Application of iterative algorithms for gas-turbine blades cooling optimization

This paper presents two iterative algorithms used to solve the inverse problem of gas-turbine blade cooling. First of them was obtained by variational calculus methods, and the second one is reduced to solving the least-square approximation problem. To determine the temperature distribution on the inner boundary of the blade (of the multiply-connected region), a combination of trigonometric functions defined on the boundary of a unit circle was used. Both algorithms are presented in two variants: the first one is about reducing the number of trigonometric functions, and in the second one, coefficients of trigonometric functions are regularized in the process of iteration. Results of calculations indicate that both algorithms operate more effectively in the variant where coefficients of linear combination of trigonometric functions are regularized.