Aerodynamic Optimization and Inverse Design of 2D and 3D Turbine Cascades Using the Discrete Adjoint Method

Abstract

The adjoint method has significant advantage in sensitivity analysis because its computation cost is independent of the number of the design variables. In recent years it has been applied greatly in aerodynamic design optimization of turbomachinery. This paper developed the discrete adjoint method based on the authors’ previous work and demonstrated the applications of the method in the aerodynamic design optimization for turbine cascades. The Non-uniform Rational B-Spline (NURBS) technology was introduced in the current design optimization system and a flexible parameterization method for 3D cascade was proposed. Based on the parameterization method, the stack line and the blade profile are parameterized together by using NURBS curves. During the design process, the control points of the profile, the stack point and the stagger angle of the blade on each section can be taken as the design variables. Moreover, the flow solver and the discrete adjoint solver were extended towards the turbulent flow environment by adopting the k – ω turbulence model. Based on the optimization design system, several applications including two optimization design cases and two inverse design cases for 2D and 3D turbine cascades were implemented with the mass flow ratio constraint. The gradient verification and the numerical cases showed the correctness and accuracy of the discrete adjoint solver. The numerical results demonstrated the validity and efficiency of the design optimization system based on discrete adjoint method.