Optimization of Surface Heat Fluxes and Tem­peratures for Minimum Coolant Flow Rate

As a by-product of the aerodynamic inverse design using Navicr-Stokcs computation of the hot gas flow field (with the specified temperatures as thermal boundary’ conditions on the hot sur­face) the corresponding hot surface heat flux distribution can be obtained. Since one of the global objectives is to minimize the coolant mass flow rate, the total integrated hot surface heat flux must be minimized. This can be achieved efficiently by utilizing a hybrid genetic evolution/gra – dient search constrained optimizer |267| and a reliable thermal boundary layer code. Input to such a code can be the hot surface temperature distribution This temperature distribution can be discretized using (3-splines [268] so that the locations of р-splinc vertices (control points) can serve as the design variables. Each perturbation to the location of the P-spline vertices will create different hot surface temperature distribution. Wherever the computed hot surface local temper­atures arc larger than the maximum allowable temperature specified by the designer, they can be explicitly locally reduced to the maximum allowable temperature.

This temperature distribution and an already optimized hot surface pressure distribu­tion can be used as inputs to the thermal boundary layer code. The hot surface beat flux distribu­tion predicted by the thermal boundary layer code will be integrated to obtain the net heat input to die 3-D structure. After the hot surface temperatures have converged to their values that arc compatible with the minimum net heat input to the structure, the aerodynamic shape inverse design Navier-Stokes code can be run again subject to these optimized hot surface temperatures. The resulting 3-D aerodynamic external shape will be slightly different than after the first inverse shape design and if necessary, the entire hot surface thermal optimization will be repeated with the redesigned external shape.

This repetitive simultaneous minimization of the integrated hot surface heat flux and the truncation and maximization of the hot surface local temperatures will converge to the final

acrodynamically optimized 3-D external shape that satisfies optimized surface pressure distri­bution. maximum allowable surface temperature, and compatible hot surface thermal boundary conditions. The minimized integrated hot surface heat fluxes imply a minimized coolant flow rate requirement. Notice that this entire process does not require knowledge of the thermal field and the coolant flow passage configuration inside the internally cooled structure.