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`Mathematical Problems in EngineeringVolume 5 (1999), Issue 2, Pages 97-119doi:10.1155/S1024123X99001015`

# Shashishekara S. Talya,1J. N. Rajadas,2 and A. Chattopadhyay1

1Department of Mechanical and Aerospace Engineering, Arizona State University, Tempa 85287-6106, AZ, USA
2Department of Manufacturing and Aeronautical Engineering Technology, Arizona State University, Tempa 85287-6106, AZ, USA

Received 29 July 1998; Revised 2 November 1998

Copyright © 1999 Shashishekara S. Talya et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Design optimization of a gas turbine blade geometry for effective film cooling toreduce the blade temperature has been done using a multiobjective optimization formulation. Three optimization formulations have been used. In the first, the average blade temperature is chosen as the objective function to be minimized. An upper bound constraint has been imposed on the maximum blade temperature. In the second, the maximum blade temperature is chosen as the objective function to be minimized with an upper bound constraint on the average blade temperature. In the third formulation, the blade average and maximum temperatures are chosen as objective functions. Shape optimization is performed using geometric parameters associated with film cooling and blade external shape. A quasi-three-dimensional Navier–Stokes solver for turbomachinery flows is used to solve for the flow field external to the blade with appropriate modifications to incorporate the effect of film cooling. The heat transfer analysis for temperature distribution within the blade is performed by solving the heat diffusion equation using the finite element method. The multiobjective Kreisselmeier–Steinhauser function approach has been used in conjunction with an approximate analysis technique for optimization. The results obtained using both formulations are compared with reference geometry. All three formulations yield significant reductions in blade temperature with the multiobjective formulation yielding largest reduction in blade temperature.