Minimization of the Number of Coolant Flow Passages

Thermal boundary condition inverse determination В EM codes can than use the hot surface tem­peratures and heat fluxes and non-iterauvely predict the distribution of temperatures and heat fluxes on walls of the coolant passages. Convective heat transfer coefficients can then be com­puted on the walls of the coolant passages. These coefficients might locally exceed the realistic values attainable with the coolant flow in smooth passages. The locally varying heat convection coefficients should, therefore, be limited to their maximum allowable values The corresponding modified heat fluxes on the walls of the coolant passages can then be determined. These "cold" heat fluxes and temperatures will then be submitted to the BEM inverse code that will determine the corresponding “hot* temperatures and heat fluxes. The resulting computed hot surface tem­peratures and heat fluxes will be different from the optimized hot surface values. The difference between the computed and the previously optimized hot surface temperatures and heat fluxes will then serve as the forcing function in a constrained optimization code. It will drive the sizes of unnecessary coolant passages to zero, while relocating, resizing, and reshaping the minimum necessary number of the passages until the differences in the computed and the optimized hot surface heat fluxes and temperatures arc negligible. Minimum allowable distances among the coolant passages or from the thermal bamcr coating interface will serve as constraints (Figure 86 and Figure 87).

Figure 86 Minimization of the number of circular cross-section coolant passages inside a ceramically coated turbine blade airfoil: a) target geometry ; b) initial guess, and c) an almost converged final result of the inverse shape design [245).

 

Figure 87 Geometric history of the optimization of a single coolant flow passage in a three-dimensional turbine blade showing sections at (a) r * 0, (b) r ■ 0.25, <c) r » 0.75, and (d) г = 1.0 subject to the specified temperatures and heat fluxes on the blade hot surface and temperatures on the coolant passage wail [2531, [254J.

 

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