Choice of reference plane orientation depends on specific nozzle geometry, with different configurations requiring different reference plane systems. In addition, for given configuration several reference systems may be used in different regions of flow field, so each system is locally aligned with flow

Dash, S.

Ferri, A.

Guidice, P. D.

Roffe, G.

English

NASA Technical Reports Server

• December 1974	 B74-10236 
NASA TECH BRIEF 
Langley Research Center 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
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be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.C. 20546. 
Numerical Program for Analysis of Three-Dimensional

Supersonic Exhaust Flow Fields (CHAR 3D) 
.
The problem: 
The achieving of optimum performance in a scramjet-
powered hypersonic aircraft, where the propulsion 
system is a dominant portion of the vehicle structure, 
requires sophisticated vehicle-propulsion system inte-
gration. The engine exhaust may be underexpanded due 
to physical area limitations, thus requiring the use of the 
vehicle undersurface to provide additional expansion. 
This results in an interacting internal flow/external flow, 
three-dimensional, nozzle flow field. 
The solution: 
A numerical method based on a reference plane 
characteristic technique is used to analyze this flow. 
How it's done: 
In the reference plane method, the orientation of the 
reference planes is chosen so that the primary flow 
variations occur within the reference planes while the 
coordinate normal to them describes the local cross-
flow. The governing equations are written in this 
reference coordinate system, with the terms representing 
derivatives normal to the reference planes treated as 
forcing functions. The characteristic directions are those 
of the two-dimensional system in the reference plane, 
and the compatibility relations differ from those of the 
two-dimensional system by the inclusion of cross-
derivative terms. Flow variations must be continuous 
in the crossflow direction, while wavelike discontinuous 
flow is permissible in the reference planes. 
The choice of the reference plane orientation depends 
on the specific nozzle geometry, with different config-
urations requiring different reference plane systems. In 
addition, for a given configuration several reference
systems may be used in different regions of the flow 
field, so that each system is locally aimed with the flow. 
The numerical procedure in a given reference plane 
employs a Hartree-type numerical grid, with the stream-
line projections being traced in the individual reference 
planes. This approach affords excellent flow visualiza-
tion through the tracing of these quasi-streamlines and 
provides self-enforced mesh controls. 
The gas mixture considered consists of air and 
combustion products (with hydrogen as the fuel) and is 
assumed to be inviscid and in chemical equilibrium. 
Three parameter curve fits (p, 0, and h) have been 
developed for the necessary thermodynamic properties. 
The flow may be rotational and nonhomentropic. The 
overall numerical approach is second order. 
Notes: 
1. This program was written in FORTRAN IV for the 
CDC 6000-series computers. 
2. Inquiries concerning this program should be directed 
to:
COSMIC 
112 Barrow Hall 
University of Georgia 
Athens, Georgia 30601 
Reference: LAR-1 1596 
Source: Sanford Dash, Paul del Guidice,

Antonio Fern, and Gerald Roffe of

Advanced Technology Laboratories, Inc.

under contract to

Langley Research Center

(LAR-1 1596) 
Category 09, 03,06 
This document was prepared under the sponsorship of the National
	
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Government nor any person acting on behalf of the United States
	
will be tree from privately owned rights.
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Numerical program for analysis of three-dimensional supersonic exhaust flow fields (CHAR 3D)

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