Industrial Applications of Genetic Algorithms:Optimization of a Porous Liner for Transpiration Cooling Using a Genetic Algorithm

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Shortcomings in Traditional Approach to Transpiration Cooling

Before discussing transpiration cooling in detail, the general definitions of each type of cooling technique mentioned must first be briefly defined.

  Regenerative cooling - A cooling method in which one or more of the propellants are fed through passages in the thrust-chamber wall to provide cooling before being injected into the combustion chamber.

  Film cooling - A cooling method in which a thin film of coolant or propellant is introduced through the injector. Additional coolant or propellant may be introduced through orifices around the thrust-chamber wall or near the throat. This method has also been used in conjunction with regenerative cooling.

  Ablative cooling - A cooling method in which a wall material on the combustion-gas-side of the thrust-chamber is deteriorated by means of melting, vaporization, and chemical changes in order to dissipate heat. In addition, the ablative material usually serves as a good thermal insulator, keeping the heat transmitted to the thrust-chamber wall to a minimum.

  Transpiration cooling - A cooling method which introduces a coolant through a porous wall at a sufficient rate to maintain the desired wall temperature for the system.

In the late 1950s through the 1960s, engineers at NASA and other organizations analyzed various coolant designs for the budding space program. One such idea was a transpiration-cooled system which developed from the flow analysis of fluids through porous media. Kelley and L‘Ecuyer’s paper [1] about transpiration cooling theory and application details several attempts at preparing analytical equations for the coolant required for a specified set of hot-gas and coolant parameters. For instance, Kelley and L’Ecuyer detail some early work by Rannie [2] in reference to an oversimplified model of the basic theory behind transpiration cooling. Kelley and L’Ecuyer go on to explain others who have taken up Rannie’s simplified model and developed it further. A primary example is the theory of Rubesin [3] which included accounting for skin friction (and heat transfer) due to transpiration cooling. The opening segment of Kelley and L’Ecuyer’s paper deals primarily with an overview of the theoretical work performed on transpiration cooling up to 1966.

Earlier in the same year, Terry and Caras [4] of the research branch of the U.S. Army Missile Command, Redstone Arsenal presented a paper on the latest theoretical and experimental work on transpiration cooling at that time. Similar to Kelley and L’Ecuyer’s paper, Terry and Caras presented the current (1966) status of transpiration cooling along with the latest technology involved with the materials used for transpiration cooling. Although not directly citing individuals in the field, many of the theoretical developments given correspond to those of Kelley and L’Ecuyer’s work.

Studies were also conducted experimentally using the technology available at that time. Referring to a work presented earlier, Kelley and L’Ecuyer [1] discuss the experimental work that had been performed in the area of transpiration cooling before 1966. The primary benefit of this section of Kelly and L’Ecuyer’s paper was to compare empirical formulae with theoretical concepts. Similarly, Terry and Caras [4] analyzed the empirical data developed prior to 1966. However, their analysis deals primarily with material choice for the porous medium, coolant choice, and comparisons based upon these choices.

The papers presented in the previous paragraphs all lead to one main conclusion: there has been little development of transpiration cooled systems such as those described in this project since the late 1960s. Barring some minor developments in the 1980s and 1990s, little evidence has appeared as a breakthrough in the technology for transpiration cooling. Several of the papers discuss explicitly the lack of adequate, uniform materials and analytical tools necessary to make such a cooling technique effective. However, with current technologies, these hindrances no longer necessarily apply. These technologies include new uniform porous materials and simpler yet more effective designs. Improvements also exist in the state of computer design and optimization techniques which could benefit the study of transpiration-cooled systems greatly.

The Genetic Algorithm Approach

Through various conversations with representatives at MSFC’s propulsion lab as well as Dr. Charles Karr, no evidence of research has been found in the area of GAs and transpiration cooling of rocket thrust-chamber assemblies. One piece of information obtained relating to transpiration cooling is found in a 1994 paper presentation by Kacynski of Lewis Research Center and Hoffman [5] of Purdue University. The primary discussion in this paper was the development of a computer code called Tethys.

Tethys is a modification of an earlier code known as Proteus. The code consisted of a, “Complete multispecies, chemically reacting and diffusing Navier-Stokes equations, including the Soret thermal diffusion and Dufour energy transfer terms.” [5]. Tethys is basically an analytical tool for predicting flow characteristics, including Mach number and temperature profiles, along a chemically reacting rocket engine. This paper provides a description of the assumptions, equations, and conditions used in the development of the Tethys code. It also provides a comparison of the Tethys predictions with experimental tests of a film-cooled and transpiration-cooled rocket engine. Although providing great insight into the method with which to undertake the current project, the Tethys code relies on user-provided information and numerical computations. Unlike a GA, it does not perform search and optimization. It might, however, develop into a beneficial coding scheme for a GA.

As a result, a GA has the potential of creating an efficient, expeditious method of generating initial design dimensions for the coolant system of a transpiration-cooled liquid rocket engine. Using the hot gas flow data, as well as required coolant flowrates, the genetic algorithm is capable of varying the required design parameters in a way to create an efficient, low cost thrust chamber assembly for use in future rocket applications.

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