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

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TRANSPIRATION COOLING

The term transpiration cooling can be described by the following definition which states, “Transpiration (or sweat) cooling involves low speed injection of coolant through a porous wall.” [6] Transpiration cooling provides at least two principal heat reducing mechanisms. First, heat is absorbed by the cooling fluid (conduction) as it travels through the coolant channels against the direction of heat flow, from a reservoir to a surface of higher temperature and consequently lowers the wall temperature. Secondly, as the fluid emerges from the surface of the wall, it forms an insulating layer, or blanket, between the surface of the wall and the hot gas [3]. This insulating blanket is capable of reducing skin friction on the surface.

The goal of the current project is to design and analyze an engine that utilizes transpiration cooling. The basic concept here is to use a porous material as a liner through which the engine coolant can “seep” through to cool the thrust-chamber and nozzle. As can be seen in Figure 5.1, the coolant flows through channels behind the porous material. The coolant then flows with low velocity through the porous material to cool the hot gas side of the porous wall.

Figure 5.1 Basic concept of transpiration cooling through a porous material.

PROJECT GOAL

The primary goal of this project is to use a GA to optimize the design of a porous liner for a liquid rocket propulsion system. Now that the concept of transpiration cooling has been defined, the details of how GAs can assist in the design of such a system can be undertaken. This discussion involves the determination of the primary optimization parameters as well as the computer model and fitness function necessary to achieve this optimization.

In order to adequately design the transpiration cooling system, several parameters need to be adjusted to provide optimum performance in three categories. The parameters include items such as the material choice for the liner, the porosity of the liner material, the hole size for the pores, and the dimensions of the coolant channels which bring the coolant to the porous liner. Each of these variables affects certain aspects of the performance of the liner and the engine. The fitness function for this GA will be based on these performance aspects.

The major performance criteria selected for the GA are the following:

  1. Minimize the pressure drop across the coolant circuit.
  2. Minimize the injection velocity of the coolant from the porous liner into the hot-gas flow.
  3. Develop a simple, yet effective design.

The coolant in the injector is delivered through a coolant circuit behind the hot-gas wall. In order to reduce the number of design parameters considered in the problem, a copper material has been chosen for the porous liner. This material, developed by Alabama Cryogenic Engineering (ACE), can be formed with cylindrical, parallel, microscopic capillaries of varying sizes and porosities. These uniform capillaries greatly simplify the problems associated with naturally porous materials. The material simply adds the consideration of hole size and spacing. Along with the sizing of the coolant channels, these variables must be optimized to provide an adequate amount of coolant flow while preventing too large or too small a pressure drop in the coolant system. Considerations must also be made for the required low injection velocity of the coolant.

There are varying definitions for the porosity of a material. Experiments are usually required to obtain an accurate estimate of porosity for naturally porous materials. However, the uniform profile of the material presented here greatly simplifies this problem and lends itself to the following definition for porosity. The porosity of a material such as this can be described by the following equation:

The maximum/minimum values for the porosity are 90% and 0%, respectively. These values are set by ACE.

The important point to note here is that the porosity is the ratio of the open area of the material to its total surface area. Thus, porosity is a function of the capillary diameter and the number of capillaries. Porosity will also be important in other factors affecting the fitness function. Another important item to note is that the porosity can be changed as necessary along the length of the assembly. However, for simplicity, the changing of porosities has been limited to three distinct regions along the thrust-chamber and nozzle.

The capillary diameter is another parameter with limits set by the material manufacturer. In this case, the maximum/minimum values for the capillary diameter are 1000 micrometers and 5 micrometers, respectively. This range will be mapped into the alphabet used in the multi-parameter, fixed-point, binary coding scheme described later.

Also of importance in this design is the thickness of the liner material. An important fact to note is that as the liner increases in thickness, the weight of the entire system increases. The thickness also affects some of the important parameters listed earlier in the problem statement. Another parameter affecting the problem is the associated cost increase that occurs when the consideration of varying thickness is included. The range of values for the thickness of the material is a maximum/minimum of 1 inch and 0.125 inches, respectively.

The final two parameters which are critical in the design of the coolant system are the height and width of the coolant channels that flow behind the porous medium. These channels can be used to assist in the regulation of how much coolant flows to certain regions of the thrust-chamber assembly. The maximum/minimum dimensions for these parameters are 0.250 inches to .125 inches.

One consideration in the actual design of a transpiration-cooled liner is the pressure drop from the injector to the hot-gas wall. The pressure must be large enough to ensure that pressure fluctuations will not cause combustion to occur in the liner and coolant channels. A literature search was conducted to determine relations governing drops in pressure across a porous boundary. This resulted in several equations relating pressure drop to other fluid parameters. The equation used in this case will be Equation (5.2). This equation is developed using a model of identical parallel capillaries in the material. Using the definition of porosity (Equation 5.1), the pressure drop can be related to the geometry of the material, the flowrate of the coolant, and the fluid properties of the coolant.

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