Chapter 5
Optimization of a Porous Liner for Transpiration Cooling Using a Genetic Algorithm

Jeremy S. Lang

Department of Aerospace Engineering and Mechanics
129 Antioch Road
Somerville, AL 35670
e-mail: jlang@eng.ua.edu

ABSTRACT

In recent decades, rocket engine cooling has largely developed into a regeneratively cooled field. However, a resurgence of old concepts is playing a new role in current design ideas. The idea of transpiration cooling, mostly abandoned after development in the 1950s and 1960s, is once again being explored with new technology and materials. The technology presented here involves using a genetic algorithm to develop and optimize a liner for use in a proposed rocket engine. This liner allows an adequate amount of coolant to impinge on the hot-gas flow while maintaining a low injection velocity and pressure drop across the liner. The parameters the genetic algorithm manipulates include the height and width of the coolant channels behind the porous thrust-chamber wall, the porosity of the porous wall, and the diameter of the uniform capillaries in the wall. The genetic algorithm incorporates three main operators: roulette-wheel selection, single point crossover, and basic mutation. The genetic algorithm proves to be a successful tool in optimizing the coolant system with a proportional increase in fitness values over the generations created.

NOMENCLATURE

φ	porosity
ρ	density
Aopen	open area in the porous material
Asurface	area of the entire liner surface
Atc	area to be cooled
c*	characteristic velocity
Cmax	maximum value of a fitness parameter
Cpc	coefficient of specific heat for the coolant
f(x)	fitness function to be maximized
g(x)	fitness function to be minimized
g	gravity
hgx	hot-gas transfer coefficient
n	number of capillaries
D	diameter of the capillaries
Dt	hydraulic diameter
L	length of the capillaries
Q	volumetric flow rate
ΔP	change in pressure across porous surface
p	static pressure
Pr	Prandtl Number
R	nozzle radius of curvature at throat
T	temperature
V	injection velocity
	mass flowrate

SUBSCRIPTS

INTRODUCTION

Basis for Work

Research in the field of genetic algorithms (GAs) has expanded exponentially in a relatively short period. These search algorithms have been applied in a diverse array of disciplines, and the benefits resulting from these efforts have been numerous. Thus, GAs have the potential to benefit the area of design and analysis of liquid rocket propulsion systems. In this case, the liquid rocket propulsion system is being developed by the National Aeronautics and Space Administration (NASA) George C. Marshall Space Flight Center (MSFC) Propulsion Laboratory.

It is well known in the liquid propulsion field that current coolant systems primarily make use of regenerative, film, and ablative cooling techniques. Due to the proven technology and material development for these systems, they have been used in such designs as the Space Shuttle Main Engine (SSME, which is regeneratively cooled), and the test-bed engines for the X-34 reusable launch vehicle program (which utilize a combination of film and ablative cooling techniques.) However, the National Aeronautics and Space Administration’s (NASA) current goals for future engine designs are based on the ideology “reliable, reusable, inexpensive hardware.” Thus, engineers at NASA’s George C. Marshall Space Flight Center are looking back to the past for alternative cooling methods which may benefit their ideology.

Since the late 1960s, the transpiration-cooled system has not been rigorously examined. This is largely due in part to the lack of materials available as well as the lack of technology to develop such materials. With the technology available today, NASA has developed a renewed interest in the transpiration-cooling concept for possible future liquid propulsion systems. The result is an effort to develop an ultra low-cost assembly by adding a porous layer of material to effectively create a transpiration cooled thrust-chamber and nozzle. The ultimate goal is to improve the knowledge of and design procedures of transpiration-cooled rocket engines for future programs.