基于控制理论的气动优化方法的计算量与设计变量无关,可快速精确地完成控制变量的灵敏度分析.本文以出口熵增最小为目标函数,详细推导了二维 N-S 方程伴随系统的偏微分方程组及其相应的边界条件和敏感性导数的表达式.以拟牛顿算法为优化求解器,利用 CFD 方法求解流动变量,采用时间推进方法求解伴随方程,建立了基于黏性伴随方法和 N-S 方程的二维叶栅气动优化设计算法.
A computational complexity of design optimization of aerodynamic shape based on control theory is independent of the number of design variables, and it can realize the quick and exact sensitivity analysis of control variables. Being considered as the cost function, the minimization of outlet entropy generation is applied to a direct design, and the adjoint partial differential equation (P.D.E) of the 2D N-S equation, as well as its boundary conditions, and the finial expression of sensitivity gradient are deduced in detail. Combining quasi-Newton method as an optimization solver,using CFD method to calculate flow variables, introducing time-marching method to solve an adjoint equation, we develop design optimization of an aerodynamic shape algorithm based on viscous adjoint method and N-S equation for 2D turbine blades.
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