GASP and
WASP computer programs are such that they can be use as (1) above with no

additional work.

AIR THERMODYNAMIC AND TRANSPORT PROPERTIES

Thermodynamlc and transport properties for air are presented 1n figures 61

to 80 for a range of temperatures from 340 to 500 K and pressures from 1 to

500 atm. Real to perfect sound speed squared ratio varies from 1.0 to 1.65,

the perfect to real gas constant ratio varies from 1.0 to 1.85, and compressibility varies from 1.0 to 1.31. As previously discussed, the enthalpy and

entropy are not zero at their respective reference temperatures e.g., 298 and

0 K. The quantities of Cp/R and CV/R approach their theoretical limits

of £ + 2/2 = 3.5 and 1/2 = 2.5 respectively, where 5 = 5 1s the number

of molecular degrees of freedom. Real gas properties are given by Hansen

(ref. 16) and Hansen and Helms (ref. 17).

MIXTURE PROPERTIES

For real gases, most of the thermodynamlc and transport properties are

functions of temperature and pressure. Using the static properties given by

Jackson (ref. 18) see table II, the following property variation was

calculated 1n this study:

8.00 < C_ < 8.08 ~

 J

p - "•*"' g_K

1.375 < y < 1-378

1.073 < -^~ < 1.076

R

act

c

2

1.04 < ~^~ < 1.05

"

 Cact ~

0.278X10"3 < w < 0.293X10"3 ~ -?— ~ ~ cm-s

0.563 < P < 0.565

0.396X10"2 < k < 0.419x10

 2

cm-s-K

From the above, the variation 1n the gas properties are: the gas constant 1s

about 7.5 percent lower than the Ideal gas constant, the actual speed of sound

1s about 2 percent lower than the Ideal, viscosity decreases by about

5 percent, and thermal conductivity decreases by 5 percent through the turbine.
AIR EQUIVALENT CONDITIONS

A1r equivalent conditions can be used as a performance reference,

(ref. 19). A1r equivalent conditions of the H2/H20 mixture were obtained

for the Inlet conditions. The Reynolds number and total temperature were held

fixed between the gas mixture and the air equivalent case. The total pressure

and hence mass flow are thus changed. The air equivalent calculation 1s necessitated by the boundary layer program requirement that polynomials of v, Pr,

and k be supplied. (These polynomials for the H2/H20 mixture were previously unknown.) Further, perfect gas assumptions are extensively used 1n

the three computer programs of Interest (refs. 1 to 3).

Equivalent conditions are obtained when (see also refs. 18 and 19).

'tin

N

_ equivalent

equivalent

The air equivalent conditions are listed 1n table III and the definitions are

given below for reference:

^

Ve

where

e =

'

 va 1 = 2^RZTt

_

v

a,stdj (Y * DC'

'tin

tstd

c =

'std Ustd * 1

2 Vr/(Y-D

T17TTJ
Table III lists the Rocketdyne mixture values, the previous study air

equivalent values (ref. 20), and the present study mixture values and air

equivalent values.

The equivalent conditions DO NOT account for real gas effects. They

account for different (constant property) gases. Real gas affects can only be

quantified by accounting for real property changes 1n the thermodynamlc process. This has not yet been accomplished.

The use of GASP and WASP provides, for the first time, a capability to

determine real gas mixture thermodynamics and transport properties. The air

equivalent performance limitation has been removed.

SSME FUEL TURBINE PERFORMANCE CALCULATION

The computer programs TSONIC, MERIDL, and BLAYER have been used to compute

the air equivalent performance of the SSME turbine (see refs. 20 and 21). The

TSONIC computer program solves for the 1nv1sdd flow 1n the blade to blade

frame, the MERIDL computer program calculates the flow 1n the hub to tip midchannel frame, and the BLAYER computer program computes the boundary layer on

the blades and the endwall friction losses and the mixing losses. The solution

1s quasi-three-dimensional. The downstream whirl distribution and total pressure losses were adjusted, outside the programs by manual Intervention, to

match the (suction and pressure) boundary layer edge velocity at the trailing

edge. The TSONIC and MERIDL programs assume the gas to be Ideal and perfect,

1nv1sc1d, and 1rrotat1onal.

The SSME fuel turbine first stage stator has 41 blades, the first stage

rotor has 63 blades, the second stage stator has 39 blades and the second stage

rotor has 59 blades. The SSME fuel turbine mid channel blade geometry 1s

represented schematically 1n figure 81. The computed relative velocities at

the hub, mean, and tip are shown 1n figure 82. The flow stagnates at the

leading edge. At the trailing edge the suction and pressure side edge of

boundary layer velocities meet at the trailing edge. There are no known

experimental data for comparison.

The loss analysis 1s given 1n table IV for previous calculations (ref. 20)

and the current study. The loss analysis methodology 1s given 1n reference 4.

As shown 1n table IV the largest losses for the stators 1s the profile and

mixing loss. The tip clearance loss 1s the largest loss for the rotors. As

shown 1n table V the first stage efficiency calculated here 1s 0.902 versus

0.893 from reference 20, and for the second stage the calculated efficiency 1s

0.915 versus 0.900 from reference 20. The aerodynamic performance Information

1s presented 1n table V. Computed pressure, temperatures, flow angles, and

velocity ratios are given for hub, mid, and shroud locations for the air

equivalent case.

SUMMARY OF RESULTS

The study has developed thermodynamlc and transport real gas data for the

SSME mixture of H2 and ^0. The GASP and WASP computer programs were modified

and run together to determine mixture properties. The programs are general 1h

that they can handle several gases over a range of pressure and temperature.
The current SSME capability at NASA Lewis 1s United to running equivalent

air, quasi-three-dimensional turbomachlnery performance. An air equivalent

case was calculated using constant real gas thermodynamlc properties. This

study has provided the tools to calculate the performance for the SSME mixture

of H2/H20.

Future studies are recommended to Include variable real gas thermodynamlc

and transport properties 1n the TSONIC, MERIDL, and BLAYER computer programs.

REFERENCES

1. Katsanls, T.: FORTRAN Program for Calculating Transonic Velocities on a

Blade-to-Blade Stream Surface of a Turbomachlne. NASA TN D-5427, 1969.

2. McNally, W.D.: FORTRAN Program for Calculating Compressible Laminar and

Turbulent Boundary Layers 1n Arbitrary Pressure Gradients," NASA TN

D-5681, 1970.

3. Katsanls, T.; and McNally, W.D.: Revised FORTRAN Program for Calculating

Velocities and Streamlines on the Hub-Shroud,Mid-Channel Stream Surface of

an Axial-, Radial-, or Mixed-Flow Turbomachlne or Annual Duct, I-Users

Manual. NASA TN D-8430, 1977.

4. Boyle, R.J.; Haas, J.E.; and Katsanls, T.: Comparison Between Measured

Turbine Stage Performance and the Predicted Performance using Quasl3-D Flow and Boundary Layer Analyses. AIAA Paper 84-1299, June 1984.

5. HendMcks, R.C.; Baron, A.K.; and Peller, I.C.: Gasp: A Computer

Code for Calculating the Thermodynamlc and Transport Properties for Ten

Fluids: Parahydrogen, Helium, Neon, Methane, Nitrogen, Carbon Monoxide,

Oxygen, Fluorine, Argon, and Carbon Dioxide. NASA TN D-7808,.1975.

6. Hendrlcks, R.C.; Peller, I.C.; and Baron, A.K.: WASP: A Flexible

Fortran IV Computer Code for Calculating Water and Steam Properties. NASA

TN D-7391, 1973.

7. Goldberg, F.N.; and Haferd, A.M.: Numerical Procedures for Cal- culatlng

Real Fluid Properties of Normal and Parahydrogen. NASA TN D-4341, 1968.

8. McCarty, R.D.; and Hord, J.; and Roder, H.M.: Selected Properties

of Hydrogen. NBS Monograph 168, Feb. 1981.

9. Hllsenrath, J.; and Klein, M.: Tables of Thermodynamlc Properties

of A1r 1n Chemical Equilibrium Including Second V1r1al Corrections

from 1500° to 15,000* K. AEDC TR-65-58, Mar. 1965. (AD-612301)

10. Svehla, R.A.: Thermodynamlc and Transport Properties for the

Hydrogen-Oxygen System. NASA SP-3011, 1964.

11. JANAF Thermochemlcal Data, Compiled and Calculated by Dow Chemical,

Midland, MI.

12. Raznjevlc, Kuzman: Handbook of Thermodynamlc Tables and Charts.

Hemisphere Publishing Co., 1976.

10
13. Roder, H.M.; and McCarty, R.O.: A Modified Benedict-Webb-Rubin Equation

of State for Parahydrogen-II. NBSIR 75-814, June 1975.

14. W1lke, C.R.: A Viscosity Equation for Gas Mixtures. J. Chem. Phys., vol

18. no. 4, Apr. 1950, pp. 517-519.

15. VanOverbeke, T.: Private Discussions, 1985.

16. Hansen, C.F., "Approximations for the Thermodynamlc and Transport

Properties of High-Temperature A1r," NASA TR-50, 1959.

17. Hansen, C.F.; and Helms, S.P., "A Review of the Thermodynamlc, Transport,

and Chemical Reaction Rate Propretles of High Temperature A1r," NACA

TN 4359, July 1958.

18. Jackson, E.D.: Rockwell International Letter to L. PovlnelH of NASA

Lewis, Feb. 16, 1984 (84RC01708).

19. Glassman. A.J., ed.: Turbine Design and Application, Vol. 1. NASA

SP-290-VOL-1, 1972, pp. 45-62.

20. Haas, J.E.: Fuel and Ox1d1zer Turbine Loss Analysis. Advanced High

Pressure 02/H2 Technology, S.F. Morea and S.T. Wu, eds.,

NASA CP-2372, 1984, pp. 560-570.

21. Haas, J.E., "Unpublished SSME notes," Feb. 1984.

11
ORIGINAL PAGE IS

OF POOR QUALFTY

TABLE I. - RANGES OF TEMPERATURE

AND PRESSURE FOR GASP AND WASP

COMPUTER PROGRAMS

(ref., Hendricks 5 and 6)

N2

02

AR

CO?

H-,

Air

H20

atm

0.1

.1

.1

.1

.001

.1

1.0

Phigh'

atm

500

1000

500

500

1000

500

1000

Tlow

64

54

87

216

13.8

54

273

v1000

500

1000

1000

3000

500

1750

TABLE II. - COMPUTED BLADE ENTRANCE SSME TURBINE THERMODYNAMIC PROPERTIES, H2/H20 MIXTURE

Total

Stator 1

Rotor 1

Stator 2

Rotor 2

T

p

T

P

T

p

T

P

T

P

a

l!05 K a

376 aim

a

!071

a

330

a

!053

a

305.2

a

!026

a

272

a

!011

a

2S4.1

1989.9 'R

5525.8 Ibf

ft*

1928.4

4855.5

1896.2

4487.1

1846.1

3997.9

1819.2

3736

g/cm-s

0.302xlO-3

.293x10-3

.289xlO-3

.282x10-3

.278x10-3

Ibm/ft sec

0.203xl(T4

.197xlO-4

.194xlO-4

.190xlO-4

.187xlO-4

Pr

0.566

.565

.564

.563

.563

kM

cm s k

0.433X10-2

.«19xlO-2

.412x10-2

.402x10-2

.396x10-2

k

'Btu

ft sec 'R

0.695xlO-4

.674xlO-4

.662xlO-4

.645xlO-4

.636xlO-4

C

2

 /C2

L

Id' cact

1.060

1.054

1.050

1.045

1.042

Z

1.057

1.050

1.047

1.042

1.039

Y

1.373

1.375

1.376

1.377

1.378

R

I

*a7T

1.076

1.076

1.075

1.073

1.073

Cp,

0

g3T

8.117

8.080

8.057

8.024

8.005

Cp,

.Btu

Ibm R

1.940

(1.879)a

1.931

(1.869)

1.926

(1.864)

1.918

(1.857)

1.913

(1.853)

aRocketdyne values, letter to Povinelli (ref. 18).

n H2 , 0.8687 n H20 = 0.1313 R . 376.5 ft-lbf/lbm R M , 4.1164

0/F . 1.0364

TABLE III. - SSME INLET CONDITIONS AND PROPERTIES, BALANCE AT

FULL POWER LEVEL

Tt, -R

Pt, atm

e

o), Ibm/ sec

n, rpm

Re

Weq, Ibm/sec

N , rpm

Neq , rpm

Y

Cp, BTU/ Ibm R

T

u, Ibm/ft-hr

R ft-lbf

Ibm R

H2/H20

(Rocketdynea)

1990

376

28.2

177.7

13 890

1.022

2.18x10'

2.565

36 742

6918

1.34

1.879

1.0587

.069

376.5

Air

equivalent3

(ref. 19)

1990

220

4.0

274.3

14 541

1.022

2.183x10'

2.565

36 742

6918

1.34

.27

1.07

.106

53.35

H2/H20

(This study)

1990

376

24.9

177.7

13 890

1.01

2.06x10'

2.384

36 742

7363

1.373

1.940

1.057

.07297

349.1

A'r K equivalent"

(This study)

1990

224

4.0

259.5

1 548

1.025

2.06x10'

2.384

36 742

7363

1.34

.27

1.07

.106

53.35

aRocketdyne, Feb. 1984 (ref. 18).

''Same Reynolds number and total temperature as SSME.
ORIGINAL PAGE IS

OF POOR QUALITY

TABLE IV. - SSME FUEL TURBINE LOSS ANALYSIS

This study

Losses

Profile and mixing

Endwall friction

Secondary flow

Incidence

Tip clearance

An blade row

ptinlet'Psexit

1st stage.

stator

0.012

.006

.0050

.001

0

0.024

1.17

1st stage,

rotor

0.014

.001

.008

.003

.050

0.076

1.18

2nd stage,

stator

0.013

.007

.003

.001

0

0.024

1.21

2nd stage,

rotor

0.014

.002

.008

.004

.034

0.062

1.15

Previous study, reference 20

Profile and mixing

Endwall friction

Secondary flow

Incidence

Tip clearance

fin blade row

Ptinlet'Psexit

0.014

.007

.005

.001

0

0.027

1.19

0.016

.002

.oog

.007

.046

0.080

1.17

0.013

.007

.004

.001

0

0.025

1.24

0.017

.002

.009

.013

.034

0.075

1.19

TABLE V. - AERODYNAMIC PERFORMANCE INFORMATION, AIR EQUIVALENT

Stator 1

Rotor 1

Stator 2

Rotor 2

Stator 1

Rotor 1

Stator 2

Rotor 2

In

Out

In

Out

I n

Out

I n

Out

In

Out

I n

Out

In

Out

In

Out

H u b

deg°

0

-72.9

-52.2

+65.1

34.6

-70.9

-53.8

+61.9

Pt, -

lbf/ft '

474041

471155

471120

367041

357038

364694

364353

284188

W ,

ft/ sec

286

1082

549

926

426

1172

637

821

T

f

R

1990

1990

1990

1877

1877

1877

1877

1769

W/Wc r

0.15

.55

•.28

.48

.22

.61

.34

.44

R

P

0.994

.779

.994

.779

M i d

deg13

0

-70.5

-36.7

+65.9

33.7

-69.5

-42.1

+61.9

W,

ft/sec

298

991

453

954

398

1063

499

867

T

tout' Ttin

0.943

.942

W/Wcr

0.15

.50

.23

.49

.21

.55

.26

.46

"stage

0.902

.915

Shroud

B,

deg>>

0

-68.3

-20.7

+66.7

33.2

-68.2

-28.3

+63.5

«t/Pt

0.0061

.0197

.0064

.0101

W,

ft/sec

310

924

407

1004

377

988

414

908

U/Ucr

0.16

.47

.21

.51

.20

.51

.22

.48

Exi t

swirl ,

ft 2/sec

-401

-93

-425

-50

Btu = Cp iTt . 54

TES~ 1

,8; Btu = Cp &Tt = 52.39 Btu; Total = 107.2 Btua

iSm

Blade row

Si

»1

52

4

Blade

angle,

deg

0

-36.6

21.0

-35.6

Incidence,

deq

0

.1

12.7

6.5

Exit design

relative

angles"

-67.5

64.5

-66.5

60.5

Deviation,

degb

-3.0

1.4

3.0

1.4

"Rocketdyne value of work (with Hj/HjO mixture) - 314.6 Btu

T6T5

bPositive angles are center-clockwise, see figure 81.
19000

18000

17 000

16000

s 15000

14000

13000

12000

11000 !

800 850 900 950 1000 1050 1100

Temperature, K

Figure 1. - Enthalpy versus temperature.

1150 1200
ORIGINAL PAGE IS

OF POOR QUALITY

90

O

D

A

O

O

85

80

Pressure,

atm

1

10

50

100

200

250

300

350

400

500

>O

75

70

65

60

55

—A

_.-6)

850 900 950 1000. • 1050 1100

Temperature, K

1150 1200

Figure 2. - Entropy versus temperature.
15.5

850 900 950 1000 1050

Temperature, K

1100 1150 1200

Figure 3. - Specific heat at constant pressure versus temperature.
11.3

11.2

11.1

11.0

TM 10.9

10. i

10.7

10.6

H2

o

n

A

Q

O

Pressure,

atm

1

10

50

100

200

250

300

350

400

500

800 •:; 850 900 950 1000 1050

Temperature, K

1100 1150 1200

Figure 4. - Specific heat at constant volume versus temperature.
60000 -

= 55000

50000

S 45000

I 40000,

5 35000

30 000.

850 900 950 1000 1050

Temperature, K

1100 1150 1200

Figure 5. -Partial derivative of pressure with respect to density at constant temperature

versus temperature.
ORIGINAL PAGE IS

OF POOR QUALITY

.00023

. 00022

.00021

.00020

. 00019

.00018

.00017

800 900 950 1000 1050

Temperature, K

1100 . 1150 1200

Figure 6. - Molecular viscosity versus temperature.
Pressure,

atm

.014

.012

.010,

.008

.006

.004

.002

800 850 900 950 1000 1050 1100

Temperature, K

Figure 7. - Density versus temperature.

1150 1200
ORIGINAL OF

1.400

1.395

1.390

1.385

.2 1.380 -

1.375

1.370

1.365

800 950 1000 1050 1100 1150 1200

Temperature, K

850 900

Figure 8. - Ratio of specific heats versus temperature.
290 000

210000

800 850 900 950 1000 1050 1100 1150

'' Temperature, K

Figure 9. - Real sound speed squared versus temperature.

1200
.0055

.0035

800 850 900 950 1000 1050 1100 1150

Temperature, K

Figure 10. - Thermal conductivity versus temperature.

1200
Pressure,

atm

850 900 -950 1000 1050

Temperature, K

1100 1150 1200

Figure 11. - Partial derivative of pressure with respect to temperature at constant density

versus temperature.
.692

.690

686

.684

-o

D

A

0

O

Pressure,

aim

1

10

50

100

200

250

300

350

400

500

.682

.680'

.678

.676

.674

800 850 900 950 1000 1050 ' 1100 1150 1200

Temperature, K

Figure 12. - Prandtl number versus temperature.
Pressure,

atm

1.14

800 850 900 950. 1000 1050 1100 ' 1150 . 1200

. . .Temperature, K

Figure 13. - Real/perfect sound speed squared versus temperature.
ORIGINAL PAGE IS

OF POOR QUALITY

1.030

1.025

1.010

1.005

1.000- 0 --

800 ! 858500 . . 9 90( 0 950 1000 1050 1100 1150

Temperature, K

Figure 14. - Perfect/real gas constant versus temperature.
1.14

1.02

1.00

Pressure,

atm

800 900 950 1000 1050 1100

Temperature, K

Figure 15. - Compressibility versus temperature.

1150 1200
ORIGINAL PAGE IS

OF POOR QUALITY

1.01

1.00

B .99

800 850 900 950 1000 1050 1100 1150 1200

Temperature, K

Figure 16. - Enthalpy/lspecific heat x temperature) versus temperature.
Pressure,

atm

800 900 950 1000 1050

Temperature. K

1100 1150 1200

Figure 17. - Enthalpy/(gas constant x temperature) versus temperature.
ORIGINAL

Pressure,

atm

850 900 950 1000 1050 1100 1150 1200

Temperature, k

Figure 18. - Entropy/gas constant versus temperature.
3.76

3.58

800 850 950 1000 1050

Temperature, K

1100 1150 1200

Figure 19. - Specific heat at constant pressure/gas constant versus temperature.
ORIGINAL PAGE IS

OF POOR QUALITY

2.74

2.72

- 2.70

2.68

2.66

2.64

2.62

2.60

2.58

800 850 950 1000 1050

Temperature, K

1100 1150 1200

Figure 20. - Specific heat at constant volume/gas constant versus temperature.
4600

4400 —

4200 —

4000 -

3800 -

3600 -

3400

3200

3000

2800

850 900 950 1000 1050 1100

Temperature, K

1150 1200

Figure 21. - Enthalpy versus temperature.
ORIGINAL PAGE" IS

OF POOR QUALfif

Pressure,

atm

800 850 900 950 1000 1050 1100 1150 1200

Temperature. K

Figure 22. - Entropy versus temperature
850 900 950 1000 1050

Temperature, K

1100 1150 1200.

Figure 23. - Specific heat at'constant pressure versus temperature.
ORIGINAL

1.6

800 850 900 950 - 1000 1050 1100 1150

Temperature, K .

Figure 24. - Specific heat at constant volume versus temperature.
5500

H20

i

^^^^

1000..;

850 900 950 1000 1000

Temperature, K

1050 1100 1150

Figure 25. - Partial derivative of pressure with respect to density at constant temperature

versus temperature.
.00050

.00025.1—

850 900 950 1000 . 1050

Temperature, K

1100 1150 1200

Figure 26. - Molecular viscosity versus temperature.
.25

.20

H20

Pressure,

atm

.15

I,

.10

.05

0

:

800 900 950 1000 1050

Temperature, K

1100 1150 1200

Figure 27. - Density versus temperature.
ORIGINAL PAGE IS

OF POOR QUALITY

1.4

1.2

850 900 950 1000 1050

Temperature, K

1100 1150 1200

Figure 28. - Ratio of specific heats versus temperature.
85000

80000

75000

5T

70000

3 65000

60000

55000

850 900 950 1000 1050 1100 1150

Temperature, K

Figure 29. - Real sound speed squared versus temperature.

1200
ORIGINAL PAGE fS

OF POOR QUALITY

r

E

.0020

.0018

.0016

.0014

.0012

.0010

Pressure,

aim

800 850 900 950 1000 1050 1100 1150

Temperature, K

Figure 30. - Thermal conductivity versus temperature.

1200
900 950 1000 1050

Temperature, K

1100 1150 1200

Figure 31. - Partial derivative of pressure with respect to temperature at constant density

versus temperature.
850 900 950 1000 1050

Temperature, K

1100 1150 1200

Figure 32. - Prandtl number versus temperature.
1.00

1

850 900 950 1000 1050

Temperature, K

1100 1050 1200

Figure 33. - Real/perfect sound speed squared versus temperature.
ORIGINAL PAGE IS

OF POOR QUALITY

850 900 950 1000 1050

Temperature, K

1100 1150 1200

Figure 34. - Perfect/real gas constant versus temperature.
1.00

O

o

850 900 950 1000 1050

Temperature, K

1100 1150 1200

Figure 35. - Compressibility versus temperature.
ORIGINAL PAGE fS

OF POOR QUALITY

2.5

2.0

1.5

I

t 1.0

.5

H20

800 850 900 950 1000 1050 1100 1150 1200

: Temperature, K

Figure 36. - Enthalpy/lspecific heat at constant pressure x temperature) versus temperature.
10.0 -rr.

7.5

850 900 950 '1000 1050 1100 1150

Temperature, K

Figure 37. - Enthalpy/(gas constant x temperature) versus temperature.

1200
800 850 900 950 1000 1050 1100

Temperature, K

Figure 38. - Entropy/gas constant versus temperature.

1150 1200
c

2

850 900 950 1000 1050. 1100 1150 1200

Temperature, K

Figure 39. - Specific heat at constant pressure/gas constant versus temperature.
. 3.6

800 850 900

Figure 40. - Specific heat at constant volume/gas constant versus temperature.

950 1000 1050 1100 1150 1200

Temperature, K
10500

10000

9500

1? 8500

6500

800 850 950 1000 1050

Temperature, K

Figure 41. - Enthalpy versus temperature.

1100 1150 1200
ORIGINAL PAGE IS

OF POOR QUALITY

Pressure,

atm

800 850 900 950 1000 1050

Temperature, K

1100 1150 1200

Figure 42. - Entropy versus temperature.
10.0

800 850 900 950 1000 1050 1100 1150 1200

Temperature, K

Figure 43. - Specific heat at constant pressure versus temperature.
850 900

Figure 44. - Specific heat at constant volume versus temperature.

950 1000 1050 1100 1150

Temperature, K

1200
28000

14000.

850 900 950 1000 1050

. Temperature, K

1100 1150 1200

Figure 45. - Partial derivative of pressure with respect to density at constant temperature

versus temperature.
.00033

.00032

.00031

.00030

.00029

g .00028

s .00027

fe

 .00026

.00025

.00024

.00023

.00022

0.8687;

= 0.1313.

o

D

A

Q

O

&

a

6

Pressure,

atm

1

10

50

100

200

250

300

350

400

500

I

800 850 900 950 1000 1050

Temperature. K

1100 1150 1200

Figure 46. - Molecular viscosity versus temperature.
.035

.030

850 900 950 1000 1050

Temperature, K

Figure 47. - Density versus temperature.

1100 1150 1200
ORIGINAL PAGE IS

OF POOR QUALITY

1.54

1.52

1.50

1.48

1.46

1.44

1.40

1.38

1.36

= 0.8687;

= 0.1313

\

O

a

A

a

o

Pressure,

atm

1

10

50

100

200

250

300

350

400

500

850 900 950 1000 1050 1100

Temperature, K

Figure 48. - Ratio of specific heats versus temperature.

1150 1200
260000

250000

240000

1 230000

220000

210 000

200000

19001

850 900 950 1000 1050 1100 1150

Temperature, K

Figure 49. - Real sound speed squared versus temperature.

1200
.0048

.0046

nH =0.8687;

nHj,- 0.1313

.0044

.0042

.0040

.0038

.0036

.0034

.0032

.00301

800

O

D

A

Q

O

Pressure,

atm

1

10

50

100

200

250

300

350

400

500

850 900 950 1000 1050

Temperature, K

1100 1150 1200

Figure 50. - Thermal conductivity versus temperature.
850 900 950 1000 1050

Temperature, K

1100 1150 1200

Figure 51. - Partial derivative of pressure with respect to temperature at constant density

versus temperature.
ORIGINAL PAGE FS

OF POOR QUALITY

.52

100 850 900 950 1000 1050 1100

Temperature, K

Figure 52. - Prandtl number versus temperature.

1150 1200
50 900 950 1000 1050 1100 1150

Temperature, K

Figure 53. - Real/perfect sound speed squared versus temperature.

1200
1.40,

nH =0.8687;

n

° 0-1313

1.35

8

iSI

*S

1.30

1.25

.20

1.15

1.10

1.05

800 850 900

O

D

A

-D

O

&

a

6

Pressure,

atm

1

10

50

100

200

250

300

350

400

. 500

950 1000 1050 1100

Temperature, K

Figure 54. - Perfect/real gas constant versus temperature.

1200
1.07

1.06

1.05

1.04

1.03

1.02

1.01

O

D

A

Q

O

Pressure,

atm

1

10

50

100

200

250

300

350

400

500

nH =0.8687;

n = 0.1313

850 900 950 1000 1050

Temperature, K

1100 1150

Figure 55. - Compressibility versus temperature.
ORIGINAL

OF POOR

800 850 900 950 1000 1050 1100 1150 1200

Temperature, K

Figure 56. - Enthalpy/lspecific heat at constant pressure x temperature) versus temperature.
4.34

4.32

4.14

850 900 950 1000 1050 1100 1150 1200

Temperature, K

Figure 57. - Enthalpy/(gas constant x temperature) versus temperature.
ORIGfWAL PAGE fS

OF POOR QUALITY

21

20

19

18

S 17

° 16

15

Pressure,

aim

14

13

12

"800 850 900

Figure 58. - Entropy/gas constant versus temperature.

950 1000 1050 1100

Temperature, K

1150 1200
800 850 900 950 1000 1050 1100 1150 1200

Temperature, K

Figure 59. - Specific heat at constant pressure/gas constant temperature.
3.00

2.95

nH2= 0.8687;

"H20 ' 0.1313

2.70

850 900 950 1000 1050

Temperature, K

1100 1150 1200

Figure 60. - Specific heat at constant volume/gas constant versus temperature.
360 380 40

0 420 440

Temperature, K

460 • 480 500

Figure 61. -Enthalpy versus temperature. ,
ORiGfNAL PAGE fS

OF POOR QUALITY

Pressure

atm

3.0

360 380 400 420 440

Temperature, K

Figure 62. - Entropy versus temperature.

460 480 500
1.30

1.25

1.00

Pressure,

atm

340 380 400 420 440

Temperature, K

460 480 500

Figure 63. - Specific heat at constant pressure versus temperature.
ORIGINAL PAGE S3

OF POOR QUALITY

.720

360 380 400 420 440

Temperature, K

460 480 500

Figure 64. - Specific heat at constant volume versus temperature.
Pressure,

atm

360 380 400 420 440

Temperature, K

460 480 500

Figure 65. - Partial derivative of pressure with respect to density at constant temperature

versus temperature.
.00036

.00034

. 00032

.00030

.00028

o . 00026

.00024

.00022

.00020

Pressure,

atm

1

10

50

100

200

250

300

350

400

500

340 360 380 400 420 440 460 480

Temperature, K

Figure 66. - Molecular viscosity versus temperature.

500
Pressure,

atm

340 360 380 400 420 440 460

Temperature, K

Figure 67. - Density versus temperature.

480 500
ORIGINAL PAGE S3

OF POOR QUALITY

340 360 380 400 420 440

Temperature, K

480 500

Figure 68. - Ratio of specific-heats versus temperature.
Pressure,

atm

65000

60000

55000

1ea

3

sr

"S

50000

S 45 000

40000

35000

360 380 400 420 440 460 480

Temperature, K

Figure 69. - Real sound speed squared versus temperature.

500
ORIGINAL PAGE-SS

OF POOR QUALITY

Pressure,

atm

.00065

.00025

360 380 400 . 420 440 460 480

Temperature. K

Figure 70. - Thermal conductivity versus temperature.

500
2.5

340 360

Pressure,

atm

380 400 420 440

Temperature,' K

480 500

Figure 71. - Partial derivative of pressure with respect to temperature at constant density

versus temperature.
.750

.745

360 380 400 420 440

Temperature, K

460 480 500

Figure 72. - Prandtl number versus temperature.
•§

360 380 400 420 440 460 480

Temperature, K

Figure 73. - Real/perfect sound speed squared versus temperature.

500
OF POOR

s 1.4

360 380 400 420 440

Temperature, K

460 480 500

Figure 74. - Perfect/real gas constant versus temperature.
1.35

1.30

1.25

1.20

.&

s

°t/l lie

S H5

k_

d

E

o

o

1.10

1.05

1.00:

.95

3

0

a

A

.Q

O

/^

Air mixture

s

~ * -,— _

,

- a -

!

'

... — )

""""

~

 = L

—^=\

!

|t- 1

P= ^

i — r >

_^ • "

. '

— •

+

&

a

—

1

•

—

Pressur

atm

1

10

50

100

200

250

300

350

400

500

a

—

!

JO 360 380 400 420 440 460 480 50

Temperature, K

Figure 75. - Compressibility versus temperature.
360 380 400 420 440. 460 480 500

Temperature, K

Figure 76. - Enthalpy/lspecific heat at constant pressure x temperature) versus temperature.
340 360 380 400 420 440 460 480

• Temperature, K

• Figure 77. -Enthalpy/(gas constant.x temperature) versus temperature.

500
Pressure,

atm

19

360 380 400 420 440 . 460 .480

Temperature, K

Figure 78. - Entropy/gas constant versus temoerature.

500
360 380 400 420 440

Temperature, K

460 480 500

Figure 79. - Specific heat at constant pressure/gas constant versus temperature.
2.70

^ .2.65

C

8

en

5-

<u

1

1 2.60

8

<" 2.55

2.50

Air mixture

I

340 360 380 400 420 440

Temperature. K

460 480 500

Figure 80. - Specific heat at constant volume/gas constant versus temperature.
Stator 1 Rotor 1 Stator 2 Rotor 2

Figure 81. - Blade geometry for SSME fuel turbine mid channel.

Positive angles are counterclockwise, see table V.

First-stage stator First-stage rotor

Second-stage rotor

.2 .4 .6 .« 1.0 0 .2 .4 .6 .8 1.0

Chord length, percent

Fjgure 82. - Relative velocity at edge of boundary layer.
1. Report No.

NASA CR-175066

2. Government Accossion No. 3. Recipient's Catalog No.

4. Title and Subtitle

Characterization of Real Gas Properties for Space

Shuttle Main Engine Fuel Turbine and

Performance Calculations

5. Report Date

June 1986

6. Performing Organization Code

7. Author(s)

Gary 0. Harloff

8. Performing Organization Report No.

None

10. Work Unit No.

9. Performing Organization Name and Address

Sverdrup Technology, Inc.

Lewis Research Center

Cleveland, Ohio 44135

11. Contract or Grant No.

NAS 3-24105

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, D.C. 20546

13. Type of Report and Period Covered

Contractor Report

14. Sponsoring Agency Code

533-13-00 (E-2938)

15. Supplementary Notes

Final report. Project Manager, Raymond Gaugler, Internal Fluid Mechanics

Division, NASA Lewis Research Center, Cleveland, Ohio 44135.

6. Abstract

Real thermodynamlc and transport properties of hydrogen, steam, the SSME mixture,

and air are developed. The SSME mixture properties are needed for the analysis

of the space shuttle main engine fuel turbine. The mixture conditions for the

gases, except air, are presented graphically over a temperature range from 800

to 1200 K, and a pressure range from 1 to 500 atm. A1r properties are given

over a temperature range of 320 to 500 K, which are within the bounds of the

thermodynamics programs used, 1n order to provide mixture data which 1s more

easily checked (than H2/H20). The real gas property variation of the SSME

mixture 1s quantified. Polynomial expressions, needed for future computer analysis, for viscosity, Prandtl number, and thermal conductivity are given for the

H2/H20 SSME fuel turbine mixture at a pressure of 305 atm over a range of

temperatures from 950 to 1140 K. These conditions are representative of the

SSME turbine operation. Performance calculations are presented for the space

shuttle main engine (SSME) fuel turbine. The calculations use the air equivalent

concept. Progress towards obtaining the capability to evaluate the performance

of the SSME fuel turbine, with the H2/H20 mixture, 1s described.

. Key Words (Suggested by Authors))

Real gas properties

Space shuttle fuel turbine

18. Distribution Statement

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Unclassified

20. Security Classif. (of this page)

Unclassified

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