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/ '

Pratt & WhitneyFR-20282-3

25 July 1989

LARGE LIQUID ROCKET ENGINE

TRANSIENT PERFORMANCE

SIMULATION SYSTEM

CONTRACT NO. NAS8-36994

SIX MONTH REPORT

PERIOD OF PERFORMANCE

1 OCTOBER 1988 THROUGH 31 MAY 1989

Prepared for

NASA-George C. Marshall Space Flight Center

Marshall Space Flight Center, Alabama 35812

/

J. R. Mason

Program Manager

Prepared by:

/

• /_.o.Southwick-Propulsion Systems

Technology Manager

Pratt & Whitney

P. O. Box 109600

West Palm Beach, FI. 33410-9600

UNITEDTECHNOLOGIESPRATT&WHITNEY

https://ntrs.nasa.gov/search.jsp?R=19910015027 2018-07-19T08:30:02+00:00Z


CONTENTS

INTRODUCTION ...................................................... 1

SUMMARY .......................................................... 2

TECHNICAL ACCOMPLISHMENTS

SYSTEM REQUIREMENTS CHANGES .............................. 4

SYSTEM ARCHITECTURE CHANGES .............................. 4

COMPONENT/SUBMODULE OVERVIEW ............................ 4

MODULE ................................................. 4

SUB-MODULE ........................................... 5

SYSTEM PROCESSORS ................................... 7

SIMPLE TTBE SIMULATION ..................................... 22

APPENDIX - MODULE ENGINEERING DESCRIPTIONS ..................... 44

MAIN FUEL INJECTOR .................................... 50

INCOMPRESSIBLE FLUID FLOW IN PIPE WITH INERTIAAND LOSS ............................................ 53

INCOMPRESSIBLE FLUID FLOW IN PIPE

WITH LOSS ........................................... 55

COMPRESSIBLE FLOW THROUGH AN ORIFICE .............. 56

MAIN COMBUSTION CHAMBER ............................ 57

SIMPLE FLOW MIXER .................................... 62

ISENTROPIC NOZZLE .................................... 64

PREBURNER WITHOUT PURGE ............................ 66

PUMP MODULE FOR POLYTROPIC PROCESS ................ 70

ROTOR TORQUE BALANCE ............................... 75

SIMPLE FLOW SPLITTER ................................. 76

TURBINE ............................................... 78

LUMPED VOLUME WITH ENERGY

AND CONTINUITY ...................................... 80

- Pratt & WhitneyFR-20282-3

CONTENTS (Continued)

STEADY STATE BALANCE ROUTINE ....................... 82

TRANSIENT INTEGRATION ROUTINE ........................ 84

ISENTROPIC NOZZLE ANALYSIS ........................... 85

FLOW CALCULATION THROUGH A RESTRICTION ............ 92

PROPERTY PACKAGES ................................... 98

PUMP CHARACTERISTIC MAP FORMAT 1 .................. 139

TURBINE CHARACTERISTIC MAP FORMAT 1 ............... 151

MULTIVARIABLE ITERATION ROUTINE ..................... 160

MAP READER .......................................... 162

=,i

INTRODUCTION

Pratt & Whitney

FR-20282-3

Large Liquid Rocket Engine Transient Performance Simulation, Contract

NAS8-36994, is a program to design and develop a simulation system for rocket

engine transient performance models. The system was designed and

conceptually demonstrated during Phase I of the contract. The current Phase II of

the contract will enhance the system, develop a detailed simulation of the

Technology Test Bed Engine (TTBE), and deliver the model and system software

to the National Aeronautics and Space Administration (NASA) George C.

Marshall Space Flight Center (MSFC).The program is sponsored by NASA/MSFC

with Mr. W.A. Adams acting as project manager. The Pratt & Whitney program

manager is Mr. J.R. Mason.

The objective of the program is to apply state-of-the-art modeling and

simulation technology to the rocket engine models. This application will be used

to design, develop, and produce all liquid rocket transient simulation system

compatible with MSFC control analysis software, simulation facilities, and

computers. The simulation system will be referred to as the ROCETS (Rocket

Engine Transient Simulation) System.

The report covers the third six months of ROCETS development.

1

SUMMARY


Phase 1 of the ROCETS program consists of seven technical tasks plus provision

for reports and review; these tasks are:

1. Architecture

°

3.

System Requirements

Component and Submodel Requirements

4. Submodel Implementation

5. Component Implementation

6. Submodel Testing and Verification

.

During

Phase

of two

Subsystem Testing and Verification

Phase I, the above tasks were completed and a Critical Design Review and

I completion review were conducted at MSFC. Phase II of Rocets consists

technical tasks plus reports and reviews; these tasks are:

1. TTBE Model Data Generation

2. System Testing and Verification

During this period specific coding of the system processors was begun and the

engineering representations of Phase I were expanded to produce a simple

model of the Technology Test Bed Engine (TTBE). As code was completed,

some minor modifications to the system architecture centering on the global

variable common, GLOBVAR, were necessary to increase processor efficiency.

The engineering modules completed during Phase II are listed below:

lg

2.

3.

4.

5.

6.

7.

8.

INJTO0 - Main InjectorMCHBO0 - Main Chamber

NOZLO0 - Nozzle Thrust Calculations

PBRNO0 - Preburner

PIPE02 - Compressible flow without inertia

PUMPO0 - Polytropic Pump

ROTRO0 - Rotor Torque Balance/Speed Derivative

TURBO0 - Turbine

Detailed documentation of these modules is in the appendix. In addition to the

engineering modules, several submodules were also completed during the

reporting period. These submodules include combustion properties, component

performance characteristics (maps) and specific utilities. Documentation of the

submodules will be included in updates to the System Design Specification

2


Specific coding was begun on the system configuration processor. All functions

necessary for multiple module operation have been completed but the SOLVER

implementation is still under development. This portion of the processor has been

incorporated into an in-house system for automated verification of the

engineering modules. This system, the Verification Checkout Facility (VCF)

allows interactive comparison of module results to store data as well as provides

an intermediate checkout of the processor code.

After validation using the VCF, the engineering modules and submodules were

used to build a simple Technology Test Bed Engine (TTBE). The simple "I-I'BE

model has 55 states and 2 algebraic loops. This simulation of main-stage TTBE

operation demonstrates steady-state and transient operation of a full rocket

simulation, used the ROCETS general property package, and provided additional

information on system operation. The simple TTBE model provides a basis for

completion of the detailed TTBE model which will be used to verify the ROCETS

system.

3

SYSTEM REQUIREMENT CHANGES


The system requirements remain unchanged.

SYSTEM ARCHITECTURE CHANGES

Minor modifications to the global common structure are being implemented

during coding. These changes center around the GLOBVAR common. Instead

of breaking out all variables by type and storing them in separate arrays, all

variables are being stored in the order encountered into the global common. The

only variable types currently being used are real*4, character'4 and integer*4.

The global variable names are still be stored in the GLOBNAM common as

character'8. The changes should increase processor speed in the linked list

search which verifies variable existence.

COMPONENT/SUBMODULE OVERVIEW

Modules

Thirteen component modules have been developed for the ROCETS system.

Five modules were developed during Phase I of the contract and were used to

model a simple engine sub-system. Eight more modules were developed under

Phase II of the contract in order to model a complete rocket engine. The Phase I

modules have been slightly revised under Phase II and have been incorporated

into the rocket engine simulation (Simple Technology Test Bed Engine).

The component modules fall into two general categories -- state-derivative

modules and non state-derivatlve modules. The state-derivative modules

perform a function that can be described by differential equations. Associated

with the module are "states" whose time derivatives are calculated by the

module. Since the solver controls the value of the states, the modules require

them as inputs and use them along with other inputs to calculate the

state-derivatives which are module outputs. Non state-derivative modules have

no states associated with them and are not directly controlled by the solver. The

format for each module consists of an argument list, software identification

number, history (revision dates), interface data, a description of inputs and

outputs, a brief engineering description, a list of required subroutines/commons

and finally the FORTRAN code.

Following is a list of the component modules that have been developed or

updated, along with a brief description.

STATE-DERIVATIVE MODULES

PBRN00

o

PREBURNER MODULE. Combined combustion and volume

dynamics module using overall density, temperature and

oxidizer fraction as states.

4

* MCHB00

* INJT00

* ROTR00

* PIPE00

MIXR00

" SPLT00

VOLMO0

Pratt & Whitney

FR-20282-3

- MAIN COMBUSTION CHAMBER. Combustion and volume

dynamics module using overall density, temperature and

oxidizer fraction as states.

- MAIN FUEL INJECTOR. Perfect gas volume dynamics

using overall density, temperature and oxidizer fraction as

states

- ROTOR MODULE. Simple torque balance that handles two

supply torques, two required torques, drag torque and

extraction torque. Rotational speed is the state.

- PIPE WITH INERTIA. Updated pipe flow module using flow

as a state for incompressible flow.

- FLOW MIXER. Updated flow mixer with reverse flow

capability using density and internal energy as states.

- FLOW SPLITTER. Updated flow splitter with reverse flow

capability using density and internal energy as states.

- LUMPED VOLUME. Updated volume module with reverse

flow capability and heat transfer. Density and internal

energy are the states.

" PUMP00

" TURB00

* NOZL00

* PIPE01

" PIPE02

NON STATE-DERIVATIVE MODULES

- PUMP MODULE. Polytropic pump with an internal iteration

on density ratio.

- TURBINE MODULE. Isentropic turbine with heat transfer and

compressibility effects.

- NOZZLE MODULE. Isentropic nozzle with normal shock.

- PIPE WITH LOSS. Updated pipe flow module without inertia.

Pressure loss for incompressible flow.

- FLOW THROUGH ORIFICE. Compressible flow through an

orifice using a standard flow parameter relation.

Submodules

Twenty-one engineering submodules which are used to support the rocket

engine component modules have been created or updated during this phase of

the program. Basically, the sub-modules are divided into maps, utility and

property submodules.

The map submodules, described in Table I, consist of component maps used to

provide specific engine characteristics.

5


The utility submodules, described in Table II, consist of routines which perform

specific functions or tasks.

The property submodules, described in Table III, consist of routines and maps

used to calculate both combustion properties and real fluid properties. The

combustion property submodules which were created during this phase consist of

a system driver, model type interface routine and a series of combustion maps

which are limited to reactions involving hydrogen and oxygen as the reactants.

The real fluid property submodule was updated to meet the growing requirements

of the ROCETS systems.

TABLE I

MAP SUBMODULES

SUBROUTINE DES(_RIPTION

PMAP01 - SSME ATD high pressure fuel pump map of both head and

torque coefficients vs flow coefficient.

PMAP02 - SSME ATD high pressure oxidizer (main stage) pump map

of both head and torque coefficients vs flow coefficient.

PMAP03 SSME ATD high pressure oxidizer (preburner stage) pump

map of both head and torque coefficients vs flow coefficient.

TBMP01

TBMP02

SSME ATD high pressure oxidizer turbine map of flow

parameter vs PR with lines of speed parameter. Also,

efficiency over velocity ratio vs velocity ratio.

SSME ATD high pressure fuel turbine map of flow parameter

efficiency over velocity ratio vs velocity ratio vs PR with

lines of speed parameter. Also, efficiency over velocity

ratio vs velocity ratio.

RDMP20 - Preburner/main chamber temperature rise curves.

TABLE II

UTILITY SUBMODULES

SUBROUTINE DES(_RIPTION

CDNZ00 - Calculates the performance of an isentropic nozzle with

normal shock.

MACH03

UNIT00

Calculates Mach number

Determines all the SI/English units conversion constants

6

TABLE III

PROPERTY SUBMODULES


SUBROUTINE DESCRIPTION

COMBUSTION PROPERTIES -

COMB00 -

PGAS00

CPGM00

CPMP01

RDM12

RDMP13

RDMP21

ZGAS00

ZZMP01

PROP00

properties.

CREATED

The, combustion property driver routine

The perfect gas model interface routine

Calculate CP and gamma for the products of combustion.

The routine also allows for pressure ratio effects.

CP as a function pressure & temperature for hydrogen

Molecular weight as a function of mixture ratio

Gamma as a function of oxidizer fraction

CP as a function of oxidizer fraction

Calculates compressibility (Z) effects as a function

pressure, temperature and mixture ratio

Compressibility as a function of pressure and temperature

for hydrogen

REAL FLUID PROPERTIES - UPDATED

Provides thermodynamic properties for the five real fluid

System Processors

The configuration processor is currently under full scale development. All

functions necessary for a single module by module checkout have been

completed. The system can currently interpret a single module/multiple node

input and configure the necessary FORTRAN calls. Property capability has been

added and currently state, state derivative and additional balance capabilities are

being coded to allow multiple module checkouts to begin. Unit definition is also

definable through configuration input. A common structure has been defined and

is currently in place and is described in greater detail in the architecture section.

A linked list system is used for determining variable existence and adding new

variables to the list during configuration.

A. system was created called VCF (Verification Checkout Facility) which allows

interactive comparisonsto be made between a ROCETS module and a section of

- 7


code representing the same function in the DTM. Binary CAPA files are created

using the DTM. This allows the engineering equations to be verified during the

development phase.

J

- 8

k

Configuration Preprocessor

Praff & WhitneyFR-20282-3

\.

Data

Dictionary

\,

\

\\.

\

\\

\

\

\\

\\

\\

VCF

Input

Screen

.__/-,

Iia _

J!io

!.I

i

!oIi

!|

!g

I[-._

Configurot;o n >Input

Config urotion

Preprocessor

Generated

Model

VCF

Output

Screen

Run

Model

Standard Configuration Step

The Configuration Preprocessor and the Verification Checkout Facility combine as

illustrated above. A simple flag in the configuration input file either turns on or turnsoff the VCF system.

9


ROCETS Main System

Configuro[ion PreProcessor

First level coils from main driver routine.

ROCONF

Moln conflgurotlon

4

driver

RCONF

Main reading

routing

COMGEN

Common ¢jenerotion

routine

i . .

CODE(_EN

Code generotlor_

routine

L ,

10


J,'

RCONF

Main Reading

Block

I READMD

Module

Reading

Routine

READEQ

Equotlon

Reodlng

Routine

READPR I

Property

Reading

Routine

READUT

Unit=

Reading

Routine

!

READEX

Externols

Reoding

Routine

Run

Reodlng

Routine

IV

READST

State==

Reodlng

Routine

°

L

11


CH KVAR ,1

Unked U_dr.

Check;ng

Routine

COMGEN

Common Generotion

Block

I

GENVAR

Vorlobte

Generotion

Routine

ADOVAR

Unked U=t

Adding

Routine

12


Mo;n

Progrom

Generotor

VCFIN 1

PROMAIN

VCFOUT1

Generote

VCF Input

Ponel Coils

Generote

VCF Output

Panel Calls

CODEGEN

Code Cenerotion

Block

I

SUBROC CENVCF

Subroutine

Rooets

Cenerotlng

Routine

VCF

Input/Output

Cenerot;n( 3

Rout;he

Block Dote

Generot;nq

Routine

13

NORKING EXAMPLE

A example of the module input and the generated code follows.

-two module input, such as=

DEFINE SYSTEM

MODULE= I USING PIPEO0

NODE I IS IN ,

NODE 2 IS VOLI ;

MODULE: 2 USING PIPEO1

NODE 5 IS IN2 ,

NODE _ IS VOL2 ;

END SYSTEM

For a

The following common would have been generated by the configuration

processor=

COMMON / GLOBVAR /

x IPRPL , IUPDAT , MODN1 ,

AREAl , CFI , PTIN ,

RHOVOL1 , XLEN1 , H1 ,

NODIIN2 , NODZVOL2, CF2 ,

RHOIN2 , H2

NODIIN , NOD2VOLE,

PTVOLI , RHOIN ,

DHDT1 o MODN2 ,

PTIN2 , PTVOL2 ,


All of these variables were created using the standard+.na.Ling convention

described in the ROCETS standards.

The above input would also have resulted in the following calls to the

engineering modules as listed below,

CALL PIPEO0 ( IPRPL

NOD2VOL1 ,AREAl

RHOIN ,RHOVOL1

CALL PIPEO1 ( IPRPL

NOD2VOL2 ,CF2

H2 )

,IUPDAT ,MODN1 ,NODIIN ,i"

,CF1 ,PTIN ,PTVOL1 ,

,XLEN1 ,W1 ,DHDT1 )

,IUPDAT ,MODN2 ,NODIlN2 o ,"

,PTIN2 ,PTVOLa ,RHOIN2 ,

14

NORKING EXAMPLE (cont.)Praff &WhitneyFR-20282-3

The requirements for the property calls have recently been revised.

Previously all properties were called as the following example shows:

PROPERTY: PTVOL1 = F(RHOVOLI, UTVOL1 ) USING HYDROGEN;

PROPERTY: PTVOL2 = F(RHOVOL2, UTVOL2 ) USING OXYGEN ;

This would have produced the following code:

C

C

C

BEGIN PROPERTY CALLS

CALL PROPO0 ('HYDROGENI,I_,RHOVOL1 ,UTVOL1

DUMYVOL1,DUMYVOLtoTEMP)

CALL PROPO0 (tOXYGEN w,I_,RHOVOL2 ,UTVOL2

W DUMYVOLZ,DUMYVOL2,TEMP)

,PTVOL1 o

,PTVOL2 ,

Recently, the need for real combustion property calculations have

altered the form of the property definition to the following:

PROPERTY

PROPO0

PTVOL1 = F(RHOVOL1, UTVOL1 ) USING

COMBO0

<combustion definition>;

HYDROGEN

The combustion definition has not been resolved as of this printing.

The type of calls generated would be exact like those listed above

for PROPO0 and would be similiar for COMBO0.

_ 15

NORKING EXAMPLE (cont.)

The VCF calls to the input panels from the program main for the

above example look like:


C

C CHECKOUT VERIFICATION FACILITY

C ENTRY CALL

DO I00 I = i, 2

IRC = 0

DO 50 J = 1, ISIZE(I)

50 ARRAY(J] : ARGLIST(I,J)

IF(I.EQ. 2) IRe = -I

100 CALL VCFIN ( MODNM(I), MMNEM(I), ARRAY, ISIZE(I), IRC )

The arrays MODNM and MMENH contain the character names of the module's

actual Subroutine name and the modules mnemonic, respectively. The

array ARGLIST contains the argument lists as read from the data

dictionary and I5IZE contains the actual size of each argument list.

The variable IRC is used to verify that data was input to the simulation

and as a single to the VCF routine that the last call has occurred.

The VCF output panel is also _nvoked from the main program with the.

following calls=

C

C CALL ROUTINE TO HRITE OUTPUT DATA TO VCF FILE

C

DO 1000 I = l, 2


IARRY(J) = IPTLIST(I,J)

500 ARRAY(J] = ARGLIST(I,J)

1000 CALL VCFHRT (MODNM(I), MMNEM(I), ARRAY, IARRY, ISlZE(I] )

C

C INVOKE VCF OUT PANEL SYSTEM

C

CALL VCFOUT

The calls to VCFHRT simply place the output from the simulation into a

location where the VCF output routine can have access to it. The _W_FOUT

routine is the actual output panel driver. The double assignment of

ARRAY will be removed at next update since it is redundant.

16

Praff & WhitneyHORKING EXAMPLE (cont.) FR'20282-3

An example of what the VCF input screen would look like for the first

module configured in this example:

5

67

8

9

1011

12 XLEN1

13 H1

lq DHDT1

Verification Checkout Facility

19 Jul 1989 ======================== Input :::::::::::::::::::::::: 3:28:37pm

Module: PIPEO0 Mnemonic: 1 DTM: O_8010DTM Time: 0 Page 1

ROCETS I/O DTM

1 IPRPL1

2 IUPDATl

3 MODNIl

NODIINl

NOD2VOLIl

AREA1I

CF1I

PTINI

PTVOL1I

RHOINI

RHOVOL1I

I

I

An example of what the VCF output screen format would look like for the

first module configured in this example (without values filled in)=

Verification Checkout Facility

19 Jul 1989 ======================== Output Map) ......... ========== 3=28:37pmModule= PIPEO0 Mnemonic: 1 DTM: O_8010DTM Time= 0 Page 1

ROCETS_VAR DTM_VAR ROCETS_VAL DTM_VAL DELTA XDELTA1 IPRPL2 IUPDAT

3 MODN1

NODIlN5 NODZVOLI

6 AREA17 CF1

8 PTIN

9 PTVOL1

10 RHOIN

11RHOVOL1

12 XLEN113 HI

1_ DHDT1

,!

-- 17

This is an. full and current example of a configuration input file=

DEFINE RUN

VCF = ON

END RUN

DEFINE EXTERNALS

PTIN , HTIN , PTEX,

CFLIN1, HTEX , VOLVOL,CFLIN2;

END EXTERNALS

DEFINE SYSTEM

MODULE= 1 USING PIPEO0

NODE I IS IN ,

NODE 2 IS VOLI ;

MODULE= 2 USING PIPEOINODE 3 IS IN2 ,

NODE _ IS VOL2 ;

PROPERTY= PTVOLI = F(RHOVOLI, UTVOL1 ) USINGPROPERTY= PTVOL2 = F(RHOVOL2, UTVOL2 ) USING

EQUATION= PT = PS • 2000/22.2 • TTINT;

END SYSTEM

HYDROGEN;OXYGEN ;


18

THIS IS THE FORTRAN THAT NOULD BE CURRENTLY PRODUCED BY THE CONFIN

FILE LISTED ON THE PREVIOUS PAGE:

PROGRAM MAIN

COMMON / ARGLST /'ARGLIST( 2• I_)

COMMON / ARGVAR / IPTLIST( 2, I_)

COMMON / MODULE / MMNEM( 2)•MODNM( 2)

COMMON / COMSIZ / ISIZE( 2)

CHARACTER_8 A , ARGLIST , ARRAY(S0) , MODNM , MMNEM

INTEGER IPTLIST , IARRY(50)

C

C CHECKOUT VERIFICATION FACILITY

C ENTRY CALL

C

C

C

DO IO0 I = I• 2

IRC = 0

DO 50 J = I• ISIZE(I)

50 ARRAY(J) = ARGLIST(I•J)

IF(I.EQ. 2) IRC = -I

lOO CALL VCFIN ( MODNM(I)• MMNEM(I), ARRAY• ISIZE(I)• IRC )

CALL READER ROUTINE TO BRING IN VALUES

CALL VCFREAD

CALL MAIN SIMULATION SUBROUTINE

CALL ROCETS

CC CALL ROUTINE TO NRITE OUTPUT DATA TO VCF FILE

C

DO 1000 I = 1, 2


IARRY(J) = IPTLIST(I•J)

500 ARRAY(J) = ARGLIST(I,J)

1000 CALL VCFWRT ( MODNM(I), MMNEM(I), ARRAY, IARRY, ISIZE(I) )

C

C INVOKE VCF OUT PANEL SYSTEM

C

CALL VCFOUT

END

SUBROUTINE ROCETS

C

COMMON / GLOBVAR /

C

IPRPL • IUPDAT •AREA1 , CF1 •

x RHOVOL1 , XLEN1 ,

w NODIIN2 • NOD2VOL2,

RHOIN2 , g2

CHARACTER_

x MODN1

x •PTIN2

MODN1 • NODIIN •

PTIN , PTVOLI ,

HI , DHDTI ,

CF2 • PTIN2 •

•NODIIN ,NOD2VOLI •NOD2VOL2

C CALL UNIT DEFINITION ROUTINE

C

C

C

C

CALL UNITOO('ENGLISH I)

BEGIN PROPERTY CALLS

CALL PROP00 ('HYDROGENI•lq,RHOVOLI •UTVOL1

DUMYVOLI•DUMYVOL1,TEMP)4_

,PTVOLI

,t,"

NOD2VOLI•RHOIN ,

MODN2 ,

PTVOL2 •

•CF2


CCC

C

C

C

C

C

C

C

C

CALL PROPO0 (tOXYGEN I,I_,RHOVOL2 ,UTVOL2 ,PTVOL2

x DUMYVOLZ,DUMYVOLZ,TEMP)

BEGIN MODULE CALLS

PT = PS _ 1000/21.2 _ TTIN

CALL PIPEO0 ( IPRPL ,IUPDAT ,MODN1NOD2VOLI ,AREA1 ,CF1 ,PTIN

RHOIN ,RHOVOLI ,XLEN1 ,N1

,NODIIN

,PTVOL1

,DNDT1

RETURN

END

SUBROUTINE VCFREAD

COMMON / GLOBVAR /

IPRPL ,

AREA1 ,

RHOVOL1 ,

NODIIN2 ,

x RHOIN2 ,CHARACTER_4

MODN1

x ,PTIN2

NAMELIST / ROCK /

w IPRPL ,

w AREA1 ,

RHOVOL1 ,NODIIN2 ,

RHOINZ ,

IUPDAT , MODNI , NOD]IN ,

CF1 , PTIN , PTVOLI ,

XLENI , H1 , DHDTI ,

NOD2VOL2, CF2 , PTINZ ,

W2

,NODIIN ,NOD2VOL1 ,NOD2VOL2

IUPDAT , MODN1 , NODIIN ,

CF1 , PTIN , PTVOL1 ,XLEN1 , H1 , DHDT1 ,

NOD2VOL2, CF2 , PTIN2 ,

W2

DO I00 I = 1, 2100 READ (IS,ROCK)

RETURN

END

SUBROUTINE VCFHRT (MODNM,MMNEM,ARRAY,iARRY,ISIZE)

COMMON / GLOBVAR /

IPRPL , IUPDAT ,

AREAl , CF1 ,

RHOVOLI , XLEN1 ,NODIIN2 , NOD2VOL2,

X RHOIN2 , H2CHARACTERw_

MODNI

,PTIN2

,NODIIN

MODN1 , NODIlN ,

PTIN , PTVOLI ,

HI , DNDTI ,

CFZ , PTIN2 o

,NOD2VOLI ,NOD2VOL2

COMMON / VARTYP / TYPE( 22)

CHARACTERw8 MODNM,MMNEM,ARRAY(_)

REAL_ VAL( 22)

INTEGER TYPE

INTEGER IARRY(_)

IO

EQUIVALENCE (IPRPL ,VAL(1))

HRITE(16,10) MODNM,MMNEM

FORMAT('MODULE:',AS,' MNEMONIC=',AS)

DO 50 I = 1,ISIZE

.IF (TYPE(IARRY(I)).EQ.3) GOTO 20

IF (TYPE(IARRY(I)).EQ.2) GOTO 30

HRITE(16,100) ARRAY(I),VAL(IARRY(I))

GOTO 5020


NODZVOL1,

RHOIN ,

MODN2 ,PTVOL2 ,

•CF2

NOD2VOLIp

RHOIN ,

MODN2 oPTVOL2 ,

NOD2VOL1,

RHOIN ,

MODNZ ,PTVOLZ",

C

C

C

C

C

30 NRITE(16,140) ARRAY(I),VAL(IARRY(I))

50 CONTINUE

100 FORMAT(3X,AS,'=w,IX,F15.5)

120 FORMAT(3X,AB,'=',IX,A8)

140 FORMAT(3X,AS,'=',IX, I4)

RETURN

END

BLOCK DATA ONE

COMMON / GLOBHAM / A( 22)

COMMON / VARTYP / TYPE( 22)

COMMON / ARGLST / ARGLIST( 2, 14)

COMMON / ARGVAR / IPTLIST( 2, 14)

COMMON / MODULE / MMNEM( 2),MODNM( 2)

COMMON / COMSIZ / ISIZE( 2)

CHARACTER_8 A o ARGLIST , MMNEM , MODNM

INTEGER IPTLIST


DATA A /

x aIPRPL ', 'IUPDAT ', 'MODN1

x 'AREA1 ', 'CF1 t, 'PTIN

W tRHOVOL 1 t 'XLEN1 ', 'N1

tNODIIN 2 o ,NOD2VOL2 I, ICF 2'RHOIN2 t 'N2 '/

t 'NODLIN ', tNOD2VOLlt,

', 'PTVOL1 ', 'RHOIN w! IDHDT 1 ', 'MODN2 I

i tPTiN 2 I 'PTVOL2.. ',

DATA ARGLIST /

X 'IPRPL o tIPRP L

'MODN2 t, 'NODIlN

'AREA1 ', 'CF2'PTVOL2 v, IPTVOL1

'RHOVOL1 ', '

' ', 'DHDT1

. olUPDAT o olUPDAT ', 'MODN1 to

i INODIIN Z g WNODZVOL1 t, fHOD2VOLZ',

w 'CF1 e oPTIN 2 a IPTIN tq, 'RHOIN2 t mRHOI N ', 'H2 ',

'o IXLEN1 ', ' ', 'H1 ',

m e w t/

DATA IPTLIST /

w ..1, 1, Z, 2, $,

w 15, 4, 16, 5, 17,6, 18, 7, 19, 8,

20, 9, 21, 10, 22,

w 11o O, 12, O, 13,w O, 14, O/

DATA I,g'lNEM /o/

DATA MODNM /

'PIPEO0 ', 'PIPE01 '/

DATA ISIZE /

w lq, 10/

DATA TYPE /

2, 2,

1, 1,

1, 1,

w 2, 3,

1° 1/

END

3, 3, 3,

1, 1, 1,

1, 1, 2,

3, 3, I,

21

Simple TTBE Simulation


In order to complete system testing and module verification, a simple model of

the Technology Test Bed Engine (TI'BE) was completed. The simple TTBE

demonstrates the ability to model a complete engine using the ROCETS

methodology of combining generic engineering modules with an implicit solver.

Figure 1 shows a schematic of the simple TTBE along with the 42 specific stations

in the simulation. By using generic code, only the following 13 componet modules

are required by the simulation:

.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

INJT00 - Main Injector

MCHB00 - Main Chamber

MIXR00 - Flow Mixer

NOZL00 - Nozzle Thrust Calculations

PBRN00 - Preburner

PIPE00 - Incompressible flow with inertia

PIPE01 - Incompresisble flow without inertia

PIPE02 - Compressible flow without inertia

PUMP00 - Polytropic Pump

ROTR00 - Rotor Torque Balance/Speed Derivative

SPLT00 - Flow Splitter

TURB00 - Turbine

VOLM00 - Volume

The modules described above were hand processed into the simple TTBE

simulation along with required property relationships and numerical utilities.

There are 55 state variables and 2 algebraic loops required in the simulation

as shown in Table IV. State derivatives and outputs are calculated from model

inputs and states. The simulation employs the multivariable Newton-Raphson

solver, SMITE, to simultaneously drive all state derivatives and algebraic loop

errors to within a certain tolerance. SMITE operates on the matrix equation:

Ay = J,_t,X

Where Ay is the amount that the errors need to change to be zero and ,_X is

the required change in the state or algebraic loop parameter. J, the solver

Jocabian, is the matrix of partial derivatives for the states and algebraic loops.

The J matrix is evaluated by perturbing each state and balance parameter. Then

the J matrix is inverted and the new X values are calculated until the Y variables

are within tolerance.

Using initial guesses from data of the Digital Transient Model (DTM) run at 100%

RPL, SMITE successfully drives all T-I'BE model state derivatives and algebraic

loop parameters to within a specific tolerance. This demonstrates the capability

22


of the ROCETS system to converge a rocket simulation to a steady-state point

without running a transient.

Transient capability was demonstrated by running the simple TTBE simulation

with small perturbations of valve areas about the 100% RPL point. Figures 2-3

show the results of stepping the oxidizer preburner valve open then closed.

Figures 4-5 show the results for the same type of movement of the fuel preburner

valve.

Additional algebraic loops (balances) were placed in the model to set preburner

valve coefficients at points other than 100% RPL. The fuel preburner valve

coefficient was iterated until chamber pressure (PTMCHB) was equal to the

request:

PTMCHBRequest = PTMCHBloo RPL X RPL

The LOX preburner valve coefficient was iterated until chamber oxidizer fraction

(OFRMCHB) was equal to a constant value of 0.865. (This is equivalent to a

mixture ratio of 6.407). Figure 6 shows main chamber pressure and oxidizer

fraction as a function of RPL. A series of steady-state points between 60% and

119% RPL were then run with the solver iterating on valve coefficients until

chamber pressure and LOX fraction were satisified. This demonstrates the ability

of the model to use the solver as a means to set a model parameter based on

an input constraint. Output of the run gives a reference steady-state operating

characteristic for the model and provides data for SMITE guess curves. Figure

7 shows fuel and LOX preburner valve coefficients and Figure 8 shows turbine

speeds as a function of RPL.

The data shown in Figure 7 for valve coefficients as a function of RPL was

tabularized and used to construct and open-loop control with RPL request input

and valve data area requests calculated from the table. The valve requests were

put through a first order lag to simulate actuator dynamics. Gross throttle

transients were run by inputting an RPL request as a function of time and using

the open-loop control to provide valve areas. Figures 9-13 show results of a

run from 100% to 65% RPL decel and figures 14-18 show a run from 65% to

109% RPL.

- 23


24


TABLE IV - Simple TTBE Simulation States and Algebraic

Loops

STATE DESCRIPTION

OFRFPRB

OFRMCHB

OFRMFI

OFROPRB

RHOFMCO

RHOFPBI

RHOFPRB

RHOFIOS

RHOMCHB

RHOMFI

RHOMOI

RHOOPBI

RHOOPRB

RHOPBSF

RHOPBSO

RH010

RH012

RHO15B

RH08

SNF2

SN02

TTFPRB

TTMCHB

TTMFI

TTOPRB

UTFMCO

UTFPBI

UTFIOS

UTMOI

UTOPBI

UTPBSF

UTPBSO

UTIO

UT12

UT15B

U,T7S

UT8

Fuel Preburner Oxidizer Fraction

Main Chamber Oxidizer Fraction

Main Fuel Injector Oxidizer Fraction

Oxidizer Preburner Oxidizer Fraction

Volume FMCO Density

Fuel Preburner Injector Density

Oxidizer Preburner Injector Density

Volume FIOS Density

Main Chamber Density

Main Fuel injector Density

Main Oxidizer Injector Density

Oxidizer Preburner Injector Density

Oxidizer Preburner Density

Preburner Fuel Splitter Density

Preburner Oxidizer Splitter Density

Volume 10 Density

Volume 12 Density

Volume 15B Density

Volume 8 Density

Fuel Turbomachinery Speed

Oxidizer Turbomachinery Speed

Fuel Preburner Temperature

Main Chamber Temperature

Main Fuel Injector Temperature

Oxidizer Preburner Temperature

Volume FMCO Internal Energy

Fuel Preburner Injector Internal Energy

Voume FIOS Internal Energy

Main Oxidizer Injector Internal Energy

Oxidizer Preburner Injector Internal Energy

Preburner Fuel Splitter Internal Energy

Preburner Oxidizer Splitter Internal Energy

Volume 10 Internal Energy


Volume 15B Internal Energy

Volume 7S Internal Energy


25


STATE DESCRIPTION

WCCVWFPHI

WFPOV

WFTI

WFTID

WF10

WMFV

WMOV

WOPHI

WOPOV

Wll

W16

W20

W21

W4

W7

W9

Coolant Control Valve Flow

Fuel Preburner Fuel Flow

Fuel Preburner Oxidizer Flow

Line FTi Flow

Line FTID Flow

Line F10 Flow

Main Fuel Valve Flow

Main Oxidizer Valve Flow

Oxidizer Preburner Fuel Flow

Oxidizer Preburner Oxidizer Flow

Line 11 Flow

Line 16 Flow

Line 20 Flow

Line 21 Flow

Line 4 Flow

Line 7 Flow

Line 9 Flow

ITERATION VARIABLE DESCRIPTION

WFTRB

WOTRB

Fuel Turbine Flow - Iterated until equal to calculated value

LOX Turbine flow - Iterated until equal to calculated value

26


FUEL PREBURNER VALVE FLOW (Ibm/sec)

80 78 76 74 72 70 68

0

.B',FIIOI--I=FIO0 _07:1qA7VA _3NEI_8%Id 7:113-1

F-(,0

oI1

"0t--

e'-(D

0

0

.-. 0

_ oI---"4 U.

c--

.Q

n

Ob

Ii

I

.__U.

-- 27

MAIN CHAMBER OXIDIZER FRACTION


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.......•+.............. -+...._..._-•_.... f.-_ _.. l ..... J--4-.+1+-t- 7.t....t....?.._............ +.---+-..,-.l • : 1 ....

0C3 L£ O0 L£ 0_0£ 000£ 0_6Z

(VlSd) :ll:lrlSS:l_d EFIS_VHO NIV_

28

34

LOX PREBURNER VALVE FLOW (Ibm/sec)

WOPOV32 ,30 28 26


24

oO

0

-- 29



0,872 0.870 0.868 0.866 0.864

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43

0

Pratt & Whitney

FR-20282-3

APPENDIX

44

Pratt & Whitney

FR-20282-3

3,4.2 ENGINEERING MANUAL

3.4.2.1 Module Cross Reference

3,4.2.2 Map Cross Reference

3,4.2.3 Map + Module Compatibility

3,4.2.4 Detailed Module Descriptions

1. Modules

A. Actuator

B. Auxiliary/Special

C. Control

D. Heat Exchanger

E. Injector

1. INJT00

F. Line/Pipe1. PIPE00

2. PIPE01

3. PIPE02

G. Main Chamber

1. MCHB00

H. Mixer

1. MIXR00

I. Nozzle

1. NOZL00

J. Pre-burner

1. PBRN00

K. Pump General Description

1. PUMP00

L. Rotor

1. ROTR00

M. Secondary FlowN. Sensor

O. Splitter

1. SPLT00

P. Turbine

1. TURB00

Q. Valve

45

Page

3.4.2.1

3.4.2.2

3.4.2.3

3,4.2.4

_w

E-1

F-1

F-2

F-3

G-1

H-1

I-1

J-1

K

K-1

L-1

O-1

P-1

Pratt & Whitney

FR-20282-3

R. Volume/Accumulator/Tank

1, VOLM00

S. System Utility

1. SSBL03

2. TRAP03

3, UNIT00

2, Sub-Modules

A. Component Sub-modules

1. CDNZ00

2. MACH03

3. FLPM02

B, Property Sub-modules

1. PROP00

2. COMBO0

C. Map Sub-modules1. PMAPXX

2. TBMPXX

D. Utility Sub-modules

1. SMIT01

2. SUNB01

3. PRPL00

4. ITER01

R-1

S-1

S-2

mw

2A-1

2A-2

2A-3

2B-1

2B-2

2C-1

2C-2

2D-1

2D-2

46


3.4.2.1 Module Cross Reference

E-1 INJTO0

F-1 PIPEO0

F-2 PIPE01

F-3 PIPE02

G-1 MCHBO0

H-1 MIXRO0

I-1 NOZLO0

J-1 PRBNO0

K-1 PUMPO0

L-1 ROTRO0

0-1 SPLTO0

P-1 TURBO0

R-1 VOLMO0

- Main fuel injector

- Incompressible fluid flow in pipe with inertia

- Incompressible fluid flow in pipe with loss

- Compressible flow through an orifice

- Main combustion chamber

- Simple flow mixer

- Isentropic nozzle

- Preburner without purge

- Pump module for polytropic process

- Rotor

- Simple flow splitter

- Turbine

- Volume/Accumulator/Tank

t

&

47

Pratt & Whitney

FR-20282-3

3.4.2.2 Map Cross Reference

1, PMAP01

2. PMAP02

3. PMAP03

4. TBMP01

5, TBMP02

- Pratt and Whitney SSME High Pressure Fuel

Pump

- Pratt and Whitney SSME High Pressure

Oxidizer Pump (main stage)


Oxidizer Pump (Preburner stage)


Oxidizer Turbine

- Pratt and Whitney SSME High Pressure Fuel

Turbine

48

Pratt & Whitney

FR-20282-3

3.4.2,3 Module + Map Compatibility

1. PUMP00 - PMAP01, PMAP02, PMAP03

2. TURB00 - TBMP01, TBMP02

49


INJT00

INPUTS:

NOD1

NOD2

NOD3

NOD4

NOD5

NOD6

NOD7

NOD8

NOD9

NOD10

CpF

Cpo

"/F

_/O

_/S

_yj

h'E

OF

QO

WE

Wo

Ws

WE

TF

To

OFRF

OFRo

B

B

m

I

I

m

I

D

Main Fuel Injector

F sqWF

IlloFR

Ws _ TI

Fuel Inlet Node

Fuel Inlet Thermal Node

Heat Flux Node - Fuel

Oxidizer Inlet Node

Oxidizer Inlet Thermal Node

Heat Flux Node - Oxidizer

Sleeve Inlet Node

Sleeve Inlet Thermal Node

Exit node

Exit Thermal Node

S )ecific

S

S

S

S

S

3ecific

3ecific

3ecific

)ecific

3ecific

Wo

I1

1"4553-1 WEINOD OIIII

STATES:

OFR- Oxidizer Fraction

T= - Injector Temperature

- Overall Density

Heat-Fuel Turbine Discharge

Heat-Oxidizer Turbine Discharge

Heat Ratio - Fuel Turbine Discharge

Heat Ratio - Oxidizer Turbine Discharge

Heat Ratio - Sleeve

Heat Ratio - Main Fuel Injector

S 3ecific Heat Ratio - Exit

Heat Flux - Main Chamber Cooling - Oxidizer

Heat Flux - Main Chamber Cooling - Fuel

Fuel Flowrate

Oxidizer Flowrate

Sleeve Flowrate

Exit Flowrate

Fuel Temperature

Oxidizer TemperatureOxidizer Fraction - Fuel Inlet

Oxidizer Fraction - Oxidizer Inlet

50

Pratt & Whitney

FR-20282-3

ms

TE

Vol

- Sleeve Temperature

- Exit Temperature

- Main Fuel Injector Volume

OUTPUTS:

d(OFR)

dtOxidizer Fraction Derivative

do

dtDensity Derivative

dTzdt

Temperature Derivative

CALCULATIONS:

WIN = Ws + WF + Wo

Total oxygenflow in: WOIN = OFRF X WF + OFRo x WO

DERIVATIVE CALCULATIONS:

m =Ox Vol

m

Vol

dr. (Vol) avotdo d"-_ - (m) at

dt - (Vol) 2

For a constant do dm(1)volume: dt - dt

I dQ - WIN - W°ut !dt Vol

51


ENERGY ANALYSIS:

dU 0.o + O.r + WFhr + Woho + W,h, WEbS (1)(It

dU d(mu) _tt dmd----;= dt = (m) + (u)---d-[

u = C_,TI

--_ = mC_ + CvT_(WF + Wo + Ws - WE) (2)

Substitute (2) into (1) and H = CpT and TEXtT = T I

movdT-_ I. + CvTI(WF + Wo + WS - WE) = OF + Oo + WFCpTF + WsCpTs WECpTI(71[

Solving for dTzdt

dTl 1= [WbTFTF + WoroWo + W_reTI - (TI(WF + Wo + Ws - We))I-- +

dt_ m

QF + Qo

Gym

dr, [ j"-dTt = WF(rFTF- 7"/) + Wo(7oTo - TI) + Ws(rsTs- TI) - WE(YE - 1)TI+ (QF + Qo) ] 1

52


PI.PE_ Incompressible fluid flow in pipe with inertia and loss

IaODll O_ --w-.---_ .)I'_ L =1

INPUTS:

NOD1 -

NOD2 -

A -

CF -

Pin -

Pout -

o in -

L

Inlet Thermal Node

Exit Thermal Node

Inlet Flow Area

Flow Coefficient

Inlet Pressure

Exit Pressure

Inlet Fluid Density

Length of Pipe

OUTPUTS:

STATES

dW

dt- Flow derivative

CALCULATIONS:

Definition of flow

coefficient, CF:

CF = 0 ,, G,l"6Y/_

(Qi. + qout)_aV

2

WO.-

QAV

CF = W_W / ear

W - Flow Rate

where GF = O (specific gravity)QHzO

and Q = Volumetric flowrate (USGPM)

solving for Ap •

Define o_ •

CF 2_m, a QH20

w a

qa_ 2 QH20 CF 2

c_ = PAv x CF 2

(1)

53

Pratt & Whitney

FR-20282-3

Substitute into (1): AP = w2 x const. (2)a

Equation (2) represents the steady state relationship for W and AP.

Lets call this friction loss AP_oss.


Momentum analysis:

MeF = --

gc

dV

dt

(1)

(2)

M = QAL

WW=oAV_V=--

QA

Substitute (2), (3) and (4)into (1)"

gc oA

(3)

(4)

(5)

Also: F = ( AP- APIoss) A (6)

Substitute (6) into (5) and solve for: (iw(It

= (AP - APtoss) ( where Ap = Pin - Pout )

54

Pratt & Whitney

FR-20282-3

PIPE_I - Incompressible fluid flow in pipe with loss,

INOD !r-/- W

INOD21

INPUTS:

NOD1

NOD2

CF

Pin

Pout

0 in

OUTPUT:

W - Flow Rate

(_ALQULATIONS:

Definition of flow

coefficient, CF:

Solving for W:

Define o_:

Substitute into (1)

Inlet Thermal Node

Exit Thermal Node

Flow Coefficient

Inlet Pressure

Exit Pressure

Inlet Fluid Density

CF = e " a,/67-1_e

W(2 =--

Qin

CF = _ / Oin

WzCF 2 =. Qin 1

O_n OHzO zXP

W = /_r" Oin CFZ qH20

o_ = o i. x CF 2

[W = _/a ZkP x const.J

where GF = 0 (specific gravity)QH20

and Q = Volumetric Flowrate (USGPM)

(1)

55

Pratt & Whitney

FR-20282-3

PIPEO2 _ Compressible flow through an orifice

INPUTS:

NOD1

NOD2 -

K

A

Pin

Pout

R

Tin

",/in

OUTPUTS:

W

CALCULATIONS:

PR = Pin/Pout

INOml ()

--'- W

Inlet Thermal Node,

Exit Thermal Node

Number of Head Losses

Throat Area

Inlet Pressure

Exit Presure

Gas Constant

Inlet Temperature

Inlet Specific Heat Ratio

Flowrate

Submodule FLPME_2 gives a value for FP from PR, K, "hN.

Definition of flow parameter: FP =

Solve forW ' w = FP x Phvx A.IJR _ T1u I

W _/R x TIN

PIN x A

) I"OD21

56

Pratt & Whitney

FR-20282-3

MCHBOO - Main Combustion Chamber

WFIG

_IWMFI

IOFRTc

Q

WMOI

IL_ WOIG

_ WOTH

WOUT

INPUTS: STATES:

NOD1 -

NOD2 -

NOD3 -

NOD4 -

NOD5 -

NOD6 -

NOD7 -

NOD8 -

OFRMFI -

Wou t

WFIG -

WMF I --

WMO I -

Wo_G -

WOT H -

VOL -

TF

_/

Inlet Thermal Node

Inlet Node

Exit Node

Exit Thermal Node

Exit Node

Exit Thermal Node

Main Chamber Exit Node

Exit Thermal Node

Oxidizer Fraction, Main Fuel Inj.Exit Flowrate

Fuel Igniter Flowrate

Main Fuel Injector Flowrate

Main Oxid. Injector Flowrate

Oxid. Igniter Flowrate

Other Fuel Flowrate

Main Chamber Volume

Fuel Temperature

Specific Heat Ratio (Chamber)

OFR- Oxidizer Fraction

Tc - Main Comb. Ch. Temperature

Q - Overall Density

OUTPUTS:

cI(OFR) Oxidizer fraction derivativedt

5?

Pratt & Whitney

FR-20282-3

d__Ee_ Density derivativedt

dTc _ Temperature derivativedt

CALCULATIONS:

Total oxidizer

& Fuel Flows:

m =Qx Vol

l

WOIN = WMOI + WOIG + WMFI x OFRMFI

WF1N = WFIG + WOTH + WMF1 x (1-OFRMFI)

Flow-Based

Mixture Ratio: OFw = WOIN/WFIN

Mass-basedmixture ratio: OFm = OFR/(1 - OFR)

Temperature Rise AT

Where AT = f(OFR)

T*c = TF+ AT


de

dt

For a doconstant volume:

dt

O = mlVol

_rn (Vol) avot (m)dt dt

(Vol) 2

(')(voO dmWoO= = 7

d O WFIN + WOlN - Wou t

dt Vol

Energy analysis:dUdt (WF/N + W°IN) h *

dU du dm-m_ -I.U_

dt dt dt

- (WouD h_ (i)

(2)

58

Pratt & Whitney

FR-20282-3

Substituting (2) into (1) and solving for a..E.uyields.dt

"" [= (WFm + WozN)h*dt

-(Wout) he-u-_t]/m (3)

For a perfect gas: h = OpT ==_ dh = CpclT

u = CvT =_ dU = CvclT

From continuity: m = mF + mo

drn

d'--_ = (WFIN + wOIN) - W°ut

dm

Substituting perfect gas relationships and T into (3) yields:

d'-'_" = (WFIN + WOIN) CpT" - Wout CpT¢ - CvTc(WF1N + WOlN - Wout)

d...UUdt= d(C_TC)dt = C_(-_)

Simplifying yields:

T

OFR derivative:

n3 o 1"13oOFR = _ =

mT me + mF

Assuming homogeneous volume: (OFR)

(1 - OFR)

W'rEX = WOEx

WTEx = WFEx

d(OFR) =(dmo

dt \---_-- mT _,,r )at mo / r,,_.

_ 1 r dm_o dmT

mT L dt dt

59


(OFR) dt J

dmo

a--i- = w°m - W°Ex = WOlN - (OFR)WTE X

(1)

(2)

dmT

dt - WTIN - WTEx(3)

Substituting (2) and (3) into (1) yields:

d(OFR) --_T[dt = W°IN- (OFR)WTEz- (OFR) (WTI N - WTEx) ]

Simplifying: [d O R>,[ ]at = m"-T W°IN- (OFR)WTIN

6O

TEMPERATURE RSE VS. OXIDIZER

Pratt & Whitney

FR-20282-3FRACTION

OO

li:i: *_ii .....i_i _ : ._: ,_ ....

f i _ ;T"{ ..... ! i _[ ! "i i r ' " _ ! : v ..... : I r': .... ! t " : : : " " " " : " _ " ! " "•''''!-!!t''_;f_: ...... : ...... |-'!!'|':''i:t'':'f .... I L) "1-'"

O(DO"I.D

LIJI---

CDO

C'q

OO

O

0.0 0.2 0.4 0.6 0.8 1.0OXIDIZER FRACTION

61


MIXR_ Simple Flow Mixer

IN°DII __I

iNOD21 W l ----..

W2

INOD41 --I

INPUTS:

NOD1 -

NOD2 -

NOD3 -

NOD4 -

NOD5 -

NOD6 -

hi

h2

h3

hmix -

Wl

W2

W 3

VOL -

Inlet 1 Thermal Node

Inlet 1 Node

Inlet 2 Thermal Node

Inlet 2 Node

Exit Node

Exit Thermal node

Inlet Stream 1 Enthalpy

Inlet Stream 2 Enthalpy

Exit Enthalpy

Mixer Enthalpy

Inlet 1 Flowrate

Inlet 2 Flowrate

Exit FIowrate

Mixer Volume

OUTPUTS'

'_--£ - Density Derivativedt

dl, l

chInternal Energy Derivative

Q

U W3INOD51

INOO61

Q

U

STATES:

- Mixer Density

- Mixer Internal Energy

62

Pratt & Whitney

FR-20282-3


m = e X vol

dm

e-S- =w_ +W2 -W3

mLO = n

Vol

dVol

dt Vol 2

For a constant

Volume:

I de (W_ + Wz - W_) I= Vol

Energy:

dU

dt- Wl hi + W2h2 - W3hmix (assuming no heat transfer) (1)

dU d(mu)= _dt dt _ at ]

Substituting (2)into (1):

Solving for d__u.dt

l_ dt ]

kdt] + \ dt ] =Wlhl+W2h2-W3hmix

(2)

63

Pratt & Whitney

FR-20282-3

NOZLOO - Isentropic Nozzle

INPUTS:

Wt

NOD1 -

NOD2 -

PIN -

POUT -

TIN -

AR -

AREA -

3'R

CS -

Inlet Thermal Node

Exit Thermal Node

Inlet Pressure Main Chamber

Exit Pressure (Ambient)

Inlet Temperature

Area Ratio

Throat Area

Specific Heat Ratio

Gas Constant

Loss Coefficient

OUTPUTS:

Fg - Gross Thrust

SI - Specific Impulse

Me "- Mach Number At Exit

WT - Flowrate At Throat

CALCULATIONS:

PR = PIN / POUT

Submodule CDNZE_O gives values for FP and CF.

Wt TinxDefinition of flow parameter: FP - v.,

AREA x Phv

Solve for Wt: Iw, = (FP)v/_(R)(TtN)(Pj,v)(AREA)]

64

Pratt & Whitney

FR-20282-3

Thrust: _g =em x AREA x C_ where CF is a thrust coefficient

Specific impulse: [sl = Fg / W_

-- 65

Pratt & Whitney

FR-20282-3

PBRNOO - Preburner without purge

I NOD2 J

INOD31

WF

INPUTS;

NOD1 -

NOD2 -

NOD3 -

NOD4 -

OFLT -

T F

VOL -

WF

WO

WOUT -

_/

Oxidizer Inlet Flow Node

Fuel Inlet Flow Node

Fuel Inlet Thermal node

Exit Flow Node

Mixture Ratio (Light Level)

Fuel Temperature

Preburner Volume

Fuel Flowrate

Oxidizer Flowrate

Exit Flowrate

Specific Heat Ratio

OUTPUTS:

d(OFR) Oxidizer fraction derivativedt

d_dt

Temperature derivative

d---E°- Density derivativedt

CALCULATIONS:

Flow - Based

Mixture Ratio ' OF., - Wo / WF

I NOD1 IWo

_/oI l-• _ TO

0

-[_Wout

INOD41

STATES:

OFR

T¢

Q

- Oxidizer Fraction

- Preburner Temperature

- Overall Density

66

Pratt & Whitney

FR-20282-3

Mass - Based

Mixture Ratio • OFm = OFR / (1-OFR)

Temperature Rise (AT): Tc" = TF + AT

Where

OF

AT = /(OFR) if preburner is lit

AT = const, if preburner is not lit


o = rn/Vol

clm (VOL) _ dVo..._L(rn)dO dt dt

dt (VoI) 2

For aconstant volume: d O "_t (VOI) dm( 1 )

dt - (Vol) z - dt -_

d_aot= wr + w° - w°"t ]vol

Energy analysis:

Substituting (2)into

For a perfect gas:

ct_.u__u= (WF + Wo) h" - (Wo.t) hc (1)dt

au du am (2)d-"_ = m---_- + u---_-

du yields,(1) and solving for 7

,u [ dm ]-_t = (Wr + Wo)h" - (Wo.t) hc - u--_-t /m (3)

h = CpT ,=_ dh = CpdT

u = CvT =_ du = CvdT

From continuity:

Substituting perfect

m = mF + mo

clm-- = (WE + Wo) - Wout

dt

gas relationships and d.-.Y--minto equation (3) yields:dt

d.__uuat= [ (WF + Wo) CpT'c- WoutCpTc-CvTc(WF + Wo- Wout) ]("-_)

dt dt

67

Pratt & Whitney

FR-20282-3

] at

OFR derivative:

mo moOFR =_ =

mT mo + mF

Assuming homogeneous volume: (OFR) WTEx

(1-OFR) WTEx

= WoEX

= WFEx

d(OFR) =(dmo dmT )dt _ dt mr dt mo / m}.

-- 1 [l _0 dm T mo]mT L dt dt mT

_1 Faro dmT]

rat L dt (OFR) dt J(1)

dmo= Wo - WoF.xdt = Wo - (OFR)WTEx (2)

dmT

dt = WTIN - WTEX(3)

Substituting (2) and (3) into (1) yields:

a(OFR) "-_T[dt = Wo- (OFR)WTEx- (OFR) (WTI N - WTEx) ]

dt - raT' Wo - (OFR)WTINi

68

Pratt & Whitney

TEMPERATURE R SE VS. OXIDIZER FRACT --OP_-20282-3

o

0o

wtmovcD

oI, i ,_-Go

rY

LUp,/

F-

rYbD13-

LMH-

OO

CN

OCDO

O

-.:!:,-!i,- :: '':i;_/ ' ': _ "{ "

_i_i__i_ ! i_i.... i: , ii _i _: __, _ !_ ti !l!i _ti •t_ _ i _t__t_0.0 0.2 0.4- 0.6 0.8 1.0

OXIDIZER FRACTION

--:-. 69

Pratt & Whitney

FR-20282-3

PUMPOEI - Pump Module For Polytropic Process

W

1

LJ/I

W

INPUTS:

NOD1 -

NOD2 -

NOD3 -

NOD4 -

W -

PIN -

Q IN -

hlN -

N

Flow Node

Inlet Thermal Node

Exit Thermal Node

Shaft Work Node

Flowrate

Inlet Pressure

Inlet Density

Inlet Enthalpy

Rotational Speed

OUTPUTS:

POUT

hooT

0 OUT

ToRe

- Discharge Pressure

- Discharge Enthalpy

- Discharge Density

- Torque Required

OOUT IThis module iterates on\ O--_--'N1 until the exit pressure that results from the

property call using hoot and Q OUT equals the exit pressure calculated from the

polytropic equation (iterate until POUT = PouT¢).

CALCULATIONS:

Submodule MAP gives values for H (head) and Torque from W, o OUT and N.

work out (w) (H) (gr)rl--_

work in (N) (Torq) (gc)where gr = acceleration due to gravity

(H) (gr)_xh -(,1) (sc)

70

Pratt & Whitney

FR-20282-3

hou T = hlN + Ah

A property call using QOUT and hou T gives a value for POUT. TO get POUTc lets look

at a polytropic process:

Polytropic Headrise

For a Polytropic Process

_1 2H = headrise = vdP

H_1 2

= vdP

P. v n = C (1)

P° v l/n= c1/n (2)

v = C 1/n p-1/n (3)

(4)

Substitute (3) into (4)

2 1/n p-1/nH = C dP

H = C 1/n_1 2 p-1/n dP

H : (C1/n P21.1/n-c1/n P11-1/n) (-'_-I)

('__1)(C 1/n P21-1/n - C 1/n pll -l/n)H

(5)

Substitute (2)into (5)

1In _ v 1 P_In p11-1In]

H= v2e 2 -

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FR-20282-3

processFor a po_y_roplcn =kp°v

or

P1 vl n = P2

n1J2

P1 u2

tP-_ = n In t_'1"1In p_ u 2

n=

atso from 3:

In

PI vl Lv2) ul

P1

P1

n=

_z- I = ( 1 -n)"U1)

In (-pP;_

1-

a)

(1)

(2)

(3)

(4)

(5)

72


letn

8-n-1

n-1

1

,o(_)

n

/3-1

v2 P2 v2

n

n-1

P2 v2 v2

,nr(_=_f"=_]-In(.--_1)LkP1/\ vl / _P1)

n-1

Q2 Q1

]-/ + -Q_ Q2

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If fl = n I n- in-1 /_ n

PI =02 +

Module implementation with o and P instead of v and P

H PIN ]POUT c = OOUT "_ + omJ

FORTRAN implementation of/7 calculation

then

74

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FR-20282-3

ROTROO -

INPUTS:

NOD1 -

NOD2 -

NOD3 -

NOD4 -

TT1 -

TT2 -

Tm -

Tp2 -

m D

TXT R -

nT1 -

nT2 -

np1

rip2 -

RXT R -

Ip

Rotor Torque Balance

INOml

TT2

INOD21

High Pressure Turbine Node

Low pressure Turbine node

High Pressure Pump Node

Low Pressure Pump Node

High Pressure Turbine Torque

Low Pressure Turbine Torque

High Pressure Pump Torque

Low Pressure Pump Torque

Drag Torque

Extraction Torque

High Pressure Turbine Gear Ratio

Low Pressure Turbine Gear Ratio

High Pressure Pump Gear Ratio

Low Pressure Pump Gear Ratio

Extraction Gear Ratio

Polar Moment of Inertia

OUTPUTS:

dNROTOR

dt

CALCULATIONS:

Rotor speed derivative

T.Tn = IF_

dNrotor0, = ----

dt

Substituting (2)

into (1) ZTn = Ip dNr°to-----_'Crdt

dNrotor _,Tn

dt Ip

[ NOD3 I

T(R(D ((P,

_) TP2

NROTOR i NOD4]

STATES:

NROTO R - Rotor Speed

(I)

(2)

.dNrotor (TT1 nT1 + TT2 nT2 - TP1 nP1 - TP2 nP2 - TD - TXTR nXTR)Idt Ip I

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SPLT00 - Simple Flow Splitter

INPUTS:

NOD1 -

NOD2 -

NOD3 -

NOD4 -

NOD5 -

NOD6 -

hi

h 2

h3

hSPLT

VOL -

Wl -

W2

W3

Inlet Thermal Node

Inlet Node

Exit Node

Exit Thermal Node

Exit Node

Exit Thermal Node

Inlet Enthalpy

Exit Enthalpy

Exit Enthalpy

Splitter Enthalpy

Splitter Volume

Inlet Flowrate

Exit Flowrate

Exit Flowrate

OUTPUTS:

do

dtDensity derivative

du

dtInternal energy derivative

CAL(_ULATIONS:

m = e x vol

d__m_._= Wl -W2 -W3dt

m

Q = Vol

STATES:

_> -

U -

Splitter Density

Splitter Internal Energy

dVol=dt Vol 2

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For a constant

Volume:

la_ = (w, , w_- w,).ivot

dU

dtWl hi - W2hsPLT - W3hsPLT (assuming no heat transfer) (1)

dU d(mu) m( d_.uuI u( dm Id-T = at t at ) + t'-EF) (2)

Substituting (2) into (1):_, dt ] k dt ] Wlht - W2hsPLT -W3hsPLT

Solving for au.dt

I'" I ( 11t at/j

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TURBOO- Turbine

INPUTS:

NOD1

NOD2

NOD3

NOD4

R

,yZ

PIN

TiN

POUT

N

QDOT

QFRC

MAP

W

tQ DO_'_

U W

- Inlet Thermal Node

- Discharge Thermal Node- Heat Transfer Node

- Shaft Work Node

- Inlet Gas Constant

- Inlet Specific Heat Ratio

- Inlet Compressibility Factor- Inlet Pressure

- Inlet Temperature

- Exit Pressure

- Rotational Speed- Heat Transfer Rate Into Turbine

- Fraction of Heat That Goes To Turbine Work

- Turbine Characteristic Map

OUTPUTS:

W

TORQ

TOUT

- Turbine Flowrate

- Turbine Torque

- Discharge Temperature

CAL(_ULATIONS:

PR" = PIN / POUT

Nra d = N (2_o)

Submodule MAP gives values for FP, Ah'

Definition of Flow Parameter: FP =

and 11

W /-R x ThvP

FP x PSolve for W: W =

/R x TIN

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Real Ah: Ah = Ah' x "q + (QDoT X QFRC)

TORQ = wz_Nrad

Exit Temperature:

(Zxh- QooT)TIN - TOUT =

Cp

(Ah - QDOT)(Y- 1)TOUT = TIN-

Y

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VOLMOO- Lumped Volume With Energy and Continuity

I NOD1 I Win_

I NOD21

INPUTS

NOD1 - Inlet Thermal Node

NOD2 - Inlet Node

NOD3 - Exit Node

NOD4 - Exit Thermal Node

NOD5 - Heat Transfer Node

Vol - Volume

hin - Inlet Enthalpy

hout - Exit Enthalpy

hvol - Volume Enthalpy

O - Heat Flux into the Volume

Win - Inlet Flowrate

Wout - Exit Flowrate

INODS]

0 _

STATES:

Q

U

Wout I NOD41

INOD3I

- Volume Density

- Volume Internal Energy

OUTPUTS:

dQ

dtDensity Derivative

du

dtInternal Energy Derivative


m = e x vol

dm

= Win- Woutdt

m

Vol

dQ )(vo,)_clt Vo/2

8O


For a constant volume:dt dt

Energy:

do Wi. - Wout Idt Vol I

dU

dt - (Win) (hin) - (Wout) (hvol) + _2 (1)

d--7 = dt - (m) + (U) (2)

substituting (2)into (1)

\at ] \ at ] = (Win) (hin) - (Wout) (hvol) +Q.

solving for d--Eu'dt -_t = (win) (bin) - (Wout) (hvoO -u a--T"

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SSBL03

SSBL03

balance

- Steady State Balance Routine

is an interface to SMIT01 which is designed to perform a steady-state

on a given model, The call list for SSBL03 is defined as follows:

ISSPNT = Print option flag

0 = No steady-state print

1 = Steady-state print to unit 6

NSTATE = Number of States

STATE = Array of State Variables

DSTATE = Array of State Variable Derivatives

SNORM = Array of normalizing values for State Variables

SNAME = Array of State Variable Names

ISON = Array of on/off codes for State Variables

0 = State not iterated

1 = State iterated

NVAR = Number of algebraic loops (balances)

XVAR = Array of balance independent variables

YVAR = Array of balance dependent variables

XNORM = Array of normalizing values for balances

XNAME = Array of names for balances

IXON = Array of on/off codes for balances

0 = Balance not iterated

1 = Balance iterated

MXPASS = Maximum number of convergence passes

ISAMAT = Same Jacobian Flag

0 = Do no use previous matrix

1 = Use previous Jacobian

ISIG = Control flag

0 = On first pass to set initialization

1 = Evaluate derivatives and errors

2 = Converged

SSBL03 provides input to SMIT01 so that both states and algebraic loop

(balance) parameters are iterated until their respective errors are within

tolerance. The error terms for states are calculated as the derivative divided by

the state and the error terms for the balance parameters are the input error terms

(WAR).

The states and balance parameters are normalized before going into SMIT01 by

the input normalization values, SNORM, and XNORM. If the input normalizing

value is zero, the initial value of the state or balance parameter will be used.

82


Values for the SMIT01 input DELTAX and DXALOW are input based on the

normalization values.

Specific states and balances may be turned on or off based on the input

switching arrays ISON and IXON. SSBL03 builds the dependent and independent

variable arrays for SMIT01 based on these inputs and the normalization

discussed above. If the switch value is 1, the variable will be included in the

SMIT01 array and therefore iterated, if the switch value is zero, the variable will

not be operated on by SMIT01,

If requested via the flag ISSPNT, SSBL03 will provide a detailed print of the

steady-state balance. The steady-state print includes the following:

1. The base point dependent and independent variables sent to SMIT01

2. The dependent and independent SMIT01 variables during the generation ofthe J matrix.

, The dependent and independent SMIT01 variables during each convergence

attempt along with the changes in each variable and the percent reduction in

the sum of the squared errors.

4, A message providing SMIT01 statistics upon completion.

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TRAP03 - Transient Integration Routine

TRAP03 is the transient counterpart of SSBL03 and has the same inputs as

SSBL03 with the following additions:

1. DT = Transient time increment

2. TIME = Transient time

TRAP03 is an implicit integration routine which can simultaneously solve

algebraic loops. The predicted STATE values at TIME = TIME + DT are the

previous time values and MSIT01 is used to solve a trapezoidal corrector. This is

performed by interfacing to MSIT01 similarly to SSBL03 except that the state

error terms become:

ESTAT E =STA TEn,out - STA TEcatcutatea

SNORM

STATEcaicu_a_ed is determined from the previous time STATE and DSTATE, the

current time DSTATE and the time increment DT as follows:

STATEcalculated = STATEprevlous + (DSTATE + DSTATEprevious) X DT/2.

Because the current derivative is used in the calculation of STATEcaJculated,

SMIT01 iS required.

Additionally, TRAP03 can solve multiple algebraic loops at the same time as

solving for the states. This is accomplished by constructing the SMIT01 input

arrays in the same manner as SSBL03, except that the error terms for the

STATEs are as ESTATE rather than DSTATE divided by STATE as in SSBL03.

The error terms for the algebraic loops are calculated in the same way as inSSBL03.

Internal checking is performed so that the J matrix used by SMIT01 is consistent.

If a state or algebraic loop is switched on or off during a run a new J matrix is

immediately evaluated. If convergence fails the SMIT01 variables are reset to the

initial values (previous converged point) and DT is reduced by a factor of

DTRDCN and convergence is attempted again. DT may be reduced a total

number MXDTRD times on any given integration step. The current values of

DTRDCN and MXDTRD are both 3 therefore allowing a factor of 27 reduction in

DT, If the point still fails, they are set equal to the initial failed values. TRAP03 will

fail when the number of failures above exceeds the value of MXFAIL. MXFAIL is

currently set at 5. DTRDCN, MXDTRD and MXFAIL are all internal variables to

TRAP03.

84

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SUBMODULE CDNZ_O : Isentropic Nozzle Analysis

Basically, all nozzles can be analyzed as an isentropic process which allows the

use of the isentropic flow rationships. Hence, the expansion process of nozzles

can be represented on an H-S diagram as drawn below:

Po

• he

h I PI

-h

/J i S°;sS

A nozzle analysis requires the following input as known conditions:

They are: PR, AR, _/, Po, To, Ath

The input parameters defined above represent pressure ratio (PR), area ratio

(AR), ratio of specific heats (_/), chamber pressure (Po), chamber temperature

(To) and throat area (Ath).

For a first test, we need to check and see if the PR is choke. The isentropic total

to static pressure can be defined as:

Po 1 + mn 2 r.-1 (1)P,

At the throat, the choked PR occures at Mn = 1

= 1 + m/'l 2 r.-1 = r.-1

CHOKED

IfPR> _ CHOKED

(2)

85


For a second test, we need to check and see if the flow parameter at the throat

(FP'rHP,OAT) iS choked. The flow parameter is defined as:

_p = w_ To = ,_ .,,, (3)

+ T inn2) r-'-T

The flow parameter defined by equation (2) is a function of X and Mn. This

relationship can also be defined as a function of _/and PR by defining Mn asfunction of PR.

Solving equation (1) for Mn as a F(PR).

_,P./

I( T' 1r_, 2 =! _ 7_1y- 1 kP,)

(4)

Now that a relationship for Mn as a F(PR) has been determined; it can be used to

define the flow parameter as function of _, and PR. Let's substitute equation (4)

into (3)

FP =

( 29" _r(Po_t _-1 1 ] --

r,._,_r_l_r,=o___1+_=,,_,,L_..,-2(p.,-1)

1

Simplifying:

FP =

L_'_ J (5)

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The choked flow parameter can now be defined by substituting the choked

pressure ratio defined by equation (2) into equation (5).

FPcHoKEO =

Ill

FPCHOKED -

1 1

k_-l J k 2 j

Let the checked pressure term be defined as CHOKED

"'" FPCHOKED \ 7- 1 ] "

Let the nozzle pressure term be defined as EXIT:

EXIT = {PR-_- 1} ½

.'. FP_,rr = ( 27 '_½ . EXIT_r-t]

Finally,

FPT#RoAT = FPExrr " AR

If FPTHROAT > FPcHOKED then the nozzle is choked.

87

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UN-CHOKED nozzle

Let's calculate the exit Mach number using subroutine Mach03 which guess

MnEXlT as a function of FPExtT,

mnExJT = F(FPExIT)

Vary MnEXlT until (FPExlT)CAL c - FPEXlT < tolerance

The above balance uses subroutine ITER01 and calculates (FPEx_T)CALC.

_-_ mnEXIT(FRExIT) CALC = #1

(1 + -_-mn 2ex, T)2(_ ')

FPrttRoar = FPzxtr * AR

Go calculate the thrust coefficient

CHOKED nozzle

IfAR < 1 then

CONVERGENT AREA

mnExrT = 1.0

FPr_Roar = FPcMoKE_ * AR

Go calculate the thrust coefficient

Else

DIVERGENT AREA

FPTHROaT = FPcHoxEo

•". FPExn" = FPcHox_D / AR

88

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Since this is a divergent nozzle, the analysis needs to check for internal shocks.

Let's calculate the exit Mach number using subroutine Mach03 which guess

MnEXIT as a function of FPEx_T,

mnExlr = F(FPExtT)

Vary MnEXlT until (FPEx_T) CALC -- FPExlT _< tolerance

EXiT PEXIT > P AMB

RPR =PR

If RPR > 1 then

The exit pressure (PExIT) iS greater than ambient pressure (PAMB) which indicates

that there is no shock in the nozzle. Go calculate the thrust coefficient.

PS2 -2yrnn2EXiT y- 1

y+l 'y+l

2nd test PEXlT

(after shock > PAMB)

= ( es2 ]RPRS \Psl ] " RPR

If RPRS > 1, then

The exit static pressure (PExIT) iS greater than ambient pressure are the check.

Hence the nozzle does not have a shock wave. Go calculate the thrust

coefficient.

A normal shock exist in the nozzle.

the shock).

mnl = 1 +

Let's guess Mn, (Mach number upstream of

(mnExtT - 1)

This allow the total to total pressure ratio (PT1 / PT2) across the shock to calculate.

89


T,l ?-ITo =1+__ ran121 2

F.......]/LPra 1 + ___mnt 2 r-t 7- 1 7+ 1

Calculating exit Mach number downstream of the shock.

FPTHFtOATFPEXIT -

PT; ) AR

MnEXlT = F (FPExlT) using subroutine Mach03

axrr = 1 +---f- mn -;-f

Vary Mnl until [(Po/PS)EXIT - (PR) ( PT2 \ PT1 )] < tolerance

(_) :_.EXIT

Go calculate the thrust coefficient.

Calculation of The Thrust Coefficient

P +Exlr 1

eo

The ideal throat coefficient { with PEX=T = PAMB) is defined as:

c_,o,+:+,{(_-_I(_--l_F,+ ,-,_l+-ipx,_,-t)k_,+t] L - (i/P,,+>-+-.,j

The ideal thrust coefficient (no real losses, but includes expansion losses) isdefined as:

90

Pratt & Whitney

FR-20282-3

/CF' = Fer.Roar mn_art g2( 1

AR ( "Psexrr 1+keo Fe 1

LOSS_.aL = CF'vac(1 - CS)

Velocity coefficient is defined as:

CV = (CF' - LOSSR.s,,u.)/CFIoL

91

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SUBMODULE FLPMO2 - Flow Calculation Through A Restriction

It is often necessary to include the effects of a flow path restriction in a simulation.

This involves developing a relationship between flow and total pressure loss.

FLOW CALCULATION:

The general problem of calculating the mass flow rate through a restriction can be

simplified considerably if the restriction is considered to be an orifice. This

reduces the scope of the problem from developing a general theory applicable to

all possible geometries to deriving a calculational procedure for only one

geometry. The general situation is thus reduced to calculation of flow through an

orifice and proper sizing of an orifice.

As flow moves through an orifice it is first accelerated until it attains a maximum

velocity at the throat. The flow is then diffused as it is decelerated to the

downstream conditions. During this process, the total and static pressures

change as depicted in Figure I. There is little loss in total pressure as the flow

nears the throat, although static pressure changes considerably due to the

increased fluid velocity. Most of the total pressure loss occurs as the fluid is

diffused downstream of the throat. The static pressure is increasing, however, as

a portion of the velocity head available at the throat is converted to pressure.

Total temperature does not change throughout the process.

Typically, the upstream and downstream total pressures and temperatures are

known, from which flow is to be determined. Since the total pressure and

temperature at the throat is nearly the same as upstream, flow could b-e

calculated using compressible flow relations if static pressure at the throat wereknown.

Static pressure at the throat can be calculated if it is assumed that the total

pressure loss across the orifice is related to the velocity head at the throat.

Numerous experiments have been conducted which justify this assumption,

although most of the empirical data is presented in terms of discharge and flow

coefficients. Discharge and flow coefficients are useful for control valve work but

are generally restricted in their range of applicability. It is more convenient,

therefore, to define a loss coefficient from which static pressure at the throat can

be determined.

Referring to Figure II, the loss coefficient is defined as:

L = Total pressure loss =Velocity head at throat

PT uo - PT DOWN

PT up - Ps THROAT

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Rearranging, the total to static pressure ratio at the throat is given by

PTUp = PR(L)

PSthroa t 1 + PR (L-1)

FlowDirection

Streamlines "-7

Pressure

I

, I

Total I

Throat Axial Location

Figure I. Total and Static Pressure Variation in an Orifice

where PR = PT up/PT down and it is assumed the orifice is not choked. If the

calculated total to static pressure ratio is greater than the choke value, then the

orifice is choked, in which case, the actual total to static pressure ratio at the

throat is equal to the choke value.

With the total to static pressure ratio known, the flow parameter (w R,/-f_t/P,A) can

be determined at the throat based on compressible flow relations;

v/2gcy (PR-_---1)W R_T =FP = _,l

eTA (r- 1) PR 7

/93


Since total temperature remains constant, and total pressure at the throat is

assumed equal to the upstream total pressure, the mass flow rate can be

determined,

W = FP (PTup)(Aeff)

R(Tt up)

PTUP

uJrr-

03ILl,.rpQ- TDOWN

PSTHROAT

VELOCITY HEAD ATTHROAT

TOTAL l_ I/_

m

I_S TOTAL PRESSURE

LOST

Lo ,_ TotalPress"-'-"'-_re Lost /

Coefficient: Velocity _ a'_ 1

Figure I1. Loss coefficient relates total pressure lost to velocityhead at the orifice throat

94

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FR-20282-3

m .

II,

a

t

m

_0

¢-

(DOO_0u3O

.. =.J

13- O

.=of

kl:l..L:l_Vt:lVd MO-I_-I

95


I !

0303O/

-r"F--

n,-WF-LU

<_rr-<Q.

O/LL

D_O_O

aflfm

I0_0_

St I! ! I

H:::II::;IAIVklVd M07-1

96


,4

Iii

LLI1_LLI©

CO

97


ROCETSREALFLUID AND COMBUSTIONPROPERTYPACKAGES

The ROCETSproperty package consists of five real fluid properties and one

"perfect gas" combustion property. Both property packages consist of a driver

subroutine and a property/model interface subroutine for each of the five fluids

and the combustion method. The driver routine is the decision maker and then

routes all information to the correct property or model interface which the

accesses the property maps for the real fluid properties or the subroutines for thecombustion properties to look up the desired results. The program logic of the

ROCETS real fluid properties and the combustion property package is shown

Figures 3.4.2.4.1 and 3.4.2.4.2 respectively. The five basic properties are

para-hydrogen, oxygen, methane, nitrogen and helium. The combustion

properties provide a perfect gas combustion analysis using hydrogen and oxygen

as the reactants. The driver has been set up such that it can be expanded to

allow real gas combustion and Brinkly combustion at some future date. The

combustion properties are from the digital transient model (DTM), but have been

upgraded to meet ROCETS software standards.

In the combustion property package, the driver receives basic inputs such as

model type (MTYPE), property option (IOPT), the independent variables (XVAR1,

XVAR2, XVAR3 and XVAR4) and the map indicies IHOLD1 and IHOLD2. This

information is then passed to the model interface which accesses the required

information from the combustion property subroutines and maps. The call

statement for the driver routine has the following form:

CALL COMBO0 (MTYPE, IOPT, XVAR1, XVAR2, XVAR3, XVAR4, OVAR1,

OVAR2, IHOLD1, IHOLD2)

It should be noted that MTYPE is a character*8 variable which defines the

method to be used. For example, if the user wishes to access combustion

properties using a perfect gas model, they would define MTYPE = 'PGAS '

Once the combustion property model type has been defined, the correct model

interface is accessed. The model interface routines have the following form:

CALL XGASAA (IOPT, XVARI, XVAR2, XVAR3, XVAR4, OVAR1, OVAR2,

IHOLD1, IHOLD2)

The single character prefix X defines the model to be used and two character

suffix defines the version number. The following models are available or are

planned: P-perfect gas model (available), R-Real gas model (not available) and

B-Brinkly model (not available). A complete list of all options and parameters

used in the argument list are defined in Table 3.4.2.4.4 and the units are defined

in Table 3.4.2.4,5.

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The perfect gas model interface defined above obtains property information in

both subroutines and property maps from the Digital Transient Model (DTM).

However, the subroutines found in the DTM have been upgraded to ROCETS

software standards and the maps which are from the DTM input file were put into

subroutine format. Basically, the subroutines which are called from the model

interface access results from tabular data which are in uni-variant or bi-variant

form. The univariant maps re set up in x-axis and y-axis coordinate system and

use a linear map reader (SUNBOO) to interpolate. The bi-variant maps are set

up in an x-axis, y-axis and z-axis coordinate system and use a corresponding

point map reader (CPMRO2) to interpolate. The map indices IHOLD1 and

IHOLD2 care used to track the corresponding map locations and are responsible

for a significant reduction in the cost of accessing the maps.

At this stage of development, the real gas and Brinkly gas combustion models

are not available. However, as they are implemented into the ROCETS system,

these models will be discussed in greater detail.

The ROCETS combustion property package has 7 property maps that are used to

drive the perfect gas model interface. The real gas and Brinkly gas interface

have not yet been implemented. The following tables define the subroutines and

maps which are used.

COMBUSTION PROPERTY ROUTINES

PERFECT GAS REAL GAS BRINKLY GAS

CPGMOO

CPMPO1

RDMP13

RDMP21

RDMP12

ZGASOO

ZZMPO1

NONE NONE

These maps are presented in figures 3.4.2.4.27 - 3.4.2.4.31. The perfect gas

combustion property package allows the calculation of basic thermodynamic

properties which are corrected for compressibility effects for the hot gas system

components such as the preburner, turbine, injectors and the main chamber.

In the basic fluid property package, the driver routine receives basic property

inputs such as fluid type (FLUID), property option (IOPT), the independent

99

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FR-20282-3

variables (XVAR1 and XVAR2) and the station niumber (KSTA). The user

supplied information is then passed to the particular property interface which

accesses the required information from the property maps, The call statement

for the driver routine has the following from:

CALL PROP00 (FLUID, IOPT, XVAR1, XVAR2, PVAR, OVAR1, OVAR2, KSTA)

It should be noted that FLUID is a character*8 variable which defines the fluid by

name. For example, if the user whishes to access hydrogen property data, he

would define FLUID = 'HYDROGEN'.

Once the fluid property has been defined, the correct property interface can be

accessed. The property interface routines for the five basic properties have the

following form:

CALL XXPROP (IOPT, XVAR1, XVAR2, DVAR, OVAR1, OVAR2)

The two character prefix XX defines the fluid to be used. The following fluids are

available: H2 - para-hydrogen, 02 - oxygen, N2 - nitrogen, HE - helium and ME

- methane, A complete list of all options and parameters used in the argument list

are defined in Table 3,4.2.4.1 and units are defined in Table 3,4,2.4,2.

Each property interface defined above obtains property data from a series of real

fluid property maps. The call statements to the maps follow a basic format which

uses a one letter prefix to define the fluid, a three character map variable name

and two character version number. The map variables define how a particular

map is set up. Let's consider an example for a hydrogen map. The fluid prefix is

H. Hence, the call for a hydrogen map whould have the form HXYZAA, A

hydrogen map call would have the collowing form:

CALL HXYZAA (XX, YY, ZZ, IOPT, IHLD1, IHLD2)

All property maps are set up in an x-axis, y-axis and z-axis coordinate system

and uses a corresponding point map reader (CPMR02) to interpolate. The

advantage of a corresponding point reader is that a family of discontinuous

curves such as a property map can be adequately handled. The map reader has

two options. Option one determines zz as a function of xx and yy. Option two

determines xx as a function of zz and yy. The integer variables IHLD1 and IHLD2

are map indicies which are stored internally for each call to a particular property

interface routine by specifying KSTA.

These indicies significantly reduces the amount of CPU time required to access

information from the maps.

100

Pratt & Whitney

FR-20282-3

The ROCETS property package has 19 property data maps that are used to drive

the interface routines. The following table defines the maps which are available:

REAL FLUID PROPERTY ROUTINES

PARA-HYDROGEN OXYGEN METHANE NITROGEN HELIUM

HRHP01 ORHP01 MRPH01 NRHP01 ERHP01

HRUP01 ORUP01 MTPH01 NPHT01 EPHT01

HPUT01 OPUT01 MHPS01 NHPS01 EHPS01

HHPS01 OHPS01 MCPT01

MCVT01

These maps are presented in plot form in Figures 3.4.2.4.3 - 3.4.2.4.26 and are

restricted to the pressure and temperature ranges defined in Table 3.4.2.4.3. It

should be noted that MCPT and MCVT define Cp and Cv as a function of

temperature with lines of constant pressure.

This particular property package has also been optimized to minimize cost, This

was accomplished by tracking the indices of the property maps for up to 100 calls

for each fluid by storing unique integer values assigned to KSTA for each call to a

particular fluid. A speed trial was performed which ran 100,000 calls to PROP00

for para-hydrogen on the IBM 3083 for both an iterative and noniterative solution.

The iterative solution required 510 seconds of real time and 1.14 CRU's of

execution time. The noniterative solution required 207 seconds of real time and

0,46 CRU's of execution time.

101

Pratt & Whitney

FR-20282-3

TABLE 3.4.2.4.1

PROPERTY INTERFACE PARAMETERS OPTIONS

IOPT XVAR1 XVAR2 DVAR QVAR1 QVAR2

1 PRES TEMP ENTH DENS TEMP

2 PRES TEMP ENTR DENS TEMP

4 PRES ENTH, ENTR DENS TEMP

5 PRES ENTR TEMP DENS TEMP

6 PRES ENTR TEMP DENS TEMP

7 PRES TEMP DENS DENS TEMP

8 PRES TEMP CP GAMMA DENS

9 PRES TEMP TH CONDVISC DENS

10 TEMP DENS PRES ENTR ENTH

11 PRES DENS ENTH TEMP ENTR

12 DENS ENTH PRES ....

13 PRES ENTH DENS ....

14 DENS INT, ENERGY PRES ....

15 PRES INT.ENERGY DENS ....

NOTE: Of

available.the eleven options above, only (9) for helium and methane are not

102

Pratt & Whitney

FR-20282-3

TABLE 3.4.2.4.2

PARAMETERS AND UNITS USED IN XXPROP

PARAMETER

PRESSURE

TEMPERATURE

DENSITY

ENTHALPY

INTERNAL ENERGY

CP

THERM.COND.

VISCOSITY

ENTROPY

UNITS

ENGLISH

- Lbf/IN 2

- DEG R

- LBM/IN" "3

- BTU/LBM

- BTU/LBM

- BTU/IN-SEC-DEG R

- BTU/FT-HR-R

- LBM/FT-SEC

- BTU/LBM-DEG R

t

SI

N/m 2

DEG K

KG/m 3

J/Kg

J/Kg

J/Kg - DEG K

J/m - SEC - DEG K

KG/m - SEC

J/Kg - DEG K

103


TABLE 3.4.2.4.3

NBS PROPERTY PRESSURE AND TEMPERATURE LIMITS

FLUID PROPERTY

Para-hydrogen

Oxygen

Nitrogen

Helium

Methane

PRESSURE RANGE

' (Lbf/iN 2)

0.0 - 17,404

0.0- 17,404

0.0 - 20,000

0.0- 14,500

1.7 - 10,000

TEMPERATURE RANGE

(DEG R)

24.8 - 720.0

97.8 - 720.0

113.7 - 3420.0

5.4 - 20700.0

163.2 - 900.0

104


TABLE 3.4.2,4.4

COMBUSTION PROPERTY INTERFACE PARAMETER OPTIONS

XVAR_1 _ _ XVAR_4 OVARI_

1 PT "IT OFR PR CP

2 OFR NA NA NA RGAS

3 PT TT OFR NA Z

4 RHO "IT OFR NA PT

GAMA

XMW

NA

RGAS

105

Pratt & Whitney

FR-20282-3

TABLE 3.4.2.4.5

PARAMETERS AND UNITS USED IN XGASAA

PARAMETER (ARG)

PRESSURE (PT)

TEMPERATURE (TT)

DENSITY (RHO)

GAS CONSTANT (RGAS)

SPECIFIC HEAT RATIO (GAMA)

SPECIFIC HEAT (CP)

COMPRESSIBILITY (Z)

MOLECULAR WEIGHT (XMW)

PRESSURE RATIO (PR)

OXIDIZER FRACTION (OFR)

ENGLISH

Lbf/lN 2

oR

Lbm/IN 3

Lbf IN/Lbm °R

D'LESS

Btu/Lbm°R)

D'LESS

Lbm/Lbm-MOLE

D'LESS

D'LESS

Sl

N/m 2

oK

Kg/m 3

N/m/(Kg°K)

D'LESS

J/(Kg°K)

D'LESS

Kg/Kg-MOLE

D'LESS

D'LESS •

106

Pratt & Whitney

FR-20282-3

SUBROUTINE

ZZMPO1

RDMP12

CPMPO1 (1)

RDMP21

RDMP13

NOTE: (1)

TABLE 3,4.2.4,6

SUBROUTINE PARAMETERS AND RANGES

PARAMETER RANGE UNITS

PT 14.7 - 2000 Lbf/IN2

TT 50 - 400 °R

77 0.45- 1.55 D'LESS

OFR 0 - 9999 D'LESS

XMW 2 - 32 Lbm/Lbm-mole

PT 50 - 5000 Lbg/IN2

TT 100 - 2000 °R

PR 1 - 4 D'LESS

GAMA 1.4 D'LESS

OFR 0- 1.0 D'LESS

CP 0.22 - 3.6 Btu/(Lbm°R)

OFR 0 - 1.0 D'LESS

GAMA 1.2- 1.4 D'LESS

Cp agrees with H2 (NBS) within +/- 2% when inlet pressure (for

turbines) is less than 2000 PSIA and within +/- 60% when inlet

pressure is less than 5000 PSIA.

107

0

0

°_,-_

c_

F_

00

1,08,


r

c_

Oc_

O

O°p.._

O

0

1

=4.._ G_

,_°_._J O..

Z_t L

>.-_ LLIt_JI,,_1_ ,--o .J

t;JZ_UJ_ 1X_ UQ-

Z_3__Ot_3b3

Pratt & Whitney

FR-20282-3

/3 (_IT Ol

Z " U_>--I

0 --_ b.II

_I

:z: I I !

_ _-'_ ml

o

NN

_J

_ cM

dd_

109

ORIGINAL PAGE IS

OF POOR QUALITY


PRATT &: WHITNEY

HYDROGEN PROPERTY MAP

DENSITY VS PRESSURE AT CONSTANT U

00

C_0cN

000

I'M

Z

1.1_

--I00

I o

0_

00

0

....

i i . : i

0 2 4 6 . 8DENSITY - LBM / FT"_3

....-g-110

FIGURE 3.4.2.4.3

DENSITY

o°

PRATT & WHITNEY.


VS PRESSURE AT CONSTANT

Pratt & Whitney

FR-20282-3

ENTHALPY

OC;O

Z

00

0

0 1 2 ,3 4 5 6 7DENSITY - LBM ,/ FT'*3

111

FIGURE 3 4.2.4.4

PRATT & WHITNEY

HYDROGEN PROPERTY

PRESSURE VS TEMPERATURE AT.o

Pratt & Whitney

FR-20282-3

MAP

CONSTANT U

O' I : . !

I

i.,jO ............

0 I O0 200 300 " 4-00PRESSURE - LBF ,/ IN*'2

112

FIGURE 3.4.2.4.5

PRESSURE

Pratt & Whitney

FR-20282-3PRATT &: WHITNEY


VS TEMPERATURE AT CONSTANT U

..... ; " | ...... "; .... I " ' : "" " :'"'!

0 .5000 10000 15000 20000

PRESSURE - LBF / IN*'2

113

FIGURE 3.4.2.4.6

ENTROPY

-.

PRATT & WHITNEY


VS ENTHALPY AT CONSTANT

Pratt &Whitney

FR-20282-3

PRESSURE

==•.-m0 .

I

-rc;

(5

0 5 10 15

ENTROPY - BTU /

I !

20 25 30 35

(LBM DEG R)

o.

114

FIGURE ,3.4.2.4.7

DENSITY

PRATT & WHITNEY

OXYGEN PROPERTY MAP


Pratt & Whitney

FR-20282-3

U

0

0

0 2O 40 60 80DENSITY - LBM / FT**3

-100

115

FIGURE 3.4.2.4.8

DENSITY VS

PRATT & WHITNEY

OXYGEN PROPERTY MAP

PRESSURE AT CONSTANT

Pratt & Whitney

FR 20282 3

ENTHALPY

¢-q

Z

--0

L,-C_a3-J

I

,,,°o

t_ ,--

L_

Q.

00

C_

0

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! t

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'/l.ttlttlfItl#fi....""" lfltl. Ittt .,.

gtlttl; tltttlttt}_.

,,

!0

0 20 40

DENSITY - LBM

6O 80 .I O0

/ F'I'** 3

_°

116

FIGURE 3.4.2.4.9

PRESSURE

Pratt &Whitney

FR-20282-3

PRATT &: WHITNEY

OXYGEN PROPERTY MAP


0

Q

Lf3.

o-4

0

O.

13_TM

(.9

hl

I.,0

::3'--

l---

l.l.l

:=i

I.I

J"O

0

i

• L i , i , ±

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•:-.. _.........J _.,- .::.._,.i--:;..--,._.-._i+:.....::......:_'H*I '_::: ;'__ '; :....

C3

"t .... ='l ........ '1 ........ ' _'•i ...... I ..... ':_ i ....... i" r ':'. _ , _ i !- :'r! : ...... I .... ? i 1 ..... : "_ ....... i ' : i .............

' :*,, ::.! :, ::: Ii 1i::i}i:-,:! ::,, !: :l: _:!,::::,: !; 1I: '._: ......:::. :: :: ..... : ................

0 100 200 300 400 500 600 700 .800PRESSURE - LBF / IN**2

117

FIGURE 3.4.2.4.10

PRESSURE

Pratt &Whitney

FR-20282-3

PRATT &: WHITNEY

OXYGEN PROPERTY MAP


OO

0

O-

0

0 5000 10000 15000 20000 25000

PRESSURE - LBF / IN*'2

3000035000

118

FIGURE 3.4.2.4.1

Pratt & Whitney

FR-20282-3

PRATT & WHITNEY

OXYGEN PROPERTY MAP

ENTROPY VS ENTHALPY AT CONSTANT PRESSURE

0

0

00

c_

0

0.0

. f. i..-..i.---._:: ............. i";"'! ........................... 1 .._...."!', i

. .:p._,....:...ll_ ......... ;'" "_ "';....... "" "'''--''l'''' " " '! "_''':"

.. g.,L....i....',...... L...L ..L i ........................... '_-i" --!-""}

f i i " : . ;....;..i i.--_........_..._4-!...................................,...........

,..L....L. L i ,:........ 2

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.'- i-_ ...... _-..._......

....+.i.,-..i-- , ' ; • ; ,,i

i

:........._.:

0.5 1.0 1 .5 2.0

ENTROPY - BTU ,/ (LBM DEG R)

-2.5

119

FIGURE 3.4.2.4.12

Pratt & Whitney

FR-20282-3

PRATT & WHITNEY

METHANE PROPERTY MAP

DENSITY VS PRESSURE AT CONSTANT ENTHALPY

2 •

0

0 5 10 15 20 2,5 30DENSITY - LBM ,/ FT**3

120

FIGURE 5.4.2.4.15

ENTHALPY VS

PRATT & WHITNEY


TEMPERATURE AT CONSTANT

Pratt & Whitney

FR-20282-3

PRESSURE

C_ .......;..i .J-..÷.4-,i.-_,= +._-.; .;.

i!:,:_ii::j! i _

t._ , " : : _¢11/I

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0 100

!.:': i.:: i:..;_,• ;/i: ;.i; ;:i! !: i! '; ! !: ::i:_::: : i i_i

i i _ i i i _ ii _ i i_ ii iii i ii _iiiii

: • . : . , _ , ;

200 .300 400 500 600 -700

ENTHALPY - BTU / LBM

o.

121

FIGURE 3.4.2.4.14

ENTHALPY VS

PRATT & WHITNEY



Pratt & Whitney

FR-20282-3

PRESSURE

0o.

0O-O0

0O-

E3 0

_-gw

I.=lI-- 0

o

oorQ

00

o0

:.:i_,., ...... _;--4.;ii. ,_E..:-, : : .__|L:_-i _ ,';_i':i ::;i = - -_! : ........",: " .

iiii: !i'it iilii0 100 200 300 400 500 600 700 .800

ENTHALPY - BTU / LBM

,...-..=.,o°

122

FIGURE 3.4.2.4.1,5

ENTROPY

°.

PRATT &: WHITNEY



Pratt & Whitney

FR-20282-3

PRESSURE

0 °

0

0

i ..........

...... , ....

"" t ..................

.0 I .5ENTROPY

2.0D BTU

L. '

i : •

2.5/ (LBM

! .....

3,0DEG R)

.3.5

123

FIGURE 3.4.2.4.16

PRATT &: WHITNEY


TEMPERATURE VS CV

Pratt & Whitney

FR-20282-3

.... i

0 200

T....

400 600:TEMPERATURE - DEG

8OO I 000

124

F GURE 3.4.2.4.17

PRATT & WHITNEY


TEMPERATURE VS CP

Pratt & Whitney

FR-20282-3

QO • : k,F ........ t ...... ! -" t ..... _ T ...... _ " I ...... :' It T " " ! .......... 1 "': :

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0 200 400 600 800 1.000:TEMPERATURE - DEG R

°°.

125

FIGURE 3.4.2.4.18

DENSITY

PRATT & WHITNEY

NITROGEN PROPERTY MAP


Pratt & Whitney

FR-20282-3

ENTHALPY

0 10 2 0 30 40 50

DENSITY - LBM / FT**3

60 70

126

FIGURE 3.4.2.4.19

PRESSURE VS

PRATT & WHITNEY



Pratt &Whitney

FR-20282-3

ENTHALPY

.. :.,._....r..I.....

....'-'-;-'- iiiii iiiiiii1111117..... i: i:i.:i i i-ii II i I

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................ ti _._.... i........:....

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ur'3 . .

.................................... _ _ ........... !........ _........ ; "' '_ T ! ............ " " _ ! ...... ;

......? .......! ....... i ) .....:= ........................._ _......£..2......... ' i ::_' " i....................... :..... : ............

0 1 O0 200 300 400 -500PRESSURE - LBF / IN"'2

..•

127

FIGURE 5.4.2.4.20

PRESSURE VS

PRATT & WHITNEY



Pratt &Whitney

FR-20282-3

ENTHALPY

I::E

l,,iJ

l.iJ

23I--

LIJ

I:L

i.iI,--

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i ; : i : ' " "; . - e - • " t,_",rr_, u, ........ i i

" i i I I iIII I IIl"l I

O

0 5000 10000 15000 20.000

PRESSURE - LBF / IN**2

. FIGURE 3.4.2.4.21

128

ENTROPY

PRATT & WHITNEY



Pratt &Whitney

FR-20282-3

PRESSURE

o.....!i_;__........,i!_i!'_"_ti__::I'...._!_;.!!_"-_'_............__......."-_.....0

...._ ....... i....... . .... i .!.._ .i..i .:, i.._,..._..;.,,i., '_....

........... !

oo0

Ii0.5 1.0 1.5 2.0 2.5 J-,.O

ENTROPY - BTU / (LBM DEG R)

, FIGURE 3.4.2.4.22

°o.

129

Pratt & Whitney

FR-20282-3PRATT &: WHITNEY

HELIUM PROPERTY MAP

DENSITY VS PRESSURE AT CONSTANT ENTHALPY

%

0

0 2 4 6 8 10 12DENSITY - LBM / F'T*=3

130

FIGURE 3.4.2.4.23

O"

0I.iJ

L,.J o

p-<:0¢I,.iJO.

i.iI--

_"_o

0

Pratt & Whitney

FR-20282-3PRATT &:: WHITNEY

HELIUM PROPERTY MAP

PRESSURE VS TEMPERATURE AT CONSTANT ENTHALPY

o o

'i ; . ._ i- ; ._ _''i ...... r ' ! "" :"1 .......... ' f....... I ' " ?

.--_. :...: ; , ........ .-' ...... , _..... : :.................:. ......... "_--_ .... +.--t ....... -" = ................. : :."] : :

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i,ll

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FR-20282-3PRATT & WHITNEY

HELIUM PROPERTY MAP

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FR-20282-3

PRATT &: WHITNEYCOMBUSTION PROPERTY MAP

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FR-20282-3

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138


PMAPXX - Pump Characteristic MAP Format 1

INPUTS:

IOPT - MAP Option

Q - MAP Density

N - Pump SpeedW - Flow

SFSP - Speed Scale FactorSFW - Flow Scale Factor

SFHD - Head Scale Factor

SFTQ - Torque Scale Factor

OUTPUTS:

HD - Pump Head

TORQ - Pump Torque

DESCRIPTION OF MAP OPTION:

(I) (IOPT = -1) : Values returned in call list are design values (100% RPL).

(11) (IOPT=O) : Scale factors are calculated from the input values. (HD and

TORQ are inputs when this option is chosen).

SFSP = NDEs/N SEW = WDEs/W

SFHD = HDoEs/HD SFTQ = TORQDEsFFORQ

(111)(IOPT = 1) • MAP is read (curve fit) by using input values and given scale

factors from call list.

CALCULATIONS:

NMA P = N/SFSP

WMA P = W/SFVV

(MAP Speed)

(MAP Speed)

Speed (in radians): /2_rNR= NMAP 6-O

Tip speed is defined as:2_r

u=D(-6-O)NMAP2

Flow coefficient (_) is

defined as:dp = A@(Sh°wn below)

139,

Pratt & Whitney

FR-20282-3

Dimensional analysis:

By relating the speed of rotation, pump diameter and volumetric

flow rate the following equation results:

Q - CONSTANTND 3

We know that:

Substituting yields:

U a NDandA a D 2

Head rise coefficient can now be read from the MAP using flowcoefficient and s_eed as inputs:

Torque coefficient can be read from the MAP using flow coefficient as aninput:

NOTE:

CTRQ _ .-

ii_

For option Ill (IOPT=I) scale factors are applied to the inputs beforereading the MAPS as defined under Option II above.

14Q


PUMP HEAD:

Dimensional analysis for pump volumetric flow rate, pressure loss,density and diameter yields:

D 2 Q= CONSTANT

Q2 z_ = CONSTANT (1)Squaring yields 1)2 e

Pump head is defined as:AP

Hp = -- (2)£gr

We know that: Q a UD 2 (3)

Substituting (2) and (3)into (1) •U2D +

D4HpGr= CONSTANT

IHMAP gr

PUMP TORQUE:

Dimensional analysis of pump area, diameter, tip speed and densityrelated to pump torque yields the following:

QADU 2TMA P - x CTRQ

gc

For Option III (IOPT = 1) scale factors are applied to the head and torque.

Hp = HMAP x SFHD (pump head)

Tp = TMAP X SFTQ (pump torque)

141 ,

Pratt & Whitney

FR-20282-3

PMAP01 - Pratt & Whitney SSME High Pressure Fuel Pump

Pump Map Format 1

142

Pratt & Whitney

FR-20282-3

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143

Pratt & Whitney

FR-20282-3

0

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PMAP02 Pratt & Whitney SSME High Pressure LOX Pump

(Main Stage) Pump Map Format 1

145


• J MAIN STAGE HEAD COEFFICIENT

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146

Pratt & Whitney

FR-20282-3

: I '

MAIN STAGE TORQUE COEFFICIENT _+1_1_0.01 0.02 0.03 0,04 0.05 ' I i I

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147

Pratt & Whitney

FR-20282-3

PMAP03 Pratt & Whitney SSME High Pressure LOX Pump

(Preburner Stage) Pump Map Format 1

148

Pratt & Whitney

FR-20282-3

-0.2

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FR-20282-3

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150

Pratt & Whitney

FR-20282-3

k

SUBMODULE TBMPXX - Turbine Characteristic MAP Format 1

INPUTS:

IOPT

N

TIN

PIN

PEX

_/R

SFSPD -

SFPR -

SFPSI -

SFETA -

OUTPUTS:

MAP Option

Rotational Speed

Inlet Temperature

Inlet Pressure

Exit Pressure

Specific Heat Ratio

Gas Constant

Speed Scale Factor

Pressure Ratio Scale Factor

PSI Scale Factor

Design Point Efficiency Adder

FP

11z_h'

- Flow Parameter

- Efficiency- Ideal Delta h

OPTION ONE (IOPT = -1)

This option will return design conditions (100% RPI_) for all arguments in the call

list.

OPTION TWO (IOPT = 0)

This option will calculate the scale factors based on the input conditions and the

design conditions as follows:

SFSPD = NDes/N

SFPR = (PRDES- 1)/PRDEs

(eR- 1)/?R

SFPSI = PSI / PSIDES

SFETA = (r I - TIDES ) (SFSPD) 2

OPTION THREE (IOPT = 1)

This option reads the MAP using the input parameters and input scale factors to

calculate the MAP parameters (actual numbers used when reading the maps).

151


CALCULATIONS •

Speed parameter: Npm -N

_/-RX TIN

= Cp(TIN- TouT)

Ah' = - Cp TIN ( TOUTTIN

TOUT = ( POUT'_'_"

T,N \--_IN )

Cp= yR7-1

,) (I)

(2)

(3)

Substitute (2) and (3)into (1)

Tip Speed:

Axial velocity:

Define PSI:

.... x (_2 2

U

Axial velocity, C is obtained from the kinetic energy term in the

energy equation such that:

0 2

2gc

ic =,/2gc

PSI = velocity ratio

I PSI = U/C I

152


For option 3 (IOPT = 1 ) MAP parameters are calculated:

PRMAP = PR/[PR(1 - SFPR) + SFPR]

SNMAP = Npm x SFSPD

PSIMAP = PSI x SFPSI

Flow parameter can now be read from the MAP using pressure ratio and speed

parameter as inputs:

F I SNMAP

PRMAP

Efficiency can be determined by reading -qMAP/PSIMAP as a function of PSIMAP

TIMAP

/PSIMAP

EFFICIENCY:

PSIMAP -

= T_MAP "t" SFETA x (SNMAP / SNDES )2

153


TBMP01 - Pratt & Whitney SSME High Pressure Oxidizer Turbine

Turbine Map Format 1.

154


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FR-20282-3

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156

Pratt & Whitney

FR-20282-3

TBMP02 - Pratt & Whitney SSME High Pressure Fuel Turbine

Turbine Map Format 1.

157

Pratt & Whitney

FR-20282-3

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159

Pratt & Whitney

FR-20282-3

SUBMODULE SMIT01 - Multivariable Iteration Routine

Utility submodule SMIT01 is a multi-variable iteration routine using a modified

Newton-Raphson technique. The matrix equation used in SMIT01 is as follows:

AY = JAX

Where deltaY is the amount that the errors, or dependent variables, need to

change to be zero; and deltaX is the associated change in the independent

variable. J, the solver Jacobian, is a matrix of partial derivative generated with the

model. SMIT01 makes a number of passes equal to the number of iteration

variables plus 1 through the model to generate the Jacobian. The first pass is kept

as a base point and the each of the next n variable passes generates a column of

the J matrix by perturbing one of the independent variables and observing the

changes in the dependent variables from the base point. The perturbation size

for each of the independent variables is set through the SMIT01 inpt array

DELTAX. Each element of DELTAX is the perturbation magnitude of the

corresponding independent variable. The J matrix is then inverted, and changes

in the independent variable values, deltaX, are calculated as follows:

AX = j-I AY

The SMIT01 input array DXALOW is used to limit the change in the independent

variables along the same direction as the deltaX vector. This is done to prevent

excessive changes in independent variables on a single pass. This process is

iterated until the dependent variables are within a specific tolerance. The

maximum number of iterations allowed is input to SMIT01 as the variable

MXPASS. The tolerance for each variable is set in the SMIT01 input array TOL.

The arrays XVAR and YVAR contain the independent and dependent variables

respectively. XVAR is input to SMIT01 and changed as above until each YVAR is

within the specified tolerance. The number of variables is input as NVAR.

To improve the efficiency of SMIT01, Broyden's algorithm for updating the

inverse J matrix j-l, is incorporated. Broyden's method updates the inverse J

matrix without evaluating or inverting a new matrix providing a large savings in

number of total passes through the model. The matrix is updated with a secant

method and can be performed during a convergence attempt. Broyden's

algorithm is applied whenever the reduction in the sum of the squared errors is

less than the SMIT01 input SSEBRD. It may still be necessary to evaluate a new J

matrix if SMIT01 fails to converge at an acceptable rate. If the improvement in

the sum of the squared errors is less than SSEJAC for greater than MXFAIL

160

Pratt & Whitney

FR-20282-3

consecutive passes, a new J matrix is evaluated. SSEJAC and MXFAIL are

SMIT01 inputs.

Other SMIT01 inputs are defined as follows:

1. IPNT = Print flag

0 = No print

1 = SMIT01 statistics output at completion

2. KFILE = Logical unit number for print output

3. ILOOP = Loop number for nesting SMIT01. Two SMIT01 loops can be

nested; ILOOP is used to distinguish internal variable for each

loop.

4, ISAMAT = Flag to use previous J matrix

0 = Do not use stored J matrix

1 = Used stored J matrix

o IDTYPE = Pertubation type for J matrix calculation

1 = Backward difference

0 = Central difference

+1 = Forward difference

The flag ISIG is used to control the program flow. It is set as 0 on the first call to

SMIT01 and is set by SMIT01 on subsequent passes as follows:

1 = New X's returned in an attempt to converge

2 = Perturbation pass to create Jacobian matrix

3 = Iteration has converged

4 = Jacobian is singular

5 = Maximum iterations failed to converge

Additional parameters are output as statistics on SMIT01 operation as follows:

PCTRDN = Percent reduction in the sum of squares error for convergence attempt

KOUNT = Convergence attempt counter.

KTOTAL = Total pass counter (including J matrix passes).--

KJACOB = Number of J matrices generated

KBROYD = Number of Boyden updates

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Pratt & Whitney

FR-20282-3

$UBMODUt,.E $UNB01 -Univariant or bi-variant sunbar-type map reader with

option to read map in any direction and either extrapolate or return corner values.

INPUTS

A = Array containing map

X = Absicssa value. Normally first independent variable

Y = Family value. Normally second independent variable

(Not used for univariant curve)

T = Ordinate value. Normally dependent variable

IOPT = OPTION CODE

1 = X and Y are input, T is returned

(X only for univariant)

2 = T and Y are input, X is returned

(T only for univariant)

3 = X and T are input, Y is returned

(Not applicable for univariant)

OUTPUTS:

IERRX = Error code describing the absicssa

0 = Normal return

1 = X value too small. Lowest X used.

2 = X value too small. Extrapolated value used.

3 = X value too large. Largest X used.

4 = X value too large. Extrapolated value used.

IERRY = Error code describing the family

0 = Normal return

1 = Y value too small.

2 = Y value too small.

3 = Y value too large.

4 = Y value too large.

Lowest Y used.

Extrapolated value'used.

Largest Y used.

Extrapolated value used.

Method of setting up the A array

Absicsssa = X

Ordinate = T

Family = Y

A (1) = Storage space for X position indicator --initially zero

A (2) = Storage space for Y position indicator -- initially zero,

or curve identification number

A (3) = Number of X values defining each line

162


A (4) = Number of Y values (must be zeero for univariantcurve) then,beginningwith A(5), the map is input as:

A (5)-A (5+NX) -

4(4+NX) = X values in ascendingorderA(4+NX+NY)= Y values in ascending orderA (5+NX+NY)= T for X1,Y1

A (6+NX+NY) = T for X1,Y2

A(2*N¥+NX+4) = T for X1,YNY

A(2*NY+NX+5) = T for X2,Y1

A(2*NY+NX+6) = T for X2, Y2

A(3*NY+NX+4) = T for X2,YNY

A(NX+NY*NX+NY+4) = T for XNX,YNY

NOTE: In the above setup, NX=number of X°S, NY=number of Y'S for bivariant

curve. Curve for univariant, A(5) - A(4+NX) contains the X values,

A(5+NX) - A(2*NX÷4) contains the T values..

COMMENTS:

1 For normal reading (IOPT=I), X is bracketed first, followed by Y bracketing.

Since X and Y are bracketed independently, care must be exercised when

setting up maps to ensure correct values will result. If maps are not fairly flat,

a corresponding point map reader should be used.

2. For reading X as a function of T and DY (IOPT=2), Y is bracketed first,

followed by T bracketing. When corner values are returned, they look as if X

and T were swapped.

3. When reading Y as a function of T and X (IOPT--3), X is bracketed first,

followed by T bracketing. This option is invalid for univariant curves.

4. Univariant and Bivariant curves are calculated similarly but there are noY-calculations.

5. Multiple valued functions (more than 1 T for given X and Y) should not be read

with Option 2.

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