基于特征值理论的轴流跨声速压气机失稳预测

Axial Transonic Compressor Flow Instability Prediction Based on Eigenvalue Theory

流动失稳问题是叶轮机械所面临的严峻挑战之一,而旋转失速是轴流压气机及压缩系统中普遍存在的一种典型流动不稳定状态。基于特征值理论发展了一个轴流压气机流动失稳开始点预测模型,应用谱方法和奇异值分解(SVD)算法求解所建立的特征值方程,通过特征频率的虚部判断压缩系统的流动稳定性。并通过一个高速单转子在高低两个转速时的算例,定量分析了流动压缩性对跨声速压气机流动失稳开始点预测的重要影响。该模型可在合理的精度范围内,以工程应用可接受的计算资源消耗来预测跨声速单级压气机旋转失速的开始点流量,同时不应用大量经验数据,为压气机设计阶段的稳定性评估提供指导。

Flow instability is a great challenge in turbomachinery,and rotating stall is one major type of flow instability in compression system of aero-engine.In the present paper a rotating stall inception model based on a general eigenvalue theory of flow stability is developed with an emphasis on flow instability onset in axial transonic compressors.After solving the established eigenvalue equation using the spectral method and the singular value decomposition （SVD） method,the onset point of flow instability is determined by the imaginary part of the resultant eigenvalue.The significant effect of flow compressibility on the stall onset point calculation for a transonic rotor is studied by comparing the prediction results for a high speed single rotor at both high and low rotational speeds.The capacity of the present model to predict the stall inception point is assessed against the experimental data of a transonic single stage compressor.It is verified that this model is capable of predicting the mass flow at the stall onset point of a multi-stage transonic compressor flow with reasonable accuracy without numerous empirical data,and it is sustainable in terms of computation cost for industrial application.