Transpiration cooling

The comparative ratio of interest in the heat-transfer case is thus 

This equation is plotted in Fig. 12-4. It may be noted that the magnetic fiejld will increase the heat-transfer rate for positive values of the Eckert number (7X T ) and decrease the heat transfer for negative Eckert numbers (T 7T). This behavior results from the fact that the magnetic field tends to heat the fluid, thereby reducing or increasing the temperature gradient between it and the plate. 

It is necessary to caution that the foregoing analysis is a highly idealized one, which has been used primarily to illustrate the effects of magnetic fields on heat transfer. A more realistic analysis would consider the variation of electrical conductivity of the fluid and take into account the exact velocity profile rather than the slug-flow model. A survey of more exact relations for heat transfer in MFD systems is given in Refs. 1 and 2. 

For incompressible flow without viscous heating and for zero pressure gradient, the boundary-layer equations to be solved are the familiar ones presented in Chap. 5 when the injected fluid is the same as the free-stream fluid  

The boundary conditions, however, are different from those used in Chap. 5. Now we must take 

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Transpiration Cooling Cooling by this method requires the coolant flow to pass through the porous wall of the blade material. The heat transfer is directly between the coolant and the hot gas. Transpiration cooling is effective at very high temperatures, since it covers the entire blade with coolant flow. This method has been used rarely due to high costs. 

The trailing edge of the strut develops the highest creep strain. This strain occurs despite the sharp stress relaxation at the trailing edge projection. The creep strain in the strut is well balanced. Transpiration cooling requires a material of porous mesh resistant to oxidation at a temperature of 1600°F (871.1 °C) or more. Otherwise, the superior creep properties of this design... 

Figure 9-20. Temperature distribution for transpiration-cooled design, °F (cooled).

This design has the highest creep life next to a transpiration-cooled design, and it has the best strain distribution between leading and trailing edges. It is the closest to optimum. 

Behning, F.P., Schum, El.J., and Szanca, E.M., Cold-Air Investigation of a Turbine with Transpiration-Cooled Stator Blades, IV—Stage Performance with Wire-Mesh Shell Blading, NASA, TM X-2176, 1971. 

Although the correlations given by Eq. (6.48) are useful for practical evaluation of heat transfer to a wall, one must not lose sight of the fact that the temperature gradient at the wall actually determines the heat flux there. In transpiration cooling problems, it is not so much that the injection of the transpiring fluid increases the boundary layer thickness, thereby decreasing the... 

In the last section, convection in a two-dimensional porous medium is presented as a physical problem. Porous media is important in environmental heat transfer studies, transpiration cooling, and fuel cells, as some examples. Using the slug flow assumption, the energy equation is solved using an alternating implicit method to show its effectiveness. 

The boundary-layer equations may be solved by the technique outlined in Appendix B or by the integral method of Chap. 5. Eckert and Hartnett [3] have developed a comprehensive set Of solutions for the transpiration-cooling problem, and we present the results of their analysis without exploring the techniques employed for solution of the equations. 

An important application of transpiration cooling is that of plane stagnation flow, as illustrated in Fig. 12-8. Solutions for the influence of transpiration on heat transfer in the neighborhood of such a stagnation line have also been worked out in Ref. 3, and the results are shown in Fig. 12-9. As would be expected, gas injection or suction can exert a significant effect on the temperature recovery factor for flow over a flat plate. These effects are indicated in Fig. 12-10, where the recovery factor r is defined in the conventional way as... 

How do the boundary conditions for transpiration cooling differ from those for ordinary flow over a flat plate ... 

Other reactor concepts show similar features (see [1] and [4]), which include boundary layer control and internal recirculation. Reference [5] proposes boundary layer control utilizing transpiration cooling. 

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