Rotor Cascade Shape Optimization with Unsteady Passing Wakes Using Implicit Dual-Time Stepping and a Genetic Algorithm

Abstract

An axial turbine rotor cascade-shape optimization with unsteady passing wakes was performed to obtain an improved aerodynamic performance using an unsteady flow, Reynolds-averaged Navier-Stokes equations solver that was based on explicit, finite difference; Runge-Kutta multistage time marching; and the diagonalized alternating direction implicit scheme. The code utilized Baldwin-Lomax algebraic and $k$- $\epsilon$turbulence modeling. The full approximation storage multigrid method and preconditioning were implemented as iterative convergence-acceleration techniques. An implicit dual-time stepping method was incorporated in order to simulate the unsteady flow fields. The objective function was defined as minimization of total pressure loss and maximization of lift, while the mass flow rate was fixed during the optimization. The design variables were several geometric parameters characterizing airfoil leading edge, camber, stagger angle, and inter-row spacing. The genetic algorithm was used as an optimizer, and the penalty method was introduced for combining the constraints with the objective function. Each individual's objective function was computed simultaneously by using a 32-processor distributedmemory computer. The optimization results indicated that only minor improvements are possible in unsteady rotor/stator aerodynamics by varying these geometric parameters.