Computer program uses Bernoullis formula and Newton-Raphson method to provide steady state fluid flow analysis of line pressure drop in a system with six outlets for each of two main storage tanks. Program flexibility arises in the ease with which changes in the fluid line geometry can be made

Clark, R. L.

English

NASA Technical Reports Server

November 1967
	 Brief 67-10414 
NASA TECH BRIEF 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Computer Program Provides Steady State Analysis for Liquid 
Propellant Propulsion Systems 
The problem: 
To design a computer program that will provide 
performance analysis in the application of steady state 
fluid flow theory to determine line pressure drop in a 
system with six outlets for each of two main storage 
tanks. It was desired to make a study of the engine 
performance of the Apollo reaction control system in 
variable firing modes. When considering the mathe-
matical model setup of the pressure drop relations 
between each of the six engines under consideration, 
given by an extension of Bernoulli's formula for pres-
sure drops between two points, a problem was pre-
sented in that two unknown variables appeared in 
each relationship. 
The solution: 
The application of Bernoulli's formula for pressure 
drops between two points provides the main aspect of 
the theory of fluid flow for the solution. The applica-
tion of a numerical scheme referred to as the Newton-
Raphson method presents an iterative solution 
to Bernoulli's pressure drop relations in a manner which 
results in fast execution time by the computer. 
Execution provides computed output of chamber pres-
sures, thrusts, mixture ratios, injector pressures, line 
pressure drops, flow rates, and characteristic velocities 
for all engine modes fired. Program flexibility arises 
in the ease with which changes in the fluid line geom-
etry can be made, i.e., line length, diameter, and shock 
losses. 
How it's done: 
The problem of solving for the flow rates of each 
engine is readily adaptable to solution by numeric 
methods. A common method of obtaining these solu-
tions is that of starting with an initial approximation
to the solution that is desired and employing a recur-
rence formula to construct a sequence of successive 
approximations which will converge to the desired 
solution. The Newton-Raphson method is an iterative 
scheme which obtains a solution in the manner 
described. 
The equations to be solved are formulated from 
pressure drop relations found by Bernoulli's formula. 
The pressure drops are found from the propellant 
tanks to each of the six engines. Each equation is 
then set to zero by transposing the pressure drop to 
the right hand side giving 12 equations in which the 
unknown variables are the flow rates and chamber 
pressure. 
Notes: 
1. This program is written in Fortran IV for an IBM 
7094 computer. 
2. Inquiries concerning this program may be di-
rected to:
COSMIC 
Computer Center 
University of Georgia 
Athens, Georgia 30601 
Reference: B67-10414 
Patent status: 
No patent action is contemplated by NASA. 
Source: R. L. Clark 
of North American Aviation, Inc. 
under contract to 
Manned Spacecraft Center 
(MSC-10064) 
Category 06 
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19670000414 2020-03-11T21:09:56+00:00Z


Computer program provides steady state analysis for liquid propellant propulsion systems

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