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International Journal of Rotating Machinery
Volume 9 (2003), Issue 5, Pages 353-361

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

1Turbomachinery Group, Korea Aerospace Research Institute, Taejon, Korea
2MAIDO Program, Department of Mechanical and Aerospace Engineering, UTA Box 19018, The University of Texas at Arlington, Arlington, TX 76019, USA
3Institute of Environmental Studies, Graduate School of Frontier Sciences, University of Tokyo, Tokyo, Japan

Copyright © 2003 Hindawi Publishing Corporation. 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.


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-ε 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.