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_INAL REPORT

IMPROVED

TWO_DIMENSIONAL KINETICS (TDK)

Computer Program

Contract Number NAS8-35046

October 1983

t

Prepared For

George C. Marshall Space Flight Center

Marshall Space Flight Center, Alabama 35812

Prepared by

Gary R. Nlckeroon

Lanh D. Drng,

Software and Engineering Associates, !no.

1560 Brookhollow Drive, Suite 203

Santa Ana, CA 92705

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

b
i SN-54

i

FINAL REPORT

IMPROVED

TWO-DIMENSIONAL KINETICS (TDK)

Computer Program

Contract Number NAS8-35046

October 1983

t-

: 1

: Prepared For

George C. Marshall Space Flight Center

,, Marshall Space Flight Center, Alabama 35812

Prepared by

Gary R. Nickerson

Lanh D. Dang

Software and Engineering Associates, Inc. i

1560 Brookhollow Drive, Suite 203

i "

Santa Ana, CA 92705

'i

1

,,_.

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION _

i

!

|
®

FORWARD

•,,_ report describes work performed by Software and Engineer- _.

ing Associates, Inc. (SEA) under NASA contract NAS8-35046,

k

titled Improved Two-Dimenslonal Kinetics (TDK) Computer Program.

The TDK computer program is a primary tool in applying the

JANNAF liquid rocket engine performance prediction procedures.

" The purpose of this contract has been to improve the TDK computer program so that it can be applied to rocket engine designs ,,

of advanced type. In particular, future orbit transfer vehicles i

(OTV) will require rocket engines that operate at high expansion i

ratlo_ i.e. in excess of 200:I. Improvements to the TDK computer program are necessary if it is to be applied engines of

the OTV type. Thls study represents a first step in extending

the TDK computer program so that it can be used for these

operating regimes. ,}

j

_ The method of approac1_ used in this study has been to :

transfer technology from the Solid Performance Program (SPP) to _k

• the TDK computer program. The SPP was developed by SEA for the _ "

Air Force under contract F04611-77-C-0046. In this manner, the

. TDK computer program has been equipped wtth a boundary layer !

analysis, and a limited capability for treating two-phase flow _

,' • (

In addition, a method has been added that will automatically

calculate the effects of regneratlve cooling on thrust chamber

performance.

Project manager for this project has been Mr. Gary R. Nickersor. Dr. Lanh Dang has performed the computer programming i

and has provided engineering support. The project was very much

aided by the helpful support of the contract monitor, Mr. Klaus

:-!.Gross, and by Mr. A. Krebsbach.

0

i }

..
J, TABLE OF CONTENTS

" SECTION PAGE NO.

._ FOREWORD

_ ABBREVIATIONS

I. INTRODUCTION I

_ 2. METHOD OF APPROACH 5

_. 3- TECHNICAL DISCUSSION 7

" 3.1 Fluid Properties 7

3.2 The Boundary Layer Module (BLM) 15

• 3.3 Regenerative Cooling 17

4. CONCLUSION 20

5. RECOMMENDATIONS 22

t

5.1 Chemistry 22

_ 5.2 Low Density Flow Effects 24

,_ 5.3 Test Cases 25

k 5,4 Input and Output for TDK 26

•_.; 5.5 Documentation 28

REFERENCES

APPENDIX A - Revised TDK User's Manual

¢,

.g

1

1
'i

t

! ABBREVIATIONS

j BLIMP Boundary Layer Integral Matrix Procedure, JANNAF

, ccmputer program. _ _

' BLM Boundary Layer Module, computer program

JANNAF Joint Army-Navy-NASA-Air Force

M_C Method of Characteristics, module of SPP and TDK

_DE One-Dimensional Equilibrium, moGdle of SPP and TDK

.. ODK One-Dimensional Kinetics, module of SPP and TDK

PSS Performance Standardization Subcommittee of JANNAF

SEA Software and Engineering Associates, Inc.

' SPP Solid Performance Program, JANNAF computer program

TDE Two-Dimensional Equilitrium, module of TDK

TDK Two-Di_enslonal Kinetics, JANNAF computer program

|

I
I. INTRODUCTION

The Two-Dimensional Kinetics (TDK) I computer program is a

primary tool in applying the JANNAF liquid rocket thrust chamber

performance prediction methodology. 2 This computer program and

the performance prediction methodology were originally developed

under the auspices of the Performance Standardization Subcommittee (PSS) of the JANNAF. The goa. of the PSS is the development

of a methodology that includes all ,spects of rocket engine performance from analytical calculation co test measurements, that

is physically accurate and consistent, and that serves as an

!

industry and government reference.

f

l

Recent interest in rocket engines that operate at high

expanslcn ratio, such as most OTV designs, has required an

extension of the analytical methods used by the TDK computer

program. The study reported here is a first attempt in

extending TDK so that it is applicable to the operating

conditions imposed by these high perfo,mance OTV designs.

, High performance can be obtained with large area ratio

thrust chambers using oxygen with either hydrogen or hydrocarbon

[ fuels. Due to the large area ratios, the combustion products F

! are expanded to low pressures such that condensed phases of water may form in addition to soot particles with hydrocarbon fuel

,!! application. The existing TDK analytical nozzle flow model for

' liquid rocket engines did not possess the capability of particle

i flow simulation• However, a recently developed Solid motor {

r Ref. I. Nickerson, G. R., Coats, D. E., and Bartz, J. L.

"The Two-Dimenslonal Kinetic (TDK) Reference Computer

Program," Engineering and Programming Manual, Ultrasystems, Inc., December 1973, prepared for Contract No.

NAS9-12652, NASA JSC.

Ref. 2. "JANNAF Rocket Engine Performance Prediction and Calculation Manual" CPIA 246 April 1975

i

• t

l

|

I
[

Performance Program (SPP) does contain the simulation of particle flow 3. This capability, which assumes gas-par_c!e

._ equilibrium, has b_n _-_-°_.._..__,, from bhe SPP to the TDK

computer program.

{

The engine specific impulse value includes boundary layer

' losses. At present, this loss is identified by feeding results

from the TDK program solution to a boundary layer code which

calculates friction losses along the wall and heat energy

transferred through the wall. In a regeneratlvely cooled

engine, most of the heat energy transferred to the wall is

returned to the main combustion chamber in the form of increased

propellant enthalpy. In addition, the friction effect requires

a displacement of the wall contour in order to conserve mass

flow through the nozzle. Both phenomena necessitate the

.. recalculation of the two-dlm_nslonal flow field at least one

time to achieve a mass flow and energy balance. At present,

this process is conducted by iterating using two computer

programs, the two-dimenslonal kinetics (TDK) and the Boundary

Layer Integral Matzlx Procedure (BLIMP) program 4. Both of these

programs are quite complex, especially the boundary layer code,

and they must be run in series.

For study purposes, a simplified approach is very useful,

especially when many computer runs are required with only one ur

!! a few input parameters to be changed at a time The

Ref. 3. Nickerson, G.&R., Coats, D. E., Hermsen, R. W., "A Computer Program for tile Prediction of Solid Propellant

Rocket Motor Performance", Volumes I, II, III, Interim

Technical Report, for Air Force Rocket Propulsion Laboratory, AFRPL-TR-80-3_, April 1981.

Ref. 4. Evans, R., "Boundary Layer Integral Matrix Procedure"

BLIMP-J User's Manual, Aerotherm Division/Acurex Corporation, Prepared for NASA George C. Marshall Space

Flight Center under Contract NAS8-30930, July 1975.

g.

2

l
On_-Dimenslonal Equilibrium (ODE) module, the One-Dimenslonal

Kinetics (ODK) module, and the Two-Dimenslonal Equilibrium (TDE)

module are such simplified options within the TDK computer

various simplified options. However, the program has a large

computer core demand, needs long execution times, and the input

is rather difficult to prepare.

Recently, a new Boundary Layer Module (BLM) was developed

for solid motor nozzles. This program holds all the essential

analytical and operating features to produce an efficient coupling with the TDK program. As part of the study reported here,

the BLM was taken from the SPF and coupled to the TDK program.

The capability of treating regeneratively cooled nozzle walls

was a_ded to both BLM and TDK.

The work carried out in this study is summarized below.

a) The current method of condensed phaJe flow treatment in

the ODE and ODK modules of the SPP program have been

incorporated in the TDK program with appropriate

changes. Specific attention has been given to the

presence of water droplets and ice crystals and of

solid carbon particulates.

b) Using subroutines existing in the SPP, the ODE module

of TDK has been modified so that it will compute transport properties for the nozzle exhaust composition.

This information is required by the BLM. Numerous other

features contained in the SPP, such as wall contour

options, have also been transferred to TDK.

c) The ODE module of TDK has been modified so that it will

provide tables of gas properties versus temperature for ;

the stream tube mixture ratio adjacent to the nozzle

wall. This information is required by the BLM.

i

J

3
I

d) The Boundary Layer Module (BLM) of the SPP has been

i

i coupled with the TDK _rogram such that it will auto- .}

_ r,,atically calculate the wall boundary layer after

,_ execution of t_e TDE ur TDK modules, if so desired. The

] resulting wall displacement and the heat transferred

the wall the level of the through increasing energy

,I cooling propellant are used to repeat a TDE or TDK

i

, cal_ulatlon once with the appropriate parameters

(wall contour and propellant enthalpy) updated.

e) The boundary layer module has been equipped with a

feature to account for the heat transfer along wall

contour sections where regenerate cooling takes place.

The wall heat flux, as determined by the BLM, is

integrated and the result (multlpled by an input

efficiency factor) is returned to the maln combustion

chamber in the form of increased propellant enthalpy.

f) Two proof cases have been run on the revised program

for the purpose of verification. The first case Is a

Pratt _ Whitney RL-IO engine configured to operate at

an expansion ratio of 205. The second case is a

Rocketdyne Advanced Space Engine (ASE) configured to

operate at an expansion ratio of 400. Performance

measurements exist for both of these engines.

g) A User's Manual has been prepared for the improved TDK

program. Thls has been done by revising Section 6 of

Reference I. A copy of this User's Manual is attached

as Appendix A. !

h) The Improved TDK computer program has been delivered to

NASA-MSFC for use on the UNIVAC 1100/82 computer. _he

program is also operational at SEA on the DEC VAX/780

computer. l

Technical details of the above work items are reported in

Sections 2 and 3. !

4

®
2. METHOD OF APPROACH.

|

! Prior to the work performed during this contract: two

_ versions of the TDK program have been generally available. The

' first of these is the version documented in Reference I. A

number of improvements have been made to this program by SEA,

such as those described in Reference 5. However, the basic

program is as presented in Reference I. A second version of the

TDK program has been developed by NASA-MSFC and has been

distributed by them. This version of TDK contains many

, programming modifications. For the most part, these

modifications are improvement_ to the internal structure of the

program and its input and output features. The basic analytical

models have not been changed. The program is undocumented.

For this contract it was necessary to combine the best

. , features of both of tne above programs, fo-mlng a "baseline"

computer program, and to then transfer advanced features

contained in SPP to this baseline program. Most of the features

of interest are contained in the ODE and ODK modules of SPP and

concern fluid chemistry.

_ : Features of SPP other than the fluid chemistry were also j

transferred to TDK. In particular, the wall geometry options in

SPP were installed into TDK. First, all of the wall geometry

options were moved forward in the code and unified in one

Ref. 5. Nickerson, G. R., "Modification to the Two-Di_,enslonal

. Kinetics (TDK) Computer Program", Software and Engineering Associates, Inc., prepared for NASA George C. |

Marshall Space Flight Center, under Contract No. :

NAS8-31988, October 1976.

i :

i 5 t '

: i -
Namelist input data set, called $DATA. Next, the splJn_ £1t

option for ODK was modified so that the ODK printout could be

requested at input values of area ratty. _ ^-+_ ......... _::+n for a cofle

with specified end point was added to ODK. An option for a wall

defined by a skewed-parabola was transferred from SPP and added ] _

to both ODK and TDK. These geometry options are described in "t !:

the revised User's Manual, Section 6.3.3 (see Appendix A).

The "problem card" feature of TDK was replaced with _

"module selection" feature of the type used by SPP, i.e., module

selection by using input flags. This method allows greater

flexibility than the "problem card" method, and is described in

the revised User's Manual, Section 6.3.1.

Wi;h the completion of the transfer of technology from SPP,

the condensed flow capability and the transport propertv

calculations items 1.a and 1.b) were essentially complete. A

discussion of the ga_-partlcle properties now used in TDK is

presented in Section 3.1.

The requirements for coupling BLM with TDK go well beyond

the usage of BLM in SPP. SPP does not require a second pass

through the Method of Characteristics (MOC) solution, and there

is no regen cooling to consider. These two topics, BLM and

regen cooling, are discussed in Section 3.2 and 3.3.

Further work is being carried out on TDK by SEA under

contract NAS8-34974. The work being done is primarily concerned

with adding a shock-wave capability to TDK. Work is being

coordinated between the two contracts so that one final computer

program will result.

L
3. TECHNICAL DISCUSSION.

!

The technical effor_ t_ discussed under the three topics

_' .... below

!

I Fluid Properties,

The Boundary Layer Module, and

Regenerat_ve Cooling.

r

i

3.1 Fluid Properties.

In order to expand the fluid property capabilities of TDK,

changes of three basic types were made to the program, as

follows:

a) The calculation of transport properties (gas vlscosity_

conductivity, and Prandtl number):

_" b) The calculation of gas properties adjacent to the

nozzle wall, and

b

c) Core flow gas-particle equilibrium chemistry for the

ODK, TDE, and TDK modules, i

Each of thes, items is discussed in the following subsections.
i 3.1a Near Wall Gas Transport Propertie3.

i

i Values of gas viscosity, u , gas conductivity, < , P_andtl

number, Pr, are required by BLM. These transn_et, prnp_,_oo_ ,._r_._

evaluated along the wall streamline as a function of temperature

using the ODE module. It zs assummed that the expansion is in

i_ equilibrium, including condensed species. 2n the model these

.!

:i properties are then computed as "frozen" properties using the

local gas composition with condensed phases included.

'i The viscosity and thermal conductivity of the individual gaseous

species are calculated from formu]as given in Reference 6 as

-!

! follows:

|

!

4 "158 22 x _0 -8 V,-_wiT OORFI(_A POOLR QUALITY PAGZ

_i = 2

_iR CP i

<i = M--_--i('45 + 1.32 (_/Mw.1))

The requi,ed Lennard Jones parameters, (qi,f2i) are internally

stored in the computer program for 206 5as phase species. (See

Subroutlne MUK, Volume II, of Reference 3, for a list of the

species.) The viscosity of the mixture is c_iculated from

Wllke's semi-,mplrical formula 7. i

U = =I _i (I + I ¢iJ X-_.)

J_i

where N is the number of species, xi the mole fraction of

species i, and _iJ is defined by:

Ref. 6. Svehla, R. A., "Estimated Viscosities and Thermal Conductivlties of Gases at High Temperatures," NASA

TR-132, 1962.

/

Ref. 7. Bird, R. B., Stewart, U.E., and Lightfoot, E. N.,

Transport Phenomena, John Wiley & Sons, 1960.

[

3

i
I ORI_NAL PAGE i/_ 2

I J _,,= _._,m_ conductivity, _, is based on _i_ equativn given by

i" Mason and Saxena 8 which is a sl:ght modification of Eucken's

relation,

:, N N xj ] -I

,

i=I j=1

J_

x

i J

The results calculated as described above are used to

. provide the BLM with properties uslnF the following procedure.

.. The viscosity at the nozzle throat, u*, and the

corresponding temperature, T*, are calculated. Using these

values, an exponant,_ , is computed such that the expression

p : p* (T/T*)_ i

provides a best fit in a least square manner to the chamber and

)'L

e.:it values for viscosity. Next, a constant value for Prandtl J,

number is computed as I

Pr :

where _ , _ , and Cp are evaluated at the nozzle throat. The

i "frozen" Cp value is used. The values transmitted to BLM are

. then _*, T*, _ , and Pr*. Actually, BLM only uses the ratio

,, Pr/u, and does not require K or the frozen C versus T. I

D p , t

Ref. 8. Mason, E.A., and Saxena, S. C., Physics of Fluids,

Vol. I, No. 5, pp. 361-369, 1958.

I

I _ :
3.1b Near Wall Gas-Particle Mixture Properties .

Values of specific heat at ccnstant pressure, Cp, and ratio

u_ specific heat_, Y , static en_haipy, h , and the gas constant

R, are required by BLM. These properties are evaluated along

! the wall streamline as a function of temperature using the ODE

module. The tables are prepared using a series of (T,S)

: equilibrium calculations, where T varies from 600°R to 7000°R at

200°R increments. The chamber entropy value is used for S.

Values at I00°R are then extrapolated and added to the table.

; The table is printed with the BLM output. An example of this

output is presented in Figure I.

Since the ODE module did not contain a (T,S) option, it was

ad6ed using the following procedure. Using known values of Pa'

'" Ta, and Ya' and the given value of temperature, T, a first

estimate for pressure p(1) was found as

ya/ ( Ya-1 )

p(1) = Pa (T/Ta)"

The (T,P) option of ODE is used to obtain S(i) as a function of

_: p(i). The procedure is iterated using the secant method

: (subroutine ITER plus a driver) to find p(i) such that

l(s(i)-Sc)/J<Sc5 E-5

where Sc is the chamber entropy. The procedure is repeated for

each temperature in these tables. The procedure is internal to

. the program and not callable through the ODE input.

J

If the chemical system contains a condensed phase, then

equilibrium solutions made during phase change can yield values

; for Y that are unacceptable to BLM, e.g., values of Y < I.

i

i

I0
t

OF POOR QUALITY

_QO_O_Q QQ Q_ OQQQ_ QO _

m

_ o_00000o0_o0_0000o_000_oo_o_0

_ _°o_o°oo °° oo°_°°o°o °_°=° °°o°_°°°°_°°° °**° °.°°___°°

_ _0 0_ 00 0_000 000_

_2_222_222_gg_gggggg;;,1¢_g;d_gg

.

__77_ | :_:::: II1.*I °°-°°-_*II_::'*II*II*IIII °°°° 011 _°°°°°°°°°°°° °°°° °.°°°°

_0_0 000_ 00000 00 0000

__ a "'''""''"' '"""""'" '_ "_

• , _ _0___ _____

. "_:::'®-= oo °o

iIIIIIiIIIIIiIIIIIIlillllltll {

©

I _ ;

!i "

eeo_oe_eoeooe ee_eoeeeelo_oo_eol_e

{ ' :;

! ,

i '

.... s , ,
Since condensation is an isothermal process, using (T,S)

solutions avoid this problem. It also avoids the "temperature

out of range" problem that can occur had other, existing options

!

The fluid properties shown in "able 1 are h, _ , <, Cp,y ,

and R versus T°R. The values of u and < are prepared as

! described in Section 3.1a. The values for h, Cp, y , and R are

_' prepared as described above, i.e., they are equilibrium

properties Including condensed phases (no gas particle lag).

• !

I

I

12 _
, 3.1c Core Flow Gas-Partlcle Equilibrium Chemistry.

The TDK program described in Reference I contains only the }

I mosU rudimentary capability to compute the effects of two-phase

l flow (gas plus condensed phases) on nozzle performance. In that

program only the ODE module is capable of considering the

existence of different phases. This is done by treating the

entire chemical system as if it were in chemical equilibrium and

the particulate and gas phases as if they were in dynamic and

thermal equilibrium. For high pressure systems and where the

characteristic particle sizes are small, the above assumptions

are quite reasonable. For systems where there is a significant

departure from either of the above assumptions, then the TDK

code described in Reference I does not have the capability to

even assess the importance of these effects, let alone to

quantitatively predict the magnitude of them. Systems whe.'e

two-phase flow phenomena could be of importance are those with

soot formation using hydrocarbon propellants, and with the m

formation of water droplets and ice in low pressure, high

expansion ratio H2/O 2 systems.

In order to improve the capability of TDK with respect to

_ two-phase flow, the ODK module of SPP was installed in TDK. The J •

chemistry subroutines of ODK also serve the same function for i

TDK, so that TDK has been given the same two-phase flow (no lag)

' capability as ODK. Unlike TDK, the SPP has no two-dlmensional

kinetics capability.

The Two-Dimenslonal Equilibr Jum (TDE) option has been

: updated to consider two-phase flow in the same manner as the ODE

_ . module, but for a two-dlmensional calculation. Source flow , i

calculations were carried out to verify the program. Under this

|

, assumption TDE was shown to calculate the same results as ODE ,

"-. for all streamlines. The TDE capability allows the user to ,

_T

)

assess the effect of particles on specific impulse, and also to

; indicate the possibility of the onset of condensation. Further

:' _ development along these lines would require the generation of 1

!

't 13 '

t_m v -.. __.
P

kinetic models to predict both condensazion and mass transfer

; between phases and is beyond the scope of this study. Implicit

i in the above is the assumption that gas-particle lag effects are

................... _w_,, is violated Lhen the _ coae should

be used to estimate the performance loss because the two-phase [

flow loss becomes the major thrust loss in the system.

++

&2

,I

'+ '+

z , .

+

J

14
3._ The Boundary Layer Module (BtM)

The BLM was developed for SEA by CBC Enterprises.

Documentation for the BLM as delivered to SEA is presented in

Reference 9. The purpose of the BLM ks to compute compressible

laminar and turbulent flows in axisymmetric nozzles. It can

also be used to calculate two-dimensional and axisymmetric

external flows. The method utilizes an efficient two-point

finite difference method developed by Keller and Cebeci I0. r

Turbulence modeling is achieved through the use of the

Cebeci-Smlth eddy-viscosity formulation 11 which has been tested

for a large class of flows with various boundary conditions.

The BLM has been modified by SEA to interface automatically i

with the SPP and with the TDK programs. TDK supplies all of

the input:, required by BLM.

In order to be able to use BLM for large expansion ratio

k nozzles, the boundary layer calculation was divided into

adjacent axial segments, and the calculation restarted

automatically at each segment. This feature is also useful when

nozzles with regen cooling are being analyzed. A segment can be

_i_. placed at the start (or end) of the cooling circuit where there

_ is a discontinuity in the wall temperature (or heat flux), and I

< the calculations can be restarted with an integration step size _ !

i

, change.

Ref. 9. Cebeci, T., "Boundary Layer Analysis Module", prepared

for Software Engineering Associates, Inc., January

1982.

Ref. 10. Keller, H. B., and Cebeci, T., "Accurate Numerical Met-

, hods for Boundary Layer Flows, Part 2, Two-Dimenslonal

Turbulent Flows", AIAA J., 10, 1972, p. 1193. i

o Ref. 11. Cebeci, T., and Smith, A. M. 0., Analysls of Turbulent

. Boundary Layers, Academic Press, N.Y,, 1974.

• !

v t

i 15 L

!
At high expansion ratio , it is possible for the gas density

in the boundary layer to become very low. If the mean free path

in the boundary layer approximates the wall roughness height,

the non-sliP condition at the wall can break down. io ald in

the assessment of this condition, the mean free path, _ , at the

edge of the boundary layer is calculated and printed, where

: 1.26 U/ ( P%/_ ) (ft)

1,

At the end of the nozzle, the Knudsen number, Kn, based on

displacement thickness, _*, is printed so that the approach to

ratified flow can be monitored, where

, i

Kn : _/ 6

e

The following options for plotted output have been added to

the BLM by SEA:

I) Momentum thickness, e, versus axial position.

7 2) Displacement thickness, 6", versus axial position.

• 3) Wall temperature, Tw, versus axial position

4) Velocity profiles at specified are ratios, or at

_- specified axial locations.

" 5) Temperature profiles at specified area ratios, or at

, specified axial locations.

The analysis used by the BLM is described in Reference 9.

Usage of the program within TDK is descrlbed in Section 6.8 of

the User's Manual (see Appendix A), as follows:

: 6.8.1 BLM Ga3 Properties

6.8.2 Boundary Layer Edge Conditions

6.8.3 Integration Step Size Control !

6.8.4 Regenerative Cooling Heat Transfer

6.8.5 BLM Plotted Output

16
3.3 Regenerative Cooling

When an engine is cooled using a regenerative device,

__ .............. y _) i_ routed around the nozzle so that

,

heat is transmitted from the boundary layer to the coolant .

This heat is then returned to the combustion chamber in the form

of increased propellant enthalpy. When the nozzle wall

temperatures are assumed known (IHFLAG = 0 option), the BLM will

calculate the heat flux from the boundary layer to the wall,

_w(BTU/ft -sec). These values can also be input directly

(IHFLAG = I option). If the coolant circuit extends from

position xo to position xe and operates at an efficiency, _ ,

then the propellant enthalpy entering the chamber will be

increased by

" X

e

AH : _ _ / _wdA (BTU/Ibm)

k: _T Xo

where

_T is the total engine mass flow rate :

•" dA is the nozzle surface area differential, 2_rdx

Using the method outlined above, the BLM will compute increments

of propellant enthalpy for up to 3 fuel or oxidizer circuits and

print out the resultant enthaipy increments. These can be added

to a later computer run by using the DELHI(1) input array. If

BLM is to be automatically rerun, then the enthalpy increments

will automatically be stored into DELHI(1) for the second pass

_ through ODE, ODK, and TDK. These enthalpy increments can be

'i calculated in two ways. If the enthalpy increase is distributed

I equally throughout the chamber, then

l

: * Heat c,m be extra, rod from the boundary layer as a fun_tlon

of length (BLM analysis). The core flow (TDK analysis) does

not include heat transfer effects other than to modify the

t

initial value for chamber enthalpy used by TDK .

L

17

i
!(9 0

: /

AH= = AH

I

i.e.

DELHI(1) : AH, AH, .... etc.

:' The second method is to assume that a fuel circuit adds

enthalpy only to fuel, and an ox circuit adds enthalpy only to

ox. It follows that

for a fuel circuit i

i

r+1

"'._ AH i = (r-_T) AH

a. and for an ox circuit

_= r+1 rl

• AH i = (r-q-_) _- AN

)._! where r i is the mixture ratio of zone i and r is the overall

" chamber mixture ratio.

, For either method, the steady state engine cycle balance can

be approximated as follows. First, calculate "adjusted tank

enthalpies" for the fuel and for the oxidizer and input these on

the reactant cards. These values must approximate the energy

content of the propellant entering the main combustion chamber 'i

accounting for all energy gains and losses, except heat returned ir ":!

._ to the main combustion chamber by the regen cooling clrcult(s). ,

Estimates for these amounts _re to be entered using the DELHI(1) i

input array. An estimate o' zero is usually satisfactory. Corrected estimates will be calculated by BLM and stored in
i DELHI(1) for a second pass through TDK (or TDE). A second pass

using these values will be executed automatically if IRPEAT = I

i was input in the SDATA namelist.

i A second pass can be made without adjusting the enthalpy by

1 ",

setting IRPEAT = 2. In this case neither the ODE nor ODK runs

: will be repeated. The nozzle wall, however, will be displaced

for TDK (or TDE). This option is useful If an adiabatic wall

•, (zero heat flux) case is run.

The boundary layer calculations are automatically started at

the downstream end of the combustion chamber (position ECRAT of

Figure 6-I, Appendix A). However, an option has been provided

that allows the user to input values for the upstream boundary

layer edge conditions and then start the boundary layer further

upstream (see item IOFF, Section 6.3.2, Appendix A). This

option can be important when calculating heat trrr-fer for the

chamber-throat wall assembly. %
4. CONCLUSIONS.

Work items a) through h) described in Section I of this

report have been completed T_ _3 _...._^_ '.... technical

, improvements to the TDK computer program that are discussed

below.

TDK has been equipped with a limited capability (zero

P velocity and thermal lag) for treating rocket nozzle exhaust

flow containing condensed phase species. This hae been

accomplished by a transfer of technology from the SPP 3 to TDK.

i

A boundary layer program, known as BLM 9, has been installed

in TDK as a module. The BLM was developed for SPP in response

to requirements set forth by experts in the field at the 2nd SPP

Workshop 12. Further development of this module has been carried

out by SEA to make it applicable to high area ratio liquid

rocket engines with regen cooling.

TDK has been modified to incorporate a capability for calculating the effect of regen cooling on engine performance. The

nozzle wall temperature (or heat flux) profile must be specified

_ by the user. The engine cycle balance must also be performed

J

external to the program.

The CPIA 246 standard procedure for computing engine

performance 2 has been automated within TDK; but with BLM 9

t

substituted for BLIMP 4. A complete TDK-BLM-TDK calculation can

be carried out in one computer run with a minimum of user input.

Two sample cases were run for the purpose of demonstrating

the program. These are I) the Pratt and Whitney RLI0 engine ,

operating at an area ratio of 205.03:1 and 2) the Rocketdyne
i

! Advanced Space Engine (ASE), operating at an area ratio of

I 400.71:1. Results of these computer runs have been sent to

! NASA-MSFC for evaluation.

The improved TDK program has been delivered to NASA-MSFC

converted for use on the Univac 1100/80 computer using the FTN

compiler. The program Is available from SEA for the DEC VAX 780

computer_

A User's Manual for these programs are presented in Appendix

A.

f

!,

!

.!

!

q

', !

i

21 !
5. RECOMMENDATIONS.

Recommendations concerning the followlng topics are discussed Oelow: chemistry, low density, flow effects, test c__ses:

, Input/output, and documentation. No recommendations are m, de

: here regarding SHOCK waves since TDK is currently undergoing

modification for this purpose under Contract NAS6-34974.

5. I Chemistry.

The TDK program contains two chemistry modules, which are I)

the chemical equilibrium solution subroutines of ODE, and 2) the

streamline chemical kinetics subroutines of ODK. These latter

subroutines are also used in a modifte4 form to compute klnet_cs

in a TDK calculation. No improvements to the ¢DE chemistry are

recommended. However, several important improvements are

recommended for the ODK (and TDK) chemistry.

ODK should be modified to Include input of "global" reactions and "hetrogeneous" reactions. For example, hydrocarbon

decomposition can be characterized by r_actlons such as:

. (CnH m) --_ CH_, H2, other fragments. !.

.

In order to effectively model the chemistry of propellants such

as LOX/RP-I, it is often necessary to include reactions of this

type. Further examples are the condensation of water, and also

the kinetics of soc_ formation. These processes can be

important in rocket engines. Further work is needed which will

' allow ODK to be used to assess the effects of these proceesses

on rocket engine performance.

', A more advanced reaction rate processc,- is available in the

GKAP computer program. It Is recommend_.d that tnis processor be

installed in ODK. This will add the following capabilities to

ODK:

b

i

-I

t :

"' 22 : i

4 D

I
a) Improved treatment of third body type reactions (rate

: ratios asslgn_d with each reaction).

I , b) Input of reaction rates of the Landau-Teller form

i _necessary for _st T-V and V-V reactions).

._ c) radlatlv_ r_action_, such as

HF(I) --- HF(O) + PHOTON

_ The new rate processor will provide a firm basis for

expanding the chemical kinetics capability of ODK.

Other recommendations in the chemistry area are: I) providing thermodynamic data for' the temperatures below 100°K, 2)

replacing the thermodynamic data library with the latest data

available from the NASA LRC, 3) updating of the kinetic rate

data for reactions in the CFHNO systems that are important in

rocket performance calculations. These items should be done on a

.. "first cut" "'-sis and then reviewed by the JANNAF membership.

|

i

23 _ ,,
5.2 Low Density Flow Effects.

Exhaust nozzle designs for future space engines may operate

at expansion r_tios so high that low density flow effects must

be considered. If so, the following questions must be examined:

a) At what conditions do low density effects at the nozzle

wall require that a sllp condition be imposed?

b) Where does transition to free molecular flow cause a

breakdown of the continuum flow assumptioz?

o) Is the boundary layer interaction with the core flow

sufficiently weak so that the JANNAF procedures can be

used with confidence?

Questiors a) and b) above, can be answered in part by examining the mean free path based on the average gas molecular

weight. This item has been added to the BLM output along the

boundary layer edge. For the boundary layer, question b) can be

answered in part by examining the Knudsen number based on

displacement thickness. This item has also been added to the

b

BLM output.

Question c) is more difficult in that it requires an

analysis of the boundary layer-core flow interaction. It is

recommended that an analysis of this interaction be conducted.
5.3 Test Cases.

The JANNAF standard performance prediction procedure was

applied to two engines (the RLI0 and the ASE) using the Imoroved

TDK program. Th_ BLM was used rather than BLIMP-J 4. Input data

i

for the cases, including data on the engine cycle balance, was

provided by NASA/MSFC.

It is recommended that further cases be run for the purpose

of obtaining estimates of the accuracy of ODK, TDK, and BLM as a

function of items that control the numerical methods. Cases

, should be run to determine if all of the program options work

properly.

Cases should also be run for the purpose of determining the

role of the boundary layer in performance prediction. The

?- following questions need to be addressed:

i, I) How do the BLM predictions compare with BLIMP-J?

" 2) How do BLM calculations with regen cooling compare with

, adiabatic wall calculations?

4.

3) What is the magnitude of performance gains due to

"enthalpy pumping" in regen cooled engines?

i

i

!
i

5_4 Input and Output for 7DK.

i

I The following recommendations are made with respect to input

and OutPut fOP TDI( and it._ m_dn')_q

I

• a) A summary pa_.e should be added at the end of the output

Which lists in a clear format all of the key

performance results. This page would correspond to the

summary page listed by the SPP.

, b) Some, or all, of the following computer plots should be

added to the program:

Isp versus Xwall and e

• " Owall, rwall versus Xwall

_ P,V,M, versus Xwall and Xaxis

P and M con;our plots

_._ P,V,M, versus r at Xexit

J

MOC plots for a window

c) The linkage data files of S[_ have been installed in

TDK (see Reference 3, Volume III, Section 2.9). This

capability allows a module of TDK to be run from a file

)

i

!

26
++ .

generated on a previous run. To _e completely

effective the file structure and programming must be

modified specifically for TDK, and documented. This is

recommended.

d) The BLM output should be reviewed for the purpose of

improving the format and to determine which quantities

should be added, or deleted.

J

+

,

/ !

t

i

i

I

i

+ i

|

J

p

I | ,

: i "-
5.5 Documentation.

A complete set of manuals for TDK should be written which

............... _ topics:

I) Methods of analysis (all modules).

2) Program structure and subroutine write-ups.

3) User's Manual.

The documents should be written so that new users of the

computer program can be systematically guided through the principles involved in the analysis. The analytical procedures

should be related to the thrust chamber performance prediction

methodology defined in CPIA 246, Reference 2. Test cases should

be included that demonstrate the differen, yroblem types solved

by the program. Text shouiu be included describing each test

case; its purpose, the engine type and c aracteristics, unique

features,interpretation of output -esul_s, etc.

!

i

28
REFERENCES

II I. Nickerson, G. R., Coats, D. E., and Bartz, J. L. "The

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

Engineering and Programming Manual, Ultrasystems, Inc., De-

: cumber i973, prepared for Contract No. NAS9-12652, NASA

JSC.

;' 2. "JANNAF Rocket Engine Performance Prediction and Calculation Manual", CPIA 246, April 1975.

• [

_

'_,_ 3. Nickerson, G. R., Coats, D. E., Hermsen, R. W., "A Computer

,_ Program for the Prediction of Solid Propellant Rocket Motor

: Performance", Volumes I, II, III, Interim Technical Report,

: for Air Force Rocket Propulsion Laboratory, AFRPL-TR-80-34,

, April 1981.

4. Evans, R. M., "Boundary Layer Integral Matrix Procedure",

BLIMP-J User's Manual, Aerotherm Division/Acurex Corporation, Prepared for NASA George C. Marshall Space Flight

Center under Contract NAS8-30930, July 1975.

] 5. Nickerson, G.R., "Modification to the Two-Dimensional

i Kinetics (TDK) Computer Program", Software and Engineering

, Associates, Inc., prepared for NASA George C. Marshall

_i Space Flight Center_ under Contract No. NAS8-31988, October

I 4976.

; 6. Svehla, R. A., "Estimated Viscosities and Thermal Conduc-

: tivities of Gases at High Temperatures," NASA TR-132, 1962. ,

7. Bird, R. B., Stewart, U. E., and Lightfoot, E. N., Transport "

;_ Phenomena, John Wiley & Sons, 1960.

8. Mason, E. A., and Saxena, S. C., P_ysics of Fluids, Vol. I, I

.i No. 5, pp. 361-369, 1958.

i 9. Cebeci, T., "Boundary Layer Analysis Module", prepared for

I Software Engineering Associates, Inc. January 1982. !

! 10. Keller, H. B., and Cebeci, T., "Accurate Numerical Methods

' fcr Boundary Layer Flows, Part 2, Two-Dimensional Turbulent

i Flows" I , AIAA J., 10, 1972, p. 1193.

!

11. Cebeci, T., and Smith, A. M. 0., Analysis of Turbulent

i Boundary Layers, Academic Press, N.Y., 1974. _ :

J 12. Minutes for the Second Workshop Conference,Improved Solid , '

'1 Performance Program, 7 September 1978, Essex House, Lancas- i

ter, CA, available from AFRPL. _]

|

!

I

t
r

APPENDIX A

Section 6

Engineering and ProgrammingManual

TOE

- Two-DimensionalKinetic Reference

t

Computer Program

_-

J

_.tL

G. R. Nickerson

, D.E. Coats

, L.D. l_.g ,

i

!

Software and EngineeringAssociates,Inc. I

: 1560 BrookhollowDrive, Suite 203

Santa Aria,California 92705

L_

,i
6.0 PROGRAM USer'S MANUAL 6-01

6.1 T_ermodynamlcData 6-04

6.1.1 ThermodynamicData Below 500OK 6-10

6.2 Title Cards 6-13

6.3 DATA Directive and $DATA Namelist Input 6-14

6.3.1 Specificationof Modules to be Executed 6-15

6.3.2 Inputs for Control for the Program 6-18

I 6.3.3 Specificationof Nozzle Geometry 6-19

6.3.3.1 Exhaust Nozzle Geometry Specification, 6-22

, for _DK and the _ Modules

t

i 6.4 _DE Input Data 6-24

! 6.4.1 Reactants Cards 6-24

f

6.4.2 _IT and INSERT Cards 6-28

i

6.4.2.1 _MIT Cards 6-28 E

6.4,2.2 INSET Cards 6-28

6.4.3 _DE Namellst Input 6-._0

6.4.3.1 Option to Punch Tables for Boundary 6-34

Layer Program Input

6.5 _K Input Data 6-35

6.5.1 Species 6-35 ,

6.5.1.1 _OK Option for Input of Initial Species 6-36

Concantratl_--

6.5.2 REACTIONS 6-37 I

%

6.5.2.1 REACTIONS Card 6-38

6.5.2.2 Reaction Format 6-38

6.5.2.3 E_D TBR FLFAX 6-39

6.5.2.4 LAST REAX Card 6-39

6.5.2.5 Reaction Rate Data 6-40

6.5.2.6 Inert Species Option 6-40

6.5.2.7 _lird Body Reaction Rate Ratios 6-40 _

6.5.3 _)DK Namellst Input 6-44 _,

6.5.3.1 Specificationof Nozzle Geometry 6-44 '

6.5.3.2 IntegrationControl 6-45

6.5.3.3 Print Control 6-46

6.5.3.4 Species Selectionand Mole/Mass 6-48 _

Fraction Check _

6.5.3.5 @DK Problem Input 6-49

6.5.3.6 Mass Averaged _K ISP 6-50 ;

i
Page No.

( 6.6 S/RANS Namellst Input 6-51

6.7.1 CharacteristicsMesh Control 6-54

6.7.2 Print Control 6-55

6.7.3Inputs_romDER 6-56

6.7.4 Exit Plane Option 6-57

_ 6.7.5 Punch Initial Line 6-57

6.8 Boundary Layer Module (BLM) Input Data, SBLM 6-.58

6.8.1 BLM Gas Properties 6-59

6.8.2 Boundary Layer F_ Conditions 6-61

6.8.3 IntegrationStep Size Control 6-63

6.8.4 Regenerative.Cooli_ Heat Trensfer 6-64

6.8.5 BLM Plotted Output 6-67

6.9 Special Options 6-72

6.9.1 Constant Properties Gas Option 6-72

6.10 InitialValues for _ $_K, $TRANS, and STDK Inputs 6-74

J,
LIST OF FIGURES

No. Title PaKe No.

6-I Nozzle Geometry, all Coordlante Values are Normalized 6-20

by RSI = rt

6-2 Boundary Layer Momentum Thickness vs. Axial Position 6-68

6-5 Bom_ary Layer displacement Thickness vs. Axial 6-69

Position

6-4 Wall Temperature (Input) vs. Axial Position 6-70

6-5 Velocity and Temperature Profiles at a Given Area 6-71

' Ratio

LIST OF TABLES

• No_. Title Pa_e No..

J

6-1 Input Data Set Description 6-02

: 6-2 Format for ThermodynamicData Cards 6-06

i 6-3 Thermo Data Cards for an 02/H2 Propellant 6-07 :

6-4 Species with Thermody_ImicData Provided 6-08

_._.6..-_ _o_=_ ¢, _,_ _ _o_ o_j_ _1_ Propellant

6-6 Usage of the Module Flags 6-16

,, 6-7 Reactants Cards 6-25

6-8 Listing of Sample Reactants Cards 6-26

6-9 Variables in _DE Namelist 6-32

6-10 Reactionsand Rate Data for C, CL, F, H, N, and 0 6-41

Systems

• 6-11 Listing of Sample Reactions Cards for an 02/_ 6-43

=' Propellant

6-12 Sample Case for the Constant PropertiesGas Option 6-75

I
i 6.0 R_XR&_ USER'S MANUAL.

, Descriptionof the ComputerProgramInput.

The TDK computerprogramconsistsof fivemodules,ODE, ODK,TRANS,MOC, and

, BLM. All of these modules are required to perform a complete two dimensional

non-equilibrium nozzle performance calculatior,with a boundary layer. Various

options exist in the program, however, which exercise the above modules alone, in

part, or in combination.

Data is readby the programsequentiallyin the orderrequiredfor the executionof the modules. _is orderis as follows:

_ermodynemlcdata,

Datecommonto the modules,

ODE moduleinputs,

., ODKmodule ir@u+a,

TR_S module inputs,

_: MOC moduleinputs,and

BLM moduleinputs.

A more detailed descriptionof these input data sets is presented in Table 6-I.

[" The documentation in which each of the data sets is completely described is also

indicated in Table 6-I

Of the data sets listed in Table 6-I, only the $DATA data set is required for

every computer run. Input of the other data sets is required only if the options

they contain are to be used. For example, input of the thermodynamicdata is not

required if an existing thermodynamicdata file is to be used.
Table 6-1. Input Data Set Description

Card Input Section No.t Description

6.1, thermodynamicdata cards, see Tables 6-2 and 6-3

e

e

D_

LOW T CR_S 6.1.1, extension of thermodynamicdata to temperatures

. below _O°K, see Table 6-5

e

END LOW T CI_S

TITLE 6.2, one or more title cards

DATA 6.3, data directive card

$DATA 6.3, data namellst for module selection, and geometry

SEND

REACTANTS 6.4, reactantsdirective card

• 6.4.1, reactantscards, see Tables 2-6 and 2-7

• 6.4.1, b1_nk card required to end reactants cards

0MIT 6.4.2, cards to omit species

INSE_T 6.4.2, cards to insert species

_AMELIST3 6.4.3, _DE directivecard

SODE 6.4.3, _DE ham,list

SPECIES 6.5.1, species cards for _DE

e

w

REACTIONS 6.5.2, reaction cards for _DK

@

e

LAST REAX

INERTS 6.5.2.6, inerts cards for _DK. (to inert those species that

• are not named in reactions) ',

@

!

t }

< i

6-2
i@

Card Input Section No., Description

THIRD BODY 6.5.2.7, reaction rate ratios for thlr_ h_!es

LAST CARD

$ODK 6.5.3 _DK module namelist

$TRANS 6.6 _RANS module namelist

SEND

SMOC 6.7 M_C module nsmelist

SEND

SBLM 6.8 BLM module namelist

SEND

' Table 6-I can be used as a guide when preparing input for given problem• It

_ lists the data sets in the order in which they must appear in the data deck, and

also shows the special cards which must appear in each s&t (first card, last card,

etc.) if the program is to function properly. The table is basically self-explana-

" tory when used together with the detailed input descriptionswhich follow.

) ,

Certain special options to the computer program are described separately '_

Section 6.9•

An input data card listing for a sample case i_ presented in Section 7, followed by the correspondingcomputer output. In preparing input to the computer prugram it is useful to review this input card listing.

' Successivecases can be run using the computer program but complete data should

be input for each case.

I I

6-3

t 0
!Q- !

6.1 Thermodynamic Data.

Ordinarily, a thermodyrmmicdata file is available for use with the program,

i and is assignedto logicialunit 25. 'I_e input described here can be used to genei rate a thermod).-lamicdata file if one.is not available.

_his dawa set is identicalto the THERMO DATA described in Appendix D of NASA

SP-273 (i.e.Reference9).

Uslr_ this data set, thermodynamicdata curve fit coefficientsmay be read from

cards. _e curve fit coefficientsare generated by the PAC computer program described in NASA _ D-4097 (i.e. Reference22).

_e thermed_" data (i.e. _p , etc.) are expressed as functions of tempe_a- T

ture using 5 least squarescurve fit coefficient (at_5) and two integration

constants (a6_7)as follows:

-r = a!" 2_+a3_ _ _ 

a2T a6

HOT al + + + +-- +

[• -_-= s°T a1 1_ a3_* a4_ -r- *T-as_ ! 

; For each species, two sets of coefficients (al_ 7 and al_ 7) are specified for

two adjacent temperatureintervals, lower and upper respectively. For the data

availablein Reference9 the lower temperature interval is 3000 to 1000°K and the

upper temperatureinterval is 1CO0°K to 5000°K. !

" i

, !

Ref. 22. McBride, B.J., and Gordon, S., "Fortran IV Program f_r Calculation of

lhenmdynamic Data", NASA TN-D-4097,Aug. 1967.

(

,! f

•_ 6-4 _ :

t .'-

I '
The input format required for this thermodynamicdata is defined in Table 6-2.

Data cards for the species AR, H, _, H20, N2, O, OH, and 02 are listed in '_ble

{ 6-5 as examples. The_odynamic data c_efflclents for many chemical species are

supplied with the computer p_ 6ram. A list of these species is presented in Table

6-4.

Data Tape Generationand Usage:

A computer run using thermodynamicdata card input will generate a data tape on

logical unit JANAF. This tape may then be saved and used at a later time. The

program writes the _ data card images on unit JANAF as read but with two minor

exceptions. _e THE_K) code card and the card numbers in card column 80 are

omitted.

If thermodynamicdata cards are not input, the program assumes the thermodynamic data is on logicalunit JANAF. Logical unit JANAF is currently assigned a

value of 25.

: •

r '

f

!

I 6-5 :
i'

TABLE 6-2 FORMAT FOR THERI_ODYNAMIC DATA CARDS

,p - . .

t

; _. ii i

Card Contents Format Card

: order co] urnn

llV i • i ii ii Hi ii J i i | j ill i

1 THBRMO " 3A4 1 to 6

2 Temperature ranges for 2 sets of co-.. 3F10.3 1 to 30

efficie_+s: lowest T, common T, and.

highest T

3 Species name 3A4 1 to 12

Date 2A3 19 to 24

Atomic sFmbols and formula 4(A2,F3.0) 25 W 44

Phase of species (S,L, or G for solid, A1 45

liquid, or gas, respectively

i Temperature range 2F10.3 46 to 65

i

l Integer 1 I1S 80

! 4 Coefficients a; (1 = 1 to 5) in equations 5(E15.8) 1 to 75

(6-I) to (6-3)"

(for upper temperature interval)

Integer 2 I 5 80

5 Co_fflc!ents in equations (6-1) to 6-3) 5"'" _'

(a_, a_ for upper temperature interval

an_ a1' a2' and a3 for lower)

Integer 3 15 80 )

6 Coe/flcients in equations (6-1) to (6-3) 4(E15,8) 1 to 60 !

(aa,a_,a 6, a7 for lower temperature inte_aL_

Integer 4 ][20 80

(a) Repeat cards numbered 1 to 4 in cc 80

for each species

(Final END (Indicates end of thermodynamic 3A4 1 to 3

card) data) i

.... | ii ,, ,

aGaseous species and condensed species with only one condensed phase can be

!

In any order, However, the sets for two or more 'condensed phases of the same

species must be adjacent, If there are more then two condensed phases of a :. .

species that: sets must be either in increasing or decreasing order according '

to their temperature intervals, _. .

'r L

i

i

6-6 _ ':
ORIGIflAL PAGE IS

OF POOR QUALITY

TABLE 6-3. THERMO DATA CARDS FOR AN O2/H 2 PROPELLANT

+ " (sp,Cte_A_.H.H_.H20.N2, O.OH_,._d02) ,,

THERNO

300.000 1000.000 S000.000

AR L S/66AR lO0 000 000 OG 300,000 SO00.O00

0,2SOOnOOOE Ol O. O, O, O,

o0.?4537502E 03 0.63660006E 0| _.25000000E 01 0. 0.

O, O, °0,74537_9RE 03 0,63660006E O!

H J 9/65H 100 000 000 OG 300eO00 So00,O00

O,2SO00000E Ol O, O,

0,2S+Tt62,E 0S-0,+6011763E 00 _:25000000E O! :: O.

O, O, 0.2S_71627E 05°0,_6011762E O0

H2 J 3/61H 20 O0 O0 OG 300,000 5000,000

0,31001901E Ol 0,51119664E-03 _+52646210E-07-0,34909973£-10 0,369_5345E-1_

+0+87738042E 03°0,19629421E nl 0o30576451( 01 0,26765ZOOE°O2-O,S8099162E°OS

O,§5210391E-OS"O,18122739(°ll-_,98R90_74E 03-0,22997056E O1

H20 J 3/6;H 20 ZOO 000 OG 300.000 5000.000 0+27167633E Ol 0,29_51374E 02-o,BO22437_E.06 0,10226_82E. -09 0,_847214SE-|4

-0,2990SR26E 05 0,66305671E 01 n,_OTO1275E 01°0,11084499Eo02 0,_1521180E-05

' ).2963740,E-08 0.S0702103E-]2-_.30279722E ..fl_-n.e....+...__fln*'r 00

-" N2 U 9/6SN aO O0 O0 OG 300,000 5000,000

0o28963194E Ol O,lS156866E°o2-_,S7235277E-06 0,99807393EolO-O,652235SSE-14

;+i+ -0,9058_18_E 03 0.616151_8E 01 0.367_82_1E 01"0.12081S00E°02 0.23240102E'u5

-. -0.63217559E-09-0.22577253E-12-0.1061158BE 04 0.23580_2_E 01

•" 0 J 6/6_0 ]00 000 000 06 300.000 5000.000

0.25_20596E 01-0.27550619E-0_-0.31028033E-08 0._S51067_E-II-0._368051SE°15

0,29230803E 05 O._9?03nBOE Ol _.2966_287E 01-0,16381665E°02 0,26210316E°05

+ "0,16028432E'08 0,38906964E'12 0,291476_E 05 0,29639949E Ol

OH J 3/660 IH I00 000 OG 300,000 SO00,O00

0,29106_27( O10°95931650E-f13-_°19441702(°O6 0°137566_6E-I0 0.1_224542E°15

0,39353815E 04 0,5_234_5E Ol _,383759_3E 0!°0,10778858E-02 0+96830378E-06

0.|8713972E-09-0.2257109_E-12 0.36_12823E 04 0._9370009E 00

02 J 9/650 20 00 O0 0G 300_000 5000,000

0,36219535E Ol 0°7361826_(-03-_,1965222RE-06 0,36201558E°_o°o,28945627E-14

' -0.l_019R25E 04 0.36150960E 01 0.36255_BSE 01-0.1878218_E*02 0.705545_E.05

.0._7635137E-08 0.21555993E-ll.0.10475226E 04 0.43052778E 0|

FNO

v

i

! ' 6-7
O

RISfNALPAGEI_

OF POOR QUALITY

Table6-4. SPECIES W]TH THERMODYNAMIC DATA PROVIDED

,AL (S) BCL BEO(S) C2H FECL2(S) KOH

AL(L) BCL+ BEO(L) C2HF FECL2 G,)v_u,e_

--- ,_bV.'b6 %"_I

,AT., B(_F BEO C2H2 FECL2 KOH_)

AL+ BCL2BEOH C2H4 FECL3(S)K2

ALBO2 BCL2+ BEOH+ C2N FECL3 (L)K20(S)

ALCLBCL2- BEO2H2 C2N2' FECL3 LI(S)

ALCL+ BCL3BE20 C20 FEO(S, LI(L)

ALCLF BF BE2OF2 C3 FEO(L) LI

ALCLF2 BF2 BE202 C302 FEO LI+

ALCL2BF2+ BE303C4 FEO2H2(S) LICL(S)

ALCL2+•BF2- BE404 C5r'EO2H2 LICL_L)

ALCL2- BF3 BR CL FEO3H3 (S)LICL

ALCL2FBH BR2(i) CL+ FE203(S) LIF(S)

ALCL3(S) BHF2 BR2 CL- FE304 (S) LIF(L)

ALCL3 (L)BI42 C(S) CLCNH LIT

ALCL3 BH3C CLFH+ LIF2-I

ALF BN(S) C+ CLF3 H- LIFO '-

ALF+ BN C- CLOHALOLIH(S)

.- ALF2130 CCL CLO2HBO LIH_)

ALF2+ BOCL CCL2 CL2HBO+ LLq

ALn- BOF CCL3 CL20HBO2UN

iALF3(S) BOF2 CGL4 CS(S) HCLUO

ALF3(S)BO2 CF CS (L) HCNUO-

: ALF3 BO2- CF2 CS HCO LIOH(S)

ALH KS CF3 CS+ HCO+ LIOH(L)

_ALN (S) B2 CF4 CSc_.(._I HCP LIOH

:ALN B20 CH CSCL_') HF LION

_= ALO B202 CH2 CSCL (L)HNO LI2'_

-.ALO+ B203 (L) CH20 CSCLHO2 LI2CL2'

" ALOCLB203 CH3 CSF(S) H2 LI2F2

ALOF B303CL3 CH4 CSF(L) H20(S)LI20(S)t

" ALOH B303F3 CN CSF H20(L) LI20(L)i

ALOH_ BE(S) CN+ CSO H20 LI20_

ALOHBE{L) CN- CS2 H202 LI202 ALO2 BE CN2 CS2CL2 H2S LI202H2 ' ALO2- BE+ .CO CS2F2 H38306 '.

: ' LI3 CL3,

ALO2H BEBO2 CCCL CS2C HE LI3F3 AL2CL6 BECL CCCL2 E HE+ MG(S)

. AL2F6BCL+ CCFF K(s)MG0.)

AL20 BECLF COF2 F- K(L) MS

"_AL20+BECL2(S)COSFCNK MG+i!

AL202 BECL2 (L) CO2 FOK+ MGCL

AL202+ BECL2CO2-FO2KCL (S) MGCL+i

-j AL203 (S)BEF CP F2KCL (L) MGCLF_.

AL203 (L) BEF2 (S) CS F20 KCL MGCL2 (S)

}AR BEF2(S) CS2, FE(S)KF(S) MGCL2 (L) ! AR+ BEF2 eL) C2 F_(S) KF(L) MGCL2 I B(S) BEF2 C2- FE(S) KF MGF

t B('L) BEH C2CL2 FE(L) KF2-MGF2(S)

,BBEH+ C2F2 FEK2F2MGF2(L)

.I_ B+ BEN C2F4FECL KO MGF2 | '

it
'r .C ....

-9

; Table 6-4. (cont'd) i: . MGH O SIN

MGN O+ SIO

.........o_ta__o/

MGO(L) OH SZO2(S)

M GO OH+SIO2 (S)

,MGOHOHS_O2(L)

,MC_H+ 02 SIO2

:..MGO2H2.02-SIS

NPSI2

NF P(S} S12C

NF2 P+ SI2N NF3 PCL3 S13

NH PF3 XE

NH2 PF5""

NH3 PH

'NO PH3

. NO+PN

NOCL PO

- NOF PS

NOF3 P2

- NO2 P4

;, NO2- S(S) NO2CL S(L)

c.. NO2FS

N2S+

.. N2C SF4

N2H4 SF6

N20 SH

N204 SN

•" NA(S)SO

• NA(L) SOF2

.NA SO2

,NA+ SO2F2 ' NACL (S) SO3 NACL(_) sz

NACLSZ(S)

_' NAF(S)SZQ.)

NAF(L) SI

NAF SI+ ' NAF2- SIC

,,NAH SIC2

,; NAO SICL

NAO- SICL2

.I NAOH(S) SICL3}

:_ NAOH(L)SICL4

'. NAOH SIF

NA2 SIF2

NA2CL2 SIF3

NA2F2 SIF4

._NE SIH

NE+SIH4

6-9_I

•L',
6.I•1 _IODYNAMIC DATA BELOW 5OO°K.

Ordinarily this data set is not required. However, for low temperaturecalcu-

•,=_=_ _ ==y be n_s_ary to extend the curve fit data in the ThermodynamicData

file (see Section 6.1). The lower temperature limit, T£, in the ThermodynamicData

suppliedwi_h the program is 500OK.

ThermodynamicData below the temperawre, T£, may be input by data cards as

described below.

card 1 L_W T CR_S Directive for start of low temperature

CR_S tables (col I through 10).

card 2 ........ n 12 character species name, left Justified, followed by the integer, n,

p_ched in column 21. The itegrer n

must be such that 1<n<3 and represent

the number of Therm_yanmic Data

PO_,_s to be input for this species.

O O O O

card 3 TIK _T HT _ 1 Fiabove rst The species, rmodynianmic putD4Fata10.0, pointI5.for the

card n+2 _nK _T _ _ nth (1<n<3) nth above_]ler species, modynamlc inpData ut 4FI0.O, point for I5. the !

• . . Repeat cards through n+2 above for each species to be input• i

Temperaturemust be T <T <T <T .

1 23£

(final END L_ T C?HS end directive (col I through 14)

c_rd)

f

J

6-10 1 :
An example of this input is given in Table 6-5 which shows a card listing extending

the ThermodynamicData for an 02/_ propellant to 100°K. Data in Table 6-5 is

taken directly from tl'eJANAF tables (Reference23), except for Argon which is

taken from NASA SF-/O01.

The quantity _ is defined as

and

' _ , cal/mole - deE K

S_ , callmole - deg K

: !

i

Ref. 23. Stull, D.R., Prophet, H., et al., JANAF Thet_ochemical Tables, _cond

, Edition, NS_S. 37, National Standard Reference Data Series, National

Bureau of Standards,June 1971.

i
ORIGINALPAGE 19

OF POORQUALITY

_' LOUT CPHS

AR 2

100,0 4.9681 -986.5 31.556 1

200,0 4.96B1 -&BT,7 36.999 2

N 2 '.

100,0 6,968 SillS, _1,965 1

200eO 6,968 51614, pS,40B 2

N2 2

100.0 5,393 "12650 _,387 1

20000 6.S18 0_62,0 78,520 2

HZO Z

|00,0 7,961 059378,9 36.396 1

200.0 7,969 058581,9 _.916 2

" N2 2

'* 100,0 7,074 -1387,0 38,113 1

_'+ 200,0 6,989 "684, 62,986 2 ,

• 0 2

+ 100,0 §,666 S8479, 32,_66 1

200,0 S,434 $9036, 36.3_0 2

' OH 2

_;_ 100,0 7.567 1879. 35.8SZ 1

;, 20000 T,309 8623, _l.OZl 2 )

OZ 2

100,0 6,958 "1381, 41,395 1

" 200'0 6,961 "685* _6'_18 2 "

ENO LOUT cPHS

i

: i

!

J ', 6-12
i 6.2 Title Cards

i This input permits labeling of runs with alphanumeric information. As many

title cards as desired may be input in sequence. Card format is as follows:

, col 1-5 col 6-77

TITLE any alphanumeric information

L It is not necessary to input title cards.

6-13 _
: 6.3 [ItTADirectiveand $DATA Namellst In_u_t.

I

i The DATA directive and the SDATA Namelist input sew described below must always

'_ be input. It is required for all problems since it contains the input that cont-

: rols which calculationmodules are to be executed.

The first input item must be a single card, called the DATA directive card.

The format of this card is as follows: the letters DATA must be punched in columns

I through 4. The DATA card is used to inform the program that the $DATA namelist

input is to follow.

The card following the DATA card must contain the name SDAT_, and all cards in

the namelist input set must start in column 2 or greater. Since Nsmelist L_ut is

card intarpretlve,J_ms can be L_ut in any order. The last card in the set must

contain $_D.

Users unfamiliar with Nemelist input are referred to their FOR_P_N reference

_ manual.

Assumed

I____ Description Uni_____ Value%s

- DATA DATA directive card

SDATA Nemelist name, reed in Subroutine

D

i

t

,! 6-14 {
6.3.I S_ecificatlonof Modules to be Executed.

; If a module is to be executed, it is necessary to indicate the fact by input of

, a module flag as desccibed below. For example, if a problem requires that the #DE

[ _dulo _ r_, it i_ necusaacy to input @DE = 1. Only certain comhlnations of

modules are allowed. These are described in Table 6-6. The module flags are:

Assumed

_' Item De.,,scrlptlon Uni__.____Value(s)

_DE = Set @DE = 1 if the ODE module is to be none O.

t executed.

_DK = Set _K = I if the ODK module is to be none O.

executed.

TDE = Set _DE = 1 if the TEE option of the none O.

M_C module is to be ex_cu1:ed

TDK = Set TDK = 1 if the TDK option of the none O.

"_ M_C module is to be executed

5

" _DF = Set TDF - I if the _DF option of the none O.

M_C is to be executed

TDKIL = Set TIKIL = 1 if the _DK option of the none O. I

M_C is to be e_cuted with an initial

: data line input as described in

_! Section 6.9.2.

C

!

BLM = Set BLM = 1 if the BLM option of the none O. 1

" M_C module is to be e_ecuted

q

PFG_ = Set PFC_ = 1 if the constant proper- none O. :

ties option of the M0C module is to be-.

executed. See Section 6.9.I for input

instructions.

' i

ii

i

[ i

!

' ; !

I 6-15
Table 6-6: Usage of the Module Flags

Mode of Execution

#DE=I, #DE is mm alone. Options other than the

rocket (Rk_T) opzlon are allowed. See

Section 6.4.3 and Reference 9.

i_)E=l,@DK=I, _)DEis run. #DK is run with _DE providing

start conditions. See Section 6.5.1.

L

_DK=I, @DK is man alone with initial conditions

supplied by the user. See Sections 6.5.1 and

; 6.5.1.1.

_DF_I, _DK=I, TDK=I, _DE is run. _DK L run wi_h _DE providing

start conditions. TIK is run with _DK and

TRANS providing M_C initial data line

conditions. The number of _DE and _DK runs

will be equal to NZ_NES.

_E=I, _DK=I, TDK=I, BLM=I, As above with a BLM run added.

52_F__1,_DK=I, TI_=I, BLM=I, As above with _DE, _DK, and TDg repeated

IRPEAT=I, using the BLM results. See Section 6.8.4.

i This option is for including the BIB results

with regen cooling.

_DE=I, #£K=1, TDK=I, BLM=I, As above except that the #DE and _ runs are

IRPFAT=2, not repeated because there is no heat input

correctiondue to cegen cooling.

_'" TDK.IL=I, TDK is run with a M_C initial data line

•: input as described in Section 6.9.2.

TDE=I, _Dt_will be run for NZ@NES. TDE is run with

_DE chemical equilibrium gas properties,and

with _RANS providing M_C initial data lin._

conditions.

TDE.1, BIM=I, As above with BLM.

TDE=I, BLM=I, IRPEAT=I or 2, As above with TDE repeated.

=,

W +

I

t

t

!

}

i

6-16 |
Table 6-6: Usage of the Module Flags (continued)

Mode of Execution

@DE=I, @DK=I, TDF=I, _E is run. @DK is Fun with @DE providing

o+..4 cc.nditic_s. However, the @DK run will

have a frozen chemical composition. TDK wl]1

also be tun with a frozen composition.

#DE=I, @DK=I, TDF=I, BIM=I, As above with BLM.

_DE=I, ¢DK=I, TDF=I, BLM=I, As above with TDF repeated.

IRPEAT=I or 2,

BLM=I, BLM is tun alone. This option requites a

large amount of input that is provided

automatically when BLM is man after TOE, TDK

or'TDF.

_=1, The T?@.NS and M_C modules are curt with

constant gas properties. See Section 6.9.1.
I

6.3.2 Inputs for Control for the Program.

Assumed

--ii Item Description Units Value(s)

IRPEAT I Set IRPEAT I I or 2 to request that a none 0

i _DK (or TDE) calculation be automatically repeatedafter the BLM module

-" has been used to calculatea displaced

nozzle wall.

8:

: If IRPEAT = I, the ODE and _3K module

execu_ions will be repeated with

ad_us%ad enthalpiesfor regen cooling,

see.Seotion 6.8.4.

If PJ_EAT -,2, the _DE and _3K module

executionswill not be repeated. The

system ent_.Ipy will be unchar4_d.

NZ_ES = Number of zones, N, to be used in the none I

anlysis. The _DE and _DK modules will

be executed N times. Zone I repre-

.. santa the flow adjacent to the nozzle

axis, and Zone N representsflow adJai cent to the nozzle wall.

" Sl = If Si = O, English units are to be none 0

u_d for input and output, if SI - I,

SI units are to be used for input and

output. T_e Sl mn_ts required for

> input are shown in parenthesis.

I_FF = W_en BLM is run with the MOC module, 0

values defin_kg the boundary layer ,|

edge conditions;Xe, Ye, Ue' Te' and

Pe are automatically calculatedend :

stored in the XIN_, RIN_, UE_, T_,

and P_ arrays. If IOFF is not input,

' then these values are stored starting

with the first entry in each array.

. If I@FF is input then these values are

' stored starting in the I_FF + 1 entry

" of each array. Values must then be

, input into entries I through I@FF.

The boundary layer calculations will

start at position XIN¢(1) of these -

arrays using the $BLM input. This

_ inpul allows the user to account for

the developmentof the boundary layer

in the nozzle chamber, upstream of

ECRAT. l_eF < I00.

If I#FF is input, do not input NXIN_

_' in BLM.

i i

6-18

t '
6.3.3 Specification of nozzle Kecmetry.

To eliminate redundancy, all geometry inputs that are common throughout the

modules are input here. Note that the center of the nozzle geometry coordinate

' normalized by the nozzle throat radius, rt. Hence, axial positions upstreom of the

throat are always negative numbers, in the figures describing the geometry, posltive angles _,reshown as counter-clockwise, and negative angles are shown as clockwise.

"w

' Geometric area ratios at which @DE and _DK print out is to be made are

specified using the input arrays ASUB(1) and ASUP(1).

The nozzle geometry is defined in Figure 6-I. The _DK calculations start at

the downstream end of t_e combustion chamber with a subsonic area ratio of ECRAT,

as shown. The circular arcs RI and RWTU cannot overlap. Thus, it is necessary .b.

that ECRAT, RI, RWTU, and THErAI be input such uhat

.: _ > 1 + (R! + RWTU) (1 - cos THETAI).

},

If this condition is not met, subroutine PRES of @DK will print the terminal error

message:

INLET GEOMETRY INCOMPATIBLE WITH INITIAL CONDITIONS.

In addition, the transonic analysis requires that a value of RWTU _> .5 be

input.

The wall geometry downstream of the nozzle tPmoat can be specified using any

W

one of several options. All of these geomet_-ies begin with a circular arc of ra-

.' diu_ RWTD which extends from the throat point through an angle of THETA. Geometries that can be input to both the #DK _,d M_C modules are described in Section

6.3.3.1. ,

I
i D

, ORtGd_!AL FAG_ ?3

_. OF POOR QUALITY

t

r : RMAX

m

z = ZMAX

, 8 = TR_'..TA

_ ¢I = THr-TAI e_

P

, / _ _n_our/

-_ / _RWTD _ Cone

• "" I

: WTU " "

b

• i i , , - , i j • , nl i - _

; (_,o) (0,_)

I

i

I

} Figure 6-i: Nozzle Geometry, all coordinate

i values are normalized by RSI : rt.

I
Assumed

Item Description Units Value(s)

PSI = Nozzle throat radiu.% - in, O.

(meters)

ASUB(1) = Subsonic area ratios at which informa- none O.

tion will be printed.

NASUB -- Number of entries in the A_JB array none O.

<50.

ASUP(I) = Supersonicarea ratios at which infor- none O.

marion will be printed. For the TDE

option, ASUP must contain an entry _>

the nozzle expansion ratio.

NASUP = Number of entries in the ASUP array none O.

<50.

ECRAT = Nozzle inlet uontractionratio for use none O.

in ¢_ and _DK calculations.

"_ RI _, Normalized inlet wall radius, none* O.

THETAI = Nozzle inlet angle, degrees O.

RWTJ = Upstream normalized wall throat radius none* O.

RWTJ_> .5 is required.

. ITYPE = Type of nozzle wall to be input, none O.

ITYPE = O, if the real wall contour is

input.

ITYPE - I, if the potential flow wall

contour is input.

, If IRPEAT = I or 2, then the nozzle

wall will be displaced by +6* as calculated by BLM when the TDK (or TDE)

calculations are repeated. _lis displacement is -_ for the real wall

(ITYPE = 0), or +6* for the potential

flow wall (ITYPE = I).

* Normalizedby the throat radius, rt

t

! 6-21 _
i+ 6.3.3.1 Exhaust Nozzle Geometry Specifloatloq,for _DK and the M_C Modules.

' Assumed

i Item Description Unit_____sValue(s)

I

: IWALL = option flag for spe_cifyir__he none O

downstreamwall.

= I cone option (input RWTD, _4ETA, and

EPS)

- 2 parabolic nozzle contour option

i (inputRWTD,THETA,_4AX,ZMAX)

-- 3 circular arc nozzle contour option

(input as for IWALS=2)

+ = 4 nozzle contour (spline)option (input RWTD,THETA,THE,RS,ZS,NWS)

= 5 cone with specified end point.

(input RW_D, P_4AX,and ZMAX)

= 6 skewed parabola option. (input

: RWlD,THETA,RMAX,ZMAX,_I_E) J.

The items required for the various IWALL options are:

RWTD = downstream wall throat radius of cur- none* O.

vature ratio*_

>_, THETA = nozzle attac_nt angle

J" I

THE = nozzle exit angle (input if IWALI=4, deg. O.

or 6) i

.

_ = nozzle expansion ratio (input if deg. O.

1"WALL1=only)

RMAX = normalized radius at the nozzle exit none* O.

plane (input if IWAL_2 or 3)

ZMAX -- normalized axial position at t/_e none* O.

noLzle exit plane (input if IWALL =

. 2 or3)

{

+ * Normalized by the throat radius rt

If a corner expansion (i.e. Prandtl-Meyer fan) is desired, a value of RWTD =

.05 is recommended. Experiencehas shown that values smaller than this give the

same result but are computationallyless efficient.

l

• !

6-22 t

D
Assumed

Item rlption value(s)

RS(2) - table of normalized wall radii down- none+ O.

stream of the nozzle tangency point

' t_-,_-.. -,'L",."_-if P#ALL=4). _ input tables

KS and ZS start with the second entry

because the first entry is calculated

automatically by the program, i.e.,

KS(1).rT and T ZS(1):,,zT in Figure 6-2.

_le T wall angle at this position is

also calculated so that the spllne

contour will be properly joined to the

nozzle t/_roatconto_-.

ZS(2) s table of normalized axial position none+ O.

downstream of the nozzle tansency

point (input if IWALL-4).

NWS - to1_l number of entries in the KS, ZS none 0

tables. Includes the first entry NWS

: <_50 (input if _AU_4).

_'i RZN_ = Optional normalizingfactor for the none. 1.

_S, ZS, P_N, ZIN tables. For example,

if RS, ZS, and RIN, ZIN were input as

•' dimensional numbers, RZN_M would be :

the t_t radius in those units.

J

+ See the input variable P_4.

j.

|

b

!
6.4 ,_DE INPUT DATA (ALL PROBLEMS SPECIFYING _DE)

The _DE Input data described here Is exactly as defined in NASA SP-273,

Reference 9, except namelists input $INPT2 and $RKIN'P have been combined into

a single list named $_DE. Any type of equilibrium calculation available with the

computer program described in Reference 9 can thus be computed using the $(_DE

; input data*. In this document, however, only the RKT option of nemelist is

: described. The RKT option differs from that of Reference 9 for problem types

2

! other then single zone _DE.

, The (_DE input data consists of the following input groups:

1. REACTANTS directive card, followed by up to 15

data cards, followed by a blank card,

specifying reactants.

2. (2tMIT and INSERT directives to omit or insert species for

equLlibrium/frozen calculations.

• 3. NAMELISTS directive card followed by input

namelist $_DE specifying input

case date.

a

6.4.1 REACTANTS CARDS

This set of cards is requlreci for all _'Dt; proDiems. The first card in the

set contains the word REACTANTS punched in card columns 1 to 9. The last card

in the set is blank. In between the first and last cards may be any number of cards

up to a maximum of 15, one for each reactant species being considered. The !

cards for each reactant must give the chemical formula and the relative amount

of the reactant. For some problems, enthalpy values are required. The format

and contents of the cards are summarized in Table 6-7. A list of some REACTANTS

J

cards is given tn Table 6-8

I

Relative amounts of reactants. - The relative amounts of reactants may be

specified in several ways. They may be specified in terms of moles, mole fraction,

or mole percent (by keypunching M in card column 53) or in terms of weight, weight i

fraction, or weight percent (blank in column 53). I

!

Relative amounts of total fuel to total oxidants can also be input. For this

situation, each reactant must be specified as a fuel or an oxidizer by keypunching an P or O, respectively, in column 72 of the REACTANTS card. The amounts

*These options include TP,HP, SP, TV, UV, or SV problems, Chapman-Jouguet detonation problems, and incident or reflected shock problems.

I

6-24
FOOR QUALITY

1

, TABLE5-7 REACTANTSCARDS

P

, Order Contents Format Card columns

, , m ,

First REACTA/_'TS 3).4 1 to 9

Any One card for inch reactant species

(maximum 15). Each card cant:zinc:

(I) Atomic srmbofs and formuia hum- 5(A2, FT. 5) I to 45

hers (maximum 5 sets) a

(2) Rel.ttlve vet_ht b or number of F'/. 5 46 to 52

moles

"_ (3) Blink if (2) is relative well:ht or AI 53

'_ M if (2) is number of moles

(4) Enth_l.oy or int_.r_i _,n-rf_ a. F9.5 54 to 62

_" cal mole

(5) State: S. L. or G for solid. AI 63

--. liquid or gas, respectively

._ (6) Temper_:ore =ss_ciated vith F8, 5 64 to 71

enthall_ in (4)

(7) F if fuel or Off o=idant Ai 72

(8) DensitT in g cn_$ (ol_iorul) FS. 5 73 to 8.}

Last Blnnk

aProl_rnm will c._lcuLlte the entl_lpv or intern.ll energy (4) for s.o,_cies in

the THERMO clara at the temperature (6) if zeros are p_,nchcd in card

; columns 37 ;rod 38. (See section React:int enthail,'y for additi_l in°

forrr=stic_.)

" bReLltil'e weight of fuel in total fuels ur c._lc_nt in tot_l nc(id_nts. All

' react:rots must be _i_-en either a!l in relative wei,.,hts or all in number

_d'moles.
¢

" t

.!

•- OF POOR QUALITY

!

TABZ,E 6-8 LISEING OF SAMPLE REACTANTS CARDS

REACTANTS

M 2. 100, O. G298.1_ F

N ,7808810 .2097954R.OQ4662 100, -7.202164G298,1S O

m[ACT&NTS

M 1, H 4, CL1, 0 4, 72,06 070730, S298,15 F

C 1, H 1,069550 .031296S .008415 1S.50 -2999.OS2L29S,lS F

ILl, t,O0 *0.0 S298,|.5 F

RGI, 0 1. ,ZO -141700, S2¢8,1S P

H 2* 0 1o o16 -6I]L?o4 _298,15 F

R[iCTINYS

N ?, .00 100, O, _298,15 F

0 2. O0 100.0 0.0 G29a,25 0

'" REACTANTS

.. M 2, H 0, C 2, SO,O 12_4,8 L296,1_ F ,7_6

N 2, K 4. 50,0 120_0, L2q6,1S F 1,00_ I

F 2. 100, ")03G.lq2_ "5,24 0 2,54 l

RE&¢TANTS

L|I, 100, O, S290,1_ F

P 2, 100. -3030,892L 85,24 0 1,54
i

1

t given on the REACTANTS cards are relative to total fuel or total oxidant rather than

total reactant.

i

i There are four options In the $_DE namelist for indicating relative

i ;_mn,lnt¢ r_/r _r,_1 _r_] to _,...=I ....,._--_ -- t_1_ ......

i 1. Oxidant to fuel weight ratio (_F Is true)

: 2. Equivalence ratio (ERA_ Is true)

3. Fuel percent by weight (FPCT is true)

!,

4. Fuel to air or fuel to oxidant weight ratio (FA is true)

For each optlon_ except _FDE with NZ_NES=I, the values are given in the

_FSKED array of $_DE (described in Section 6.4:3). For _DE with NZ_NES=I,

the MIX array is used.as described in Reference 9.

,Reactant enthal_v. Assigned values for the total reactant are calculated

automatically by the program from the enthalpies of the individual reactants.

Values for the Individual reactants are either keypunched on the REACTANTS

.: cards or calculated from the THERM_ data as follows:

Enthalpies are taken from the REACTANTS cards un/ess zeros are punched

in card columns 37 and 38. For each REACTANTS card with the "00" code, an

;: enthalpy wLll be calculated for the species from the THERM_ data for the temperalure given in card columns 64 to 71.

When the program is calculating the individual reactant enthalpy for

: values from the THERM_ data, the following two conditions are required:

1. _he reactant must also be one of the species in the set of THERM_ data.

For example, NH3(g) Is in the set of THERM_ data but NH3!_) is not. Therefore,

tf NH3(g) is used as a reactant its enthalpy could be calculated automatically,

, J but that of NH 3 (t.) could not be.

i

2. The temperature T must be in the range Tlow_l. 2 < T < ThighX 1.2 where Tlow

to Thigh Is the temperature range of the THERM_ data.

For cases with NZ_NES > 1 (see Problem card, Section 6.3) it may be de-

, sirable to modify the en*_alpy of each zone. This can be done by using the DELH

input array. For the Ith zone the tth DELH entry wLll be added to the system

6

6-27 ;
enthalpy as computed by _DE from the reactants cards (see above). /'or example,

overall system enthalpy of the propellants in the tank can be input through the reactants

cards and the. work added or extracted per zone can be input by the DELH entries.

_,-_alte,-nate met_%odwould be to input zero enthqlpy on the Reactants cards and

_put enthalpy per zone by the DELH entries.

:" 6.4.2 _MIT _qd INSERT Cards

{_MIT and INSERT cards are optional. They contain the names of particular

species in the library of Thermodynamic Data for the specific purposes discussed

below. Each card contains the word OMIT (in carpi columns 1-4) or INSERT (in

card columns 1-6) and the names of from 1 to 4 species starting in columns 16,

31, 46, and 61. The names must be exactly the same as they appear in the "4

THERM_ data.

6.4.2. l _M1T..Cords

These cards list species to be omitted frnm the T_ERMOJ cl_t_, ff OJMTT

cards are not used, the program will consider as possible species all those

species in the THERM_ data which are consistent with the chemk,_=l system

being considered. Occasionally it may be desired to specifically omit one or

more species from considerations as possible species. This may be accomplished

by means of _MIT cards.

6.4. _}.2 INSERT Card s

These cards contain the names of condensed species only. They have

been included as options for two reasons.

The first and more important reason for including the INSERT card option is

that, in rare instances, itis impossible to obtain convergence forassigned enthalp7

problems (HP or RKT) without the use of an INSERT card. This occurs when, by

considering gases only, the temperature becomes extremely low. In these cases,

i

the use of an INSERT card containing the name of the required condensed species '

can eliminate this kind of convergence difficulty. When this difficulty occurs,

the following me_sage is printed by the program: "LOW TEMPERATURE IMPLIES _

CONDENSED SPECIES SHOULD PAVE BEEN INCLUDED ON AN INSERT CARD" _ ."

! ,!

6-28
The second and less important reason is that if one knows that one or

several particular condensed species will be present among the final equilibrium

compositions for the first __ss!gned r-,,.,-,""_'**_'*--,__-,, s_,all amount of computer

time can be saved by using an INSERT card. Those condensed species whose

chemical formulas are included on an INSERT card will be considered by the

: program during the initial iterations for the first assigned point. If the INSERT Z'

card were not used, Only gaseous species would be considered during the initial

iterations. However, after convergence, the pt'ogram would automatically insert

; the appropriate condensed species and reconverge. Therefore, it usually is

immaterial whether or not INSERT cards are used. For all other ass'gned points

the inclusion of condensed species is handled automatically by the proeT_m. i,

i
t

6,4.3 $_DE NAMELIST _NP_T

_. ' The _DE subprogram contains namellst input sections $_DE

and $SHKZNP. The Namellst $_DE must be preceded by a card with NAMELISTS

punched in card columns 1-9.

•= The SBDENamelist is required if ODE:1. or TDK =1, in SDATAas

described in section 6.3.

For the _DE problem type any of nine (9) different equilibrium problems can be

solved. These are T?,HP,SP, TV, UV, SV_RKT, DETN, and SH_CK. For the gDE-

(2_DK,(_DE-(_DK-TDK, or TDE problem type, only the RKT problem can be

solved. In this section only the RKT input option ts discussed. Reference 9 is

.tobe used to prepare inputfor the other equtllbrlumproblems.

' Be variables input by the $_DE namellst are listed in Table 6-9.

"' Additional information about some of these variables follows:

- Pressure units. - The. pro_.r_m ess,,_,-.es the pressure in the P schedule to be in

; units of atmospheres unless either PSIA .= true, or SI = true.

Relative amounts of fuel(s) and oxidizer(s). - These quantities may be spect'fied by

assigning 1 to 15 values for either o/f, %F, f/a, or r. If no value is assigned

- for any of these, the program assumes the relative amounts of fue'(s) and oxidizer(s)

to be those specified on the REACTANTS cards. (See discussion tn REACTANTS

Cards, Section 6.4.1)

,p

RKT ])roblerru - Only one value for chamber pressure, P, is to be input for cases

_ with NZ_N]_S > 1 (see $DATA input:, Section 6°3). The stagnation pressure used for

the tTMzone will be the value input for P multiplied by the tth value input in the

: schedule XP. I_ not input, all XP entries are assumed equal to one. For TDK Lype

"i .,

t

i '

|

i

i .

1 :

6-30

I

t
i problems, zone one is taken about the nozzle axis of symmetry and the last

zone ts bounded by the nozzle wall. Similarly, the tth zone will have a mixture

ratio equal to the ith entry tn the O'FSICEDschedule=

Print oct will be given for the chamber pressure condition (i.e. stagnation)

and the throat condition. Print out may be requested at other conditions by use

of the PCP schedule and the $UBAR and SUPAR schedules.

The program will calculate both equilibrium and frozen performance unless

FR_Z = F or EQL = F are input. If FR_Z = F, only equLlLbritun performance will

be calculated. If EQL = F, only frozen performance will be calculated.
lit'

i

O_t_NAL Ft,_E IS

I oF Poor QU,_LrI'Y

TABLr.6-9 VARU_ES IN $¢DE NAM_IST

Variable Nc. of Type Value Definition and comments

entries befc_e

read

i i --, i i im ,ii i i i i ii

RKT I L False Rocketproblema

P 26 R 0 Assignedpressures: stagnationpres-

; sttresfor_cket problems:valuesin

"; atm un_:s':PSIA, or SI = ,T., {seebe-

, low)

-' Sl I L False aValues in P _rrayare in N/m 2

, PSIA I L False aValuesIn P array are in psla un'.ts

XP $0 R I, Multipliersforthe ith zone stagnat/onpressure{zone1 = innerzone)

I L False OxJdantto fuelweightratiosareto

, be input a

,o ERAT[_ I L False Equlvaienceratiosa;eto be i,puta

•'- FPCT 1 L Paise Percent fuel bF weight ere to be input s

- FA I L False Fuelto alrweightratiosareto be Inputa

_ _SKED 50 R 0 Fora Rocketproblem,and NZ_NE$ ._I,

_FSKED willbe used ratherthanMIX

{seeReference9), Relativeamounts of

" total oxidantto total fuel are input as

defined hy _F, ERATI_, PPCT, or FA.

_,;:. Pot _DEm_fDK-TDK and TDE problem

typesthesevalue_definethe oxidantto

fuelratiosforeach zone (zoneI =

Lrmer zone)

DKLH 50 I R 0 Correspondingto each zone thisvalue

will be added to the _ystem enthalpy ---

-- inputthruthe reactantscards. Units

, are BTU/# if PSIA=.T., Joule/kilogram

_. ifSI=.T.,otherwisecal/gram.

_ DELHI 50 R 0 Correspondingto each zonethisvalue

.: will be addedto the systementhalpy.

,. These values can be used as a ist est- !,

•" imate for the heat returned to the main ,

" combustion chamber by regen cooling !

circuits(GIFCinputin SBLM). The BLM i

; will recalculatethesevaluesand, if

IRPEAT=i in $DATA,rerunthe _DE,ODK, _

TDK (orTDE)analysis.Same units as

DELH. # :

=,, ,= ,,, ,=

|

• t

1 " elfvariableis set to be trje,

" i

6-32 t
Table 6-9 (cont'd)

i el i iii w= i

!

Variable No. of Type Value Definitionand comments i

entries bef'_re

lead

-- m nun _ , nil -

,! I_NS 1 L False Considerionicsoeclp._a v_ .

WFL_W 1 R 0 Input nozzle mass flow option for (_DE-

: (_'DK-TDKor _E problems. If _ value

_ ,vrL_W is input an expansionwith

' thismass flow will be computed. The

-_ valuesinputforP and XP are used as

; estimates for computing stagnation pressure for each zone. The program wiLl

adjust these stagnation pressures to

obtain the desired nozzle mass flow

witl-.in a tolerance of RELERR. Units

are lbs/sec Lf PSI=. T. otherwise kilograms/sec.

: RELERR 1 R o0P95 Relative dLfference between requested

and computed mass flow rate. The pro-

' gram stops Lfthis error is exceeded.

PCP 50 R 0 Compute and print solutions at these

values of chamber pressure to pressure

:" ratio (entries must be > 1.)

SUBAR 50 R 0 Compute and print solutions at these

values of subsonic area ratios (entries must # i.) ;

SUPAR 50 R 0 Compute and print solutions at these

L:- valuesof supersonicarea ratio(en-

•" triesmust _ 1)

ECRAT I R 0 Subsonic area ratio to start Q'DK calculations withcomputed equfllbrium

conditions.The SUBARinputtable ;

must include an entry equal to ECRAT.

EQI_IST ! L False To startG_K calculationswithcorn- '

puted equfllbriumconditionsat the i

nozzle throat, a

, EQL I L True Calculaterocketperformanceassure.- ,

.. ing expanesqiounLllb.rlum b , compositionduring i_,

• FR_Z l L True Calculaterocketperformanceassuming frozencompositionduring expan- i

sionb, i

LISTSP l L False List names and dates of all species _ :

residing on thermodynamic data used'.

KASE 1 I 0 Optional assigned number associated '

withcase.

I

"' _ I in I n Ji in n , - i |n inn

, allvariableisset to be true. i

bset variable false Lf these calculations are not desired.
it'

6.4.3.1 OPTION TO PUNCH TABLES FOR BOUNDARY LAYER PROGRAM INPUT

'. (DOES NOT APPLY TO BLM)

Conditions computed along the nozzle wall can be output as punched cards

for input to the BLIMP, TBL, or MABL boundary .... ]ay-re--I,,_'cs._ ompu,.ter, pr_,sms.

_hese conditionsare taken by the boundary layer computer program as being the

Invlscidflow conditionat th_ edge of the boundary layer. Tables to be punched

are: x, F, and P/Pc (i.e.the nozzle wall coordinates and the ratioof pressure

to chamber pressure along the wall). The tables are punched In NAMELIST for-

: mat readable by BLIMP (seethe punched card listinggiven at the end of the sample

. output, Section 7).

A maximum of 50 er_trles upstream of the throat are saved and punched.

_e wall point at the end of every characteristic is punched up to a maximum of

., 500 totaltable entrles. The user may specify a number by which the punched table

will be offset. Thus, the firstpoint may be output with identification5 by input

•of I(21FF=4._he use of I_ enables the user to extend the table by adding points

upstream.

: If punched cards for input to a boundary layer program are required, the

...... = ................. t--- p.'_ of .,,,. Namellst input:

Item Name Description

_:" IPTAB = If IPTAB=_ , one title card will be punched (this will

•" be the last titlecard Input as described In 6.2) )

followed by tables of X, Y, and P/P,.along the nozzle

wall. These cards are for input to t_e BLIMP or i

MABL computer programs. The first poLnt punched will

correspond to beginning of the converging section of !

• the nozzle (t.e. at ECRAT; see Figure 6-i, also

table 6-8).

I_FF = The first point to be punched will be numbered as

Igfl_+l.

: IPTBL = If IPTBL and IPTAB=I, tables of M, T/T , C , V, and

.F, p, will also be punched. These additional _ards are

, required for inputto the TBL computer program (l.e, ;

the December 21, 1973 version).

If a _Dr problem is specified, the following items mus.___atlso b_ input

when IPTAB=I: RSI, RWTU, THETAI, and RI in SDATA.

These items define the nozzle geometry,from the combustion chamber through the

,, throat as shown In Figure 6-1. For a I'D]; option |t is necessary, that IPTBL=O. L

1

6-34 ._ "

l
6.5 ODKINPUT DATA

_DK input data is required if _DK :I or TDK =I in $DATAas described

in Section 6.3. The ODKinput data consists of three data groups as follows:

SPECIES data group

REACTIONS data group

$ ODK data group

These data groups are described below in sections 6.5.1, 6.5.2, and 6.5.3,

respectivly.

)

6. $. 1 SPECIE5

Species used by the cdmputer program are determined in several possible

" ways, depending upon the problem type. Methods used to determine chemical

species foreach probelm type are discussed below.

; For _DK problems species names and concentrations must be input, see

, Section 6.5.1.1.

; _DE-_DK i

I For _DE-@'DK problems the initialstartconditions forthe kinetic e_.__-

slon are obtained from an equilibriumcalculation. The species listgenerated by
I the equilibrium calculation generally contains many more species than the 40

species for which the _DK subprogram is dimensioned. Therefore a selection

0

: processes is required to interface the (_DE cal_=l .....l_t==d =,_,,ilck,._,,-_.=s.........,,,, t6_ conditLon_

: with the _FDK kinetic expansion calculations. This selection is performed using

the following rules:

Rule 1 If a species appears in a reaction, ,it is selected for the kinetic

calculation.

Rule 2 If a species is specified using INERTS directive it is selected

for the kinetic calculations.

Rule 3 If any species has a mole fraction greater than an input criterion,

it is selected for the kinetic calculation.

Species which are selected but which do not appear in a reaction are treated as

Inert and listed as such on the output list of selected species.

.. GfDE-_DK-'rDK

' For _DE-(_DK-TDK problems species ere selected by the above rules for

"_ (_DE-_DK problems. However, for multizone TDK cases it is necessary that

_ each zone have the same species list. _hus the INERTS input (see Section 6.5.2.7)

must _ used to assure the same species are selected for each zone.

; _K w,ith,Input Initial Line Option

Species names and concentrations must be input as described in

Section 6.8.2 when TDKIL-1 is input, in $DATA.

6.5.1.1 _fDK OPTION FOR INPUT OF INITIAL SPECIES CONCENTRATIONS (APPLIES

ONLY TO THE _SK PROBLEM TYPE_

This input begins with a single card with SPECIES in columns 1 through 7

• and with either MASS FRACTIONS or M_2tLEFRA,3TI_NS in columns 9 through 22.

• 1[ the identifier for mass or mole fractions is omitted, mass fractions are assumed.

Up to 40 species cards may be input. Only those species specified by input i

species cards will,, be co,n,side.red for an _DK pro,blem.... The order of the input
species cards is independent of the order In which the species appear on the

master Thermodynamic Data file.

' A chemical species Is identified symb_l|cel]y by 12 elphen,_,mer!c ch--r- '

acters end must correspond identically with the species name as It appears

on the Thermoa:mamic Data file. A complete list of the current species names

a_e listed in Table 6-4 (condensed species, however, may not be specified In

the species list.) The species symbol may not contain the characters * or =.

Co._.! Function

1-10 Not used

11-22 Species symbol (left Justified)

23-30 Not used

31-60 Value of initial species concen_ation {if zero

must be input as 0.0) free field F or E format

61-80 User Identification if desired

L 6.5.2 REACTIONS

v.

Chemical reactions must be input if ¢DK -1 or TDK =1 in SDATA. =

_-, Up to 50 reactions with an implied third body and a total 150 reactions may

-: by input to the program. Only one card per reaction, and only one reaction per

J

card Is petrol.tied. Cards specifying third body reactions must precede cards

specifying a!l other reactions. Species names appearing In the symbolic reaction

set must correspond IdenticaLly with the species names as they appear in the .,

master Thermodynamic Data (see Table 6-4). A card listing for a sample reaction

set Is presented in Table 6-10.

• The symbolic reaction set contains directive ca_'ds and reaction/data cards

In groups as outlined below: 0

REACTIONS Directive for start of symbolic reaction _

I input i

,I ." Reactions with implied third body speices "

, END TBR REAX Directive for end of third body reactions :

_, . All other reactions :

-! I

_ r

c i

6-37
; ORI NALPAGIs

i OF pOOR QUALllW,

i

I

! LAST REAX Directive for end of reactions

i INERTS Specified Inert Species

! _-IIRD B_DY REAX RATE RATIOS Directive for start of third body reaction

i rate ratios

Thirdbody reactionrate ratios J •

]

_i LAST CARD DLrectivefor end of REACTIONS input

i_] The content,and format of each type of card is defined as follows:

:!

,I 6.5.2.1 The symbolic reaction set begins with a card containing the word

!

,j RF_CTI(_NS in columns 1 through 9. Other columns on this card can be used

__ for comments.

I

I

i 6.5.2.2 Each card ddining a reaction is divided into five fields, separated by"

"! commas. Each field contains:

' field 1 a reaction

{ field 2 A = followed by a value of A

rate parameters

•., field 3 N = followed by the value of N for the reactions

,_ field 4 B = ,,,1T^,.,°_ t.,, ,_.., v._l.... _ B

the activation energy (Kcal/mole)

i field5 available for comments

! The general form of a react.ton is:

_,

. . . = +N b-Symbol b+

"' N 1 *Symbol 1 + N 2 *Symbol 2 + Na *Symbol a . . .

I where the left hand side represents reactants end the right hand side represents

•! products, The reaction can be either endothermic or exothermic.

The multipliers, N, must be integers and represent stoichlometric cot

f efflcients. H no stoichiometric coefficient is given, the value 1 is assumed. The

,t, dlxnensioning currently in the program requLres that:

i N I + N 2 + .... < I0 1

and

,! Na +Nb+ .... _10

The chemical species (denoted by the word "symbol" In the above general

, form) can contain up to 12 characters each of which must match a species name coni tained in the thermodynamic data (see Table 6-2 card 3)

:'i ' " [

6-38 :
ORIGINAL PAGE Ig

OF POOR QUALITY

examples:

. Reaction Interpretation

NA++CL-=NACT: .,_Q'v-+-_ CI- NeCi

s+++qZ--=

Be+++ 2¢H- = Be( 2

L

The value assigned to A, N, B define the forward (i.e. left to right) reaction rate,

k, aS

k = A • T-N • e-(10008/_T)

In units of cc, °K, mole, sac.

t

All three reaction rate parameters must be input. 1he numeric value of each paremeter may be specified in either I. F, or E format. If E format is used the E must

appear before the exponent.

• 6.5.2.3 ,_e reactions with an hnplled third body must precede other types of

reactions, and must be followed by the directive (columns 1 through 12):

f

• Col 1 4.

"""' TDR RF.,AX _e

: all reactions prior to the above dlJ_=ctlve will have a third body term added to each

- side of the reaction. E.g.

J

.g

H2=H+H, . . .

._ END TBR REAX

defines the chemical reaction

l

p

H2+M=H+H+M

where M Is a generalized third body. Specific third body effects may be included

by lnputing specific third body reaction race ratios as outlined in 6.5.2.8. Cards !,

encountered after the END _ REAXdirective card do not have a third body term i

added, i

! i

i

i All other reactions are input next, exactly as described under 6.5.2.2. :

t

6.5.2._i After the last reaction has been defined, a card with LAST REAX in

columns I through 9 is input. _

6-39 ,_ '

-,_p,
O_IL_I_ALPAGZ |_

OF POUR qUALITY

i

6.5.2.5 Reaction rate data for 13 dissociation-recombination (implied third

bod_/) reactions and 35 binary exchange reactions are listed in Table 6-10 for

_,, F, N and O. Tnese rates are

taken from Reference 16 (two additional reactions from Reference 1S are included).

Cards can be abstracted from Table 6-10 for input to the computer program. For

: the implied third body reactions, the third body, for which the rate applies is in-

; dicated in parenthesis In the comment field (M represents a "g.=neralized" third

body, see Section 2 2 for ;u_her detaLls).

6.5.2.6 INERT SPECIES OPTION

Inert species (i.e. species not appearing In reactions) can be included in

the input by input of a card with INERTS tn columns 1 _rough 6 followed by a list

•" of inert species names. The species names must each be followed by a comma

and each name must written exactly as in the master Thermodynamic Data. The

"_ last comma must be followed by, the word END. See Table 6-I1 for an example.

_- The species list can continue on to the next card, but a species name can not

overlap onto t3=_J_L _rd.

6.5.2.7 THIRD BODY RFACTION RATE RATIOS

As described above in Section 6.5.2.2 for the Jth reaction only one reaction

•- rat_., kj, where :

kj = AT'NJ e-Bj/_T '

: can be input, For three body recombination reactions such as

H+._H+M l= H2(_+M i

0 the rate of reaction Is in general different for each species, M l, depending upon

• the efficiency of the species, M[, as a third body collision partner. As discussed i

In Section 2.2 the temperature dependance of a recombination rate is approximately

Independant of the third body, i.e. _r the tth third body and jth reaction:

ki j _"Al j T-Nj e-Bj/_ T

[

The third body efficiency of *he ith species for the Jth reaction is then defined as

• mlJ = All/Aj

i

i J

i

6-40 t
-' OF POOR QUALITY

TALE 6-10 REAC22ONS AND RATE DATA FOR G,CLoF,H,N, AND O S_TEMS

(FROM _U[FERENCE 16)

NF&rTT_q ¢CLFHN_ NiY _-6 1977 JANNA_ _SWG KzAT*e-N [XP(-|0n0BINT)

. _w • H_fl , JsT,_F23 • Nm?,6 * _80•• (&R) HOe ]

fl * _ t OH , AIT•0_|R • Na|, * N_0** (AR) NO*

0 * n • 0P • in|,2F|? , _ml, • R80** (AR) NO• 3

F * F • R? , AmS.7[|S , Nst• , R80•• (AN) NO• 6

W * r • _r , ao2.S[IR • Nsl, * R•0.o ¢AR) NO. S

$ N • _? , Ji6•6_17 • Net, , 810., (&P) NO• 6

rn_ • O $ CO , P82.713_ • NI4•S , AII27•_SSo (NP) NO. ?

• n • ¢_ • J83.0116 , Ns,S , Rs0,• (M) N0. 8

w • N • _ . Amlo0[lm . wsl, * _•0o* (M) NOo 9

N * _ I k_l , I•6.6F1_ , Nt.S , 8S0oO OAULCH CN_) NO• 10

¢L * _ • CLF * J•_o0[16 • NSoS , N80** (H) NO• 11

• : _ * CL m MCL * im3.a[l_ • N8•S , aN0•• IN) NO. 12

! CL 6 CL • CL_ , ill.l[lq 9 NIl. , _10., IN| NO. 13

, [NO TH_ •FAX

_ . n. m. $ 0_. . 1•1•3F!3 , N•0, , Hm0,• BAUSCHNO._S

I ON * C_ • _ * ¢_ • JeS•_[|l • N•0° • _•|oO_0* 8_U_CH NO, 6|

8JULCH NO• 4_

N * hn _ 0 *.N? • Ja3,lF|3 • N8_• , 8803369 B_ULC_ NO, _O

: N $ _ • 0 * _n • Jub•_3E9 , N•--I. , 8•6•2_0• OiUbCH NO• S]

! Off * OH • H'_* 02 , 1zl.41£13, Ns.0|S* B•,9.?6_0 NO. _

N? * r m 10P'. _ , 1•5.011? • Nm_o 88S,?000 NO, _7

i+ H: * R? • _*F- _F • lsl*?_[10* N•-,S : 8839.?390 NO, _e

; N * (_.? • WC_eCt • Js3,0F16 . NS_o • 8•_.00n* NO• _9

i N_ * _.? • _CL*_CL , lsl.Tq[l 0' NU-oS , 8865.37S NO, 30

= l'k_L*F • _*CL , An|oqF|_ • N•*.68• 0m•60fl* NOo 32

._ CL?* F • CL*CLF , _s6,2[12 , Nno,68, O•.5flfl, NO, 33

CL * r_ • r *CLK • 1•7o6E12 , _s-°_, R•,308_ N0. 3_

CLK* _ • _*CL o _81.011_ , N8-•68, _m3•_O0o HOe 3S

CLR* H • Nt_L$_ * ImS°6[12 * N•**_8* 8nl,900. NO, 36

CLr* N? • ,eL•N• , I•1.8_10 , Ns*_S , 8e4_•337, NO, 37

FP * NCL • NF*CLR * 6s!•8_10 * NI*•S * 81]9•t77. NO• 38

" ¢_F* _4_t • bHreCL2 , 1•1,8[| 0 , NIn•S I _•66°_2S9 N0• 39

" F? * (_L? • CLF*CLR * A•1•811_ * N•'•S * 88_6,?$0o NO, _0

CnP* C • C_*Cn * aSl*lEt] * N•-,S * O•6•9qS* N0. _3

C * _ • CO* _ , a•5,3_11 • wt-°S , 885.67_, _0• _4

C * NO • CO* N , asS.3111 , N•-•S , _s8.303, NO, _S

C_?* N • C_*N_ * Ssl*l[ll , _•-oS , 0•5_o6|8, N0o &6

NOC $° n?_ •• CO* N?*Q2_ ,, Jinl•0 mS.3F|__|| ,* HNm_ o-•5• •, 0• 8•7q.690, 6._S?* NNO0•• 4719 !.

° n_ • _* N • _•5.3F11 , _•-•S , BaS._PR• NO. S0 *

OH * F • I_° 0 e ls_e9112 , _•-•6R• gs°2_flo NO, S_ [

H2_$ F • HF°_H , Jg|,6_| fl , NUmeTR* 8me,tiff, NO, S3 !

OH * Ct • _CL°O * aSSo0Ett * Ni-,S , O•_,_•

L_T OF_x
Thus mij is the ratio of the reaction rate with species Mt as the third body to i

the reaction rate input on the reaction card described In Section 6.5.2.2.

H reaction rate ratios, mtj, are to be input for the dissociatlon-recombin-

! at.ton reactions, a card with THIRD B_DY REAXI_ATERATIOSin columns 1 through

27 must be input next. If this card is deleted from the input, the prog...ramassumes

_. all mlj = l___jIf this card is included in the input, it must be fol1_wed either by :

a card with ALLEQUAL 1.0 in columns 1 through 13 (which sets all mu=l) or by

SPECIES cards as described below:

The mtj, can be input using a card with the word SPECIES in columns 1 through

7. This word is followed by the name of the Ith species followed by a comma,

followed by the values mij tn F format, each followed by a comma. These mij values

can be continued onto succeeding cards. Note that the mij values depend on the

- order of input of the reaction cards, i.e. the Jth reaction is defined by the jth

card input after the REAC_NS card.

_ Table 6-11 gives a sample input for a Hydrogen/Oxygen system using third

.bodyreaction rate ratios. In this example the three body recombination rates

are input with Argon as the third body. The rate with H2 as _ third body is a

factor of 5 larger then with Ar as a third body for the first three reactions and a

_" factor of 4 larger for the fourth (Hydrogen recombination) reaction.

6.5.2.9 At thispointin thedatainputdeck a cardwithLAST CARD in columns

I through9 must be input.

-i

6-42

I '
J

,i

2

i _ TAIK,E 6-11 LISTING OF SAMPLEREAC_ONS CARDS FOR AN O2/H 2 PROPELLANT

j . . .'

' OrArT!n_ _._ u_V 3.A |a_ j_,L_Mr oS_G

H • OH • H_O • AmTtSE23 o N•_,6 o BI0oo (AR) N01

• 0 * N • 0H 0 As6,0EI8 o _sl, .,.Ou0,t (AR) HO,

M * O • 0r * A=l,2E17 o N•I, o 8m0oO (AR) HOo

M • M • M2 o Am6.6El? o Nm;o 9 B80o9 (AR) HOe

_ END TBR REAx

M2 • O. • H * H20 _ Ai2,IgE13, NiO, , 8S_olSO BAULCH HOe

OH * MN • 0 * N20 o A#SiTSE|2o NmO, o Om,7RO_ _AULCH NO,

,_ " + _M • 0 * HE o A=To33EI_, N=0, o B"7,300, BIULCH _0, E

O * 0N x H.* 0_ o Axl,3EI3 , N•0o o Ox0** BAULCH _O, ;

LAST REIX

_NERTS N_tAR,ENO

TN_RD RODY REAX RATE RATIOS

SPECIES ARoj,o|o,|,O|o_

SPECIES H2oYoOS.,S.,_o,

S_E_tES _?Ot20.,5o,_.,_O.,

" SOECtES OEo_oOSoO_.S,I.S,

'" SPECIES N_*&,#4,I4,o|,S,

SOECtES ",1_,5,12,5,12,_,_So*

S_ECTES O,IE.S*IE.S.IE.S,2SoO

S_ECIES OH*I2oS,12,_,I_,S,ZS,,

LAST CARO
6.5.3 S#DKm_LIST INPUT.

$_K Namelist input specifiesthe conditions for the kinetic expansion calculation. The ir_ut i3 read in subroutine _DKINP and consists of the followinggroups

"_ d_ _ _,,_.14._._ i.^1....

6.5.3.1 Specificationof Nozzle Geometry

6.5.3.2 IntegratlonControl

6.5.3.3 Print Control

4.5.3.4 Species Selection and Mass/Mole Fraction

Check

6.5.3.5 #OK Problem Input

6.5.3.1 Specificationof Nozzle Geometry.

All of the nozzle geometry is to be input using the SDATA Namelist input, see

_ Section 6.3.3 and Figure 6-I.

_2

An _DK calculationwill be carried out for each mixture ratio input in _FSKED

of $_DE whenever _K = 4.or TDK = 1 in $DATA.

)i

For a TDK problem, it is necessary that the _DK calculationsbe run past the

nozzle throat. Usually it is not desirable to run the _DK calculationsall the way

to the nozzle exit because the extra computer time and print out that results.

However, if this is desized on a TDK problem, it can be requested by input of item

EP as describedbelow.

Assumed

Item Description Units Value(s)

t

i

$_DK = Namelist, read in subroutine

_ _DKINP.

EP = If TDK = 1 and a value is input none O.

here for _, then each ODK will be

run to expansion ratio EP.

!

6-44

k

q _ o 3
..

OF _ Q_j_L|TY

, 6.5.3.2 INTEGRATIONCONTROL

: The int_:_rm+4r,_'_ _._..,,ro. uth,econtrolsthe step size,_uch that the relative

error in the dependent variable increments are less than a prescribed fraction,

DEL. ©nly doubling or halving of the step size is permitted, and on option,

either all the variables may be considered (IF=0), or only the fluid dynamic

variables (IF=l) may be considered.

, When the flow becomes supersonic and the area defined flulddynamic

i

equations are used, an additionalcheck on continuityis applied in the form

: (pVA)N+I - (pVA)N I < C_NDKL

" (pVA)N+I i

>_

where C_NDEL is an input relative criterion.

" The step size is he!d between the two inputbounds HMIN and I-IMAX.

Fixed step cases may be run by setting input values f_r HI, HMAX, HMIN all

equal. Assumed

: Ite__m_m Description Units Value(s) _

• $_DK namellst, read in subroutine

ODKiNP.

HI = initialstep size non;: .01

HMAX = upper bound on step slze none 0. i0001

HMIN = lower bound on step size none .005

DEL = fractionalincremental none .0f)!

efro r !!"-

°

b

!

i

-!

_-

t

I

6-45 _
ORIGINAL FA_E [_

OF POOR QUALITY

Assumed

Item .Descr,ipti on Units Value(s)

TEXPL_ = t_mperature below which OR 0

explicit integration will

start. Not recon_nend_Yi.

• C(_NDEL = relative error crite_on for none Ixi0 -6

continuity check for supersonic flow

i

IF = 0 all variables considered none 0

for step size control

= J only fluid dynamic variables none

considered for step size

control, i.e., p,u, and T

6.5.3.3 PRINT CONTROL

h

Output from .the Kinetic Expansion Calculation consists of complete

i'.. output for each print s_ation selected. The end point of the nozzle is ;'lways

. 1)tinted. P_int statfons ave selected from one of the following options:

= Assumed

!tern Descripti on Value (s_)

v 4- r [PRNT = -2 print _h.oat and Input area ratios (see ARPRNT) -2

) :. = -I print at interna!iv s__tarea ratios for conical

,., nozzle.* Print at selected wall conto,.,r pointn

forcDntoured nozzles. For t' _-sp_ine fit

option (IWALL:4), print out will occur at

each entry in ZS of $SPP. For other contours (IWAiL=2 _r 3), pri_c out will

_, occur at 20 equal!_, spaced axial locations

, along the nozzle.

= 0 print at eve_/ integr_*.ionstep

i: = +I print every ND3rd step up to the throat and then nominal 2tea ratios

= +2 print every ND3rd step over entire nozzle

x

' *For [PENT =--I _nd a conicdl nozzle (:_. I'/VALL= I), the internally set area

• ratios are : i

: ARPP_¢T(1) = 2 3, I 29 _5 "2 _8,6r) 64 _16 i20 128 200 2!0

220, , ,4C"] ' ,

6-46 " _

Ca J
_AL ?ALZ ;::

If [PRNT is +I or +2, the following must be input: OF POOR QUAL[T'{

Ite_.__mm Description

NDi = firstintegration step to be selected for -

print

ND2 = last integration step to be selected for -

print

ND3 = print every ND3rd step between NDI and -

ND2.

If [PRNT is -2, the following must be input:

Ite.__.m_m Description

ARPRNT(1) = requested area ratios for print, must be -

monotonic increasing and greater than 1.0

" If no values are input, will use

.,. values from ASUP of $SPP.

NIPRNT = number of area ratios requested for print -

• -<I00.

An extended print option may be selected as follows:

; , Item Value Description

" IDYSCl = 0 no extended print requested 0

= I extended print option selectea (not suggested)

l

l
" ORIGIn/4- t:Av.= :

OF POOR QUALITY

6.5.3.4 SPECIES SELECTION AND MOLE/MASS FRACTION CHECK

In order to interface _D_F. equ!librium calculated start conditions

with the kinetic expansion calculations, special consideration must be made

for inert species (those not appearing in the reaction set}. Inerts may be select.-

ed explicitly by use of the INERTS directive or by use of a relative selection

criterion.

! It A MULTIZONE TDK PROBLEM IS SPECIFIED INERTS MUST BE SPECIFIED

VIA THE INERTS DIRECTIVE. This is required so that the chemistry selected for

multizone cases will be compatible.

The INERTS directive is described in Section (6.5.2.6).

The relative selection criterion (_DK or 1 Zone TDK problems,)

_ is described below:

?-

Item Narn_ Function

EFSEL = all species which do not appear expI,.c,tiy

-- in the reaction set but whose mole fractions :

are greater then the input vaiue for EPSEL, will

; :, be retained forthe klnedc extension. Species

selected under this criterion_re treatedas ine:'t.

The program assumes EPSEL= I.OE-5, unless input.

_, some instances it may be desirable to use input species concentrations

wldch do not sum to unity. Species concentrations, eitherinput or from equi,'ii

; brlum startconditions, are summed and the sum checked as described below.

Item Name Function '

,t P

°, XMFTST = Input species concentrations are summed and checked i:il

, versus unity using this input criterion. If [

II -_species conc,entrationsJ<XMFTST

then the test is passed. The species concentrations

will then be no,ma!ized such that

_specles concentrations = i.

The program assumes XMFTST = 1.0E-3, unless input. i

> If the test is not passed, an error message will be given and the I

run terminated. !_

6-48 _
(+]:

: ORIGINAL P,_.QEf_

OF POOR QUALITY

6.5.3.5 ODK PROBLEM INPUT

f

This input is required when PROBLEM _ODK is specified on the

prt)blem card. A kinetic ext_n.s!on from input a:bit_a_¥ start conditions is

to be computed. In addttio_ to the input items described in section 6.5.3, an

J_OKproblem requires input of those _tems described in sections 6.$. I and 2.

:' Item Name Input Quantity _ SI Units

' PC = chamber pressure PSIA N'/M a

T - lnitia I tern peru ture °R °K

V - initial gas velociW ft/sec m/sec

JI_IAG - 0 pressure table none none

ca lculated internally

- 1 pressure table input

= ECP,A_' - lnitlal cont,actlon ratio none none

For IPFLAG = 0 option the following must be input:

Item Name Inp, ut Quantity _ SI Unlt.q

PI = initial pressure PSIA N/M z

;, PESTAR = throat pressure PSIA N/M =

For IFFLAG = 1 option the followlhg must be input:

3

,: ,ItemName Input O uanti_ Units ',

' I_B(1) = norn:altzed pressure none

,. table entries*

ZTB(I) = normalized pressure none

table coordinates**

; NTB " number of pressure none i,

table entries, < 127 [

: Z = initialaxial posltion none "" i

s

- m i j

* normalized to input chamber pressuxe, PC L :

f ** normalized to input throat radius, RSTAR

! "

.' [

,°.
\ 6.5.3.6 MASS AVERAGED _9DK IBP

A mass averaoed _)DK ISP s-mm;__,'_na_g_ F "_Y _e "_,_;-_'_at *_^ end of

, the _)DK calculations as described below:

Item Name Description

_. MAVISP =! Specifies mass averaged ISP option

': AM(l) = Ratio of mass flow rate of each zone (zone I

-" inner zone) to the totalmass flow rate.

•ho

F' i

6-50 _
6.6 STRANS NA_IST INPVf.

, When a M_C problem has been specified, the input data set STRANS is required

for the transonic calculation.

Assumed

Item Description Value(s)

STRAN = Namelist, read in subroutineTRAN 50*0

XM(1) = Ratio of mass flow rate of each zone (zone 1

= i_ner zone) to the total mass flow rate.

(need not be input if MAVISP = I option specified and XM input in $_DK).

ALl = Number of degrees initial line will be disp- 0

laced downstream. _he program assumes ALI

is zero. If ALI is not zero, a symmetric

throat is required (RWTD = RWTU).

L IBUG = If input is nonzero, intermediatetransonic 0

_ output will be printed.

The following input may be used to control the constructionof the initial line:

•', Ite..__m Description Value(s)

MP Number of points to be placed on the initial 50

line. For RWTD < PMCPLT the number of

points placed on _ initial line will be

incrementedby the largest integer of theta,

the downstream tangent angle.

PMCRIT For RWTD > _4CRIT a sirmsiodal distribution J.

is requested; i.e.

.a

' eI '

i ri = [rwSin (W.5 )] i = 0,1,2....N

w_:re N = MP and eI is EXPI described belowEditir_ is done to control the spacing.

%

If RWTD < PMCRIT an initial line distribu-

( _ion will r-esult such that the first left :

.. running characteristicintersects the wall

i at a wall angle of PMDEG degrees. :

A 6-51 _ -
i

Assumed

__ Item OescriptloA Value(s>

PMDSG = Intersection angle, in degrees, for the I.

first left running characteristicif P,._!D_<

_IT.

EXPI = ei for sinusoidal distribution. 1.2

SEND

,m

l

iv

I

i

i

i

: 6-52
6.7 SMOC NAMELIST INPUT.

_is data set contains the IL_putitems for the supersonicMethod of CT_racteristics (MOC) module. The items are divided into four types, which are described

in the following subsections.

6.7.1 CharacteristicsMesh Control

6.7.2 Inputs from SD_

! 6.7.3 Print Control

_, 6.7.4 Exit Plane Option

Often no SMOC input is necessary since the default values are usually sufflcient.

3

.,°

b

!

i : i

!

i

6-53 , c
=

:i i

'I 6.7.1 CharacteristicsM_sh Contro]

! Item Name Input Quan,tity Units

_w#iM,nrv_ - Na.mlist name, read by subroutine l

CHAR

i DS =, insertions wtU be made such none

that successive points ,along

: streamlineswillnot b_ separated by more than DS.

DWWI = insertioncontrolparameter degrees

_ef_described in Section 5.9.2.

L_W = the program will insert such none

thatthe wall end point is

located within a tolerance EFVV.

IMAX ,, th_ maximum number of interatlons none

be allowed while attempting to

achieve a relative convergence for

the flow variables of 5"10-5.

IMAXF = I the program will terminatethe case none

ffa printedpoint requL,'esmaximum

Reratlons for convergence.

or

IMAXF - 0 program wLLI continue the case after ' ,

f IMAX Iterations per p_int have occurred none '

_{PLI = inputtemperature beiow which explicit °R, °K tfSI Units

integration for the species concentra-

. tlons wltlbe used. :

ECI-II = (8for point editing as described in degrees

; Section 5.9 2, CNTRL. '

] v L

ES = _s for point editing as described In none ,

r

Section 5.9.2, CN TRL.

DTWI = &etzucriterion for ln=e.rtlon in sub- degrees

routines INPT, DSPT as described

in Section 5.9.2, CN11_.

i

: i

6-54 {,
i

r

i

I_ 6.7.2 Print Control

if Item Name .input Quanzity Units

F

i! N1 = flow parameters will be printed none

for every N1 m interior ]_oint along characteristics selected

_: for print

'r N2 = every N2 th characteristic will none

be selected for print

NC = for NC _ 0 species concentre- none

irons (partial densities) will be

printed with the flow parameters.

If NC=I the quantll_Les 4' B,_,,

heat capacity (BTUP._- R), and

enthalpy (f_/sec 2) will be append-

,_ eel to the species concentration

: print.

M,a,SSI_ = at the completion of each left running none

characteristic (LRC) the massflow is

Integrated.

If

MASSFL = 0 then no mass flow printed

MASSFL = 1 then total mass n ...... " *_^

number of points on the LRC i

ere printed for each LRC i

MASSFL - 2 then mass flow for each point

along LRC is printed

MASSFL = 3 Same as MASSFL = 2 with the !

additionof execution time at

the end cf each LRC

see Section 5.8. I, CHAR

NDS = for NDS = 1 I_IvidingStreamlinePoints none

will be,printed. (Nominal)

for I_DS = 0 Dividing Streamline Points

will be suppressed.

!

i"

!

!

6-55
°

6.7.3 Inputs from DER, Reference 10.

Item Nerne Input Quantity Units

_FBAR - Overall mixture ratio in- none

aluding condensed phases.

For print out only.

ETABAR = Overall evaporation efficiency, none

i.e. the ratio of gas flow to

total propellant flow at the

throat, total

,E,TABARISp' = 'isp, .aas

DP,PISP ,. Ratio of total condensed lhf sec/_bm

phase momentum to the mass (tf SI Units then

flow ot the throat. Not used, N sec/kg)

reserved for future use.

b "

r

=

I

!

h

i

!

E

6-56

t

I
.% _:

, 6.7.4 Exit Plane Option

On option, the TDK method of characteristics calculation will continue

the mesh construction through the exit plane of the nozzle and print a summary

' of the exit plane properties.

_ R_m Name InputOuantltY Fun_ior_

ExrrPL - ,TRUE. Exitplanecalculation

requested.

6.7.5 Punch Inlti_Li lne

Duringany calculationgeneratingan initialine,the initialllne

may be punched in a formsuitableforrunningan inputinitialineoption. The

followlnginputis required.

i Input Ouantltv Function

4

i ILPCH = .TRUE. Requests_mchin_ of

. _ InitialLine

; IPUNrr = The Fortranunitnumber

- assignedto the PUNCH.

: (_..g. on Univac 110 8

IPUNIT = -3, on the

' othermachines itmay be i

! 7, 8, etc.)

IM ?ORTAN'rNOTE

: IF IFTAB= I optionis selected,i.e. theboundarylayeredge conditions

i punched frrTBL input,the initialllnepunched cardswillbe interspersed

wRh theTBL edge conditionspunched cards.

!

SEND

i

: i

I

}

6-.57 ',

t
6.8 Boundary Layer Module (BLM) Input Data, $BLM

This J:,putdata set is required if the BLM is to be executed, i.e., if BLM=I.0

was input in the SDATA namellst. Most of the data required by the BLM is com_micat_d au_umaticaiiy Oy t21e@[_Eand/or M_C modules, or is preset as assumed values.

Hence, these data items do not necessarily need _o be input to the BLM module.

However, any value thmt is read in will override the assumed or communicated value.

_he ir_u_ da1_ items to the BLM module are as follows.

Assumed

Ite_.__m Description Unit_.___s Value (s

$BLM - Nsmelist name, read in Subroutine

INPtEB

_ ITYPE = flag to specify the type of body I.

geometry

I = I, for an axisymmetric nozzle, requlred by SPP

= 2, for an axisy_etrio external flow

)

= 3, for a two-dimensionPi external

flow starting at a stagnation

.' point.

&

= W2D' nozzle mass flow If the TD22 ib/sec O.

module was not execu+_x_, a value

can be input here _o that a boundary layer ISP decrement can be

computed

J[

6-58 t
6.8.1 2LM Gas Properties

Gas properties that are required by the BZM ar_ Y, Cp, and U versus T, and a

value for the Prandtl number, Pr"

! If tables for Cp and y are not input (_ CPO, CKI],and TO, below) then the

program will prepare these tables usLng the _DE module. The tables are prepared

! using a series of (T,S) equilibrium calcuia_,.c,_-_,where T varies from 600% to

7000°R at 200°R increments. The chambe_ .... .___.... _.a_;value is used for S. Values at

• 100°R are then extrapolatedand added to the tahl"_., The.;_ble is printed with t2m

SLM output.

if constants defining the gas viscosity,U, and if the Prandtl number, Pr' are

not input, then they will be transmittedfrom the ODE module.

'" If the TD2P and _DE modules have not been run, then the data listed below must

be input.

Assumed

Item Description Uni_____ Value(s)

CKO(1) = table of ratio of specificheats, none 101"1.4

' Y, versus T.

CPO(1) = table of specific hret at constau,t ft/sec-R 101"6OO6

pressure, Cp, versus T

_' TO(1) - temperatures corresponding to ube OR 300,....70OO

entries in CKO and CPO arrays,

above

/ I

!

6-59 i
Assumed

I_____. Description Units Value(s)

.._rA_ = _umbec uf values enrere_ in CKO, - 24

the CPO, and TO arrays. 5 < 101.

!NTAB

_ RMUI = Refere-^eviscosity, _o' where vis- Ibm/ft-sec .605954"10-4

eosity is expressed as

I

! U = Uo(T/To)_

i

TI = referencetemperature,To, for vis- OR 6032

cosity. See RMUI, above.

_MEGA = Viscosity exponant,_. See RMUI, - .66843

above.

PR = Molecular Prandtl number, Pr - .4585

6-60

®
6.8.2 Boundary Layer Edge Conditions

The coordinates for t._2_bo,_,ndao- laye_ aL-_ specified in the RIN_ versus XIN@

table. Conditions at the invisid edge are specifed in the UE_, T_, and _ versus

tables. Conditions at the wall are specified in the TQW and CQW versus XTQW

tables. The program will redistribute the input stations (up to 201 total) in

order to have 101 x-statioru_ tmiformly distributed per segment, except for the

: first five stations which are generated non-muifomly. The input values of

! Y,Ue,Te,Pe,T w (or qw ), and (pV)w are interpolated at the new x-statlons and used in

= the boundary-layer calculations.

Values of RINO versus XINO and the conditions at the invisld edge of the boundam/ layer will be automatically Zransmlttad fr_ the TD_P module if it has been

real. Otherwise, they must be input here. See the description of I_FF in $DATA.

Condltio_ at the wall must always be input here.

Assumed

: Item Description Units Value (s)

&.

XIN_(I ) = xe axial coordinate none -

RIN_(1) = Ye' radial coordinate none -

U_(1) = Ue, gas velocity at the invisid ft/se_ -

TE_(I ) = Te, gas static temperature at the o- _

invisld edge

P_(3) = Pe' gas pressure at the invisld psi -

NXi_ _ number of itemsin theXIN_,RIN_,

.. UE_, T_, and PE_ tables. NXIN <

201.

h !

|

L

6-61 _
Assumed

Item Description Units Value(s)

X_W(1) = X , axial coordinate for the TQW _ .

and CQW tables.

IHFI_G - Flag specifying wall boundary con- - 1"

dition input through TQW array.

IHFLAG = O, for temperature

IHFLAG = I, for heat flux

TQW(1) = Tw, wall temperature or _, wall OR -

heat flux, depending in IHFLAG. or 3

ibm/sec

For an adiabatic wall, set IHFLAG =

I and all TQW(q) = O.

To convert (BTU/hr-ft2) to

' (Ibm/sec5) multiply by 6.9547,

_ which is Jg/3600.

-'- CQW(1) = (PV)w, mass transfer parameter at ibm/ft2-seo 101"0

:, the wall

NTQW . Number of axial stations, Xw. Each - -

of the above tables must have this

number of entries. NTQW ! 101.

b

i

6-62 '
6.8.5 IntegrationStep Size Control.

Asm_ed

Item Description T_ J.. ._"....t.

NSEGS = Number of Segments, 1_< NSEGS < 10 none 1

NISPS(1) = Number of Integration Steps per none 10"101

Segment,< 101 per segment.

XSEG(1) = Vector containing the axial (x) io- ft -

; cations which define the wall segments. The vector is always NS_GS

+ I values long and is defaulted to

the st_rtL-4gand ending values of

the wall table supplied by the TD2P

module. (The variable XI_BL is

used to define the startLng axial

; location for the boundary layer

edge table in the STD2 namelist.

[_ The ending points for the edge tab-

_.- le is taken as the nozzle lip.)

i NTR = Station at which transition to none 3

turbulent flow is allowed. The

program starts with an assummed

bo_dary layer profile, and then

turns on the eddy viscosity terms

for Odrbulent flow at station NTR.

_, For a laminar boundary layer, set

J ,

-' NTR large, e.g. NTR > r NISPS(I).

m

6-63

I )
6.8.4 RegenerativeCooling Heat Transfer.

When an engine is cooled using a regenerativedevice, propellant (usually fuel)

is routed around the nozzle so that heat is transmittedfrom the boundary layer to

the coolant. This heat is then returned to the.combustionchamber in the form of

increasedpropellant enthalpy. When the nJzzie wall temperaturesare assumed known

(IHFLAG = 0 option), the BLM will calculate the heat flux from the boundary layer

to the wall, _(BTU/ft -sec). These values can also be input directly (IHFLAG = 1

option). If the coolant circuit extends from position xe to position xo and operates at an efficiency,n , then the propellant enthalpy entering the chamber will be

increasedby

X

e

l"

; AH . !

(BTUIlm)

xo

where

": _T is the total engine mass flow rate

•A is the nozzle surface area differential,2_rdx

) Using the method outlined above, the BLM will compute incrementsof propellant

enthalpy for up to 3 fuel or oxidizer circuits and print cut the resultantenthalpy

increments. These can be added to a later co_puter run by using the DELHI(1) input

array. If BLM is to be automatically rerun, then the enthalpy incrementswill

automatically be stored into DELHI(1) for the second pass throu_ ODE, ODK, and

T[K. These enthalpy incrementscan be calculated in two ways. If the enthalpy increase is distributedequally throughout the chamber, then

AHi = AH

• i.e.

i

: DELHI(1) = AH, AH, .... eto.

t

: 6-64

, t

l
{

The second method is to assume that a fuel circuit adds enthalpy only to fuel,

ap_ an ox clrcult adds enthalpy only to ox. It follows that

for a fuel circuit

[

: re1

t AHi = (r--_)AH

and for an ox circuit

r+1 ri

, AM i --(r-_) _- AH.

where ri is the mixture ratio of zone i and r is the overall chamber mixture ratio.

For either method, the steady state engine cycle balance can be approximatedas

follows. First, calculate "adjusted tank enthalpies" for the fuel and for the oxidizer and input these on the reactant cards. _'_me values must approximate the

_' energy content of the propellant entering the main combustion chamber accounting

4-:

for all energy gains and losses, except heat returned to the main combustion ch_-

( bet by the regen cooling clrcuit(s). Estimatesfor these amounts are to be entered

using the DELH1(I) input array. An estimate of zero is usually satisfactory. Cor-

_-i rected estimates will be calculatedby BLM and stored in DELH1(1) for a second pass

"t through TEK (or TDE). I second pass using these values will be executed automatically if IRPEAT = I was input in the SDATA namelist.

$

p

t

J

P

i

|

[

, i

{ n

_ E

:! i

i

6-65

'L
Assumed

Ita_.__mm Description Value(s)

XO(1) = the Ith entry is the starting position for 3*0

, the Ith cooling circuit*.

XE(I) = the Ith entry is the ending position for 3*0

: the Ith cooling circuit*.

[

ETA(I) = the Ith entry is the efficiency for the Ith 3"I

cooling circuit.

+

_FC(1) -- Type of coolant for the cooling circuit: 3*0

_FC(1) = O. if there is no _.th CirCuit

_FC(I) - I, if the Ith circuit is oxidizer

_FU(1) _ 2. if the Ith circuit is fuel

. <3

,- DISTRB(1) = Flag for method of distributingAH incre- 3*0

merits

, DI_fRB(I) = O. for equal distribution of

" heat to chamber

DISTRB(I) = I. for distributionof ox heat 'l

to ox in chamber, and fuel !.

heat to fuel in chamber.

._ The Ith entry is for the Ith circuit, i

* Normalized by the throat radius, rt.

,, j

{

' 6-66 I i
6.8.5 B[24Plotted Output.

%_m input described below is used to control plotted output from the BLM. The

pioZ options available from BLM are:

I

I) Momentum thickness,e, vs. axial pcsition.

2) Displacementthickness, _*, vs. axial position.

• 3) Wall Tamperature,Tw, vs. axial position.

4) Velocity profiles at specified area ratios, or at speclfi_d axial

= locatloos.

5) Temperature profiles at specified area ratios, or at specified a_.ial

locations.

Example plots are presented in Figures 6-2 through 6-5 for types I through 5,

above.

Assumed

.. Ito__m_m Description Value.(s)

IPR_ = If IPR_F = O, then supersonicarea 0

ratios are input in APR_F.

If IPR@F = I, then axial locations, x/rt, are isput in APR_F

APROF(I) = Area ratios (or axial locations, 20*0

see IPR_F) at which velocity ratio

and temperature ratio profiles will

be plotted. Two frames per area

ratio will be plotted: U/U vs.

edge

y/y and T/T vs. y/y .

edge

NPROF = Number of area ratios (or axial 0

locations) requested in APROF.

- NPROF < 20.

• KDTPLT = If KDTPLT -I, then displacement 0

thickness, 6", vs. axial location,

.' x, will be plotted.

KMTPLT = If KMEFLT _ I, then momentum thiok- 0

ness, 8, vs. axial location, x,

will be plotted.

KTW_LT = If KTWPLT = I, then wall tempera- 0

tur_.,Tw, vs. axial loc_tionwill

be plotted.

SEND 6-67
"! . ORIGtNALp,c,_

_

' OFPOOR(_IJALI'I"Y Ii
..... ®.

ORIQIN,_PLAC_F,8

,Jr r'uuff _)UALITY
o_ _ou q_UTY
)

OF POOR QUALITY

O

O

._I.U

e_311

J

L_ II II II II II II

1" ct'j

oo-'i o_-d og.d o_.d oz.d oo'_d

3k/k "_

°r-.

lg "

L

°

.0 I--

_.j e-

' I# _# 11 II I

C= _'_ :

_]0"_ 08"6 09'0 0_'_] 0Z_ 00"O=

3Ai',i,

{t6-71 (_ '
6.9 SP_rlAL OPTIONS.

6.9-I Constant _ooerties Gas Optlon.

The TDK program contains a useful option by which the real gas chemistry can be

replacedby constant properties chemistry. Multiple zones can be calculated. The

: output includes the nozzle divergence efficiency,qDIV' (see Section 5, subroutine

PRINT).

i

The constant properties gas option is man by input of PFG_PT = I in $DATA.

Sample input data for the constant propertiesgas option is listed in Table 6-12.

0nly the $DATA, ST_AN and SM_C data sets are to be input. _lese data sets are

input as described in Sections 6.3, 6.6 and 6.7, respectively,with the following

: requir_ additions to the STRANS Namelist.

G(1) -- Value of specific heat ratio,Y, for _ach zone, inner to outer, the

number of zones is specified lh $DATA.

PSA = Chamber pressure in ibs/in2. (N/m2 if SI units)

XP(1) = (From Table 6-9) All assumed = 1, if not input.

%_(I) = Chamber temperature, OR, for each zone, inner to outer. (OK ix Si

 its)

RGC(1) = Real gas constant, f+2/sec2 OR, (i.e., 49721/._ = g*J*1.986/Mw) for

: each zone, inner to outer. (m2/sec2 OK if Sl unts)

XMW(1) = Gas Molecul_r Weight. If input then RGC(1) need not be input.

?

!°

6-72
OF pOOR QUALITY

Table 6-12: Sample Case for the _onstant PropertiesGa_ Option.

TIT_E S_"LE CASE O_C

' DATA

$0_r_

: PFGOPT=te

NZO_ES=[,

: RWTU=2, Q_TO=.5.

TH[TAz]5,0738_

IWALL=_e I

Nn$:tt,

_$C2): l.[o_3,[:2b_75,l,qTq10_i.73_75*2,0_9"0'_, u5930t

Z$(2): ,]Q575w ,530080 .8;_05wi.lg_13et,b6923f_,]2795_

q,b87-17,7,68599elO,q601et],3[[_,

THE:11.581_.

SE_O

, G:1,23,

;_ PSAz[O0_

TC,5500.

• XMs[#

SE_O

: IM0¢

,!

}

i

I

!

I

I

|

6-73 _: I :
]he following defines nominal values to which variables will be set if

not input. If a variable is ,e_$isted, no nominal vaiue _s set. Variables are set

in the subroutine containing the Name.list read..

; $g_DE, set in subroutine (2fDES

DELH(I) = o.

ECRAT -- O.

' EQL - .TRUE.

EQTHST = . FALSE.

ERATI_ = .FALSE

FA - . FALSE.

). FPCT -- ,FALSE.

_z - ._.

, I(_NS = .FALSE.

ICASE - 0

LIS TSP = .FALSE.

,. _ = . r_SE.

(_FSKED(I) = O.

P(Z) = o.

, PCP (I) = 0.

PSIA = , FALSE.

REI.ERR - .0005

RKT = . FALSE.

: SI = , FALSE.

SUBAR(I) = O.

._ SU'PAR(I) = o.

WFL_Ar = 0.

, XP(I) = 1.

i ,

o

I',

r

I 6-74

| '.

r

I
$

gDK, set in subroutinegDKINP

C_Nnm=!.0E-6

DEL= .001

EPS= 0.

EPSEL= 1.0E-5•

HI= o01

HMAX= .10001

HMIN=.005

IDYSCI=0

IWALL=1

Jr'=0

JPFIAG=O

]'PRNT =- -1 TEXFLI = Oo _OV_C_) = O.

XMFTST= 1.OE-3

STRANS, set In subroutineTRAN

ALZ- 0.

IBUG=0

)

MP= 50

PMCRIT= I."

PMDEG= I.

XlVi(1)= O.

STDK, set in subroutine CHAR

DP_PlSP= O.

DS=. 15

DTWI= 2. ' ' DW'WI - 3. _ = .01

ES= .005

it!i

6-75 |
STDK (cont'd)

_ ETABAR = I.

J

ETHI = .25

_ = 10

J

IMAXF " 0

MASSFL = 1

NC " 0

NDS = 1

N1 = I000

' N2 = i000

i

• k I

!

i i 6-76 1

t

!

:L. ,®: