Optimum Design of Axial Flow Gas Turbine Stage—Part I: Formulation and Analysis of Optimization Problem

Abstract

The problem of stage design of axial flow gas turbines has been formulated as a nonlinear mathematical programming problem with the objective of minimizing aerodynamic losses and mass of the stage. The aerodynamic as well as mechanical constraints are considered in the problem formulation. A method of evaluating the objective function and constraints of the problem is presented in Part I of this paper. The optimization problem is solved by using the interior penalty function method in which the Davidon-Fletcher-Powell variable metric unconstrained minimization technique with cubic interpolation method of one-dimensional minimization is employed. Problems involving the optimization of efficiency and/or mass of the stage have been solved numerically in Part II of the paper. The results of a sensitivity analysis conducted about the optimum point have also been reported.