采用梯度方法对某型4.5级压气机最后级进行气动设计优化研究，梯度由连续伴随方法计算确定，多排伴随方程采用伴随掺混面模型进行数值求解。首先，采用基于经验修正的初步设计方法设计带进口导叶的4.5级低速、低压缩比压气机的原始气动外形。之后，在压气机近失速工况对最后级静子叶片进行伴随气动设计优化，通过优化叶型和安装角降低流动损失，目标函数定义为加权求和形式的熵增和流量偏差，优化中对流量进行约束。最后，开展基于伴随方法的多工况气动设计优化研究，改善两个不同转速条件下最后级的气动性能。优化结果表明，基于伴随方法的多排气动设计优化可以通过改变叶片气动外形提升多排全工况气动性能。
The paper presents an aerodynamic shape optimization of the last stage of a 4.5-stage com-pressor by a gradient-based optimization method that adopts the continuous adjoint approach. An adjoint mixing-plane formulation is used to compute the adjoint solutions for multi-stage turbomachines. Firstly, a conventional preliminary design method with empirical correlations are used to produce a base design of a 4.5-stage low-speed and low compression ratio compressor with an inlet guide vane. Then the last stage is redesigned by the adjoint method to reduce the flow losses at the operation condition near stall through modifying the aerodynamic shape and stagger angle of the stator blade. The cost function is defined as a weighted sum of entropy production and the deviation from a given mass flow rate, enforcing the constraint on mass flow rate. Finally, a multi-point design optimization approach by using the adjoint method is employed to improve the performance of the last stage at two different operation conditions. The optimization show that the adjoint-based multi-stage design can improve the aerodynamic performance of a multi-stage compressor by profile modifications.
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