I 

PERFORMANCE PREDICTIONS 

FOR AN SSME CONFIGURATION 

WITH AN ENLARGED THROAT 

SN 63 

November 1985 

(NASA-CR- 178743) PEBTCRNANCE FEECICTIONS N86-2 1579 - 

FOB AN SSM CCNFIfUhATICN WI'IIi AN ENLARGED 

THROAT (Softuarc atd Enqineericq Associates, 

Inc.) 44 p HC AC?/HF Ad1 CSCL 21a Unclas 

G3/20 08803 

Contract No. NAS8-35931 

By: G. R. Nickerson 

L. D. Dang 

Prepared For 

George C. Marshall Space Flight Center 

Marshall Space Fliaht Center, AI. 35812 

Software And Engineering Associates, Inc. 

1050 East William Street, Suite 402 

Carson City, Nevada 89701 
, 

TABLE OF CONTENTS 

.. . 

Nomenclature 

Abbreviations 

1. Introduction 

2. Performance Prediction Results 

3. Factors Effecting the Performance Prediction 

Results 

4. Comparison of Shock Results with other Computer 

Programs 

5. Conclusions 

5.1 Chemical Kinetics 

5.2 Transonic Analysis 

5.3 Shock Wave Prediction 

5.4 Thrust Chamber Performance Prediction 

6. Recommendations 

References 

Appendix A 

iv 

V 

1 

4 

6 

10 

12 

12 

12 

13 

13 

14 . 

34 

36 

851 106 

i 
.- 

LIST OF FIGURES 6' 

-- Page - No. . 

Figure 1: SSME Main Combustion Chamber. (MCC) 15 

Figure 2: A Comparison of Current and Large Throat 16 

SSME MCC/Nozzle Configurations 

Figure 3: TDK Input for SSME Current Design Analysis 17 

Figure 4: TDK Input for SSME "Large T h r o a t v 1 D e s i g n 18 

Anal ys i s 

Figure 5: SSME Wall Temperature 19 

Figure 6: TDK Performance Summary for SSME Current 20 

Configuration 

Figure 7: 

Figure 8: 

Figure 9: 

Figure 10: 

Figure 11: 

Figure 12: 

Figure 13: 

Figure 14: 

Figure 15: 

TDK Performance Summary for SSME "Large 

Throat" Configuration 

Flow Velocity along a Gas Streamline Behind 

an Oblique Shock. SSME "Large Throat" 

Design 

SSME Large Throat Design 

Isomach from Throat Minimum Point for Back 

Nozzle 

VNAP2 Isomach Predictions for the "Large 

Throat" SSME Design 

VNAP2 Solution Grid 

Sensitivity of Nozzle Mass Coefficient, 

Transonic Analysis 

CD 

SSME Current Design, Induced Shock 

Predictions 

-2 1 

22 . 

23 

24 

25 

26 

27 

28 

29 

851 106 

ii 
, 

LIST OF FIGURES 

Figure 16: SSME "Large Throat" Design, Induced Shock 30 

Predi ct ions 

* 

Figure 17: SSME Current Design, Shock angle vs x/r 31 

Figure 18: SSME "Large Throat" Design, Shock angle 31 

* 

vs x/r 

* 

Figure 19: Shock Strength vs x/r for Differing 32 

Transonic Start Lines 

Figure 20: Summary of Shock Strength Predictions 33 

. 

851 106 

iii 
I 

NOMENCLATURE 

cD 

ISP 

I 

SPtheoretical 

M 

r 

r 

R 

Rd 

i 

RU 

X 

’. Greek 

B 

Y 

E 

“DER 

OTDK, BLM 

0 

$ 

851 106 

flow coe cient, nozzle mass flow/l-D mass fl 

specific impulse 

specific impulse for an isentropic equilibrium 

expansion 

Mach number 

radial coordlnate. r=o at axis 

throat radius 

throat radius/r* 

downstream throat radius/r* 

upstream throat radius/r* 

axial coordinate. x=o at throat plane 

angle between shock and gas streamline, 

shock strength (see page 4) 

ratio of specific heats 

nozzle expansion ratio 

Distributed Energy Release efficiency 

aerodynamic efficiency, incl’uding chemical 

kinetics 

angle between gas streamline and axis 

angle between surface and axis 

iv 

W 

. 
ABBREVIATIONS 

BLM Boundary Layer Module, computer program 

DER Distributed Energy Release 

JANNAF Joint Army-Navy-NASA-Air Force 

LRC Left Running Characteristic 

MC C Main Combustion Chamber 

MOC Method of Characteristics 

ODE One-Dimensional Equilibrium Expansion 

' 0DF One-Dimensional Frozen Expansion 

ODK One-Dimensional Kinetics Expansion 

RRC Right Running Characeristic 

SEA Software and Engineering Associates, InC. 

SSME Space Shuttle Main Engine 

- 

TDK Two-Dimensional Kinetics, JANNAF computer program 

VNAP2 Viscous Nozzle Analysis Program, Version 2 

851 106 V 
_. 1. INTRODUCTION 

-In--this study the Two-Dimensional Kinetics (TDK) computer 

p+ogram that has recently been developed for the NASA under 

contract NAS8- 35931.was used to predict the performance of a 

"Large Throat Configurationft of the Space Shuttle Main Engine 

(SSME) (' I. Calculations indicate that the current design SSME 

contains a shock wave that is induced by the nozzle wall 

shape . In the "Large Throat" design an-even stronger shock 

wave is predicted. Because of the presence of this shock wave, 

earlier performance predictions that have neglected shock wave 

effects have been questioned. In this study the JANNAF thrust 

chamber performance prediction procedures given in Reference 3 

have been applied. The analysis includes the effects of two 

dimensional reacting flow with a shock wave. The effects of the 

boundary layer with a regenatively cooled wall are also 

included. This analysis has been made possible by the 

development of a new shock wave version of the TDK computer 

program . 

(2) 

(1 1 

In order to substantiate the calculations, a computer 

program- developed by Prof. Hoffman at Purdue University was also 

used(4). The results were run independently at Purdue with 

input data supplied by SEA, Inc. The Purdue computer program 

can compute axially symmetric supersonic nozzle flows with an 

induced shock, but is restricted to flows with a constant ratio 

of specific heats, Y . Thus, the TDK program was also run with 

this assumption and the results Of the two programs were 

compared. 

851 106 

1 
The Space Shuttle Main Engine (SSME) utilizes a thrust 

chamber that is constructed in two sections, 1) a Main 

Combustion Chamber (MCC) assembly, and 2) an expansion nozzle 

assembly. The MCC current design is shown in Figure 1. The 

nozzle assembly is bolted to the MCC at a nozzle attach flange. 

The nozzle expansion ratio at the attachment position is 5:l. 

The "Large Throat1' version of the SSME is constructed by 

modification of the MCC. The nozzle assembly is not modified. 

The current design and "Large Throat" design MCC geometries are 

compared in Figure 2. It can be seen that the enlargement of 

the nozzle throat reduces the nozzle expansion ratio from 77.5 

to 69.5:l. The chamber pressure is reduced from 3285 (109% 

power level) to 3010 psia. The distance from the nozzle throat 

to the nozzle exit is very slightly decreased. There is a 

considerable difference in throat radius of curvature, both the 

upstream and downstream values, between the two designs. 

Nozzle geometry and operating conditions- for the SSME 

.current design nozzle (109% power level) were obtained from 

NASA/MSFC and are given in Figure 3, which is an annotated 

listing of the input data. Definitions for all of the input 

data items are given in Reference 1. Those input items which 

were changed in order to run the "large throat" SSME are listed 

in Figure 4. The wall temperature profile for these engines is 

shown in Figure 5. 

The calculations were made assuming that 1) there is perfect 

mixing so that the overall engine mixture ratio of 6.05485 is 

achieved, and 2) the system enthalpy is determined from tank 

conditions. These assumptions are equivalent to assuming that 

the distributed energy release efficiency, nDER , is unity. 

851106 

2 
Results were then calibrated using measured data. That is, an 

actual value of nDERwas estimated from 

so that for the current design 

I =I 

"predict "measured 

The performance predictions results are presented in the .. 

next section. 

. 

851 106 

3 
2. PERFORMANCE PREDICTION RESULTS 

Performance prediction results are summarized in Figures 6 

and 7 for the current design and "Large Throat" designs, 

respectively. (See Appendix A for an explanation of these 

summary sheets). The measured Isp for the current design is 

known to be 452.6i-1 seconds. The distributed energy release 

efficiency for the engine is found from equation (1) as follows: 

I - 458.0 sec. 

"TDK,BLM 

= 458.01465.1 = .9847 "TDK, BLM 

Thus, it is predicted that the distributed energy release 

loss for this engine is 5.4 seconds. This value is consistent 

with the value of 5.3 seconds predicted by R. Carroll (6) using a 

full distributed energy release analysis. 

As can be seen from Figure 6, the maximum shock strength, B, 

predicted for the current design nozzle is .29. This value 

is taken at the intersection of the last Left Running 

Characteristic (LRC) surface and the shock surface. Downstream 

of this intersection the shock can not effect thrust chamber 

performance. Shock strength is defined here as 

8- (P, - p1 p1 

where 

P1 is the pressure in front of the shock, and 

P2 is the pressure behind .the shock. 

851 106 
For the large throat design the maximum shock strength is 

found from Figure 7 to be 1.13. The difference in theoretical 

performance between the two engines is (ISP (ODE) values from 

Figure 6 and 7) . 

The difference in predicted performance is (ISP (TC) *nDER from 

Figure 6 and 7) 

452.6 - 449.1 = 3.5 seconds, (with nDER = .9882) 

which is larger than expected. From the analysis presented here 

it appears that the lowered performance predicted for the "Large 

Throat" SSME design is almost entirely due to the effect of the , 

shock wave calculation. Factors that influence the performance 

calculations are discussed in the next section. 

851 106 5 
3. FACTORS EFFECTING THE PERFORMANCE PREDICTION RESULTS , 

An examination of the computed results indicate that the 

lowered performance predicted for the "Large Throat" SSME is a 

result of the shock wave calculation. In order to minimize the 

numerical error contained in the .calculation, an extremely fine 

mesh spacing was used. The number of points in the initial data 

line was set at 250. Each Method of Characteristics (MOC) flow 

fieid calculation was carried' out using approximately 100,000 

points. 

Two phenomena were examined in detail: 1) the interaction 

of the shock wave with the chemical kinetics of the flow, and 2) 

the transonic flow field. Each is discussed below. 

Across the shock front, the translational degrees of freedom 

of a gas are equilibrated within a few molecular collisions . The chemical composition of the gas is frozen during this time 

since thousands of molecular collisions are required for even 

the fastest chemical reactions. Thus a chemical excitation . 

process can occur immediately behind the shock front. Since the 

kinetic rate equations are notoriously stiff, it is necessary 

that a fully implicit integration method be used (See Ref. 1, 

Section 3.1.1). 

* 

------------- * The present analysis assumed that both the translational and 

vib.-rot. degrees of freedom are Pqi~ilihrated =crr\gg the 

shock. 

851 io6 

6 
In order to test the accuracy of the TDK integration 

procedure immediately behind a shock point, a streamline was 

selected from. the "Large Throat" SSME TDK analysis. A pressure 

defined ODK calculation was then carried out for this streamline 

starting at the back side of the shock. The shock strength was 

1.05, so that there was a considerable change in pressure and 

temperature across the shock. 

A comparison of the TDK and ODK streamline calculations are 

shown in Figure 8. Each TDK mesh point is shown. The ODK 

integration step is approximately 1000 times smaller than the 

TDK mesh size. Never the less, the two results cannot be 

separated on the scale shown in the figure. Velocity vs path 

length was chosen since velocity is a direct measure of specific 

impulse (for one-dimensional flow, optimum Isp = V/g>. A 

computer generated plot repeating this result, but with higher 

resolution, is given in Figure 9. It can be concluded that for 

this case, TDK is giving an accurate result. 

A one-dimensional frozen (ODF) calculation was also carried 

out for this streamline. There were no differences between the 

ODF and- ODK results, i.e., the frozen and equilibrium paths were 

found to be the same. Thus, in this flow regime there can be no 

dissociation of H20 or H2 due to a shock of this strength. It 

follows that no significant energy can be bound up in 

dissociated species causing a performance loss. The shock wave 

and chemistry interaction is foun4 to be negligible. 

The Transonic Flow Field 

The most important parameter effecting the transonic flow 

field is the radius of curvature immediately upstream of the 

851 106 

7 
nozzle throat. This value was reduced from RU = 1 in the 

current design to RU = .494 in the ''Large Throat" design (see 

Figure 2). The modified Sauer transonic analysis used by the 

TDK program is based on perturbation theory (see Reference 1, 

Section 2.4) and a value of Ru = .494 is at the lower limit for 

which the analysis has been validated. Because of this fact, 

the analysis was re-examined in order to assess its accuracy for 

calculating the MOC start line for the "Large Throat" SSME. In 

particular, results obtained from the analysis were compared 

with results obtained from . Two the VNAP2 computer program 

cases were examined in some detail. 

(7) 

The first case examined was the nozzle studied by L. Back, 

Reference 8, for which ample experimental data is available. 

The Back case is for air flow through a nozzle with a 

small, RU = .625, radius of curvature throat. Results of the 

analysis -are shown in Figure 10. It can be seen that both 

methods are in excellent agreement with the data in the region 

near the wall. Near the flow axis, the TDK analysis is in 

closer agreement with the data than the VNAP2 analysis. In 

general, VNAP2 predicts flow accelerations along the nozzle axis 

that are greater than seen experimentally (see Reference 8 for 

further data). 

The second case examined is the "Large Throat" SSME design. 

Results of the VNAP2 analysis are shown in Figure 11. Included 

in Figure 11 is the isomach attached to the throat minimum point 

as calculated for this case by the TDK modified Sauer transonic 

analysis. It can be seen that the agreement between this 

isomach and the corresponding isomach computed by VNAP2 is very 

similar to that measured by Back, et.al., Figure 10. A grid 

spacing of 101x34 was used for the VNAP2 runs. The VNAP2 

solution grid for the "Large Throat" SSME case is shown in 

Figure 12. 

851 106 

8 
For the prediction of rocket engine performance it is 

important to be able to accurately estimate the steady state 

mass flow rate. This parameter is both difficult to measure 

experimentally or to predict theoretically for nozzles with 

small throat radius of curvature. The mass flow coefficient, 

can be shown to be rather sensitive to the flow angle 'D ' 

distribution within the nozzle. Consider the isomach attached 

to the throat minimum point for the Back case shown 

in Figure 10. For this suface (M - 1.346) the CD depends only 

on the flow angle distribution, e(r). The CD will be maximized 

if the flow is normal to the surface (although this violates the 

wall boundary condition). On the other hand if the flow angle 

is parallel to the nozzle centerline, then the CD is very much 

reduced. Figure 13'gives computer values for CD for these two 

cases (e - 41 - - and 8 = 0). Also given is the CD corresponding 

to the flow angle distribution computed by the TDK modified 

Sauer method. This computed distribution has then been 

perturbed k 10% and values o.f CD It can be seen 

from Figure 13 that a 10% perturbation in flow angle 

distribution gives significant differences (.5 to .8%) in 

computed mass flux. Resuits obtained for CD and for the isomach 

attached to the nozzle throat minimum point are shown in Figure 

14. 

ll 

2 

determined. 

From the results discussed above it is concluded that the 

TDK modified Sauer analysis is adequate for the present 

application. 

-851106 

9 
4. COMPARISON OF SHOCK RESULTS WITH OTHER COMPUTER PROGRAMS 

The current design and "Large Throat" design nozzles were 

analyzed using a method of characteristics computer program with 

shock tracing that was developed by Hoffman . This MOC 

computer code can only analyze nozzle flows where the ratio of 

specific heats, Y, is constant . A value of Y-1.24 was selected 

for the analysis since this closely approximates the equilibrium 

value found in the region of the shock, i.e., at T = 2500 R. 

These same two cases were also run using the constant Y Option 

of the TDK computer program. A comparison of results obtained 

are presented in Figures 15 through 20. - 

(4) 

0 

The nozzle contour for the current configuration of the SSME 

is shown in Figure 15. An induced shock wave is found by both 

the TDK computer program and the Hoffman computer program , 

which is indicated in the Figures by the initials JDH. The 

corresponding plot for the "Large Throat" configuration of the 

SSME is shown in Figure 16. 

(4) 

A plot of shock strength along the shock path for the 

current configuration of the SSME is shown in Figure 17. The 

corresponding plot for the "Large Throat" configuration of the 

SSME is shown in Figure 18. 

From the above figures it can be seen that the shock begins 

as a weak disturbance. The shock path follows a Right Running 

Characteristic (RRC) surface until x/r* = 4 for the current 

design nozzle, and x/r* = 3 for the "Large Throat" design 

nozzle. The shock wave then gains in strength until the last 

LRC surface in the nozzle is reached. Downstream of this 

851 106 

10 
position the shock cannot effect nozzle performance. 

It was found that the shock strength calculation is 

sensitive to the input parameters. A sensitivity study was 

therefore carried out by J. D. Hoffman using the computer 

program described in Reference 4. The number of points on the 

initial data line was varied by doubling the spacing as follows: 

21, 41, 81, and 161. The computed values of shock strength vs 

position are shown in Figure 19. The Hoffman program uses the 

modified Hall method (’1 for transonic analysis in constructing 

the initial data line. In order to determine the effect on 

shock strength of the transonic analysis, an initial data line 

calculated by .TDK using the modified Sauer method was input 

into Hoffman’s program. The results are also shown in Figure 19. 

A sensitivity’ study was also carried by SEA using the TDK 

computer program. The purpose of the study was to examine the 

sensitivity of the performance .calculation to the pressure 

calculation behind the shock front. It was found that a 1% 

error in pressure corresponds to roughly .75 seconds in specific 

impulse. 

The Lockheed MOC program (lo) was also u’sed to calculate the 

induced shock wave in these nozzles. Both Lockheed Huntsville, 

and Rocketdyne, used their version of the program to perform 

the calculations. Equilibrium chemistry was assumed. The 

results of all of these calculations are summarized in Figure 

20. 

851 106 

11 
5. CONCLUSIONS 

As a result of the studies described in this report, the 

following conclusions are given regarding the performance of the 

SSME engine designs. 

5.1 ------------ Chemical Kinetics 

The effects of chemical kinetics are not important. The 

difference in predicted specific impulse between the ODE and ODK 

analysis is only 2/10 seconds. It is also shown that the shock 

wavq found in the nozzles do not produce a kinetic loss. 

There is no significant difference between equilibrium and 

frozen gas properties in the region of the shock. A Mach shock 

would be required to activate the flow reaction chemistry. 

Three different transonic methods were used to obtain start 

lines for the MOC calculations, 1) modified Sauer , 2) 

modified Hald9), and 3) a time dependant finite difference 

(1 1 

method('l). Each method produced a somewhat different shock wave 

solution. It is not possible to determine which transonic 

analysis is the more accurate. The modified Sauer analysis 

gives the best prediction of measured data (8). The VNAP2 

analysis, however, is based on more advanced methods. A nozzle 

design should be suspect if it shows a significant shock wave 

based on calculations using any one of these transonic methods. 

If the shock wave becomes sufficiently strong, e.g., B > 1, then , 

according to the TDK computer program the nozzle performance is 

significantly degraded. 

851 106 

12 
* 5.3 Shock Wave Prediction 

As shown in Figure 20, nozzle flow field calculations were carried 

out independently by several contractors. Each analysis predicted the 

existence of a shock wave in both the current and "Large Throat" SSME 

nozzle configurations. 

the "Large Throat" nozzle that was 2.7 times as strong.as in the current 

SSME design (see column 1 of Figures 6 and 7). Changes either in the 

transonic method, or in the MOC grid spacing were found to affect the 

shock strength as much as 50%, however, the predicted performance of 

the nozzles was little affected. 

The SEA prediction gave a shock strength for 

5.4 Thrust Chamber Performance Prediction 

The analysis implies that for the current design SSME thrust 

chamber, the performance loss due to Distributed Energy Release is 

more than 5 seconds of specific impulse. 

improvement of the injector design could recover most of this 

performance loss. 

loss for the "Large Throat" SSME configuration, as compared to the 

current design. The loss appears to be primarily due to flow divergence, 

rather than shock wave effects. Because of the small downstream throat 

radius (Rd = .2) of the "Large Throat" SSME a finely spaced MOC grid is 

required near the wall to obtain an accurate performance prediction. 

numerical accuracy of the performance predictions require further 

investigation. 

performance, but a stronger shock (B Q 1) can have an important effect 

on performance. 

near the threshold where shock wave effects become important. 

If this is true, then 

The TDK computer program predicts a substantial* performance 

The 

The calculations indicate that a weak-shock has little effect on 

The "Large Throat" SSME configuration 'appears to be 

* Loss due to nozzle aerodynamics = 3.5 - 1.9 = 1.6 seconds. 

See Section 2. (Aerodynamic Loss Includes: Divergence with Shocks and 

Boundary Layer Effects ) 

851 106 

13 
6. RECOMMENDATIONS 

It is recommended that the SSME MCC be recontoured to reduce 

or eliminate th;?' shock wave predicted for the "Large Throat" 

SSME design. This has recently been done by Rocketdyne (11,121 

by replacing the contour downstream of the nozzle throat with a 

shape designed with the aid of a Rao method ('3) computer 

program. The revised contour was run by SEA, Inc. using the TDK 

computer program, which showed the nozzle to be shock free. 

The predicted nozzle performance was increased by -3 secondsWith regard to a projected "Large Throat" SSME test program, the measurement 

of the shock location in the exit plane is recommended. A comparison of the 

predicted with the measured val ue wi 11 contribute si gni f i cant1 y to veri fy 

the current analytical calculation method. 

. 

851 106 

14 b 

 . --- . 4 --- 

. 

0 

C 

3 

C 

c 

C 
' 

TITLE SSME - COOLED UALL , CURRENT DESIGN, 10% 

DATA ' SDATA 

OOE = 1, OOK = 1, TDK = 1, ELM = 1, IRSTRT= 0, 

SHOCK = 1, 

IRPEAT = 1, 

NZONES = 1, 

ECRATd, ASUE=3,2,1.5, NASUE=3, 

ASUP = 5,10,20,30,40,50,60,77.5, NASUP=8, 

IUALL=4, THE.5.3748, THETA-37. 

Thrust Chamber 

. RSI 5.1527, RWTU 1, RUT0 = .392, THETA1 = 25.4167, RI = 1.73921, 

NUS = 18, 

RS 0, 1.426405, 1.173862, 1.255959, 1.379498, 1.551987, 

1.741611 , 1.947049, 2.186550, 2.212090, 2.226684, 

2.363046, 3.785419, 5.338208, 6.586136, 7.564615, 

8.298253, 8.803421, 

1.152396, 1.452449, 1.812502, 1.851582, 1.873954, 

2S.s 0, -2990952, .3626237, .4733999, -6422291, .8823416, 

2.085214, 4.546562, 7.947338, 11.54691 , 15.34513, 

19.34211, 23.52318, 

IOFF = 3, 

SEND 

REACTANTS 

H 2. 100. -2154. L 

0 2. 100. -3102. L 

NAMELISTS 

OODE 

RKT = 1, 

P = 3285., XP = 1, PSIA = 1, DELH = 0, 

SEND 

OFSKEO = 6.05485, 

REACT IONS 

H + OH= H20 ,Ml ,A=7.5E23 , N=2.6,E=O., 

O+H=OH ,M2,A=C.OE18 ,N=l. ,E=O., 

0+0=02 ,M3,A=1.2E17 ,N=l. ,PO., 

H+H=H2 ,MIA4.4El7 ,N=1. ,E=O., 

END TER REAX 

H2 + OH = H + H2O ,A=2.19€13,N=O. ,E=5.15, 

OH + OH = 0 + H2O ,A=5.75€12, N=O. ,E=. 78, 

H + OH =O+H2 ,A=7.33€12, N=O. ,E=7.3, . 0 + OH =H+02 ,A=1.3E13 ,N=O. ,E=O., 

LAST .REPX 

THIRD 93Cv QEAX RATE RATIOS 

M1=2~-~23.j-H2,5'32,12.5*H,12.~*0,12.5*0H, 

M2=5'HLO, S*HZ, 5*02,12. S*b, 1 2 .5*0,12.5*OH, 

M3=5*H20,~*H2,4.~*02,12.5~H,t2.5*O,l2.~*0Hf 

M4=20*H20,4*H2,1.5*02,25*H,25*0,25*OH, 

LAST CARD 

SODK 

JPRNTr-2, 

SEND 

STRANS 

MQ = 250, 

XM = 1, 

SEND 

WC 

NC = 0, 

I SHCK=l , 

IMA:;=40, IMXF=l, 

SEND 

$ELM 

EP = 77.5, 

I Regen Cooling OFC = 2, 2, DISTRB = 0, 0, 

XCE = 1.849, 23.5, 

IHFLAG = 0, 

NTQU = 27, 

xco = -2.4842, 1.85, 

I Circuits _. -- -.1941,'.1941, .is~~, .97i)4, i.5526, i.gloj, i.96oi 

5.8222, 6.7926, 7.7629, 8.7333, 9.7037, it.64u, 13 

15.5258, 17.4666, 19.4073, 21.3480, 23.523178, 

TQU = 1360, 1500, 1510, 1500, 1470, 1470, 1490, 1490, 840, 

820, 790, 760, 1450, 1260, 1060, 960, 890, 850. 830, 

765, 745, 730, 720, 715, 710, 

MTP = in 

xiiio =':i.4842, -2.40. -2.30, 

RIM0 = 3*1.73251, 

UEO = 535, 690.8, 979.2, 

TEO = 6499.7, 6496.8, 6489.5, PEO = 2918.1, 2906.3, 2877, 

NSECS = 6. 

- .3881 , 3.881 

830, 

795, 

.5a5, 

ORIGINAL PACE 1s 

WA POOR QUALITY 

CAR) NO. 1 

(AR) NO. 2 

(AR) NO. 3 

(AR) NO. 6 

EAULCH(68)LZ 

EAULCH (68) L2 

EAULCH(68)LZ 

EAULCH (69 ) L3 , Finite 3ate 

Chemisfry 

Wa 11 

Temperature 

R 0 

~-~ 

XSEG = -215. -.4658, ~658, 4.6578, 9.3155, 16.3021, 23.53, 

APROF = 50, 76, NPROF = 0, 

KDTPLT=O, KMTPLT=O, KTUPLT=O, 

SEND 

b 

Figure 3: TDK Input for SSE Current Design Analysis 

17 
TITLE SSME - LARGE THROAT DESIGN, COOLED WALL 

DATA 

SDATA 

ODE = 1, OOK = 1, TDK = 1, ELM = 1, IRSTRT = 0, 

SHOCK = 1, 

IRPEAT = 1, 

NZONES = 1, 

ECRAT=2.7, ASUB=2.7,2,1.5, NASUW, 

ASUP = 5,10,20,30,40,50,60,69.5, NASUP=8, 

RSI = 5.4417, RUN = .494, RWTD = .2, THETA1 = 25.4167, RI = 1.73921, 

IYAl.LsL. -I..-- .r 

RS =1.066583 1.11 1520 1 .la9257 

1.306235 , 1.4i9563 , 1.6i9117 , 1.8i3644 , 2.09W9 , 2.108428 , 2.237548 , 3.584382 , 6.236357 . 7.162870 . 7.857546 . 8.335885 , 

2.070426 , 5.054705 , 

ZS =0.1560446 0. 

0.4809552 , 0.708j157 

1,626081 , 1.647265 

10.80651 , 14.40301 

NUS = 17, 

THE = 5.374800 , THETA = 37. 

,2161~2 0.321 0922 , 0.9646279 , 1.248146 , , 1.847305 , 4.177936 , , 18.18771 , 22.14673 , 

1.589077 , 7.398101 , 

IOFF = 3, 

SEND 

REACTANTS 

H 2. 

0 2. 

NAMELISTS mi! 

RKT = 1, 

P = 3010., XP = 1, PSIA = 1, DELH = 0, 

OFSKED = 6.05485, 

100. -2154. L 20.271: 

100. -3102. L 90.180 

SEND 

REACT IONS 

H + OH= H2O ,M1 ,A=7.5E23 ,N=2.6,6=0. , 0 +' H = OH ,M2,A=4.OE18 ,N=l. ,E=O., 

0+0=02 ,M3,A=l.2E17 ,N=1. ,B=O., 

H+H=H2 .. .M4.A=6.4€17 .N=l. ,B=O., 

END TBR REAX 

H2 4 OH =H+HK) ,AS. 19E13, N=O . , Br5.15, 

OH + OH =O+HZO ,A=5.75€12,N=O. ,B=.78, 

H + OH =O*H2 ,A=7.33E12,N=O. ,B=7.3, 

0 + OH =H+O2 ,A=1.3€13 ,N=O. ,B=O., 

LAST REAX 

THIRD BODY REAX RATE RATIOS 

Ml=2O*H20,5*H2,5*02,12.5*H,12.5*0,12.5*OH, 

M2=5*H20,5*H2,5*02,12.5*H,12.5*0,12.5*OH, 

M3=5*H20,5*H2,4.5*02,12.5*H, 12. PO, 12.5*OH , H4=2O*H20,4*H2,1.5*02,25*H,25*0,25*OH, 

CAST CARD 

tOOK 

JPRNT=- 2, 

EP = 69.5, 

SEND 

$TRANS 

MP = 250, 

XM I, 

SEND 

NC=O. 

_- 

(AR) NO. 1 

(AR) NO. 2 

(AR) NO. 3 

(AR) NO. 6 

BAULCH(68)LZ 

BAULCH(68)LZ 

BAULCH(68)LZ 

BAULCH(69)L3 

OFC = 2, 2; DISTRB = 0, 0, 

XCO = -2.6842, 1.85, 

XCE = 1.849, 22.15, 

NTR = 10. 

XINO '2.5, -2.40, -2.30, 

RINO = 3V.6432, 

UEO = 535, 690.8, 979.2, 

TEO = 6499.7, 6496.8, 6489. 

PEO 2918.1, 2906.3, 2877; 

NSEGS = 6, 

XSEG -2.5, -.4658, .4658, 

APROF 

KDTPLT~O,KWTPLT=O,KTUPLT=O, 

NTQU = 27. 

50, 76, NPROF 8 0, 

5, 

4. ,6578, 9.3155, 16.3021, 22.16, 

-. 

xTau = -214862, -2.1348, -1.9407, -1.7467, ..9704, -.na, -.3aai, 

- .19C1, .194l, .3881 

5.8222, 6.7926, 7.76i9, 8.7333, 9.7037, 11.6444,'13.585, 

15.5258, 17.4666, 19.4073, 21.3480, 23.523178, 

TPU = 1360, 1500, 1510, 1500, 1470, 1470, 1490, 1490, 840, 830, 

820, 790, 760, 1450, 1260, 1060, 960, 890, 850, 830, 795, 

765, 745, 730, 720, 715, 710, 

.9704, 1.5526, 1.9407, 1.9601, 3.8815, 

SEND 

Figure 4: 
d 

rl 

a 

3 

.. 

In 

Q 

t 

3 

t3 

4 

5 
TDK PERFORWAKE SUUARY : s#E - COOLED UALL , WRREWT DESIGN, 109% 

REAL UALL COlTWR 1 ZOYES YLILL TW 

FIRST 

TDK/BLn SOLUTION 

SECOWD 

TDK/BLM SOLUTIOH 

THRUST CHAMBER OPERATING COIIDITIOWS 

3285 .OOO 

6609.458 

6.054850 

CHAnEER PRESS [PSIAI 

CHAnEER TEW [RI 

MIXTURE RATIO (-1 H (OXID) . fCAL/IIOLEl 

H (FUEL) fCAL/)KKEI 

DELH (AVERAGE) fBN/LBl 

DELHl (AVE) oBTU/LBl 

HCW (ODE) [BTU/L~I 

THRUST CHAnBER CEWETRY 

ECRAT I-] 

RI f-I 

rHETAl DEGREES1 

RUTU 1-1 

RSTAR [INCHES1 

RUTD (-1 

NIT [-I 

THE (DEGREES1 

THETA DECREES1 

EP (NOZZLE) [-I 

SHOCK PARMETERS 

XA (X/R*) [-I 

XB (X/R*) t-1 

SHOCK (R/R*) (-1 

SHOO: (X/R*) [-I 

SHOQ: STRENGTH [-I - 

EXIT FLW PROPERTIES 

P (AXIS,EXIT) LPSIAl 

P (UALL,EXIT) [PSIAI 

T (UALL.EXIT) [RI 

3285.000 

6543.192 

6.054850 

-3 102 .OOO 

-2154 .OOO 

-422.3787 

0.0000000E+00 

0.0000000E+00 

-31 02.000 ~. 

-21 54. OW 

-303.6657 

0.OWOOOOE+OO 

118.7092 

3 .OOOOOO 

1.739210 

25.4 1670 

1.000000 

5.152700 

0.3920000 

243.0000 

5 -374800 

37.00000 

77.50022 

2.997371 

1.739210 

25.41670 

0.W85945 

5.156323 

0.3910218 

243.0000 

5.299142 

37.00000 

76.50255 

0.23591 15 

0.0000000E+00 

2.584894 

8.834632 

0.2892100 

0.2359115 

0.0000000E+00 

2.589131 

8.839259 

0.0-00 

0 -2726767 0.275631 2 

6.161937 __- -~ 

6.109760 

2483.953 2561.766 

14149.57 

4.243621 

V (UALLiEXIT) tFl/SECl 

IIA (UALL,EXIT) [-I 

14039.21 

4.271464 

ONE-DIb!ENSIONAL FLOU PERFORMANCE 

469.2740 

469.0910 

449.4862 

ISP (ODE1 [SECONDS1 

ISP COOK) fSEMNOSl 

ISP (OOF) LSECOWDSl 

465.131 1 

464-9658 

446.7661 

TYO-DIMENSIONAL FLOU.PERFORWNCE 

0.9910184 

n68.724 

528341.6 

1136.373 

464.9368 

I. 928235 

CD [-I 

CF (TOK) [-I 

CSTAR (TDK) CFT/SECl 

THRUST (TDK) [PWNDSI 

UDOT (TDK) fLB/SECI 

ISP (TDK) [SECONDS] 

0.9896666 

1.921868 

7713.456 

526597.2 

1142.907 

460.7523 

BOUNDARY LAYER PARMETERS 

DFOPT (ELHE) CPWNDSI 8386.935 a285 .425 

O.ZI~R~~E-OI 

7829.081 

6.889535 

0.1 m33E-01 

OF (ELI~E) CPWNDSI 

DISP (ELHE) [SECONDS] 

THETA (EXIT) [FEET] 

DEL' (EXIT) [FEETI 

EP (REGEN) CBTU/SEC] saooi (REGEN) CETU/SECI 

saooi (LOSS) CETU/SECI 

793 1 -962 

6.9401 62 

0.17m33E-01 

0.2187267E-01 

T7.46112 77.16112 

56.39063 

135682.6 0.0000000E+00 

56.39063 

THRUST CHAMBER PERFORIIANCe 

THRUST (TC) CWUNDSI 518665.2 

453.3?21 

1.892919 

5205 12.5 

458.0472 

1 A99662 ISP crci CSECONDSl 

CF (TCI t.1 

Figure 6: TDK Performance Surnrr.ar;. for SF5 Currenr; ConfiguratTon 

20 
TDK PERFORMANCE SUMMARY : SSME - LARGE THROAT DESIGN, COOLED UALL 

REAL UALL CONTOUR 1 ZONES UALL TEMP 

INDUCED SHOCK AFTER XA 

FIRST SECOND 

TOK/ELM SOLUTION TDK/ELM SOLUTION 

THRUST CHAMEER OPERATING CONDITIONS 

CHAMEER PRESS [PSIAl 

CHAMEER TEMP CR] 

MIXTURE RATIO I-] 

H (0x10) [CAL/MOLEI 

H (FUEL) [CAL/MOLEI 

HCHAM (ODE) [ETU/LEI 

DELH (AVERAGE) IETU/LEI 

OELHl CAVE) [BTU/LEI 

THRUST CHAMBER GEOMETRY 

ECRAT [-I RI [-I 

THETA1 bEGREESl 

RUTU 1-1 

RSTAR [INCHES] 

RUT0 1-1 

NIT 1-1 

THE [DEGREES] 

THETA DEGREES1 

EP (NOZZLE) [-I 

SHOCK PARAMETERS 

XA (X/R*) [-I 

XB (X/R*) [-I SHOCK (R/R*) I-] 

SHOCK (X/R*I t-I 

SHOCK STRENGTH [-I 

EXIT FLOW PROPERTIES 

P (AXIS,EXIT) [PSIAI 

P (UALL,EXIT) CPSIAl 

T (UALL,EXIT) [RI 

V (UALL, EX1 T 1 

HA (UALL,EXIT) t-I 

tFT/SECI 

QE- DIMENSIONAL^ FLOW PERFORMANCE 

ISP (WE) [SECONDS1 

ISP (ODK) [SECONDS1 

ISP (OOF) [SECONDS1 

3010 .OOO 

6526.882 

6.054aso 

-3102.000 

-2154.000 

- 422.3749 

0.0000000E+00 

0.0000000E+00 

2.700000 

1.739210 

25.41670 

0.4940000 

5.44 1700 

0.2000000 

244.0000 

5 374800 

37.00000 

69.48698 

0.1203630 

0.0000000E*00 

2.637427 

a.5mi~ 

1.131168 

0. tazoo55 

6.195770 

2519.777 

13992.76 

4.229021 

463.2604 

463.0793 

444.7228 

TWO-DIMENSIONAL FLOW PERFORMANCE 

Q) 1-1 0.9802917 

CF (TDK) [-I 1 .a92262 

CSTAR (TDK) IFT/SECI 7774.756 

THRUST (TDI) [PCUNDSI 529866.9 

ISP (TDK) [SECONDS] 457.2597 

UOOT (TDK) [LE/SECl iisa.788 

BOUNDARY LAYER PARAMETERS 

DFOPT (ELME) [POUNDS] a34 1 .OM 

DISP (BLME) [SECONDS] 6.8081 u 

THETA (EXIT) [FEET] o.i7a0233~-01 

DEL* (EXIT) [FEET] 0.214239a~-oi 

OF (ELME) [POUNDS1 7889.169 . 

EP (REGEN) CBTU/SECI 69.4871 4 

SWOT (RE JEW) [BTU/SECI 135283.0 

SWOT (LOPS) IETU/SECI 0.0000000E+00 

THRUST CHAMEER PERFORMANCE 

THRUST (TC) [POUNDS] 52im.a 

ISP (TC) [SECONDS] 450.4516 

CF (TC) [-I 1.864088 

3010.000 

6591.104 

6.054850 

-3102.000 

-2154.000 

- 305.691 6 

0.0000000E+00 

116.6856 

2.69491 2 

1.739210 

25.41 670 

0.4925624 

5.44694 1 

0.1988453 

264.0000 

5.327114 

37.00000 

68.57317 

0.1203630 

0.0000000E+00 

2 -61 2652 

8.626249 

I. 138703 

0.2786561 

6.247626 

2589.486 

141 09.94 

4.210537 

467.2708 

467.0724 

447.3469 

0.9azii96 

1 .a98804 

531698. a 

7830.471 

1152.760 

46 1 -2397 

8277.303 

7a24.0~ 

6.7a725 2 

o.i7a0233~-01 

0.2142398~- 01 

69.4871 4 

0.0000000E+00 

0.0000000E+00 

523874.7 

454.4525 

1 .a70862 

Figure 7: TDK Performance Summary for SSYE "Large Throat" 

Configuration 

21 
ORIGINAL PAGE IS 

Of POOR QUALITY 

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0 

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0 

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W 

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a 

J 

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CA 

4 

0 

28 
c L" 

rn 

c, rnd 

... ___+ --i .... --~- ......... .. 

. . .............. ..... .. .............. -i ---2.. --c :.---4- j 1 ... ..-L ... .... .... 

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.... -. .,~ .... --.- ......... ... .............. , .I___. 1 _._-I 1 -_-.' ~ 

.I 

.. 

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Figure 17: SSME Current Desig; 

Shock angle vs x/r - 

y=l. 24 

Figure 18: SSME "Large Throat" Design 

Shock angle vs x/r* 

v=1.24 

31 
m 

0 co =r 0 

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-. .- - . - .............. ...... ----- -.__. .......... 

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33 
REFERENCES 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

Nickerson, G. R., Coats, D. E., and Dang, L. D., '!The 

Two-Dimensional Kinetic (TDK) Reference Computer Program", 

Engineering and Programming Manual, Software and Engineering 

Associates, Inc., prepared for Contract NAS8-35931 , NASA/MSFC, April 1985. 

Nickerson, G. R. and Dang, Lanh D., Report No. SN76FR, 

"Assessment of the SSME Nozzle Performance" Software and 

Engineering Associates, Inc., prepared for Aerojet 

Techsystems Company, March 1985. 

"JANNAF Rocket Engine Performance Predict ion and 

Calculation Manual", CPIA 246, April 1975. 

Hoffman, J. D., ?'A Computer Program. for the Performance 

Analysis of Scarfed Nozzles", U.S. Army Missile Command 

Technical Report RK-CR-84-3, prepared for Propulsion 

Directorate, U.S. Army Missile Laboratory, May 1984. 

TDK Data Package for the SSME, "Informal Communication from 

K. Gross", NASA/MSFC, received December 1984. 

Carroll, R. G., et.al., "Performance Comparison of the 

Current SSME and a New Main Injector - Main Combustion 

Chamber Configuration Using the JANNAF Methodology", 22nd 

JANNAF Combustion Meeting, 7-10 October 1985. 

Cline, M. C., "VNAP2: A Computer Program for Computation of 

Two-Dimensional, Time-Dependent-, Compressible, Turbulent 

Flow", Los Alamos National Laboratory Report No. LA-8872, 

August, 1981. 

Back, L. H., Massier, P. F., and Gier, H. L., l f C o m p a r i s o n o f 

Measured and Predicted Flows through Conical Supersonic 

Nozzles with Emphasis on the Transonic Region", AIAA 

Journal, Vol. 3, No. 9, Sept. 1965, pp. 1606-1614. 

Hall, I. . M., "Transonic Flow in Two-Dimensional' and 

Axially-Symmetric Nozzlesff, Quarterly Journal of 

Mechanics and Applied Mechanics, Vol. XV, Pt. 4, 1962, 

pp. 487-508. 

10. Smith, S. D., and Ratliff, A. W., "Rocket Exhaust Plume 

Computer Program Improvement, Vol. I, Final Report" 

LMSC-HREC D162220-I, prepared for Contract NAS7-761, June 

1971. 

11. Private communication from R. O'Leary, Rocketdyne Division 

of Rockwell International, October 1985. 

851 106 

34 
1-2. Lee, Y. C., llNozzle Flowfield and Specific Impulse (Isp) 

Calculations for Rocketdynels Shock Free Large Throat SSME 

Nozzlef1 NASA MSFC, memo ED33(45-85), September 25, 1985. 

13. Rao, G. V. R., "Exhaust Nozzle Contours for Optimum 

Thrust", Jet Propulsion, Vol. 28, No. 6, June 1958, pp. 

377-382. 

851 106 

35 
APPENDIX A 

DISCUSSION OF SUMMARY OUTPUT 

At the end of each computer run, the TDK program prints a 

table of summary output. Examples of this output are given in 

Figures 6 and 7. The first item printed is the title 

9 

TDK PERFORMANCE SUMMARY: (title) 

Next, performance parameters summarizing the results of the 

calculations are printed in three columns. The left hand Column 

identifies each item to be printed and its units. The first . 

column of results is for the first MOC/BLM solution, and second 

column of results is for the second MOC/BLM solution. 

The items labeled ISP(TDK1, THRUST(TDK1, WDOT(TDK), CD, 

CSTAR(TDK), and .CF(TDK)’ are defined as: 

--- Name Units --------- Definition ---- 

SP,2D ISP(TDK) sec Specific Impulse, I 

THRUST( TDK) lbf‘ Thrust, FZD 

WDBT(TDK) lbm/sec Mass Flow, i2D 

CD - Flow coefficient, 

CSTAR(TDK) ft/sec Characteristic Velocity, C*2D 

‘D, 2D 

CF( TDK) ‘F,2D - Thrust coefficient , 

If a TDF or TDE calculation was made rather than TDK, then 

these items will be relabeled. 

851 106 

36 
are obtained by * The values given for I and q 

evaluating the integrals discussed in the documentation for MOC 

module subroutine CHAR. The mass flow integral is evaluated 

across the MOC initial data line.. The I integral is evaluated 

across the initial data line, plus the integral of the axial 

component of wall pressure from the initial data line to the 

nozzle end point. The thrust is 

SP,2D 2D 

SP 

rh F2D = I sp,2D 2D 

The nozzle flow coefficient is calculated as 

'D,2D - i2D/ IID 

where 

A* 

* * 

'1, '1D '1D 

* 

is obtained from ODE. A is the geometric throat area. 

* 

The characteristic velocity, C , is calculated as 

* 

'2D I SP,2D g/cF, 2D 

where the thrust coefficient, CF, is defined by 

I 

'F, 2D F2D 'c A* 

* 

Again, A , is the geometric throat area. 

The items labeled DISP(BLME), DFOPT(BLME), DF(BLME), 

ISP(TC), THRUST(TC), and CF(TC) are defined as follows: 

Name -- 

DISP(BLME1 

DFOPT(BLME) 

Definition --- Units -------- 

see 

lbf 

''S~,BLM 

'amb AF~~~ for Pe= 

DF ( BLME ) lbf AF~~~ 

851 106 

37 
Name -- Definition ---- Units -------- 

ISP (TC 1 sec IS~, 2D ,BLM 

THRUST( TC) lbf F2D,BLM 

CF(TC) . 'F, 2D ,BLM 

- . 

In the above, the thrust loss calculated by the BLM is given 

by the following relation: 

AF~~~ = 2nre cos ae * 

pe 'i 'BLM 

- 2rre cos a e * (Pe - 'amb) 

* 

6BLM 

The additional items, printed are 

AFBLM/ '2D I 

''S~,BLM 

'sp, 2D,BLM. I (F2D- AFBLM) h2D 

F2D - AFBLM I 

,BLM 

I / Pc A* 'F,2D,BLM F2D, BLM 

Performance.parameters summarizing the results of the second 

MOC/BLM calculation differ from the first set printed as 

follows: 

1) The TDK and ODE results for the second (invisid 

core) run have a modified wall contour, throat area, 

and expansion ratio. Note that the system enthalpy is 

different than used in the first run if the BLM wall 

calculation is not adiabatic. 

2) The BLM results are re-calculated using edge conditions 

from the second TDK run. BLM itself is not re-run, and 

the values of 6 and 8 are not changed. 

* 

The equations used are the same as given above. 

851 106 

38