基于控制理论的压气机叶型数值优化方法
Numerical optimization of compressor blade profile based on the control theory
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摘要: 将基于控制理论的气动优化方法应用于轴流压气机叶型设计.以Euler方程作为流动控制方程,具体推导得出了其相应的伴随方程,分析了边界条件,并给出求解方法.以给定压力分布作为目标函数,将参数化叶型作为设计变量,在求得目标函数对设计变量的梯度信息后,结合BFGS优化算法得到优化方向,更新设计变量完成叶型的优化设计.通过三个算例验证了该叶型优化设计方法的有效性.Abstract: An aerodynamic optimization method based on the control theory has been applied to the axial compressor 2-D blade profile design.The correspondent adjoint equations on the basis of Euler equations and the relevant boundary conditions were deduced in detail.The solving method for the adjoint equations was also proposed.The procedure to conduct an optimized design of a compressor 2-D blade profile could be divided into three steps.First,the required surface pressure distribution is pre-specified and set as the objective function.Second,the parameterized blade profile is seen as a set of the design variables,and the gradients of objective function to the design variables can be calculated by solving the adjoint equations.Third,a new blade profile is obtained by using the BFGS optimization algorithm,and this process is repeated until a converged profile is obtained.The proposed method has been validated by three illustrations.
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