technical report fluid flow analysis of the ssme high

LMSC-HEC TR F268780

TECHNICAL REPORT

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FLUID FLOW ANALYSIS OF THE SSME

HIGH PRESSURE FUEL AND OXIDIZER TURBINECOOLANT SYSTEMS

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JULY 1989

Contract NAS8-36284

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Prepared for

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

GEORGE C. MARSHALL SPACE FLIGHT CENTER

MARSHALL SPACE FLIGHT CENTER. AL 35812

(NA'_A-C_,-!63730) FLUIO FLOW ANALYSIS OF THE

SSME HIgH PRESSI_!RF FUeL AND oxIr_IZER TUR_INF

CfIQLANT SYSTEMS (LMS£) 67 p CSCL 7'IN

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LIL_C-HEC TR F268780

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TECHNICAL REPORT

FLUID FLOW ANALYSIS OF THE SSME HIGH PRESSURE FUEL

AND OXIDIZER TURBINE COOLANT SYSTEMS

July 1989

Contract NAS8-36284

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Prepared for

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

GEORGE C. MARSHALL SPACE FLIGHT CENTER, AL 35812

by

G.A. Teal

LOCKHEED MISSILES & SPACE COMPANY, INC.

HUNTSVILLE ENGINEERING CENTER

HUNTSVILLE, AL 35807

LMSC-HEC TR F268780

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FOREWORD

This document presents the results of work performed

for NASA-Marshall Space Flight Center by the Computational

Mechanics Section of the Lockheed Missiles & Space Company,

Inc., Huntsville Engineering Center. This work was performed

for NASA-MSFC under Contract NAS8-36284, with Dr. Helen

McConnaughey serving as technical monitor.

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LOCKHEED-HUNTSVILLE ENGINEERING CENTER

LMSC-HEC TR F268780

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Section

CONTENTS

FOREWORD

INTRODUCTION AND SUMMARY

I.I Objectives

1.2 Summary

GENERAL THEORY OF FLUID FLOW RELATIONS

2.1 Flow Equations

2.2 Bearing Model

2.3 Labyrinth Seal Model

2.4 Therm_odynamic and Transport Properties

HIGH PRESSURE FUEL TURBINE COOLANT ANALYSIS

3.1 Turbine Coolant System

3.2 Model Improvement3.3 Results

3.4 Program Input Guide

HIGH PRESSURE OXIDIZER TURBINE COOLANT ANALYSIS

4.1 Turbine Coolant System

4.2 Model Improvement4.3 Results

4.4 ProEram Input Guide

REFERENCES

P a_e_

ii

1-1

1"-1

2-1

2-1

2-5

2-5

2-5

-..I

3-1

3-1

3-3

3-3

4-1

4-1

4-1

4-20

4-20

5-1

Tab ie

2-1

3-I

3-2

3-3

4-1

4-2

4-3

LIST OF TABLES

Pressure Loss Factors (K)

HPFTP Turbine Coolant Analysis (FPL)

HPFTP Turbine Coolant Analysis (I04%)

HPFTP Turbine Coolant Analysis (MPL)

HPOTP Turbine Coolant Analysis (FPL)

HPOTP Turbine Coolant Analysis (104%)

HPOTP Turbine Coolant Analysis (MPL)

PaK_

2-2

34

3-7

3-10

4-21

4-26

4-31

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LMSC-HEC TR F268780

LIST OF ILLUSTRATIONS

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3-1

4-1

4-2a

4-2b

4-2c

4-2d

4-2e

4-2f

HPFTP Turbine Coolant System Schematic

HPOTP Turbine Coolant System Schematic Diagram

Flow Passage of Hydrogen from the Coolant Manifold at

Station 6 to the Turbine Seal Region at Station 131

Flow Passage of Hydrogen from the Coolant Manifold at

Station 6 to the Struts at Stations 149 through 153

Flow Passage of Mixed Coolant from the Mixing Chamber

at Station 8 to the First Stage Rotor at Stations 22

and 28

Flow Passage of Mixed Coolant from the Mixing Chamber

at Station 8 to the Turbine Stator Region at Stations 63

and 66

Flow Passage of Mixed Coolant from the Mixing Chamber at

Station 8 to the Turbine Housing at Stations 42 through

50 and Exit Strut Region at Stations 75 through 90

Flow Passage of Mixed Coolant from the Mixing Chamber at

Station 8 to the Second Stage Rotor at Station 109

3-2

4-2

4 --14

4-15

4-16

4-17

4-18

4--19

iv


LMSC-HEC TR F268780

I. INTRODUCTION AND SUMMARY

I.I OBJECTIVES

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The objective of this study is to provide improved analysis capability

for the Space Shuttle Main Engine (SSME) high pressure fuel and oxidizer

turbine coolant systems. Each of the systems was analyzed to determine fluid

flow rates and thermodynamic and transport properties at all key points in the

systems.

I. 2 SUMMARY

Existing computer codes developed by Lockheed for NASAMSFC were used as

a baseline for these analyses. These codes were modified to provide improved

analysis capability. The major areas of improvement are listed below.

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• A review Of the drawings was performed, and pertinent geometry changes

were included in the models.

• Improvements were made in the calculation of thermodynamic and

transport properties for a mixture of hydrogen and steam.

A one-dimensional turbine model for each system is included as a

subroutine to each code. This provides a closed loop analysis with a

minimum of required boundary conditions as input.

• An improved labyrinth seal model is included in the high pressure fuel

turbine coolant model.

The modifications and the analysis results are presented in detail in the

following sections.

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\ LOCKHEED-HUNTSVILLE ENGINEERING CENTER

LMSC-HECTR F268780

2. GENERAL THEORY OF FLUID FLOW RELATIONS

The fluid flow model solves the steady state continuity, momentum, and

energy equations to obtain thermodynamic and transport properties at various

stations in the coolant systems. The models compute changes in fluid flow

properties between stations using coolant system geometrical data, pressure

loss factors, heat transfer rates, and bearing and labyrinth seal models

discussed below.

i

2.1 FLOW EQUATIONS

The mass continuity, momentum, and energy conservation equations are cast

in one'dimensional, incompressible form to describe the fluid flow from station

to station. The continuity equation states that the fluid flow rate ls con

served from station to station. The momentum equation is cast in the fot_

P = P - _p + _PT2 T1 loss cen

o

where

and

PT2 is the total pressure at the downstream station

P is the total pressure at the upstream stationT1

6Ploss is the change in pressure due to friction or turbulence

AP is the change in pressure due to centrifugal effects.cen

The term APloss depends on the type of flow passage involved and is

evaluated using the relationship

APloss = K (pV_ /2 gc )

2-1


LMSC-HEC TR F268780

where

and

p is the fluid density

VF is the fluid flow velocity (excluding centrifugal components)

g is the gravitational constantc

K is a pressure loss factor that depends on the type of flow.

The values of K for several types of flow may be obtained from Ref. 1 and are2

presented in Table 2-1. The dynamic pressure term PVF/2 gc is evaluated at

the station with the smaller flow area.

Table 2-I PRESSURE LOSS FACTORS (K)

Type of Passage I Value of K (Ref. I) Remarks!

Smooth Pipe

(Darcy Weisbach)

Mitered Bend

Sudden Expansion

Sudden Contraction

Entrance from

Large Volume

Exit to Large

Volume

K = fL/D

K = fL /De

2

K = [I - (DI/D2)2]

K = 0.50

K=0.23

K = 0.04

K= 1.0

f = 0.1841R 0"2

L = length

D = hydraulic diameter

R = Reynolds number

L = equivalent lengthe

(See page A-27 of Ref. I)

DI = smaller hydraulic .diameter

D 2 = larger hydraulic diameter

See page A-26 of Ref. 1

Sharp-edged entrance

Rounded entrance

Well-rounded entrance

V F = 0.0 (small flow velocity)

2-2

-- LOCKHEED-HUNTSVILLE ENGINEERING CENTER

LMSC-HEC TR F268780

The resultant pressure changes _Ploss may be modified by an expansion

factor (Y) for compressible fluid flows. Expansion factors for several types

of passages may be obtained from pages A-21 and A-22 of Ref. I; the change in

pressure becomes

2

_Ploss = _Ploss/Y

This expansion factor may be ignored for _Ploss/PTl values of less than 10%

and for up to 40% if the fluid density is replaced by the average density

between stations 1 and 2 (Ref. i)

The term _Ploss also includes the pressure losses that occur in

bearings and labyrinth seals. These pressure losses will be discussed in

subsequent paragraphs.

The term AP accounts for pressure changes due to centrifugalten

effects of the spinning fluid and may be computed from the relationship

2 2

_Pcen = Kc p (VT2 - VTI)/2 gc

where VTI and VT2 are the upstream and downstream tangential velocities.

The term K is a frictional loss factor equal to unity for frictionalc

dissipation.

For flow about spinning disks the pressure change is computed from the

relationship

2 2

= p w _ R dR/g cdPs s

where

dP = differential static pressures

w = shaft angular velocitys

= ratio of fluid to shaft angular velocities

R = radial distance from spin axis.

2-3


LMSC-HEC TR F268780

w

Relationships for n may be obtained from Ref, 2 for inward and outward

flows through smooth and bladed disk/housing configurations, The effect on

total pressure hP must be determined from dP and dynamic pressure.cen s

These various contributions to pressure changes also affect the energy of

the fluid through the energy equation

QI-2

HT2 = HTI + m + _Hcen

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where

HT = total enthalpy per pound of fluid

QI-2 = heat transferred to the fluid

AH = change in total enthalpy due to centrifugal effects.cen

Changes in pressure due to centrifugal effects result in a change in total

enthalpy equal to

gH = AP Ipcen cen

For spinning disks the heat generation term AH becomes (Ref. 2):cen

P (RI- R2) C

AHcen = \ 60/ _ 4 gc J m

where C is a coefficient depending on disk/housing configuration,m

and J = 778.2 Ibf-ft/Btu,

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The above equations represent solutions to the general flow equations

which will adequately describe the flow in the coolant systems.

2-4


LMSC-HECTR F268780

2.2 BEARING MODEL

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The bearing model computes the pressure drop in the fluid flowing through

ball bearings. The pressure loss term AP B is computed by solving the

quadratic equation

_(APB)2 .2- m (AP B) - _ _2 = 0

where

2 2

= 288 p gc A C

2 (2_N/60) 2

B = p (RK) 288 gc

N = shaft rpm

The coefficients A, C, R, and K are bearing constants supplied by NASA-MSFC.

2.3 LABYRINTH SEAL MODEL

The labyrinth seal model now used by the high pressure fuel turbine

coolant model is an empirical leakage prediction program for straight-through

labyrinth seals developed for NASA-MSFC by Texas A&M University (Ref. 3).

This program is included as a subroutine in the fuel turbine coolant program.

2.4 THERMODYNAMIC AND TRANSPORT PROPERTIES

The high pressure fuel and oxidizer turbine coolant systems are complex

flow systems comprising several flow paths in which the fluid is pure hydrogen

and other flow paths containing a mixture of H 2 and H20. Thermodynamic and

transport properties for hydrogen are computed from the GASP computer code

(Ref. 4).

To evaluate real thermodynamic properties for H2/H20 gas mixtures the

WASP computer code (Ref. 5) is used to calculate H20 properties. The gas

2-5


LMSC-HECTR F268780

components are assumed to occupy the entire volume at the mixture temperature

and pressure, and the thermodynamic properties are mass fraction weighted to

obtain mixture properties. The compressibility factor is assumed to obey the

law of additive volumes and is computed accordingly.

To obtain thermodynamic properties for a mixture containing H20 in the

liquid phase, the following procedure is employed:

• PM and HM are the known thermodynamic properties (except at

turbine inlet and discharge stations where PM and TM are known)

• Assume TM and compute PV

e Check if PH20 > PV (two-phase if true)

• Compute a gas phase mole fraction required to give PH20G = PV

• Compute KL and XG

• HTM = XH HH + XL H L + XG HG

• Iterate on TM until HTM = HM.

This procedure is extended to include the solid region when PM and HM are

known. However, in the solid region, the thermodynamic state cannot be

defined by PM and TM alone.

In general, the properties routine evaluates thermodynamic properties of

H20 for four separate regions:

I. TM > Tcrit

Composition is all gas, properties evaluated at PM and TM

2. TM < Tcrit' PV > PM

Composition is all gas, properties evaluated at PM and TM

.

PV < PM' PV > PH20Composition is In vapor state.

Enthalpy is evaluated by computing liquid enthalpy at PM and TM

and adding the heat of vaporization. Transport properties are

evaluated for saturated vapor only.

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LMSC-HEC TR F268780

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PV < PM' PV < PH 0

Composltion is t_o-pha_o

- Liquid/vapor

- Liquid

Vapor phase is negligible

- Solid/liquid

Vapor phase is negligible

- Solid

Vapor and liquid phases negligible

where

TM = mixture temperature

PM = mixture pressure

Tcrit = critical temperature of H20

PV = vapor pressure of H20 at TM

PH20 = H20 partial pressure based on total mixturemole fraction

PH2OG = H20 partial pressure based on gas phasemole fraction

XL

xG

HH

H L

HG

%.

= the mass fraction of liquid H20 in the

total mixture

= the mass fraction of H20 vapor in thetotal mixture

= H 2 enthalpy at PM and TM

= H20 liquid enthalpy at PM and TM

= H20 vapor enthalpy at PM and TM

= mixture enthalpy

= computed mixture enthalpy.

In the two-phase region, the mixture density computed by the program is

the homogeneous two-phase density. The compressibility factor is computed for

the gas phase only.

Transport properties are evaluated for a mlxture of gases using the method

of Wilke for computing viscosity and the method of vanderslice for computing

thermal conductivity (see Reference 6). Mixture transport properties are

evaluated for the gas phase only.

2-7


LMSC-HEC TR F268780

3. HIGH PRESSURE FUEL TURBINE COOLANT ANALYSIS

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3.1 TURBINE COOLANT SYSTEM

The existing high pressure fuel turbopump (HPFTP) turbine coolant system

flow model developed by Lockheed for NASA-MSFC was used as a baseline for this

analysis. This baseline model (shown in Figure 3-1) is documented in Ref-

erence 7. The turbine coolant system was modeled to evaluate the flow proper-

ties at each of the numbered stations shown in Figure 3-1 and to compute the

flow rates along each of the flow paths in the system. Two additional flow

paths have been added to compute flows through the turbine blade fir trees.

These are the first stage blade fir trees (stations 95 through 98) and the

second stage blade fir trees (stations 99 through I01). The model comprises

I01 stations and 25 flow paths.

3.2 MODEL IMPROVEMENT

A review of current drawings was performed and pertinent geometry changes

were included in the model. Operating clearances for the turbine blade

platform seals, labyrinth seal, and the lift-off seal were supplied by NASA-

MSFC.

A one-dimensional turbine model is included as a subroutine in the code.

This provides a closed loop analysis with a minimum of required boundary con-

ditions as input. Estimated platform seal leakage rates are input to the

turbine model, and the turbine model is executed to provide pressures as

boundary conditions for the coolant flow model (stations 35, 41, 64, and 72).

The coolant model is then executed and new leakage flows are computed. An

input option is provided for terminating the execution at this point or con-

tinuing with another pass through each model if greater accuracy is desired.

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LMSC-HECTR F268780

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An improved labyrinth seal leakage prediction program developed for

NASA-MSFC by Texas A&M University (Ref. 3) is included as a subroutine in the

turbine coolant program.

An improved properties subroutine for computing thermodynamic and trans-

port properties for a mixture of H 2 and H20 has been added to the program.

See Section 2.4 for a detailed description of this calculation procedure.

3.3 RESULTS

The fuel turbine coolant system was analyzed at full power level (FPL),

104% and minimum power level (MPL), using Rocketdyne engine balance data

obtained from Reference 8. The results of these analyses are presented in

Tables 3-1 through 3-3. These results are for a balance piston high pressure

orifice gap of 0.004 inch.

3.4 PROGRAM INPUT GUIDE

This section describes the input data file required for execution of the

HPFTP turbine coolant program.

Column Parameter Description

Line number I, Format (8EI0.4)

I-I0 GAP Balance piston high pressure orifice

gap, in.

Line number 2, Format (8EI0.4)

I-I0 RDEFO

11-20 RDEFI

21-30 XDEF

Housing radial deflection at high

pressure orifice, in.

Impeller radial deflection at high

pressure orifice, in.

Impeller axial deflection at high

pressure orifice, positive toward

turbine, in.

3-3


LMSC-HEC TR F268780

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3-12


LMSC-HEC TR F268780

I


Line numbers 3 through 103, Format (15,5X, 6EI0.4)

1-5 IP

11-20 A

21-30 D

31-40 XL

41-50 XR

51-60 XK

61-70 EFF

Flow type

Passage flow area, in2

Passage hydraulic diameter, in.

Passage effective length for frictional

losses, in.

Radial location, in.

Flow loss coefficient

Ratio of fluid to shaft rotational speed.

w

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Line number I04, Format (8EI0.4)

I-I0 BAREA

11-20 BRAD

21-30 BC

31-40 BK

Bearing area, in 2

Bearing pitch radius, in.

Empirical constant

Empirical constant.

Line number I05, Format (215, 7FI0.5)

Data for interstage labyrinth seal

1-5 N

6-10 J

11-20 CL

21-30 PL

31-40 HL

41-50 WL

51-60 DSHF

61-70 DCASE

71-80 DCL

Final tooth number, enter 4

Parameter not used; enter 0

Radial clearance from drawings, in.

Tooth pitch, in.

Tooth height, in.

Tooth width, in.

Shaft diameter, in.

Case diameter, in. = DSHF+2(CL+HL)

Change in diametral clearance at

operating conditions, in.

3-13


" LMSC-HEC TR F268780


w

Line number 106, Format (215, 7F10.5)

Data for first two teeth of turbine seal

1-5 N Final tooth number, enter 6

6-80 Same parameters as above.

Line number 107, Format (215, 7FI0.5)

Data for next three teeth of turbine seal



= ..w

= =

Line number 108, Format (215, 7FI0.5)

Data for final three teeth of turbine seal



Line number 109, blank card image.

Line number ii0, Format (815)

1-5 IOPT = 1 Fixed blade coefficient and

iterates to determine flow rate

= 2 Fixed flow rate and iterates to

determine blade coefficient

6-10 IOPTXI = 1 Enter total pressures in pump

input data

= 2 Enter static pressures in pump

input data

11-15 ITURB = I Uses programmed turbine leakage

flows and makes one pass throughturbine and coolant flow models

= 2 Uses computed leakage flows from

first pass and makes an additional

pass through each model

16-20 KPUMP = I Reads input impeller inlet and

discharge conditions and bypasses

pump head rise model

= 2 Computes impeller inlet and

discharge conditions using pumphead rise model.

3-14


LMSC-HECTR F268780

Column Parameter

Line number III, Format (8EI0.4)

I-I0 WPIO

11-20 PIOF

21-30 TIOF

31-40 POOF

41-50 TOOF

51-60 ETAP

61-70 RPM

71-80 XPL

Description

Pump inlet flow rate, Ibm/s

Pump inlet pressure, psla

Total pressure if IOPTXI = 1

Static pressure if IOPTXI = 2

Pump inlet temperature, °R

Pump discharge pressure, psia

Total pressure if IOPTXI = 1

Static pressure if IOPTXI = 2

Pump discharge temperature, °R

Pump efficiency

Pump speed, rpm

Power level ratio.

w


I-i0 PKNOWN(1)

11-20 TKNOWN(1)

21-30 RKNOWN(1)

31-40 VTKNON(1)


I-I0 PKNOWN(2)

11-20 TKNOWN(2)

21-30 PKNOWN(2)

31-40 VTKNON(2)

Impeller discharge total pressure, psia

Impeller discharge temperature, °R

Impeller discharge density, Ibm/ft 3

Impeller discharge fluid tangential

velocity, ft/s.

Impeller inlet total pressure, psia

Impeller inlet temperature, °R

Impeller inlet density, Ibm/ft 3

Impeller inlet fluid tangential

velocity, ft/s.

3-15

"- LOCKHEED-HUNTSVILLE ENGINEERING CENTER

LHSC-HEC TR F268780

. I

m

Column Parameter


I-I0 WDPB

11-20 PPB

21-30 TPB

31-40 HPA

41-50 TFTD

51-60 PFTD

61-70 ETANZ

71-80 XKB


i-i0 OF


1-80 WDLEG


1-80 WDLEG


1-80 WDLEG

Description

Turbine inlet flow rate, ibm/s

Turbine inlet total pressure, psia

Turbine inlet total temperature, °R

Turbine horsepower, hp

Turbine discharge total temperature, °R

Turbine turnaround duct discharge total

pressure, psia

Nozzle efficiency, Kn2

Blade coefficient, Kb.

Preburner mixture ratio.

Legs 1 through 8 estimated flow rate at

FPL, Ibmls.

LeEs 9 through 16 estimated flow rate

at FPL, ibm/s.

LeEs 17 through 24 estimated flow rate

at FPL, Ibm/s.


I-I0 WDLEG Leg 25 estimated flow rate at FPL,

ibm/s.

3-16


LMSC-HE¢TR F268780

4. HIGH PRESSURE OXIDIZER TURBINE COOLANT ANALYSIS

4.1 TURBINE COOLANT SYSTEM

!

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The existing high pressure oxidizer turbopump (HPOTP) turbine coolant

system flow model developed by Lockheed for NASA-MSFC was used as a baseline

for this analysis. This baseline model (shown in Figures 4-1 and 4-2) is

documented in Reference 9. The turbine coolant system was modeled to evaluate

the flow properties at each of the numbered stations and to compute the flow

rates along each of the flow paths in the system. Four additional stations

have been included in the model for computational purposes. These are at the

first stage blade exit (station 159), second stage nozzle exit (station 160),

second stage blade exit (station 161), and primary turbine seal inlet (station

162). The model comprises 162 stations and 27 flow paths.

4.2 MODEL IMPROVEMENT

A review of current drawings was performed, and pertinent geometry changes

were included in the model. Operating clearances for the interstage seal and

turbine seal were supplied by NASA-MSFC. The flow path supplying coolant

hydrogen to the turbine seal region at station 131 (see Figure 4-2a) has been

modified and now supplies mixed coolant from the mixing chamber. The cold

hydrogen supply has been blanked off, and mixed coolant is now introduced at

old station location 122 shown in Figure 4-1m. This flow path now consists of

stations 120 through 131.

A one-dimensional turbine model is included as a subroutine in the code.

This provides a closed loop analysis with a minimum of required boundary

conditions as input. Estimated leakage rates into the primary turbine flow

path are input to the turbine model, and the turbine model is executed to

provide pressures as boundary conditions for the coolant flow model (stations

29, 159, 160, and 161). The coolant model is then executed and new leakage

4-1


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LMSC-HEC TR F268780

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4-6


LMSC-HECTR F268780

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LMSC-HEC TR F268780

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LMSC-HEC TR F268780

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flows are computed. An input option ls provided for tecmlnating the execution

at this point or continuing with another pass through each model if greater

accuracy is desired.

An improved properties subroutine for computing thermodynamic and trans-

port properties for a mixture of H2 and H20 has been added to the program.

Refer to Section 2.4 for a detailed description of this calculation procedure.

4.3 RESULTS

The oxidizer turbine coolant system was analyzed at FPL, I04%, and MPL

using Rocketdyne engine balance data obtained from Reference 8. The results

of these analyses are presented in Tables 4-1 through 4-3.

4.4 PROGRAM INPUT GUIDE

Th[s section describes the input data file required for execution of the

HPOTP turbine coolant program.


Line numbers 1 through 158, Format (15, 5X, 6EI0.4))

1-5 IP

11-20 A

21-30 D

31-40 XL

41-50 XR

51-60 XK

61-70 EFF

Flow type

Passage flow area, in2

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Ratio of fluid to shaft rotational

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4-23

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4-28


LMSC-HEC TR F268780

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4-2g


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4-30


LMSC-HEC TR F268780

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4-31


LMSC-HEC TR F268780

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4-32


LMSC-HEC TR F268780

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4-34

LOCKHEED-HUNTSViLLE ENGINEERING CENTER

LMSC-HEC TR F268780

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4-35


LMSC-HEC TR F268780


Line number 159, Format (8EI0.4))

I-I0 SEALCL Primary turbine seal operating

clearance, in.


1-10 RPM

11-20 ROF

21-30 XPL


I-I0 WDPB

11-20 PPB

21-30 TPB

"- 31-40 HPA

41-50 TFTD

qm_

51-60 PFTD

6I- 70 ETANZ

71-80 XKB

Line number 162, Format (815)

1-5 IOPT

6-I0 ITURB

Pump speed, rpm

Preburner mixture ratio

Power level ratio.

Turbine inlet flow rate, Ibm/s

Turbine inlet total pressure, psia

Turbine inlet total temperature, °R

Turbine horsepower, hp

Turbine discharge total temperature, °R

Turbine discharEe total pressure, psia

Nozzle eff£ciency, Kn 2

Blade coefficient, Kb.

= 1 Fixed blade coefficient and

iterates to determine flow rate

= 2 Fixed flow rate and iterates to

determine blade coefficient

= I Uses programmed turbine leakage

flows and makes one pass throuEhturbine and coolant flow models

= 2 Uses computed leakage flows from

first pass and makes an additional

pass through each model.

4-36

"_ LOCKHEED-HUNTSVILLE ENGINEERING CENTER

LMSC-HEC TR F268780

Y

Column Parameter


I-I0

11-20

21-30

PKNOWN (2)

TKNOWN (2)

WKNOWN (2)

31-40 RKNOWN(2)

Description

41-50 VTKNON(2)

Hydrogen coolant supply pressure, psia

Hydrogen coolant supply temperature, °R

Estimated hydrogen coolant flow rate,Ibm/s

Estimated hydrogen coolant density,Ibmlft 3

Coolant supply tangential velocity, ft/s.

i


1-80 WDLEG Legs 1 through 8 estimated flow rate at

FPL, Ibm/s


1-80 WDLEG Legs 9 through 16 estimated flow rate at

FPL, Ibmls


1-80 WDLEG Legs 17 through 24 estimated flow rate

at FPL, Ibm/s

Leg 19 is no longer used, input 0.O


1-30 WDLEG Legs 25 through 27 estimated flow rate

at FPL, Ibmls.

4-37


LMSC-HEC TR F268780

5. REFERENCES

w

L _

I. "Flow of Fluids Through Valves, Fittings, and Pipe," Technical Paper

No. 410, Crane Company, 1957.

,

o

5 ,

6 ,

o

,

°

H.F. Due and W.E. Young, "Investigation of Pressure Prediction Methods for

Low Flow Radial Impellers," PWA FR-1716, Pratt & Whitney Aircraft, West

Palm Beach, FL, February 1966.

G.L. Morrison et al., "Labyrinth Seals for Incompressible Flow," Seai-4-83,

Texas A&M University, College Station, Texas, November 1983.

R.C. Hendricks et al., "GASP-A Computer Code for Calculating the Thermo-

dynamic and Transport Properties for Ten Fluids," NASA TN D-7808, February

1975.

R.C. Hendricks et al., "WASPrA Flexible FORTRAN IV Computer Code for

Calculating Water and Steam Properties," NASA TN D-7391, November 1973.

S. Gordon, B.J. McBride and F.3. Zeleznick, "Computer Program for

Calculation of Complex Chemical Equilibrium Compositions and Applications,

Supplement I - Transport Properties," NASA TM-86885, October 1984.

P.G. Anderson et al., "Fluid Flow Analysis of the SSME High Pressure Fuel

Turbopump," LMSC-HREC TR D568931, Lockheed Missiles & Space Company,

Huntsville, AL, April 1979.

M. Tamasu, "SSME Phase 2 Predicted Engine Performance," OL 87RC060638,

Rockwell International, Rocketdyne Division, May 1987.

P.G. Anderson et al., "Fluid Flow Analysis of the SSME High Pressure

Oxidizer Turbopump Operating at Full Power Level," LMSC-HREC TR D698083,

Lockheed Missiles & Space Company, Huntsville, AL, August 1980.

w

5-1


technical report fluid flow analysis of the ssme high

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