. £.

LMSC-HEC TR F042555

DUCT FLOW NONUNIFORMITIES STUDY

FOR SPACE SHUTTLE MAIN ENGINE

Technical Report

Contract NAS8-34507

August 1985

By

Jurgen Thoenes

^NASA-Cfi-17873U) DDC1 FLOW NCNUUIPOiJHITIES N86-22632

STUDY FOB SPACE SEOTTLE MAI N ENGINE

{Lockheed Missiles and Space Co.) 129 p

HC AQ7/MF A01 CSCL 21H Duclas

^ _ _ G3/20 08800

Prepared for

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

MARSHALL SPACE FLIGHT CENTER, AL 35812

by

Missiles & Space Company. Inc

Huntsville Engineering Center

4800 Bradford Drive. Huntsville. AL 35807
LMSC-HEC TR F042555

FOREWORD AMD ACKNOWLEDGMENTS

This study was performed under Contract NAS8-34507 with Mr. Heinz

Struck of NASA-Marshall Space Flight Center serving as technical monitor.

Appreciation is expressed for his critical comments throughout the course of

this investigation.

The experimental part of the study was performed by personnel of

Rockwell Tnternational/Rocketdyne Division under Subcontract No. SM80C6620M

to Lockheed with Mr. Dennis G. Pelaccio serving as principal investigator.

The cooperation and patience of Rocketdyne personnel in clarifying the many

questions which arose from the experimental effort is very much

appreciated. The summary of the experimental effort contained in the

present report was largely taken from their documentation. The

computational part of this study could not have been completed without the

help of past and present members of the Lockheed-Huntsville Computational

Mechanics Group. The author is grateful for all their contributions to this

effort.

PRECEDING PAGE BLANK HOf

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CONTENTS

Section

1

2

Table

2

3

4

5

6

FOREWORD AMD ACKNOWLEDGMENTS

INTRODUCTION AND SUMMARY

SUMMARY OF EXPERIMENTAL EFFORT

2.1 Introduction

2.2 Test Configuration

2.3 Test Results

METHOD OF ANALYSIS

3.1 The PAGE Code

3.2 Geometry and Grid Construction

3.3 Flowfield Initialization

3.4 Flowfield Analysis

ANALYTICAL RESULTS

4.1 DFNUS Nominal Configuration

4.2 Configuration Variations

CONCLUSIONS

REFERENCES

LIST OF TABLES

HGM Design Comparisons

Test Article Instrumentation Legend

Two-Duct/SSME HGM Reynolds Number Comparison

DFNUS HGM Pressure Test Data (psi)

Axisymrnetric HGM TAD Results

Results of Turnaround Duct Variations

Page

ii

1

4

4

4

12

27

27

32

46

64

64

105

121

123

6

11

12

13

65

120

ill

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LLSF OF FIGURES

F-igure

1 Two-Duct HGM Air Flow Test Powerhead Configuration 7

2 Instrument Layout 10

3 Screen Exit Static Pressure Distribution 15

A Static and Total Circumferential Pressure Variation D/S

of 180 deg Turn 16

5 Downstream 180-deg Turn Total Pressure Distribution 17

6 Downstream 180-deg Turn Static Pressure Distribution 18

7 Two Duct HGM Fishbowl Entrance Pressure Variation 19

8 Two-Duct HGM, Fishbowl Dimensionless Pressure Variation 20

9 Circumferential Static Pressure Variation at Turbine Exit 21

10 Static Pressure Variation Downstream of 180-deg Turn 23

11 Total Pressure Variation Downstream of Turnaround Duct

180-deg Turn 23

12 Stagnation Region Comparison Between Two- and Three-Duct

Configurations 24

13 Engine-Scaled Three-Duct Manifold Mach Number Profiles

Along Duct Major Axes (100 Percent Power Level Condition) 25

14 Engine-Scaled Two-Duct Manifold Mach Number Profiles

Along Duct Major Axes (100 Percent Power Level Condition) 25

Ib DFIMUS Hot Gas Manifold Turnaround Duct and Bowl

Cross-Section Definition 33

16 Definition of Transfer Duct Location Relative to Hot Gas

Manifold Bowl 34

17 Hot-Gas Manifold Bowl Inside Wall Sparse Grid . 36

18 Hot-Gas Manifold Bowl Outside Wall Sparse Grid 37

19 Hot Gas Manifold Composite Grid 38

20 Hot Gas Manifold Bowl Grid (Unwrapped Inside, Center,

Outside Surface) 39

21 Hot-Gas Manifold Bowl Cross-Section Grid 41

2? Hoi-Gas Manifold Grid, View Along Transfer Duct Axis 42

23 Modified HGM Bowl Outside Wall Sparse Grid 43

24 Modified HGM Composite Grid 44

25 Nominal Turnaround Duct Cross-Section Grid 45

'26 Nominal Turnaround Duct Inside Wall Grid 47

27 Nominal Turnaround Duct Outside Wall Grid 48

28 Nominal Turnaround Duct Composite Grid 49

29 Nominal Inside Wall Grid 50

30 DUVUS HGM Nominal Outside Wall Grid 51

31 DFNUS HGM Turnaround Duct and Bowl Cross-Section Grid 52

32. Definition of Flow Angles 53

33 HGM Bowl Center Plane Velocity Vector Plot and Streamtubes

for Initialisation 56

34 Multi-Cycle Predictor-Corrector Finite Difference Method 58

35 Effect of Boundary Condition Specification on Pressure

Contours in Turnaround Duct 62

IV

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Figure Page

36 Effect of Viscosity on Mass Flow 66

37 HGM TAD Flow - Pressure Contours 68

38 HGM TAD Flow - Pressure Contours 69

39 HGM TAD Flow - Mach Contours 70

40 HGM TAD Flow - Mach Contours 71

41 HGM TAD Flow - Velocity Field 72

42 HGM TAD Flow - Velocity Field 73

43 Turnaround Duct Exit Pressure Variation 75

44 HGM Bowl Velocity Vector Initialization Wear Inside

and Outside Wall 76

45 Behavior of Unsteady Derivatives and Duct Inlet Mass Flow

as Function of Time 77

46 HGM Bowl Center Plane Velocity Field 79

47 HGM Bowl Center Plane Static Pressure Contours 80

48 HGM Bowl Center Plane Mach Number Contours 81

49 Comparison of Computed Static Pressures to Measured Static

Pressures in Bowl 83

50 Comparison of Total Pressures to Measured Data in Bowl 83

51. Nominal HGM Bowl and Transfer Duct Flow Field 84

52 Nominal HGM Transfer Duct Flow Field Results 85

53 Comparison of Computed Transfer Duct Exit Static Pressure

Contours and Stagnation Regions from Experiment 86

54 Two Duct HGM Duct Inlet Mach Number Variation 88

55 DFNUS HGM Nominal Configuration Velocity Field 90

56 DFNUS HGM Nominal Configuration Pressure Contours 91

57 DFNUS HGM Nominal Configuration Mach Number Contours 92

58 DFNUS HGM Nominal Configuration Bowl - Transfer Duct

Flow Field 93

59 DFNUS HGM Nominal Configuration Bowl - Transfer Duct

Flow Field 94

60 DFNUS HGM Nominal Configuration Flow Field 96

61 DFNUS HGM Nominal Configuration Pressure Contours 97

62 DFNUS HGM Nominal Configuration Mach Number Contours 98

63 DFNUS HGM Averaged Pressure Along Flow 99

64 Turnaround Duct Exit Static Pressure Distribution 101

65 Turnaround Duct Exit Total Pressure Distribution 102

66 DFNUS HGM Bowl Inlet Static Pressure 103

67 DFNUS HGM Bowl Inlet Total Pressure 104

68 Transfer Duct Exit Mach Number Profiles 106

69 Modified HGM Bowl and Transfer Duct Flow Field 108

70 Nominal HGM Transfer Duct Flow Field 109

• 71 Modified HGM Transfer Duct Flow Field 109

72 Nominal HGM Transfer Duct Mach Contours 110

73 Modified HGM Transfer Duct Mach Contours 110

74 Transfer Duct Exit Static Pressure Profile 111

75 Transfer Duct Exit Total Pressure Profile 112

v

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Figure Page

/6 Twin Duct HGM - Ratio of Average Cross Flow to Average

Axial Flow Along Transfer Duct 113

7/ Turnaround Duct Variations 115

78 Turnaround Duct Cross-Sectional Area Variations 116

79 Axisymrnetric Turnaround Duct Variations, Velocity Vectors 117

80 Axisymmetric Turnaround Duct Variations, Static Pressure

Contours 118

81 Axisymmetric Turnaround Duct Variations, Mach Number Contours 119

VI

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1. INTRODUCTION AMD SUMMARY

Much of the U.S. activity in space over the coming years will be

dependent upon the Space Shuttle and its derivative versions as a principal

space transportation system. This dependence requires improved designs or

techniques to extend the life, upgrade performance, reduce weight, lower

operational costs, and generally improve the functional capability of the

main propulsion system. The engines for this main propulsion system are

advanced high pressure engines operating on oxygen and hydrogen. A need

therefore exists to investigate, develop, and define basic concepts in

support of the main propulsion system improvements. One basic area that

bears investigation is the hot gas flow nonuniformities that occur within

the manifold, duct work, and main injector. Nonuniformities result from

highly distorted and mismatched flows within the ducts which create severe

environments for the system components, thus limiting their useful life.

Development and verification tests of the Space Shuttle Main Engine

(SSMl) have shown that the three gas transfer tubes have an uneven flow

distribution with large areas of separated flow. The outer transfer tubes

each carry approximately twice as much of gas as the center tube. This

causes the energy of the gas to be much higher in the outer tubes. Flow

from the tubes impinge upon the main injector liquid oxygen posts which bend

under the static load of the gas flow, the bending being more pronounced in

line with the outer tubes. To alleviate this phenomenon and to keep the

posts cooler, shields, linking pairs of posts in the outermost row, were

installed. The design alteration enhanced the injector life; however, LOX

post failures have shown that this change alone is insufficient to grant

specified life at equal to or greater than rated power levels.

Incorporation of the shields also affects circumferential flow in the

annulus arid degrades the engine performance arid necessitates higher

operating temperatures in the turbines.

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To improve the SSME design and for future use in the development of new

generation rocket engines, a combined experimental/analytical study was

undertaken with the goals of first, establishing an experimental data base

for the flow conditions in the SSME high pressure fuel turbopump (HPFTP) hot

gas manifold (HGM) and, second, setting up a computer model of the SSME HGM

flow field. Using the test data to verify the computer model it should be

possible in the future to computationally scan contemplated advanced design

configurations and limit costly testing to the most promising design.

This report documents in detail the effort of establishing and using

the computer model, The experimental effort, performed by Rocketdyne under

subcontract to Lockheed, is described in a companion report entitled "Duct

Flow Wonuniforrnities Study, Final Report" (Ref. 1), while a shorter summary

can be found in Ref. 2.

For the benefit of the reader, a brief summary of the experimental

effort is also presented in Chapter 2 of the present report. The analytical

work, performed by Lockheed, is described in detail in the main portion of

the present report.

1 he comparison of computational results and experimental data observed

as a result of this study clearly demonstrate that computational fluid

mechanics (CFD) techniques can be used successfully to predict the gross

features of three-dimensional fluid flow through configurations as intricate

as the SSME turbopump hot gas manifold. Although gaps in the technology

remain, such as the unavailability of an accurate turbulence model for

internal flows, the principal factor which presently limits the extent to

which prediction calculations can be performed is cost. Detailed

calculations require high resolution. In spite of the great progress

achieved in the last decade both with regard to computational methodology

and facilities, such calculations must still be judged as too expensive to

be performed routinely.

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The high cost of experimental efforts, both with respect to hardware

and labor, is, of course, common knowledge. For this reason, fewer

measurements were performed than would hawe been desirable for this study.

Careful examination of the data obtained raised almost as many questions as

it answered, and pointed to the need for more detailed measurements,

particularly in places of the configuration where the nature of the flow is

uncertain.

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2. SUMMARY OF EXPERIMENTAL EFFORT

2.1 INTRODUCTION

In this study, a full-scale, modified, fuel-side SSME was evaluated

using a high-pressure, ambient-temperature, air blowdown system, which was

directed toward improving the overall flow distribution and decreasing

turbulence levels in the turbine exit, turnaround duct, and transfer duct

regions compared to the present SSME hot-gas manifold design. Detailed

steady state pressure measurement surveys were performed of the HGM fuel

side flow field, using wall static ports, total pressure Kiel probes,

directional probes, and total pressure rakes. Some high frequency pressure

measurements were also included to quantify the turbulent nature of the flow.

Data were scaled to engine conditions and were compared to similar data

for the current SSME three-duct HGM design. From these comparisons, flow

system improvement trends associated with the advanced SSME hot-gas manifold

design concept were then established.

2.2 TEST CONFIGURATION

A number of advanced HGM fuel-side design concepts were conceived and

evaluated (Ref. 1). The concept options generated were guided by two major

goals: (1) to produce a more favorable flow environment for the SSME main

combustion chamber LOX injector posts and HPFT turbine by improving transfer

duct flow distribution, velocity profile uniformity, decreasing turbulence

levels, and minimizing streamline pressure losses; and (2) compatibility

with flow conditions associated with projected increased SSME power levels.

These HGM concepts were evaluated in terms of their flow aerodynamic,

therrnodynamic, structural, system integration, and fabrication

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characteristics. From this design option task, an enlarged area, fuel-side,

two-transfer duct concept was selected as the HGM configuration that was

fabricated, tested, and analyzed in this study.

The selected design has the following key features incorporated on the

fuel turbine side of the manifold: (1) two .6.50-inch diameter ducts that

increase flow area approximately 30 percent over the current configuration

decreasing the flow dynamic head proportionally; (2) increase in turnaround

duct area, 8-deg outer wall fairing after the 180-deg turn to decrease the

flow dynamic head; (3) slightly rounded duct inlets to assist in turning the

flow into the transfer ducts; (4) slightly rounded duct outlets to assist in

distributing the flow around the main injector LOX post bundle; (5) faired

transfer ducts into the fuel preburner housing to assist in directing flow

into transfer ducts and decreasing the HPFT exit pressure gradient; (6)

faired transfer ducts into the main injector housing to assist in

distributing flow around the main injector LOX post bundle; (7) increasing

the HGM fishbowl volume by eliminating the present liner element to decrease

the flow dynamic head in this region; and (8) compatibility to incorporate

contoured turning vanes to assist in distributing flow into the transfer

ducts and decreasing the HPFT exit pressure gradient. A schematic layout of

this advanced HGM design identifying its key features is shown in Fig. 1.

A comparison of the two-duct HGM to the current SSME HGM design is

displayed in Table 1. The major area increase in the turnaround duct exit

area, fishbowl cross-sectional area, and duct cross-sectional area

associated with the two-duct HGM design tends to decrease the flow dynamic

pressure for a given operational setting, which assists in gradual turning

of the flow. These HGM design features also improve duct flow distribution,

uniformity, and decrease flow turbulence, as well as assist in producing

uniform flow conditions at the HPFT exit.

A low-cost philosophy guided the design and fabrication of the hot-gas

manifold test article. An existing surplus SSME hot-gas manifold was

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Table 1 HGM DESIGN COMPARISONS

Turnaround Duct

Turnaround Duct

Exit Area

Fishbowl CrossSectional Area

Duct CrossSectional Area

Faired Duct

Inlets1*

Faired duct

Outlets

SSME HGM

Current

Design

FPL**

29.5 in2

6.05 in2

51 in2

Yes

No

Flow Study

Design Model,

Two Ducts

RPL (FMOF)+

49.68 in2

10.6 in2

66.3 in2

Yes

Yes

Percentage

Difference

Two-Duct Design

SSME Design

—

68.5

75.3

30.0

-

-

*Slightly rounded.

x*Full power level configuration.

"•"Rated power level, first manned orbital flight configuration.

modified to produce the advanced, two-duct HGM test article. Additionally,

where applicable, internal flow simulation components and instrumentation

techniques that were successfully demonstrated in past HGM flow studies for

the present SSME engine design (Ref. 3) were used. Numerous steady-state

and high-frequency pressure instrumentation ports were incorporated in the

fuel side of the model to define the flow field in detail from the model

inlet to the transfer duct exits. The test model was designed for a working

pressure of 300 psia.

"Ihe oxidizer flow was modeled with a preburner/turbine simulator and

turnaround duct. Flow enters the oxidizer preburner, which then transitions

into an annulus passage that has six long, equally spaced blades to impart a

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ORIGINAL PAGE 13

Of POOR QUALfTY

swirl velocity component to the flow. The swirling flow is typical of

turbine exit flow conditions. The flow then enters the oxidizer turbine

exit simulator where the flow direction is changed 180 deg and exits into

the large oxidizer side HGM fishbowl region (Fig. 1). In the SSME the

oxidizer side HGM fishbowl region contains the heat exchanger component.

Flow then exits through the two oxidizer transfer ducts into the main

injector. Aluminum and Ores were the materials used in oxidizer side

simulator hardware designs. This design simulates the gross features of the

SSME oxidizer flow field but lacks proper simulation of flowfield details.

The degree of simulation designed into the test model was considered

adequate because the oxidizer flow field does not influence the fuel side

FUEL SIDE

TRANSFER DUCT

OXIDIZER SIDE

TRANSFER DUCT

OXIDIZER PREBUHNER

OXIDIZER SIDE

TURBINE SIMULATOR

A. SIDE VIEW

MCC FLOW DIRECTION

UPPER TRANSFER

OUCT

MAIN INJECTOR

TOROS IRACETRACKI

FLARED HPFT HOUSING/

DUCT INTERSECTION

MAIN INJECTOR

FLARED INJECTOR HOUSING/DUCT INTERSECTION

B. TOP VIEW

Fig. 1 Two-Duct HGM Air Flow Test Powerhead Configuration

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transfer duct flow field to a great extent. This is considered a good

assumption because only approximately 30 percent of the total HGM gas flow

goes through the oxidizer side of the HGM, while the remaining 70 percent is

passed through the fuel side during hot-fire engine operation, as previously

mentioned.

In contrast to the oxidizer side simulator design, the fuel

preburner/turbine simulation hardware was designed to simulate the SSME fuel

side flow field in detail. Like the oxidizer side simulator, the fuel side

simulator was based on a design that was successfully demonstrated in past

HGM flow studies. Past flow study test data showed that this simulator

design produced an HGM fuel side flow that correlated well with that

measured in an SSME engine. In this design, the flow enters the fuel

preburner simulator where it is manifolded into an annular passage. At the

annular passage entrance, a turbine simulator screen is placed to produce

flow effects that are characteristic of those associated with a 15 deg swirl

angle clockwise if viewed in the direction of the flow downstream of the

scroen, which is typical of SSME HPFT exit flow conditions at rated power

level. Constant velocity conditions are produced by varying the orifice

diameter as a function of radial position. The screen was designed for a

pressure loss coefficient (Ap /q) of 5.6, which is approximately 25

percent of that exibited by the HPFT while still having enough resistance to

stabilize flow exit conditions. Twelve thin fins, which span the width of

the annular channel, are positioned just downstream of the screen exit in an

equally spaced circumferential fashion. These fins simulate flow

interference blockage associated with the turbine exit coolant liner

supports. They are set at an angle of attack to the flow because of the

swirl angular velocity component, and therefore add eddy vortex (vorticity)

structure to the flow. The flow then changes direction, 180 deg, in the

turnaround duct region. The turnaround duct geometry simulates that used on

the Space Shuttle Columbia's first set of flight engines known as the First

Manned Orbital Flight (FMOF) configuration. Downstream of the 180 deg turn,

the outer wall of the annular flow channel is designed with an outward 8 deg

8

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taper. Twelve large support struts are then equally spaced

circumferentially in the annular passage at the fishbowl entrance and

simulate major structural components associated with the engine in this

region. In the design of the HGM fuel-side fishbowl, the coolant liner was

removed to increase the fishbowl volume. Two 6.5-in. constant ID ducts were

integrated into the fishbowl and main injector housing, completing the

fuel-side gas flow path to the main injector assembly. The coolant liner on

the fuel side of the main injector was removed to accommodate the large

transfer ducts. The two-duct HGM design also incorporates slightly rounded

entrance and exit duct geometries and flush internal surfaces at the outer

intersection points between the transfer ducts and the HGM fuel preburner

and main injector housing (Fig. 1). Like the oxidizer simulator hardware,

the fuel side simulation hardware was designed to be made of aluminum and

Cres material.

The SSME powerhead main injector was designed to be removable for ease

in instrumentation and configuration changes. A modified SSME main

combustion chamber (MCC), which incorporates the addition of a long throat

ASME flow metering type nozzle is bolted to the HGM main injector exit

face. The flow metering nozzle chokes the flow maintaining high pressure

within the flow model and also functions as a model total flow metering

device.

Integration of an extensive amount of pressure instrumentation was

incorporated into the fuel side test model. The model instrumentation

measurement locations were placed to give detailed steady-state flow field

definition at the model inlet, turnaround region, fishbowl entrance,

transfer duct entrance and exit planes. High frequency instrumentation was

included in the model to give a qualitative assessment of the turbulent

nature of the flow. A layout of instrumentation (location and type) is

shown in Fig. 2 and listed in the legend given in Table 2, respectively.

The upper transfer duct was designed to accept a pressure survey at the

entrance. Flow conditions are defined at both transfer duct exits (Symbols

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ORIGINAL PAG£ IS

OF POOR OiiALITY

TOP VIEW

_u

UPPER TRANSFER DUCT

0

SIDE VIEW

Fig. 2 Instrument Layout

10

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Table 2 TEST ARTICLE INSTRUMENTATION LEGEND

State Pressure Measurements

Symbol Location/Type

(7) Model Inlet/3 Static - 1 Total

2 Screen Exit - Upstream 180 deg Turnaround/Static

3 Downstream 180 deg Turnaround/Static

4 Downstream 180 deg Turnaround/Total

5 Fishbowl - Entrance Upstream of Transfer Duct (3-0 Probes) .

5A Fishbowl Entrance/Static

SB Fishbowl Entrance/Total

6 Transfer Duct Entrance/Static

7 Transfer Duct Entrance/Total

8 Transfer Duct Exit Plane/Total

9 Transfer Duct Exit Plane/Static

10 Transfer Duct Exit Inner Wall/Static

11 Transfer Duct Exit Inner Wall/Total

12 Main Combustion Chamber/Total

High Frequency Measurements

/1\ CG1P - Racetrack Flow

2 Upper Transfer Duct - Exit

3 Upper Transfer Duct - Entrance

4 Fuel Side Model Inlet

8 and I, Fig. 2) by placement of exit total pressure survey rakes. In the

lower duct, a pressure rake element was placed to measure the inner wall

region flow field at a position 1.25 in. upstream of the exit rake plane.

These total pressure rake elements were designed to be easily removable,

haue rotational capability, and be interchangeable with all rake locations.

When assembled the cross-sectional area blockage of the rakes was no greater

than 9 percent of the total transfer duct cross-sectional area. Total

pressure Kiel probes were used downstream of the 180 deg turnaround region

and three-dimensional directional probes were used to map the flow at the

fishbowl entrance plane (Fig. 2).

Detailed measurements were made of the fuel-side HGM internal surfaces

to support configuration definition for use by complementary computational

model flow analysis efforts (See Chapter 3, also Ref. 4).

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2.3 TEST RESULTS

Tests were run at three flow conditions (Reynolds number, based on

transfer duct diameter and flow conditions, approximately equal to 2 •

106, 5 • 10 , and 7 • 10 ; see Table 3) to determine the influence of

Reynolds number on the fuel-side flow field.

Test repeatability was considered quite good between individual tests

at the approximate same operating conditions. In general, little or no

Reynolds number effect was observed throughout the HGM fuel-side flow system

except at the fishbowl entrance plane where the local dynamic pressure

Table 3 TWO-DUCT/SSME HGM REYNOLDS NUMBER COMPARISON

Fuel Mass

Flow (Ibm/sec)

Re x 106

Re/D x 107

Cold Flow 2-Duct

Low

Flow

26.9

2.59

0.48

"tedium

52.3

5.08

0.94

Maximum

73.5

7.07

0.94

SSME*, Hot-Fire

65%

Throttle

90.6

4.57

1.11

100%

Throttle

151.8

7.68

1.86

109%

Throttle

173.0

8.14

1.98

*Based on Columbia SSME configuration.

circumferential variations increased by approximately one dynamic pressure

head <*t the low Reynolds number test condition (ReD = 2.6 x 10 ). These

results give confidence that at the high Reynolds number test conditions (69

percent of SSME rated power level Reynolds number), the critical Reynolds

number conditions have been exceeded as is characteristic of engine

operation. This implies that major separation and turbulent flow structure

features present in a hot gas manifold operated at engine conditions should

also be present in the hot gas manifold cold flow model when operated at

high Reynolds number test conditions.

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2.3.1 Two-Duct HGM Test Results

In order to compare test results with results to be obtained from model

calculations, experimental data in appropriate form are needed for the

entire configuration from the turnaround duct inlet (turbine exit) to the

transfer duct exit. Constraints and/or limitations with respect to the

number of probes as well as the number of channels in the data recording

system available unfortunately did not allow the taking of as many data as

would have been desirable at exactly the same overall conditions. Table 4

summarizes averaged pressure data obtained from several high Reynolds number

test runs. Since little effect of Reynolds number on the qualitative

behavior of the flow was noted, we can assume that small variations in

Reynolds number should not invalidate a compilation of data from different

runs to serve as a data base to: (1) anchor the model calculations; (2) to

Table 4 DFNUS HGM PRESSURE TEST DATA (psi)

Test 1.07 1.09 2.09

m (Ib/sec) 61.63 61.98 73.48

11

TE

TAD E

BI

TO I

TD E

p 255.03

pt 265.95

P

Pt

P

Pt

P

Pt

p 179.3

pt (182.3)

p 172.9 178.3

pt (175.1) (180.4)

2.15 3.06

71.34 72.86

244.4 247.6

254 . 4 258 . 3

176.0

188.7

190.2

209 . 9

174.7

179.0

169.5

Legend: TI = Turbine inlet; TE = turbine exit; TAD E =

turnaround duct exit; BI = bowl inlet; TD I =

transfer duct inlet; TD E = transfer duct exit.

13

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compare theory and experiment; and (3) to provide the overall total pressure

loss from the turbine exit to the transfer duct exit.

Inspection of Table 4 reveals that the pressure measurements at the

turbine exit (TE, Test 3.06) are inconsistent with those obtained at the

turnaround duct exit. The most likely cause for this is the very difficult

flow environment that exists where the swirling flow exiting the turbine

simulator impinges on the guide vanes which are aligned with the turbine

axis. Detailed prior knowledge of the flow field would have been necessary

to properly place probes in this region. The difficulty of obtaining data

in this region is also believed to be the cause for the oscillations in the

circumferential pressure distribution shown in Fig. 3. The bottom line of

this discussion is that in order to match the measured data in the

computational model, at least those from the turnaround duct exit to the

transfer duct exit, the inconsistent measured pressure data at the turbine

exit had to be replaced by estimated values based on turnaround duct exit

values and an estimate of the pressure loss through the turnaround duct.

The remaining data (Figs. 4 through 8) showing absolute as well as

x

dimensionless circumferential pressure distributions at the turnaround

duct oxit and at the fishbowl entrance were used for comparison with results

from the computational model.

2.3.2 Comparison of Two-Duct and Three-Duct HGM

The SSME HGM at the exit of the high pressure fuel turbopump imposes

considerable circumferential variations in static and total pressure on the

turbine. This effect is due to the compactness of the manifold and to its

one-sided discharge through the transfer tubes, as confirmed by SSME

hot-firing tests, as well as by past HGM air-flow test studies (Ref. 3).

Circumferential location is defined to be 0 between the transfer ducts

and 180 deg at the opposite side.

14

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

O

•3 ••-.

it. .£>

Q

Q

0)

crju

o

Q ~->

HH X

0)

o

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,-1 '-^

c« o

0)

ID to

U) O

at z;

H

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C/3

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00 00

CM CO CM

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cs

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15

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
220,

LMSC-HEC TR F042555

200

180

D

D D

Test 3.06

Re = 7.096 x 10

CO

a

0)

M

3

W

CO

CU1-1

p160

120

100

80

D

 D D ° ° °

Total

Static

60

Test 3.05

Re = 5.178 x 10

Test 3.04

Re = 2.167 x 10

180 225 270 315 0 45 90 135 180

Circumferential Location (deg)

Fig. 4 Static and Total Circumferential Pressure

Variation D/S of 180 deg Turn

16

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

td

O

Ed

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in U)

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17

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

bJ

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d /( d-d )

18

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
• Total Pressure

O Static Pressure

LMSC-HEC TR FOA2555

2001-

180

160

1AO

(0

•H

CO

P.

120

3

CO

CO

0)

100

80

60

AO

I I I

21A

213

I

180 225 275 0 85

Directional Probe Location (deg)

180

Fig. 7 Two-Duct HGM Fishbowl Entrance Pressure Variation

19

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

X

n

&

l.OOi0.98

0.96

0.94

0.92

180 225 275 0 85

Directional Probe Location (deg)

Symbo 3 l Re P , N P ,, s s(max) total(max)

lbf/in2 lbf/in2

Tic

X

fl

Q

i.oor

0.98

0.96

0.94

0.92 I I

• 2.6x10" 70.66

A 5.0x10:* 133.76

O 7.0x10 180.50

71.69

135.88

184.03

I

180 225 275 0 85

Directional Probe Location (deg)

180

Fig, 8 Two-Duct HGM, Fishbowl Dimensionless Pressure Variation

20

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

("he two-duct HGM greatly reduced the pressure (flow) nonuniformities in the

turbine exit/turnaround duct region compared to the present three-duct SSME

design. A reduction of about two-thirds of the total pressure variation

around the turbine exit region (Fig. 9) is achieved by the two-duct HGM

design.

The turbine simulator screen in the flow model enforces constant

velocity conditions implying that the static pressure distribution measured

is characteristic of the total pressure distribution. The increased

uniformity in the pressure distribution should result in the following

improvements: (1) increased turbine life; (2) decreased radial loads and

shaft movements, which tend to produce increased clearances and/or rubbing;

(3) reduction or avoidance of maldistributions of coolant flow; (4)

reduction in deformation and cracking of sheet metal; and (5) decreased HPFT

turbine temperatures for a given power level.

_,

8 3.0

O

1§

a.

UJ

<r 2.0

3

ft

UJ

cc

a.

_j

2

0

*2 1.0

UJ

2

5

z

Q

Z

O n

/

 N

* \

.s \

^-^ I * \

If^ \ 

• \

I A \ / / \ \

' ^> \ 1 / \ \ / / \ \ / / \ «.

/ / \ \

LEGEND

• THREE-DUCT AIR FLOW (Re ->~ 1.22 x 107/FT)

A HOT-FIRE TEST (RPL) (R« — 1.90 x 107/FT)

D TWO-DUCT AIR FLOW (Re ~~ 1^9 x 107/FT)

i

P - LOCAL PRESSURE |

P180 • REFERENCE PRESSURE AT 180° LOCATION |

QLOCAL - LOCAL DYNAMIC PRESSURE )

1 / \> \.

- ,v i-i . ^v

\

s'/ / / \, ^ Ss ^\ ^ ^ - ^

f / ^:

y//0 -r/

^

JJS

ISO 225 270 315 0 45 90

N

x \

-Oo\ \ \ x^\

1 1*\

135 180

CIRCUMFERENTIAL LOCATION (DEGREES)

Fig. 9 Circumferential Static Pressure Variation at Turbine Exit

21

LOCKHEED-HUIMTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

It should be noted when examining the data that a 16-cleg swirl was

induced in the fuel-side flow at the turbine simulator screen in the

clockwise direction (upper to lower transfer duct direction) when viewed

from the top (LOX dome) of the flow model. In the fuel-side simulator

region, the circumferential location was defined as 0 deg between the two

transfer ducts, the position angle increasing in the counterclockwise

direction when viewed from the top of the model.

Both the static and total circumferential pressure variation downstream

of the 180-deg turnaround duct (Figs. 10 and 11, respectively) were greatly

reduced for the two-duct HGM configuration. Examination of Fig. 10

indicates the static pressure difference, referenced at the maximum pressure

position at the 180-deg location, is approximately 25 percent of that

exhibited in the present SSME HGM design. The minimum static pressure was

recorded at the 315-deg location for the two-duct configuration while the

three-duct configuration minimum static was identified at 0 deg for HGM

air-flow tests and 45-deg for SSME hot-fire tests. The total pressure

circumferential pressure variation exhibited for the two-duct HGM is

radically different (Fig. 11) from that associated with the present HGM

design. The two-duct HGM total pressure distribution varies little and is

nearly symmetric with the maximum total pressure located between the two

transfer ducts. The increased uniformity in the turnaround duct region in

the two-duct hot gas manifold configuration would increase HGM coolant sheet

metal liner life over the present design.

The flow through the transfer duct exit planes of the two-duct manifold

was more uniform than that present in the current three-duct manifold

design. The improvement in flow uniformity should decrease main injector

LOX posts loading and increase their operational lifetime.

The percentage of the flow area stagnant is less for the two-duct

configuration. A rough comparison of stagnation areas for the two- and

three-duct hot gas manifold configurations is displayed in Fig. 12 for

22

LOCKHEED-HUNTSVILIE ENGINEERING CENTER
LMSC-HEC TR F042555

UJ

Ct

§

WJ

UJ

cr

Q.

< <

§ 8

5 §

5 °^

Is

z

~

4.0

3.5

3

rt

,u

2.5

2.0

1.5

1.0

0.5

0.0

* LEGEND

' \ / \ • THREE-DUCT AIR FLOW (Re ~ 1.22 x 1Q7

/FT)

P \ £ A HOT FIRE TEST (RPLMRe- 1.90 x107/FT)

/ \L • D TWO-DUCT AIR FLOW (Re ~ 1.29 x 107/FT)

/ A \

/ A \ \ / -• \ •.

/.• &' \\ P -LOCAL PRESSURE

(.' \ \ PIBO -REFERENCE PRESSURE AT 180° LOCATION

/ \X

 QLOCAL " LOCAL DYNAMIC PRESSURE

• 1 *

•*V * •

.^ \\

^ \

^ yP^^ ^\

-/* iy//^^^^:^--axjV

^ ~/^ ^^"n^-

180 225 270 315 0 45 90 135\ /ISO

CIRCUMFERENTIAL LOCATION ( DEGREES )^

Fiq. 10 Static Pressure Variation Downstream of 180-deg Turn

3.0

LEGEND

THREE-DUCT HGM

O E0110F CONFIGURATION

107/FT

BASELINE CONFIGURATION

R«-1.6x107/FT

TWO-DUCT HGM

DR«-1.31x107/FT

P -LOCAL PRESSURE

P

180 -REFERENCE PRESSURE AT 180° LOCATION

QLOCAL • LOCAL DYNAMIC PRESSURE

-1.0

180 225 270 315 0 45 90 135 180

CIRCUMFERENTIAL LOCATION

Fig. 11 Total Pressure Variation Downstream of Turnaround Duct 180-deg Turn

23

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
SOLID WALL HOT GAS MANIFOLD

LMSC-HEC TR F042555

LOX DOME

fit-1.22 X 107/FT

R» - 107

/FT

STAGNATION REGIONS

MCC

FLOW DIRECTION IS

INTO PAGE

LOX DOME

LTO MCC

DUCT FLOW NONUNIFORMITIES STUDY

Fig, 12 Stagnation Region Comparison Between Two- and

Three-Duct Configurations

comparable Reynolds numbers. Typical mass flow splits are 52 percent in the

UTD and 48 percent in the LTD for the two-duct system, while the three-duct

configuration exhibits typical mass splits of UTD: 52 percent, CTD: 9

percent, and LTD: 39 percent, where CTD is the center transfer duct.

Typical Mach number profiles for the two- and three-duct hot gas manifold

configuration scaled to engine RPL (100 percent) conditions are shown in

Figs. 13 and 14, respectively. The maximum Mach number observed in the

two-duct configurations is 0.16 while the three-duct HGM exhibited a maximum

Mach number of 0.26.

It can be observed from the side view profiles (Fig. 14) that there is

more flow in the upper portion of the ducts as expected because the flow has

an upward bias after coming around the 180-deg turn. The contours of these

vertical profiles are basically the same in both ducts. The top view shows

24

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

TOP

UTD

BOTTOM

TOP

CTD

BOTTOM (

TOP

LTD

BOTTOM

-1.22X107/FT

1-0 IDEAL

MACH NO.

(TYPICAL)

~ .103

0' .1 .2 .3

SIDE VIEW

OUTER

INNER

INNER

OUTER

0 7l .2 .3

TOP VIEW

Fig. 13 Engine-Scaled Three-Duct Manifold Mach Number Profiles

Along Duct Major Axes (100 Percent Power Level Condition)

TOP

R« ~ 1.29 X 107/FT

UTD OUTER

BOTTOM

0.0

TOP

111 1

.QlOJ 0.2 0.;3 MACH NO.

LTD

BOTTOM

ID IDEAL

MACH NO. ~ 0.069

(TYPICAL)

SIDE VIEW

UTD

INNER

1 1 1

0.0' 0.1 0.2 0.3 MACH NO.

OUTER LTD

INNER

TOP VIEW

Fig. 14 Engine-Scaled Two-Duct Manifold Mach Number Profiles

Along Duct Major Axes (100 Percent Power Level Condition)

25

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

that there is more flow on the outside of each duct. This is because flow

travels circumferentially in both directions around the fishbowl where most

of the flow enters the transfer ducts at the outside regions. Examination

of the corresponding Mach number profiles associated with three-duct

manifold displays that little appreciable flow passes through the center

transfer duct. In addition, the flow is nonuniforrn within each duct and

from one duct to another. This observation is true for both the vertical

and horizontal axis. The two-duct HGM configuration Mach number profiles

for both ducts approach the one-dimensional ideal Mach number condition

(0.16). This ideal Mach number uniformity condition was only approached in

the upper transfer duct in the present three-duct design. It should be

noted that the one-dimensiona} constant Mach number profile across the

transfer duct exit plane is the best flow condition achievable for a given

mass flow and transfer duct cross-sectional area. The flow through the

transfer duct exit plane, in the two-duct HGM configuration, is clearly more

symmetrical and uniform than that associated with the current three-duct HGM

design.

26

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

3. METHOD OF ANALYSIS

3.1 THE PAGE CODE

This study employed the PAGE code which evolved from the General

Interpolants Method (GIM) for constructing numerical analogs of the partial

differential equations governing fluid flow (Refs. 5 and 6). The

formulation considers the flow to be unsteady, viscous, heat conducting, and

compressible. Steady flow is treated as the asymptotic limit of the

unsteady case. Viscous effects are treated as either laminar flows or

through algebraic turbulence models. Incompressible flows, or flows at low

Mach numbers with almost no changes in density, are easily treated by use of

artificial compressibility.

The partial differential equations solved are the time-averaged

Navier-Stokes equations together with the equations for conservation of mass

and energy. These equations, written in three-dimensional conservative form

for a Cartesian coordinate system, are expressed as follows:

9y . 3E 8F 8G m

at 3x 8y 82 *• '

where

U = (p, pu, pv, pw, p£) (2)

is the solution vector of conserved variables, and E, F and G are the flux

vectors. The set of equations is completed by providing transport

properties and an equation of state relating pressure, density, and

temperature.

Boundary conditions are required to obtain a unique solution to the

above set of equations, the specific form of the boundary conditions

27

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

obviously being dependent on the problem. Generally, configurations with a

definable mass flux are assumed to have a set of specified "inflow"

conditions at some point upstream of the domain of interest. Subsonic flows

require the static pressure to be specified in some form as a downstream or

exit condition. The no-slip condition is imposed along all solid walls.

Thermal boundary conditions consist of either constant wall temperature or

adiabatic wall conditions. For elliptic problems, the integration commences

at time t = 0 with all variables initiated over the entire domain of

interest. After each time step, the flux vectors are recalculated after

evaluating the primitive variables via a decoding procedure. The solution

proceeds for a specified time or until a steady state condition is reached.

The geometric treatment uses concepts from finite element theory to

obtain discrete models of the conservation equations in arbitrary geometric

domains. Complex domains can be subdivided into a number of smaller

regions, the edges and surfaces of which can be described by analytic

functions. Intrinsic curvilinear coordinate systems can be produced by a

univalent mapping of a unit cube onto any simply connected bounded

subdomain. Any complex region can then be transformed piecewise and

assembled using blending function interpolation. While the local intrinsic

coordinates are designated n,, 19. and rj , the shape of the geometry

J. £. O

is completely defined by eight corner point functions P., twelve edge

functions, E., and six surface functions, S.. Based on previous work by

Gordon and Hall (Ref. 7), a general relationship between physical and local,

intrinsic, coordinates has been developed in the form of a general trilinear

intorpolant function:

£

2.8

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

where X(n.) denotes the Cartesian coordinate vector (x,y,z) as a function

of intrinsic coordinates r\ , r\ , n ' anc' ^ • • ^ •

 anc' ^ • are

J. .t J r ; 1 C.,1 O,l

respectively, known trilinear, bilinear and linear functions of the

intrinsic coordinates q / H_ and q . With this transformation, any

1 it. O

point with intrinsic coordinates n- can be related to global Cartesian

coordinates x,y,z.

A grid of discrete nodal points is generated using this concept of

multivariate blending function interpolation. Virtually any stretching

function can be accommodated to concentrate nodes near walls, large gradient

regions, etc. In addition, the edges of the local hexahedrals can be

segmented, thereby allowing another means of grid spacing control.

Discrete analogs of the conservation equations are derived by employing

the Method of Weighted Residuals (MWR). The procedure followed here differs

from the classical one in several ways: the weight functions are not

necessarily equal to the shape functions; the conserved variables U and

the respective flux terms E,F, and G rather than the primitive variables,

are approximated over an element. Assuming the shape functions to be

multilinear interpolants, written in intrinsic coordinates, the value of any

function Q at any point within the element can be expressed in terms of the

values of the function at the corner nodal points as

9(V

 = Si

(V

 Qi

where the shape function S. is formally identical to f .as defined in

i P,i

Eq. (3). Derivatives with respect to physical coordinates x. are then

easily evaluated from

SSL ._ ._

ax. ~ an.

2.9

LOCKHFIED-HUWTSVILLE ENGINEERING CENTER
0583R

LMSC-HEC TR F042555

where [J] is the Jacobian of the transformation obtained by differentiating

Eq.(3).

Hawing defined the variables over each element we proceed to produce a

discrete analog of the governing equations for each element using the Method

of Weighted Residuals. Accordingly,

/ W dV = 0 (6)

where w is an arbitrary weight function, and Jcx represents the differential

equation, Eq. (1). Utilizing Eqs. (4) and (5) to derive a detailed expression for the differential equation Z), and substituting into Eq. (6), we

arrive at the discrete analog for each element

I = A6. U. + B6. E. + CS.F. + D6. G. (7)

where U , E., F., G, now are evaluated at the element node points,

J ] 3 ]

and tho geometry dependent element coefficient matrices are given by

A

6

H - / Ul q -—*•£•'* •'*-'• d"n (Ha'I J J — / w j: : 'jo/«r»n\ clr i \<>&)

(8b)

f 9(sry,z)

'ij " J Wi 9(nrn2,n3)

30

LOCKHEED-HUNTSVILI.E ENGINEERING CENTER
0583 R

LMSC-HEC TR F042555

„•-/". ij J i«

3(x,y.S.) ,

-=—i-rdn (8d)

After all elements are so processed, the coefficients are assembled at all

node points which are connected to each other. This assembly is characteristic of finite element procedures and consists of a weighted Boolean sum

over the eight elements surrounding each node.

The assembled equation becomes

where

CNM

 FM

An,M = / . a A®. (10)

NM

and similar expressions are obtained for the B, C, and D matrices. The

a are a set of arbitrary element in

select a specific difference scheme.

a are a set of arbitrary element influence coefficients which are used to

At this point the weight functions W are arbitary, and therefore, Eq .

•

(9) is generally implicit in the time derivative term U. It can be shown

that, if the weight functions are selected to be equal to the shape functions, Eq . (9) represents a classical Galerkin finite element model. Any

other choice for the weight functions will result in what is now called a

Petrov- Galerkin method. Choosing weight functions which are orthogonal to

the shape functions results in a scheme which is explicit in the time

t

derivative U and thus represents finite difference schemes. In practice

such schemes have the advantage that a great wealth of experience exists

concerning their behavior during numerical integration.

The general form of the weight functions is

w. * j = a. (a. - njXb. -nz)(c. - r,3) i = i ..... 8 (ii)

31

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

where A is the determinant of the Jacobian matrix [J] . Since the weight

functions are orthogonal to the shape functions, the A(mass) matrix becomes

diagonal, which results in explicit, uncoupled time derivatives. However,

the resulting element integrals, Eq. (8), must be evaluated by quadrature.

With the goal of refining the general interpolants method a new set of

orthogonal tricubic weight functions has recently been derived by Stalnaker

(Ref. 8), viz.

k~0 k=0 k=0

The principal advantage of these weight functions is that they allow the

element matrix integrals to be evaluated analytically. Analytical evaluation introduces less numerical "noise" into the calculation than Gaussian

quadrature, and it allows a progressive assembly of generalized elements

(PAGE) to be used resulting in large savings of computer storage by not

having to store matrix coefficients in memory. Furthermore, progressive

assembly of the full domain matrices lends itself to vectorization and thus

efficient use of modern supercomputers.

3.2 GEOMETRY AND GRID CONSTRUCTION

The definition of all baseline configurations to be modeled was

obtained from drawings supplied by NASA-MSFC and/or Rocketdyne. Relevant

dimensions were extracted from these drawings and are given in Figs. 15 and

16. The schematic sketches given in these figures completely define the

flow boundaries for the turnaround duct and the fishbowl (Fig. 15), and the

positioning of the transfer ducts relative to the fishbowl (Fig. 16). The

transfer ducts were terminated at the position of the transfer duct exit

pitot probe rakes (13.315 inches from point B along the axis given by BA in

Fig. 16).

32

LOCKHEED-HUIMTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

1

u

X

C

O

•H

4J

c

o

1-1

4J

O

C/3

CO

CO

O

M

O

"S

n)

O

M

(0

M

H

CO

O

4->

O

co

O

in

60

•H

33
LMSC-HEC TR F042555

5.174

\

\

-£-- Duct

1 6.500

-H"

\\ \

7.835

Fig. 16 Definition of Transfer Duct Location Relative

to Hot Gas Manifold Bowl

34

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

Construction of the grid (as well as subsequent flowfield calculation)

was performed in several phases:

I Fishbowl and Transfer Ducts

II Turnaround Duct

III Combination of Turnaround Duct, Fishbowl and Transfer Ducts.

In all cases, the configuration geometry was assumed to be symmetric with

respect to a plane containing the HGM pump axis and a fishbowl meridional

cut between the two transfer ducts. Struts and guide wanes were neglected

in the computational model. While the actual flow field is truly

three-dimensional due to the swirl imposed on the flow exiting the turbine

simulator, neglection of the swirl in the analysis made it possible to

perform the flowfield analysis using only a half-geometry.

Geometrical detail and truth of the model (i.e., nodal density and

contour detail) is dictated by a compromise between what is needed for

reasons of computational stability and desired flowfield detail on the one

hand, and what one can afford financially on the other hand. Note that

computational cost is directly proportional to nodal density.

3.2.1 Fishbowl and Transfer Ducts

The Phase I HGM Bowl and Transfer Duct Half-Model was set up using a

total of 6798 nodes. Oblique (sparse grid) views of the complete bowl inner

wall, outer wall plus transfer duct as well as a composite view are given in

Figs. 17 through 19. The inner wall consists of a circular cylinder

followed by a cone frustum with another cone frustum of larger included

angle at the end. The HGM spherical bowl outer wall is shown in the next

illustration. Since the standard geometry module of the PAGE code only

permits simply connected surfaces to be modeled, extensive code refinements

were required to model the spherical bowl circular cylinder transfer duct

intersection. Note that the duct inlet edges are slightly rounded, which

was achieved by input of an appropriate mathematical function rather than

by tabulated data. An unwrapped view of the fishbowl grid is shown in Fig.

20.

35

cry LJI IMTOI/Ti i r~ i—ui/**Tiur-crriTM/** I"*CTIU*Y'C
LMSC-HEC TR F042555

Fig. 17 Hot-Gas Manifold Bowl Inside Wall Sparse Grid

36

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Fig. 18 Hot-Gas Manifold Bowl Outside Wall Sparse Grid

37

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Fig. 19 Hot Gas Manifold Composite Grid

38

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Fig. 20 Hot-Gas Manifold Bowl Grid (Unwrapped Inside,

Center, Outside Surface)

39

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Considerable effort was expended to construct the grid network keeping

economy of the calculations in mind. By this we mean using a relatively

coarse grid in regions where relatively small gradients are expected, with

an orderly transition to a higher nodal density for regions with rapid

changes in the flow properties. Given the constraints of the formulation of

the geometry module of the PAGE code it is extremely difficult to satisfy

all requirements simultaneously. Stability problems were expected and

encountered, particularly at the top end of the bowl where inner and outer

wall converge, and in the region of the transfer duct inlet, where highly

distorted (skewed) elements could not be avoided entirely, particularly on

the outside where the transfer duct wall joins the bowl contour almost

tangentially, as shown in Fig. 21.

For reasons which will become clear after discussing the flowfield

results, a second version of the HGM was investigated. This second version

incorporates a modified transfer duct inlet geometry. Specifically, a much

larger radius of curvature of the duct inlet contour in the lower inner duct

quadrant was provided with the goal of preventing flow separation in this

region. The modified geometry is illustrated and compared to the nominal

geometry in Figs. 21 and 22. Again, the modified duct inlet geometry was

implemented using functional input rather than tabulated data. Overall

views of the outer wall and the assembled HGM (sparse) grid are shown in

Figs. 23 and 24, respectively. No changes were made to the dimensions of

the fishbowl and the transfer duct and its position relative to the fish

bowl as specified in Figs. 15 and 16.

The next step (Phase II) of the geometry effort was to establish a grid

structure for the turnaround duct using the dimensions given in Fig. 15.

Grid structures were set up first for an axisymmetric configuration to be

used in conjunction with the testing of certain inlet and exit boundary

conditions to be discussed later. A typical cross-section using 270 nodes

is shown in Fig. 25.

40

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a. Nominal Configuration

b. Modified Configuration

Fig. 21 Hot-Gas Manifold Bowl Cross-Section Grid

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a. Nominal Configuration

b. Modified Configuration

Fig. 22 Hot-Gas Manifold Grid, View Along Transfer Duct Axis

42

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Fig. 23 Modified HGM Bowl Outside Wall Sparse Grid

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Fig. 24 Modified HGM Composite Grid

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Fig. 25 Nominal Turnaround Duct Cross-Section Grid

45

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Having accomplished this, the grid structure for a three-dimensional

turnaround duct was set up to be matched to the fishbowl at x = 0

(turnaround duct - fuel bowl interface, see Fig. 15). Various oblique views

of this three-dimensional turnaround duct are given in Figs. 26 through 28.

In Phase III of the geometry effort the turnaround duct grid was joined

to that of the fishbowl - transfer duct to form a 14703 node assembled grid

structure for the complete DFNUS hot-gas manifold from the turbine exit to

the transfer duct exit. The inner wall of the turnaround duct and fuel bowl

is displayed in Fig. 29, while Fig. 30 shows the outer wall of the complete

HGM. A typical flow channel through turnaround duct and fuel bowl is shown

in Fig. 31.

3.3 FLOWFIELD INITIALIZATION

Integration of the governing equations in time requires initial values

in the spatial domain for all nodal points. The large number of nodes to be

evaluated in these problems requires a sizable amount of computer time, and

the cost of integration can be minimized by providing an initialization

which is as close as possible to the solution of the flow field. A

systematic initialization procedure for all nodes was implemented by

utilizing the interpolative capability already built into the geometry

module.

Variables which must be initialized include the density, the three

velocity components and the pressure. For a perfect gas, the temperature is

then determined from the equation of .state. In the case of the SSME fuel

turbo pump HGM we are dealing with nearly incompressible flow (Mach number £

0.3). Under these circumstances, temperature changes are expected to be

minimal and we therefore assumed the flow to be isothermal. The

initialization is greatly helped by some knowledge of the flow field to be

calculated, either by intuition or by examining measured data and flow

visualization results. The initialization is implemented in two steps as

follows.

t

45

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Fig. 26 Nominal Turnaround Duct Inside Wall Grid

47

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Fig. 27 Nominal Turnaround Duct Outside Wall Grid

48

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Fig. 28 Nominal Turnaround Duct Composite Grid

49

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Fig. 29 Nominal Inside Wall Grid

50

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ORIGINAL PAGE IS

OF POOR QUALITY

Fig. 30 DFNUS HGM Nominal Outside Wall Grid

51

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1-1

o

c

o

•H

to

i

to

CO

o

§

PQ

•o

o

M

rec

n

H

O

re

CO

t>0

•H

52

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

Step one takes place in the geometry module where we make use of the

aforementioned built-in interpolation capability to assign flow angles 8

xy

and 9 (see Fig. 32), total pressure and the magnitude of the velocity to

all nodal points. This is achieved by assigning values for all four

quantities to zonal and/or sectional corner points as well as to all edge

segmentation points. Values for all nodes along edges are then obtained by

interpolation. Further interpolation over surfaces and interior spaces

completes the process.

Initial flow angles clearly must be specified in a manner such that the

resultant velocity vector is first, tangent to the walls involved, and

second, in the general direction of flow as perceived or as obtained from

flow visualization for the location in question.

w

Fig. 32 Definition of Flow Angles

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To set up the total pressure initialization, either experimental data must

be available, or preliminary calculations must be performed using simplified

methods. In the present study, total pressure values were used wherever

available from experiment, and for nodal point locations where no

experimental data were available values were estimated.

Assuming that the mass flow through the configuration is known, we can

use the total pressure data in conjunction with cross-sectional area values

from the geometry to arrive at velocity data by using a one-dimensional

stream tube analysis.

Given the equations of continuity and state as well as Bernoulli's

equation, i.e.,

PV = m/A (13)

p/p = RT (14)

p + (P/2) V2 = pt (15)

we can eliminate p from Eqs. (14) and (15) and solve for p and V. The

result is

r

 2RT

and

2RT

Pt

v = p (J)

While the procedure just described is straightforward in the turnaround

and the transfer ducts, it is a little more difficult in the fuel bowl.

Inspection of the situation in the fuel bowl shows that there must be two

stagnation points, one each at <p = 0 and one at 9 = 180 deg in the fuel bowl

symmetry plane at the top of the bowl. This implies that another stagnation

point must occur in the region of 30 _< 9 £ 60 deg at the top of the fuel

bowl above the transfer duct. Along the stagnation streamlines the

54

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
LMSC-HEC TR F042555

velocity, according to potential flow, decreases linearly to zero. Hence,

for the purpose of initialization, we assign zero velocity at the corner

points at x = x , and at the third stagnation point with assumed

max

approximate values at edge segmentation points inbetween.

To establish initial values in the interior of the fuel bowl, it is

useful to define streamtubes (approximately) on an unwrapped grid of the

bowl as shown in Fig. 33. Local streamtube cross-sectional areas can then

be calculated from the known geometry. Application of Eqs. (16) and (17) to

individual streamtubes then leads to initial values for the interior of the

fuel bowl. Values thus established for the two flow angles, the velocity

magnitude and the total pressure are saved as part of the output from the

geometry module.

Step two of the initialization process takes place in the integration

module which uses as input the output from the geometry module.

As a first step, we use the velocity magnitude and the total pressure

to solve Eqs. (14) and (15) for the density p and the static pressure p.

Secondly, we use the velocity magnitude and the flow angles to compute the

three velocity components u, v, and w. Further, we can use p, p, and V to

compute initial values for the total internal energy

2

c* — _. —ELTM i jL— /1 o \ E

 - P(Y-D

 + 2 (18)

The final step in the process is to set the velocity components to zero

at all wall nodes in order to satisfy the no-slip boundary condition. This

completes the initialization process.

3.4 FLOWFIELD ANALYSIS

The PAGE code, as described in Section 3.1, represents a rather general

methodology to process the fluid flow governing equations so that they can

55

LOCKHEED-HUNTSVILLE ENGINEERING CENTER
CO

u

lJ

•rt

u

LMSC-HEC TR F042555

180 r*

150

120

60

30

•V

\

»

\

\' ^ > « \ \ .» * < I I

\ I \

)

\ \

I

w

Fig. 33 HGM Bowl Center Plane Velocity Vector Plot

and Streamtubes for Initialization

56

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LMSC-HEC TR F042555

be solved by numerical integration. Actual numerical analysis requires the

specification of a finite difference algorithm, thermodynamic, and transport

properties as well as a procedure to implement the boundary conditions.

This section will briefly discuss the treatment of all these topics.

3.4.1 Finite Difference Algorithm

For most of the cases calculated in the course of this study the

two-step predictor-corrector MacCormack procedure was used which is one of

the built-in finite difference schemes in the PAGE code. The time step used

was generally a certain fraction of the (inviscid) smallest permissible CFL

time step. The reduction factor was determined such that, depending on the

local rate of change, a specified relative change in any of the primary flow

variables was not exceeded. Modal properties exhibiting unstable behavior

in spite of the precautions taken, and which were encountered mainly in the

region of the fuel bowl - transfer duct juncture due to highly skewed (i.e.,

nonorthogonal) grid elements in this region, were handled by averaging or

interpolation.

As the study progressed, a multi-cycle predictor-corrector finite

difference scheme (as illustrated in Fig. 34 for the two-dimensional case)

was introduced. In conjunction with this, a time step routine which

evaluated a local time step based on the local CFL condition, was

implemented. This combination proved to be much superior to the previously

used scheme and allowed us to get by with a very minimum of interpolation or

averaging. It should be noted that the limitation of computational

resources forced us to pursue these calculations using a rather coarse grid

structure.

3.4.2 Transport Properties

Transport properties are specified in terms of dynamic viscosity and

Prandtl number for turbulent flow. Effects of turbulence were modeled first

57

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LMSC-HEC TR F042555

4

„ J *-

+

~"ir-

- — \ — .*- i

^-J• —

Step

0

©

©

©

Predictor Corrector

x y x y

F F B B

B F F B

: F B B F

B B F F

Fig. 34 Multi-Cycle Predictor-Corrector Finite Difference Method

58

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LMSC-HEC TR F042555

in simple form by applying an appropriate multiplier to the laminar

viscosity, and second, by using a Prandtl-Van Driest algebraic turbulence

model in which the turbulent viscosity is evaluated as a function of a local

mixing length and the three-dimensional vorticity.

The magnitude of the effective turbulent viscosity in the hot-gas

manifold can be estimated by applying Prandtl's mixing length hypothesis to

the flow in the transfer duct. According to Prandtl (Ref. 9)

du

dn

where p is the density, H the mixing length, u the mean velocity and n the

direction normal to the wall. For turbulent pipe flow (Re > 10 ) we can

make use of the correlation established by Nikuradse (Ref. 9).

I 2 4

- = 0.14 - 0.08 (1 - J-) - 0.06 (1 - *) (20)

where y is the distance normal from the wall and R is the pipe radius.

The mean velocity gradient in the transfer duct is (approximately)

du

dn

m . 1

pirR

r

duct radius of R = 0.271 ft, we obtain

2 R (21)

For a given mass flow of 36 Ib/sec per duct, a density of 1.0 Ib/ft and a

dn

~ 6 - 102 (sec

 l) (22)

For y/R = 0.5, Eq. (20) yields a mixing length of t = 0.031 ft.

Substituting these values into Eq. (19), we obtain p = 0.6 Ib/ft-sec,

59

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LMSC-HEC TR F042555

while the laminar viscosity of air at ambient temperature is approximately

M = 1 -10 Ib/ft-sec. Therefore

= 6 • 10 (23)

10

indicating that the effective turbulent viscosity is roughly four orders of

magnitude higher than the laminar viscosity.

The Prandtl-Van Driest turbulent viscosity model is obtained by

replacing the magnitude of the mean velocity gradient in Eq. (19) with the

magnitude of the vorticity so that we can write

(24)

where

V

2 2 2 ,3u 8vN ,9" 3w. ,9w 9u,

. . % ~ -x-> + <8z ~ 8y) + (8x ~ 8Z>

and A is determined by Nikuradse1s correlation, Eq. (20). For flow passages

with non-circular cross-sections, the geometric radius is replaced by the

hydraulic radius.

3.4.3 Boundary Condition Treatment

In any attempt to solve the fluid flow governing differential equations

careful attention must be given to the specification of boundary

conditions. They must be physically correct and mathematically consistent.

These general constraints still leave the investigator with a surprising

variety of ways in which boundary conditions can be implemented. Some

arrangements appear to work better than others depending on the flow

configuration to be analyzed or on the nature of the flow.

60

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In all calculations the no-slip conditions were enforced along all

solid walls, in conjunction with appropriate thermal boundary conditions.

No problems were encountered with these conditions. Difficulties, however,

were encountered with the implementation of inflow and outflow boundary

conditions which merit discussion. For the sake of simplicity for this

discussion, we assume isothermal flow so that we deal with only four

differential equations, namely the continuity and the three momentum

(Navier-Stokes) equations.

Initial calculations of the nominal DFNUS HGM (fuel bowl - transfer

ducts, but without turnaround duct) were performed by imposing all boundary

conditions at the inflow boundary. Specifically, the four primary

variables p, u, v, and w were held fixed. This implied that static pressure

and mass flow were also held constant at the inlet. Eventually, integration

in time starting from an appropriate initial condition should produce a

solution for which the exit mass flow equals the inlet mass flow and for

which the exit pressure is such that the average pressure gradient along the

flow is consistent with specified mass flow and viscosity. Experience has

shown that this convergence process may take considerable time (large number

of time steps). In order to shorten the process, a "convergence

acceleration" condition was generally applied at the exit. This meant that

after each time step the three velocity components were scaled such that the

exit mass flow would be equal to the inlet mass flow. For the fuel bowl and

transfer duct configuration this set of boundary conditions appeared to work

well. However, when applied to the turnaround duct, the result was a

buildup of pressure waves both near the inlet and near the exit accompanied

by a very discontinuous velocity field near the turnaround duct outflow

boundary as illustrated in Fig. 35a. The boundary conditions were therefore

reexamined.

We implemented a revised set of boundary conditions as follows. At the

inlet flow boundary the total pressure and the flow angles (i.e., the flow

vector direction) are specified and held fixed. While the density (and

61

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LMSC-HEC TR F042555

• H

0!

a.

o\

«M

O

<N

tfl

c

O

• H

-a

O

1-1

(fl

•O

C

O

03

T3

OJ

v|

O

• -H

in >

O CL)

r-( OS

W

a

a

ca

O

c

o

(0

•a

o

PQ

•H

00

•H

J-l

o

3

(/I

7)

0)

i-l

o

a

o

•H

a

CD

a,

C/3

C

O JJ

•H O

•U S

•H a

•a

c -o

o a

0 3

O

>> ti

ti CO

(fl C

•O Vi

C 3 d H

o

pq C

O <a

3

O

U-l C

u-i o

u a

oo

•H

62

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LMSC-HEC TR F042555

therefore the static pressure) is determined from the continuity equation,

tn«> thrto momentum equations arc ignored. Instead, the magnitude of the

velocity is computed from the definition of the total pressure and then

resolved into its three components by using the specified flow angles. At

the outflow boundary the static pressure is specified and held fixed. This

implies that the density is fixed, and the continuity equation is therefore

ignored. Using the density, the three velocity components are obtained from

the momentum equations. Note that in contrast to the previously used

boundary conditions, the mass flow at both flow boundaries is floating.

Experience has shown that both inlet and exit mass flow smoothly converge to

the same value which only depends on the specified viscosity and the imposed

pressure gradient. A solution for specified mass flow is then easily

obtained by changing the viscosity. Increased viscosity produces a reduced

mass flow and vice versa.

The iteration on mass flow can be avoided by imposing a fixed mass flow

at the inlet boundary. Again, the density (and thus the static pressure) is

determined from the continuity equation. As before, the three momentum

equations are ignored and the inlet velocity components are determined from

the given flux terms. In this case convergence is reached when the floating

exit mass flow converges to the value of the fixed inlet mass flow. Both

variations of the new boundary conditions produced physically reasonable and

stable results.

Typical pressure distributions obtained with the original boundary

conditions and with the revised boundary conditions can be compared in Fig.

35a and 35b, respectively.

63

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4. ANALYTICAL RESULTS

4.1 DFNUS NOMINAL CONFIGURATION

4.1.1 Turnaround Duct

In order to check out the previously described revised boundary

conditions in conjunction with the multi-cycle finite difference scheme and

the local time-step routine, axisymmetric turnaround duct calculations were

performed. Although the real turnaround duct flow is not axisymmetric due

to swirl and a nonuniform circumferential pressure distribution, the

assumption of axisymmetric flow permitted us to perform a reasonably

realistic calculation with a minimum number of 270 nodal points in a flow

plane. A series of calculations was performed for specified constant

upstream total pressure and downstream static pressure, for which

approximate values were taken from the experimental effort. The viscosity

was varied until the calculated mass flow through the turnaround duct was in

agreement with the measured mass flow. Specified data and calculated

results are summarized in Table 5.

The convergence of inlet and exit mass flow to a common value after

starting the integration with initial values representing the anticipated

nominal result (Case 3, m = 72 Ib/sec) is shown in Fig. 36. All cases

behaved as expected showing a rnonotonic increase in mass flow as the

viscosity is gradually decreased. The viscosity is constant for each

calculation and equal to the sum of the scaled laminar viscosity and a

numerical viscosity added to supply additional stability for the coarse grid

calculations. The numerical viscosity scale factor e^ was chosen such as to

render the numerical viscosity roughly equal to the laminar viscosity.

64

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Table 5 AXISYMMETRIC HGM TAD RESULTS

Case

1

2

3

4

Specified

^L

(Ib/ft-sec)

0.6

0.3

0.1

0.05

C M

0.5

0.25

0.05

0.025

m

(Ib/sec)

30.0

45.0

72.0

82.0

Calculated

max

(ft/sec)

209.0

315.1

591.2

786.3

P

(psi)

165 - 203

165 - 201

153 - 191

139 - 188

M

max

0.184

0.276

0.497

0.656

All Cases: P. _ . . = 205 psi

t,Inlet

Exit

= 164 psi

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100,-

u

0)

<o

•e

Case

Case 2

Case 1

20 - Inlet

Exit

1

0 2

1

4

1

6

1

8 1C

Iterations (thousands)

Fig. 36 Effect of Viscosity on Mass Flow

66

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The following figures illustrate pressure contours, Mach number

contours, and velocity vector plots for the cases calculated. The change in

pressure contours (Figs. 37 and 38) from Case 1 with highest viscosity to

Case 4 with lowest viscosity is particularly obvious, showing the gradual

transition from highly viscous flow with strictly favorable pressure

gradient to almost inviscid flow with distinct local pressure minima and an

unfavorable pressure gradient downstream of the 180 deg turn.

While the Mach number contours (Figs. 39 and 40) appear to be very

similar for the four cases, some distinctive features develop as the

viscosity is decreased and the average flow velocity increases. Note the

development of high speed regions at the inside wall upstream of the bend

and on the outside wall downstream of the bend. Case 3 and Case 4 show

detached Mach contours at the inner wall downstream of the 180 deg turn

indicating the possibility of flow separation. This is confirmed in the

velocity vector plots (Figs. 41 and 42) which show very slow flow for Case 3

and reverse flow for Case 4 in that region. While the turnaround duct exit

shows the typical viscous laminar velocity profile for all cases, note that

at the inlet, as the viscosity is decreased, the velocity retains more and

more its initial plug flow profile.

4.1.2 Fuel Bowl and Transfer Ducts

In the spirit of tackling problems successively rather than

simultaneously, calculations for the fuel turbopump HGM were first performed

for the fuel bowl and transfer ducts without the turnaround duct. The grid

for this configuration was illustrated in Figs. 17 through 19. To account

for the effects of the turnaround duct on the flow in the bowl (and possibly

the transfer ducts) turnaround duct exit experimental data were used to

impose initial conditions at the bowl inlet. In fact, boundary conditions

(aside from the no-slip wall boundary conditions) for these calculations

were all imposed at the bowl inlet forming the upstream boundary, as

discussed previously.

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Case 1

Case 2

Fig. 37 HGM TAD Flow - Pressure Contours

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Case 3

Case

Fig. 38 HGM TAD Flow - Pressure Contours

69

JLQCKHREB—HTINTSUTT.T.E F.TJnT'ME'E'P TMn
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Case 1

Case 2

Fig. 39 HGM TAD Flow - Mach Contours

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Case 3

Case 4

Fig. 40 HGM TAD Flow - Mach Contours

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Case 1

Case 2

Fig. 41 HGM TAD Flow - Velocity Field

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Case 3

Case 4

Fig. 42 HGM TAD Flow - Velocity Field

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Experimental data for the static and total pressure taken at the

turnaround duct exit are shown in Fig. 43, indicating a circumferential

distribution which deviates from the average by at most +2 percent. For the

bowl inflow boundary condition we simplified the experimental distribution

by assuming constant total pressure and static pressure linearly varying

from the relatively high value at the back side (180 deg position) to the

relative minimum at the front side (0 deg position) between the two transfer

ducts, as also shown in Fig. 43. Bowl inlet boundary conditions for the

velocity components were calculated such that all conditions were consistent

with the available experimental data.

The entire flow field was then initialized as described previously.

Figure 44 illustrates the velocity initialization in the bowl in terms of

flow vector plots near the inner and near the outer bowl wall.

Integration of the fluid flow governing equations was performed using

the two-step MacCormack predictor-corrector finite difference scheme. While

the mass flow at the transfer duct exit was inforced through appropriate

scaling of the velocity vector, convergence to the steady state solution was

monitored in two ways.

Ideally, the unsteady terms of the governing equations should vanish as

the steady state solution is approached. In practice, however, a

discretized set of equations is solved, rather than the original partial

differential equations. Hence, taking this into account, as well as other

sources of error accumrnulation, one looks for a vanishing slope of the time

derivative terms. The level at which these terms stabilize relative to

their initial value is then a measure for the quality of the

initialization. The behavior of the unsteady terms with time is shown in

Fig. 45 in the form of the normalized sum of the squared time derivatives

(summed over all nodal points).

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0.06 r0.04

0.02k

-0.02

-0.04

• Total Pressure

O Static Pressure

Total Pressure

Static

) Experiment

} GIM Code Input

i i i

90

180 -— - -

270

i

180 225 270 315 0 45 90 135

Circumferential Location

180

Fig. 43 Turnaround Duct Exit Pressure Variation

75

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->-»«» x

\ l V k tt k > I t

I t > I tl * I II

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x > , \ \ I »*»'»» "

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__ • ^ _ „ „ r ' ' *

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LMSC-HEC TR F042555

• •* >» x -x x

\ \\\\\\Xtl\k» l i

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'Ml

// ;.'„„ '''».•'. '

Fig. 44 HGM Bowl Velocity Vector Initialization Near Inside and Outside Wall

76

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4-1

0)

•d

Duct Inlet Mass Plow

10 -

10

-3

1000 2000 3000 4000

Number of Time Steps

5000 6000

Fig. 45 Behavior of Unsteady Derivatives and Duct Inlet

Mass Flow as Function of Time

77

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It is also clear that once a steady state is reached, the mass flow

through any definable cross-section along the flow must equal the inlet

and/or exit mass flow. Therefore, as a secondary convergence criterion, the

mass flow at the transfer duct inlet was monitored as a function of time.

As seen in Fig. 45, the normalized transfer duct inlet mass flow exhibits a

decaying oscillatory behavior, eventually reaching a steady value of unity

after several thousand time steps, thus indicating that the duct inlet mass

flow has settled on a value which is equal to that of the required steady

state mass flow.

Flowfield results for the fishbowl are shown in Figs. 46 through 48 in

terms of velocity vector plots, static pressure and Mach number contours,

respectively, for a flow surface centered between inner and outer wall.

Several prominent flow features can be identified from these plots.

First, almost the entire rear half of the bowl (within an angle of

roughly 60 deg to either side of the symmetry plane) forms a region of

rather constant static pressure in which the flow is gradually decelerated

to stagnation conditions at the upper end of the bowl. Second, the highest

velocities are encountered at the bowl inlet at an angular position of 30

< <p 1 60. Another region of relatively high velocity is seen to occur near

the top of the bowl between 9 = 60 and 9 = 90 deg where the flow from the

rear half experiences a relatively high acceleration as it enters the

transfer duct.

Third, and as expected, a secondary stagnation region can be identified

at the top of the fishbowl at an angular position of approximately 30 deg.

Finally, the high velocity (high momentum) of the flow at the angular

position of the transfer duct inlet causes the flow to "pileup" at the upper

transfer duct wall where it is redirected in various directions, thereby

causing a swirl pattern and a region of flow separation in the transfer

ducts as will be shown later.

78

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180

150

120

e

o

•H

4J

•H

<A

O

^ 90

C

(Uij

0>

60

30

k I . . . .

M i \ ' . . " V.vVi1

x //.

 M 1 j / j i*

M l ' / n,,

^ \ \ i j / i ., \ \ \ \ i * ' ••

x X V V ' " '•

« « l«

« « 11

t*..

HOTlAS MANIFOLD - 6798 NODE 6RIO BOUL CIR

Fig. 46 HGM Bowl Center Plane Velocity Field

79

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180 r

150

120

o

(0

o

Ol

0)

Vt

0)

o

1-1

•H

O

90

60

30

/U\ \ V

HOT~6AS MiMIFOLD - 6798 NODE 6RID BOUL CTR PUNE

Fig. 47 HGM Bowl Center Plane Static Pressure Contours

80

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180

150

120

o

W

o

0)

y

i-i

90

o 60

30

OL

HOT GAS MANIFOLD - 8798 NODE 6RID BOUL CTR PLANE

Fig. 48 HGM Bowl Center Plane Mach Number Contours

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Flowfield results in the fishbouil can be compared with pressure

distributions obtained experimentally. The comparison of static and total

pressures versus circumferential location is shown in Figs. 49 and 50,

respectively. Here "Model I" refers to the simple turbulence model

consisting of the scaled up constant laminar viscosity only. "Model II"

refers to the Prandtl-Van Driest model as described in Section 3.4.2. The

computed circumferential pressure distributions for both turbulence models

are seen to be in close agreement with the experimental data. The

computational results provide additional detail in the vicinity of the

transfer duct inlet in the form of distinct static pressure minima due to

relatively higher velocities as the flow anticipates the turn into the

transfer ducts. Other velocity and pressure results in the bowl were also

surprisingly close between the two turbulence models. The reason for this

close agreement is believed to be the fact that in this configuration the

geometry is the main cause for large scale turbulence and that therefore the

details of the turbulence models are of lesser importance in this case.

An overall view of the flowfield in the bowl and the transfer ducts is

presented in Fig. 51 in terms of velocity vectors in the bowl center flow

plane and an oblique flow plane in the transfer ducts. The particulars of

the flow in the transfer ducts are shown in more detail in Fig. 52,

presenting velocity vectors and Mach number contours. The flow separation

and recirculation region found in the inner lower quadrant of the transfer

duct is clearly visible. IMote the corresponding low Mach number "bubble" in

the Mach contour plot. These transfer duct flow features are in excellent

qualitative agreement with the experiment which showed stagnation regions in

the inner lower quadrants of the transfer ducts, as indicated in Fig. 53.

Also shown in this figure are static pressure contours near the transfer

duct exit, indicating the highest static pressure (i.e., a correspondingly

low absolute velocity) in the inner lower quadrants.

An attempt was made to compare measured Mach number profiles in the

transfer duct entrance to computed profiles. No agreement was found for

82

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i.oo

0.98

0.96

P/P

max

0.94

0.92

0.90

0.8B

180 240 300 0 60 120

Circumferential Location

180

Fig. 49 Comparison of Computed Static Pressures

to Measured Static Pressures in Bowl

I.OO

0.98

0.96

P /P

t t,max

0.94

0.92

0.90

0.88

1

•""S

80

\

\X/(Tu?

V

\v

\\

\ \

\

CIH Code

• Rocke tdyne

Experiment

bulence Hod

(Turbulenc

^

el 1)

e Model II)

^

/'/

>/

II

II

1

1 I

1

' 5

-»•

180 -[- •

/ ^

10

I F7

| Li

VH

270

1

2*0 JOO 0 60 120 18

Circumferential Location

Fig. 50 Comparison of Total Pressures to Measured Data in Bowl

83

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Fig. 51 Nominal HGM Bowl and Transfer Duct Flow Field

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Velocity

Vectors

a. Velocity Vectors

Mach

Contours

b. Mach Number Contours

Fig. 52 Nominal HGM Transfer Duct Flow Field Results

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STAGNATION REGIONS

TWO DUCT MANIFOLD

LOX DOME

MCC

PRESSURE CONTOURS ITERATION 8800

HOT GAS MANIFOLD - 6798 NODE GRID DUCT EXIT

Fig. 53 Comparison of Computed Transfer Duct Exit Static PressureContours and Stagnation Regions from Experiment

86

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these data as illustrated in Fig. 54. The reasons for the disagreement must

be attributed to shortcomings in both the computational model and the

experiment. While it is difficult to point to any single feature of the

computational model which might be responsible, the coarse grid (i.e., lack

of resolution) and the absence of a detailed turbulence model must certainly

be considered contributing factors. Concerning the experiment, the data

points were obtained using pitot probes aligned with the transfer duct

axis. Flow visualization as well as the computational results indicate that

the flow in this region is anything but aligned with the duct axis. Thus,

anytime that pitot probes are not properly aligned with the direction of

flow, the validity of the pressure data taken must be questioned.

For probably similar reasons, the computational model was not able to

reproduce the details of the measured Mach number profiles at the transfer

duct oxit.

4.1.3 DFIMUS HGM

This section describes the computational results obtained from the

analysis of the complete hot gas manifold from the turbine exit to the

transfer duct exit. The geometrical configuration was described previously

and is illustrated in Figs. 29 through 31.

The multi-cycle predictor-corrector finite difference scheme was used

to integrate the governing equations toward steady state. Turbulent flow

was simulated using a high laminar viscosity at the value established for

the solution of the flow in the turnaround duct, except for a slightly

increased value of the numerical damping, which merely increases the

effective viscosity by an amount proportional to the velocity. Inflow and

outflow bound-sry conditions were imposed in terms of circumferentially

constant total pressure at the turnaround duct inlet and constant static

pressure over the transfer duct exit plane. Values for both were taken from

87

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r^\ \'< \ \ '• '• '• \

\•.•.\\\\\v-.- . ' \» \ i i » • • . \ \ • . i * «\»' • *

\ ' . ' I « \ \ \ N ' •

\ • . \ \ \ \ \ \ \ ^

CO

•

o

c

o

•H

•H

M

(0

l-i

0)

A

a

3

88

4=

U

ro

•

O

0)

r-1

c

U

Q

o

a

bd

•H

IX.

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the experimental data . The resulting mass flow through the manifold was

<3>t the required value which means that, under the adopted assumptions, the

effective viscosity was consistent with the imposed pressure gradient.

Figures 55 through 57, representing a cut at <p = 45 deg through the

turnaround duct and the bowl, joined to a center cut through the transfer

duct, indicate an overall agreement with results discussed previously. From

the velocity vector plot is is seen that a small region with nearly

stagnating flow is found just downstream of the transfer duct entrance. The

pressure contour plot confirms that this is a region of adverse pressure

gradient and the Mach number contour plot indicates that a state of

incipient separation has been reached at the bottom of the transfer duct.

Figure 58 shows a cut through the transfer duct (in a plane which is

roughly perpendicular to the one shown previously) adjoined by a cut through

the bowl normal to its axis. Apart from some small regions of instability

manifesting itself in the form of "wiggly" velocity vectors and a

concentration of high gradients in the contour plots, the results are

largely as expectod. No flow separation is found in this plane. Note that

the flow component which has to negotiate the sharp turn from the bowl into

the transfer Juct is already small upstream of the turn (small Reynolds

number per unit length).

Flow properties in an oblique cut at 45 deg relative to both previously

shown cuts are illustrated in Fig. 59. Just as found in the earlier

calculations, there is a relatively large region of very low velocity in the

inner lower quadrant of the transfer duct. Although this velocity vector

plot does not show any flow reversal as encountered previously, the present

results are qualitatively in agreement with the earlier calculations.

^Recent experimental data indicate that the static pressure is not constant

over the duct exit plane.

89

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Fig. 55 DFNUS HGM Nominal Configuration Velocity Field

90

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PRESSURE CONTOURS

1

7.

J

4

5

0

7

8

e

10

ti

12

13

M

15

18

17

18

19

21

21778 7758

22183.2745

225*8.7749

22931.2735

233* 3 7730

23C97 2724

24eee 7719

24*64.. 2714

2484? 7709

25231 2704

253H 7699

25098 2004

20381.7080

267B5 288S

27148. 7678

27532 2673

27015.7688

28299.2603

28682 7658

29060.2653

Fig. 56 DFNUS HGM Nominal Configuration Pressure Contours

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HACH NUMBER CONTOURS

ID

I

?

3

4

s

!

8

9

18

I I

ii

14

N/kCH

8144

.8433

1722

.1811

. 1290

"588

1877

.2166

.2454

.2743

.3CJ2

.3321

J699

3898

IS

Fig. 57 DFNUS HGM Nominal Configuration Mach Number Contours

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b. Pressure Contours

c. Mach Number Contours

Fig. 58 DFNUS HGM Nominal Configuration Bowl - Transfer Duct Flow Field

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a. Velocity Field

b. Pressure Contours

c. Mach Number Contours

Fig. 59 DFNUS HGM Nominal Configuration Bowl - Transfer Duct Flow Field

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Figures 60 through 62 present an overall view of velocity vectors,

static pressure and Mach number, respectively, in the bowl and turnaround

duct as viewed from the side and slightly above. The information content is

similar to that shown for the earlier calculations in an unwrapped view

(Figs. 46 through 48), and close examination reveals many similar features

in the two sets of figures. It will be noticed that the later contour plots

lack the smoothness of the former ones. This smoothness in the earlier

calculations was achieved by constantly monitoring the stability of the

calculations. Properties at any node which exceeded a given tolerance of

deviation from the mean among its surroundings were recalculated by

averaging. In contrast to this, the more powerful and more stable

multi- cycle finite difference scheme used in the latest calculations made it

largely unnecessary to resort to averaging, but by itself did not achieve

quite the same smoothness in the results. Secondly, the computational grid,

in the rear half of the bowl (90 < <f> < 180) as used in the latest

calculations was somewhat coarser than the grid used in the earlier

calculations, for reasons of economy.

3n Fig. 63 a comparison is made between experimental and computed

static and total pressure data as a function of distance along the flow.

The experimental data are those for the highest mass flow (i.e., highest

Reynolds number) cases as previously compiled in Table 4. The computed data

are presented in terms of local maxmimum and minimum values, i.e., all

computed results are contained within the bands shown. As mentioned

previously in the summary of the experimental effort, the total pressure at

the turbine exit (f.E.) used as the upstream boundary condition was

estimated since the experimental data at this station must be considered

incorrect.

Not surprisingly, but believed to be in agreement with general

engineering knowledge, the relatively highest total pressure loss occurs in

the bend of the turnaround duct. The computed pressure loss from the exit

of the turnaround duct (TADE) to the bowl inlet (B.I.) appears to be

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VELOCITY VECTOR S

VMA X * 481 47

ITERATION 15000

4

1

»

1

\

ill

1

^

4

9

t

f

1

*

*

4

i i

! Nt^

lul

•&f

\ \

Fig. 60 DFNUS HGM Nominal Configuration Flow Field

96

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LMSC-HEC TR FOA2555

ID

1

I

3

4

5

e

7

8

9

(0

I I

12

13

M

IS

16

17

18

19

28

21779

22163

22546

22931

23313

23897

24988

24464

24847

25231

250 M

25098

28381

287f5

27148

27532

27915

28299

28682

29866

7759

2745

7740

2735

7738

2724

7719

2714

7789

2784

7099

2604

7880

2693

7678

2S73

7688

2683

7658

2653

Fig. 61 DFNUS HGM Nominal Configuration Pressure Contours

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ID

I

2

3

4

S

9

I B

I I

12

13

M

IS

HACH

0433

9722

101 I

1290

1588

1877

2186

2454

2743

3332

.3321

3689

3890

.4187

Fig. 62 DFNUS HGM Nominal Configuration Mach Number Contours

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MI TE TAD E

260

240

Bend

.TAD

O

A

220

W

Q.

200

w

w

a>

a

O

v

A

O

BI

Bowl

Sym. Test

1.

1.

2.

07

09

09

2.15

3.06

TDI

I

I Transfer

1 Duct

TDE

m

61.63

61.98

73.48

71.34

72.86

Total Pressure (PAGE Code)

180

160

Static Pressure

(PAGE Code)

I

0.2 0.4 0.6 0.8 1.0

 r

Flow Distance (ft)

0.2 0.4 0.6

Fig. 63 DFNUS HGM Averaged Pressure Along Flow (Open symbols

indicate static pressure; solid symbols indicate

total pressure).

Legend:

= Model inlet

= Turbine exit

= Turnaround duct exit

= Bowl inlet

= Transfer duct inlet

= Transfer duct exit

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smaller than that indicated by the experimental data. From there to the

transfer duct exit (T.D.E.) the computed pressures are roughly in line with

the experimental data. The overall computed total pressure loss from the

turbine exit to the transfer duct exit lies between 15 and 19 percent (of

the assumed initial total pressure), and between 33 and 50 percent of this

loss occurs in the turnaround duct.

Next, computed circumferential pressure distributions at the turnaround

duct exit are compared with experimental data and the pressure distributions

assumod as upstream boundary condition in the earlier calculations. Figure

64 shows that the computed static pressure distribution straddles both the

experimental data and the previously assumed linear distribution with the

maximum at the back side of the manifold and the minimum at the front side

between the transfer ducts.

The corresponding computed total pressure distribution is shown in Fig.

65. Mote that the total pressure is practically constant over the front

side of the bowl displaying a small increase toward the back side.

Both distributions display noticeably larger oscillations on the back

side of the bowl (90 < 9 270) than on the front side (2.70 £ <p < 90) due to

the already mentioned coarse grid on the back side, especially in the

circumferential directjon. Nevertheless, the results do seem to justify the

previously adopted assumption that the effects of the flow in the turnaround

duct on the flow in the bowl and transfer duct can be simulated (without

including the turnaround duct) by using appropriate upstream boundary

conditions.

Circumferential distributions of static and total pressure at the bowl

inlet (a cross-section just passing through the lower edge of the transfer

ducts) are again compared with experimental data in Figs. 66 and 67. The

computed results are seen to follow the trend of the experimental data. In

spite of the oscillations from grid plane to grid plane in the

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0.06

0.04

-0.02

-0.04

-0.06

180

Rocketdyne Experiment

Assumed for Bowl/Transfer Duct Calculation

Result for Complete HGM Calculation

I I

240 300 360/0 60

Circumferential Position, <p

120 180

Fig. 64 Turnaround Duct Exit Static Pressure Distribution

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0.06,-

0.04

> Rocketdyne Experiment

-— Assumed for Bowl/Transfer Duct Calculation

— Result for Complete HGM Calculation

0.02

4J

ia

-0.02

-0.04

-0.06

180

I I I

240 300 360/0 60

Circumferential Position,

120 180

Fig. 65 Turnaround Duct Exit Total Pressure Distribution

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Rocketdyne Experiment

Calculation (PAGE Code)

l.OOCH

0.98L

0.86

180 240 300 360/0 60

Circumferential Location, <P

120 180

Fig. 66 DFNUS HGM, Bowl Inlet Static Pressure

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Rocketdyne Experiment

Calculation (PAGE Code)

l.OQt0.98U

0.90U

0.88

180 240 300 360/0 60

Circumferential Location,

120 180

Fig. 67 DFNUS HGM, Bowl Inlet Total Pressure

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circumferential direction, the expected minima in the static pressure just

upstroam of the turn into the transfer duct (<p ~ 45 deg) are clearly

v/isible. Both static and total pressure display local maxima between the

transfer ducts and absolute maxima on the opposite side of the bowl, in

agreement with the experimental data.

As a final comparison between analysis and experiment, Mach number

profiles at the transfer duct exit are illustrated in Fig. 68. Dashed and

solid curves represent the results from the earlier calculations without the

turnaround duct, while the dash-dotted curves represent the results from the

analysis of the complete HGM. Neither one of the calculations reproduces

the details of the experimental profile. However, qualitatively at least,

results from the later calculations do indicate a slight minimum near the

duct center, so prominently displayed in the experimental data.

4.2 CONFIGURATION VARIATIONS

4.2.1 Modified Transfer Duct Inlet

Having demonstrated that available numerical analysis is capable of

producing results which agree with experimental data, another goal of the

effort undertaken here was to use the analysis to explore changes in the

geometric configuration which would result in more favorable flow behavior.

Figures 21 through 24 illustrated a computational grid of the hot gas

manifold incorporating a greatly increased radius of curvature of the

transfer duct inlet fairing, especially in the region just upstream of the

duct flow separation region found in both analytical and experimental

studies of the nominal HGM configuration. Neither the transfer duct

location, nor its orientation nor its size was affected by this

modification. Flowfield calculations for the modified configuration were

then performed using initial and boundary conditions identical to those

previously used for the nominal configuration.

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90 270

180 180

0.3 0.3

M . M

> Rocketdyne Experiment

(Turbulence Model I) ~)

(Turbulence Model II) J

Complete HGM Calculation

Bowl/Transfer Duct

Calculation

Fig. 68 Transfer Duct Exit Mach Number Profiles

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Results are shown in Figs. 69 through 75. Figure 69 gives the same

overall view of the HGM flow field as shown for the unmodified manifold in

Fig. 51. Note the absence of any flow recirculation in the present case.

Details of the velocity vector plots and Mach number contours in the oblique

longitudinal cut through the transfer duct are compared in Figs. 70 through

73 for the two configurations. Hence, a significant result of decreasing

the curvature in the transfer duct inlet fairing is the elimination of flow

separation in the duct.

The effect of the transfer duct inlet modification on the duct exit

flow properties is shown in terms of relative static and total pressure

profiles across the duct exit plane. Figure 74 shows a significant

reduction in static pressure nonuniformity, and the same holds for the total

pressure distribution shown in Fig. 75,

Flow visualisation experiments as well as computational analyses have

shown certain swirl patterns to exist in the transfer ducts. Although the

present rplativoly coarse grid analysis shows good agreement with

experimental pressure distributions we believe that it is not accurate

enough to predict swirl patterns reliably. Nevertheless, an attempt has

been made to compare the swirl encountered in the present analysis for the

two HGM configurations in terms of the ratio of average cross flow to

average axial flow along the transfer duct. The results, displayed in Fig.

76, show that, in the transfer duct inlet region, swirl is somewhat higher

for the modified inlet configuration. In the cylindrical portion of the

ducV.^ however, the situation is reversed. At the duct exit, swirl in the

modified duct is found to be almost 35 percent lower than that calculated

for the nominal duct.

4.2.2 Turnaround Duct Variations

A limited study was performed to explore the effect of slight changes

in the geometry on the flow properties in the turnaround duct relative to

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Fig. 69 Modified HGM Bowl and Transfer Duct Flow Field

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Fig. 70 Nominal HGM Transfer Duct Flow Field

Fig. 71 Modified HGM Transfer Duct Flow Field

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ORIGINAL PAGE IS

OF POOR QUALfTY

Fig. 72 Nominal HGM Transfer Duct Mach Contours

Fig. 73 Modified HGM Transfer Duct Mach Contours

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Nominal Transfer Duct Inlet

Modified Transfer Duct Inlet

0.05 0.051—

la

/—\ la

i

ft

-0.05 I I I I I -0.05

180 270

Fig. 74 Transfer Duct Exit Static Pressure Profile

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Nominal Transfer Duct Inlet.

Modified Transfer Duct Inlet

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0.051—

0.05

0.05 i i i I i

270

Fig. 75 Transfer Duct Exit Total Pressure Profile

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0.5

0.4 -

0.3

l>

CO

CO

o

l-l

u

0.2

0.1

LMSC-HEC TR F042555

Nominal Transfer Duct Inlet

— _ Modified Transfer Duct Inlet

10 15

Grid Surface

Fig. 76 Twin Duct HGM - Ratio of Average Cross Flow

to Average Axial Flow Along Transfer Duct

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the nominal DFIMUS turnaround duct configuration. The changes implemented

affected mainly the wall contours in the 180 deg bend while the dimensions

of the inflow and outflow cross-section were held at the values for the

nominal duel.

The modified geometries are compared to the nominal geometry in Fig.

77. The first change implemented (Version 2) was to slightly decrease the

curvature of the bend while keeping the cross-sectional distribution versus

flow distance near that of the nominal configuration (Fig. 78). For the

second change (Version 3) we used the outer wall from Version 2 while

retracting the inner wall so as to open up the narrowest passage in the

bend. The result is also shown in Fig. 78, indicating an increasing flow

area through most of the bend with a local minimum at the exit of the 180

deg turn.

Axi.synvitetric flowfield calculations were performed using 510 nodes in

the grid pL*ne. Inflow and outflow boundary conditions were specified in

terms of inlet total pressure and exit static pressure, and were the same

for all thr^e cases. A relatively high effective viscosity was used to

simulate turbulent flow resulting in a calculated mass flow at approximately

50 percent of the experimental value. The viscosity was the same for all

throe cases.

Velocity vector plots are compared in Fig. 79. Differences between the

throe cases are very subtle and hardly noticeable. Some slight quantitative

differences can be detected in the static pressure contours shown in Fig.

80. The most noticeable effect appears in the Mach number contour plots

shown in Fig. 81. For the first two cases the highest velocity is found in

the second half of the bend, i.e., just downstream of the narrowest flow

passage. In contrast, for Case C, the flow velocity is much more uniform

throughout the bend reaching a maximum just downstream of the 180 deg turn.

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Version I (Nominal)

Version II

Version III

Fig. 77 Turnaround Duct Variations

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oo

I

00

u

c

(0

4J

(0

0)

c

I-J

0)

*J

c

0)

U)

o

CD

•H

n>

nt

c

o

•H

*->

U

<u

CO

I

VI

U)

o

1-1

o

4-1

(J

T>

c

3

o

3

H

oo

t>o

•H

in

CM

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a. Nominal DFNUS

~ - L =..=.=• LMSC-HEC TR F042555

b. Version II

c. Version III

Fig. 79 Axisyiranetric Turnaround Duct Variations, Velocity Vectors

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a. Nominal DFNUS

b. Version II

c. Version III

Fig. 80 Axisymmetric Turnaround Duct Variations, Static Pressure Contours

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a. Nominal DFNUS

b. Version II

c. Version III

Fig. 81 Axisymmetric Turnaround Duct Variations, Mach Number Contours

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Table 6, in which some numerical results are compared, indicates that

the static pressure gradient is practically the same for all three cases.

In terms of mass flow, however, version 3 allows a 14 percent higher mass

flow relative to the nominal duct, at the same pressure gradient and

viscosity. It is concluded, therefore, that opening up the flow passage in

the turn where the highest flow losses are to be expected results in a more

efficient configuration. This is a preliminary conclusion and should be

explored further in the future.

Table 6 RESULTS OF TURNAROUND DUCT VARIATIONS

Case

Nominal

Version 2

Version 3

_ p_

pinlet

0.2312

0.2317

0.2320

m

32.3

32.8

36.9

m

m . , nominal

1.0

1.015

1.142

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5. CONCLUSIONS

It was experimentally demonstrated that a new twin-duct SSME high

pressure fuel turbopump hot-gas manifold yields improved flow uniformity as

compared to the original three-duct design. This advanced HGM design shows

promise in leading to longer life and higher power level versions of the

SSME.

Major flow improvements were accomplished in the turbine

exit/turnaround duct region by increasing the annular path cross-sectional

area downstream of the 180 deg turn, the fishbowl volume, and by contouring

the two larger transfer ducts with the outer fishbowl housing. These

increases, in general, decreased the local dynamic pressure and allowed the

flow to turn more gradually into the transfer ducts. This substantially

reduced the circumferential pressure gradient at the turbine exit and

downstream of the 180 deg turn. Although flow separation in the transfer

ducts could not be eliminated, it was substantially reduced with the result

of much improved flow uniformity at the transfer duct exits.

The Lockheed PAGE code was used to computationally model the new

twin-duct HGM and to compare calculated flow field characteristics with

experimental data. It was found that computed pressure distributions agreed

well with measured circumferential pressure distributions downstream of the

180 deg bend in the turnaround duct and in the fishbowl entrance just below

the transfer ducts. Furthermore, the computer model correctly predicted

flow separation and flow reversal in the lower inner quadrant of the

transfer ducts. The computer model did not reproduce the details of the

Mach number distributions in the transfer duct as obtained from experiment.

As there are known shortcomings in the model as well as known uncertainties

about the validity of these particular measurements, the clarification of

this disagreement must await further study.

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Using the PAGE code, a study was performed on configuration variations

with the goal of flowfield improvement. Computational results for the flow

in a modified HGM with much improved fairing of the flow contour at the

junction of the transfer ducts to the fishbowl outer wall predict that

through proper inlet contouring it will be possible to further substantially

reduce the extent of the stagnation/recirculation regions in the inner lower

quadrants of the transfer ducts, or to perhaps eliminate them altogether.

The same calculations also resulted in more uniform static and total

pressure distributions over the transfer duct exit cross-section.

From a study of variations in the wall contours of the turnaround duct

it is concluded that enlarging the cross-sectional area in the 180 deg bend

where the largest losses occur should result in decreased pressure losses

for a given mass flow or increased mass flow for a given pressure loss,

i.e., a more efficient flow configuration.

Computational fluid dynamics has been applied to realistic flow

problems in the SSME and found to be a useful tool for analysis. These

results are, in fact, expected to influence the actual design of improved

hardware. The three-dimensional flowfield calculations performed under this

effort demonstrate what can be achieved with present computational

technology. They require an intimate knowledge of the computational

analysis on the side of the investigator and the most up to date

computational resources available. To the designer, however, the

computational analysis can provide details of the flow conditions which,

previously, were largely inaccessible. Once a computational model has been

set up, variations in the flow parameters or modifications in the flow

geometry can be implemented with relative ease, helping future designs to be

optimized before rather than after constructing the hardware.

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6. REFERENCES

1. Pelaccio, Dennis G., "Duct Flow Nonuniformities Study," Final Report

RI/RD83-160, Rockwell International, Rocketdyne Division, 30 June 1983.

2. Pelaccio, D.G., F.F. Lepore, G.M. O'Connor, G.V.R. Rao, G.H. Ratekin,

S.T. Vogt, "Experimental Evaluation of an Advanced Space Shuttle Main

Engine Hot-Gas Manifold Design Concept," 20th Joint Propulsion

Conference, AIAA Paper 84-1463, June 1984.

3. Lepore, F.F., and Vogt, S., "Solid Wall Hot-Gas Manifold Testing Series

IV Test Results," Rocketdyne Briefing No. ATU-83-006, Canoga Park,

Calif., 13 January 1983.

4. Rosen, R., P.Y. Liang, Y.H. Quan, G.V.R. Rao, and T.T. Yang,

"Investigation of a Complex Rocket Engine Manifold Flow to Determine its

Major Characteristics," presented at AIAA/SAE/ASME 20th Joint Propulsion

Conference, Cincinnati, Ohio, Paper No. 84-1462, June 1984.

5. Prozan, R.J., L.W. Spradley, P.G. Anderson, and M.L. Pearson, "The

General Interpolants Method," AIAA Paper 77-642, Albuquerque, June 1977.

6. Spradley, L.W., J.F. Stalnaker, and A.W. Ratliff, "Solutions of the

Three-Dirnensional Navier-Stokes Equations on a Vector Processor," AIAA

J_L, Vol. 19, No. 10, October 1981.

7. Gordon, W.J., and C.A. Hall, "Construction of Curvilinear Coordinate

Systems and Applications to Mesh Generation," J. Numer. Math., Vol. 1,

1973, pp. 461-477.

8. Spradley, L.W., J.F. Stalnaker, M.A. Robinson, and K.E. Xiques, "Finite

Element Algorithms for Compressible Flow Computation on a Supercomputer,"

Finite Elements in Fluids, Vol. 6, Edited by Gallagher, Corey, Oden, and

Zienkiewicz, John Wiley, New York, 1984.

9. Schlichting, H., Grenzschicht-Theorie, 3rd Edition, Verlag G. Braun,

Karlsruhe, 1958.

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