Subject: A parametric study of a plug nozzle, using the Liquid Propellant Program (LPP) CodeBy: Stuart S Dunn, Douglas E Coats, Software and Er.gineering Associates, Inc.

Abstract

The Liquid Propellant Program (LPP) computer code is a super-set of the industry

standard Two Dimensional Kinetics (TDK) computer code, which has been developed by

Software and Engineering Associates, Inc. (SEA, Inc.) over the past twelve years. The TDK

code uses a Two-Dimensional Method of Characteristics solution with fully coupled finite rate

kinctics for axially symmetric nozzles. The chemical reactions are modeled with a generalized

reaction package that includes 3rd body efficiencies and four reaction rate forms. The code

performs optional solutions for frozen or equilibrium flow. TDK evaluates discrete shocks, both

attached or induced. The Transonic module models variable mixture ratio profiles fl'om the

combustion chamber injector. The Mass Addition Boundary Layer module (MABL) calculates

the boundary parameters with the same chemistry options, and includes transpiration or tangential

slot injection of gas at the wall.

The LPP upgrades include: planar nozzles, scarfed nozzles, plug nozzles, and scrarnjct

nozzle configurations. The code evalu_.tes both upper and lower wall flow simulation, and

includes the interaction with the external flow. The MABL module evaluates equilibrium

radiation heat transfer for both upper and lower walls. In addition, the LPP code models

combustion effects due to injector inefficiencies with the Spray Combustion Analysis Program

(SCAP) module. The LPP package provides extensive post plotting capabilities for flow

visualization. The LPP is sufficiently fast and robust to provide performance predictions for

extensive parametric studies and sufficiently accurate to provide flow field and performance

solutions for detailed studies.

The evaluation of a planar or axially symmetric plug nozzle has received recent interest

dtte to the SSTO studies. The LPP code allows easy modeling of a plug nozzle configuration,

since the user is allowed to input an arbitrary inner and outer wall geometry (referred to as the

plug and the cowl). The transonic analysis models both planar or axially symmetric annular

flow, including straited and variable mixture ratio profiles. When the internal flow reaches the

exit of the outer wall, a PrandtI-Meyer fan allows the flow to expand to the external pressure.

At this point, a pressure boundary condition is apl2lied for either quiescent sub-sonic, or super-

sonic external flow. The MABL analyses is subsequently performed to evaluate the boundary

layer losses for both the inner and outer walls. Following JANNAF standard procedures, the

characteristic analysis is automatically repeated with the boundar) layer compensated wall

geometry.

The above procedure was employed to parame_.rically evaluate the performance of several

plug nozzle configurations at different flight conditions. The altitude compensating effects are

evaluated and related to ideal conventional nozzle performance. An optimization technique Js

presented, which includes chemistry, divergence, and boundary layer effects. Graphical output

includes flow field contours, and wall properly profiles.

791

https://ntrs.nasa.gov/search.jsp?R=19960029260 2020-06-10T02:16:54+00:00Z

o_

o_

0

_9

0C_

C_04

© OU _

Cxl"n° _ ;Aooo_

°_-_ !

0

_ t-¢3

Z _ _ _iiiiiiiiiiiiiiiiiiiiiiii_iiii,i_¸ _.

t21

792

it.0t-.o

o0-

09

tn

o4

ILl09

c,O)opmq

©v----q

c_

c_ e::xC)

794

elum

©©

©

795

opU

0

©

©

o _ _

©

0

m

=IC._ °v--I

.v-,l

-_D

I I I I

00 0

0 0 ._

797

o.ot-

o

I.Lot-._o

tn

t-

tt_o)

4

l.tJ0_

o_

¢¢©

E

mare

ttt

-jqmelul

m

0

Z

0I

In

0II

CD

0

_ LL rn "_

c-

o CD 00-;-' CD

a X _.._ LLIn

0

0

0II

0 CDn-

u_

0 Q.. _r__rn

799

QI.t.0

¢...o

t.-,or_

t-

¢0

o_

_bt_

IJJ09

i

Z

J

.Jm

_0

• • • •

8OO

O)

ub

mintCY)

om

o_

I

|

I_. 0 0 0 0 0I_ 0 I_ 0 _ 0m _ ,_- _I" CO LY)

801

0(.(3

U')

C

m

C

o1.1_0c._o

LoOC_ a.

_....

(3)

W

o.o

III

Ol"l

-,Ill

,,Ill

r_

CO co

I

I

I

00

I I_

I

I

0Lrj

00

0

_lF

,1'

L

00

802

t_c,i

¢,¢

I

,.-. ¢_

aIi

0c'-

.--iO.

0 £IX.

0 _=

tbi'M

¢Cttl

_.Jn_

cotoL_

(3_

I--

_E

O3

(I

n_

I

rr

L__J

Ncoz

0

u13_

cy

c_J-t-

o

o3o3

co o_ LO(.0 C,,I ---,r--

• 0o0co ,-_ c,,I

(xJ (.0 0

_0__0

N_-_

O 0-) (_1 ,-,ZooLU • 0'3 (.13

C._ "_" ---, O0

__J O0 (_ .--

O0

oo

or)tO

(0

U3O0

O_O_O_

C,J

803

L_

n_

LUn-

O-

eo

U_

GO

l--

n-

n_

C_

J

J

UO

_1

N

Z

O

.J13_

C_

C_

I---U-3

-_

._

0_0_Zo"

.,

O'l

o°

1.0O0

O_O-nr

804

00" 9£

U/U

C_0

N

00

0C_

0

0

O0

oo

1",,,4

,,,--,I

;:=r,..3

00"0# 00"9_T

00"SZ

_(X3Oq

CDO

Oq

CDO

_(El)O4

CDED

_(_O

£D(Z3

_04

CDCD

B

QO

£D£D

B

(Z3tED

B

00" "Iz;_

n-.-

x

805

[._

,,,z

oo

i-4

,_1,_1I,--I

[._

I

O0"_G S/S

806

CD

_COO4

EDED

O,J

EDED

_EDO,,1

ED

_LID

X

EDED

_04

EDED

B

00

EDO

"<1-

EDC)

00"_8

oo

.,<

i-i

;:=

00"T

017]

00" SE:

807

00"T

C3CD

O0"#S

oo

00"_

_COCxJ

CDED

EDED

CxJ

EDO

_OD

OE

X

EDED

EDO

m

(DE)

C)O

EDED

m

00"_

808

ep_l

r_

!

!

I

t

I tl

D= 0 0 0 0

809

00CO

00

i

01.00_1

01.00_i

0

001.0

Q.

o

o0

.o

.mQ.o

O_

co

14)

o,I4-

LLIO_

0.m

r_

.m

0

.ilI

r_

@ _ ._m

i

¶ !

L

\ !

I

i

12. 0 0 0 0 0

810

000

O4

00

d

0O0

,.Q

.o

o,II.D _.

0')

r_

O4.o

• • • •

811

o¢-

o

It_ot.-o

o12.

cO.T.tt_

ub

lid09

©o_-_

©

©

0

0

0

812

I •