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another practical optimization problem (IOSO vs Genetic Algorithm)

Dear Colleagues,

Let us continue viewing the efficiency of the application of various optimization methods on practical optimization problems.


 A constrained optimization oflocations and discrete radii of a large number of small circular cross-sectionstraight-through coolant flow passages in internally cooled gas turbine vanewas developed. The objective of the optimization was minimization of theintegrated surface heat flux penetrating the airfoil thus indirectly minimizingthe amount of coolant needed for the removal of this heat. Constraints werethat the maximum temperature of any point in the vane is less than the maximumspecified value and that the distances between any two holes or between anyhole and the airfoil surface are greater than the minimum specified value. Aconfiguration with maximum of 30 passages was considered. A parallelthree-dimensional thermoelasticity finite element analysis (FEA) code from theADVENTURE project at Universityof Tokyo was used toperform automatic thermal analysis of different vane configurations. The finiteelement analysis codes and tools for mesh generation, mesh partitioning, andothers (Fig. 1) are freely available as a part of the ADVENTURE project leadby the Universityof Tokyo. The finiteelement solvers are geared towards large-scale parallel analysis and are wellsuited to the efficient analysis of complicated geometries.









Figure 1: Modules used forautomatic parallel FEA.


The objective is to minimize the total amountof heat transferred to the vane (integrated heat flux on the hot surface of thevane) while maintaining a maximum temperature, Tmax, which is lower thanthe maximum allowable temperature, Tallow. This objective indirectlyminimizes the amount of coolant required to cool the vane. The minimization ofthis objective could result in the reduction of the number of cooling passagesas well.   

         Theouter vane shape is considered to be fixed and to be provided by the user atthe beginning of the design optimization. The design variables include theradius of each circular passage, ri, and position of the passage center,<xi,yi>, in the vane cross-section. The passage center isallowedto move normal to the outer contour within a specific region as shownin Figure 2. For 30 passages, this parameterization leads to a total 90variables. Examplemesh is shown in Figures 3. A typical mesh had around 80.000 nodes.


 Figure 2. Region wherecoolant passage centers are allowed.        Figure 3: View of a surfacemesh.

For both PGA and IOSO method,40 simultaneous analyses were run per iteration. The convergence history inFigure 4 shows that for this example the IOSO method outperforms the PGAmethod.










Figure 4 Objective functionconvergence history.


 As a total IOSO required only 800calls of the calculation model to achieve the convergence. The outer surfacetemperature on the optimized design is much closer to Tallow than in theinitial design as shown in Figure 5.



 Figure 5: Temperaturedistribution on suction side for initial design (left) and IOSO optimized bestdesign (right).

Full paper source Optimization of a Large Number of Coolant Passages Located Close to theSurface of a Turbine Blade (George S. Dulikravich, Dennis, B. H., Egorov, I. N. andYoshimura, S.), ASME paper GT2003-38051, ASME Turbo Expo 2003, Atlanta,GA, June 16-19, 2003.


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