基于突变理论的压气机失速边界预测新方法

The theoretical prediction and numerical determination of stall points and stall boundary of compressor “abrupt stall” is still one of the biggest challenges for fluid mechanics. The difficulty lies in: 1) the “catastrophe” of stall process and the “hysteresis” of recovery process can cause the discontinuous change of the system state, non-differentiable in mathematical description, which result in theoretical modeling become extremely difficult; 2) For the dynamic incentive of “catastrophe” and “hysteresis” in the entire process of abrupt stall and the key factors which impact the change of “hysteresis loop”, there is still a lack of systematic theoretical analysis and experimental study. The above mathematical and physical problems lead to the determination of stall points and stall boundary still can only rely on the limited experimental measurement data. This item is committed to the experimental study and theoretical analysis of dynamic characteristics of the complete stall change process, reveal the effects of different physical variables on the compressor stable and unstable state and the change rule; based on catastrophe theory, develop the cusp catastrophic model which can be used to describe the complete stall process of abrupt stall; through the development of the solution method of model equation, acquire the technical approach of determining the catastrophe points of the system state; based on topology analysis, explore the topological mapping relationship between the compressor stall and the standard cusp catastrophic model, and establish the prediction method and criterion of the compressor stall points and boundary.

压气机“突变型失速”失速点及失速边界的理论预测和数值判定仍是流体力学所面临的一大难题。其难点在于：1）失速过程的“突变性”和恢复过程的“迟滞性”造成系统状态变化的不连续，在数学描述上不可微，导致理论建模变得极为困难；2）对于突变型失速完整过程发生“突变”和“迟滞”的动力学诱因以及影响“失速环”变化的关键因素，仍缺乏系统的理论分析和实验研究。上述数学物理两类问题的存在，导致压气机失速点及失速边界判定仍严重依赖于有限的实验数据。本项申请将致力于完整失速变化过程动力学特性的实验研究和理论分析，揭示不同物理变量对压气机稳定和非稳定状态的影响及变化规律；基于突变理论，发展适用于突变型失速完整过程描述的尖点突变模型；通过模型平衡曲面方程的求解，获得判定系统突变点的方法；在拓扑学分析基础上，探索压气机失速与标准尖点突变模型的拓扑映射关系，建立压气机失速点及失速边界的预测方法和判定准则。

压气机“突变型失速”失速点及失速边界的理论预测和数值判定仍是流体力学所面临的一大难题。项目研究针对这一核心问题，完成了四个方面的研究工作：（1）失速非线性流动特性的实验和理论分析：借助翼型“post-stall”恢复特性数值模拟以及突变型失速完整动态变化过程的模型实验，探究了失速过程“突变性”、“迟滞性”等非线性流动特征，并结合经典的Moore-Greitzer模型分析了影响压气机失速迟滞性的关键控制参数及物理机制；（2）失速非线性过程描述的理论建模：对比压气机的压升特性和尖点突变模型的空间拓扑，发现二者具有相似的拓扑性质，由此基于尖点突变模型的构成原理，构建了压气机系统的平衡曲面方程，通过选取多条控制线探究了压气机系统在多参数影响下的模式转化特性，并通过求解该平衡曲面方程，建立了压气机失速点的判定方法；（3）压气机失速边界预测方法：利用RBF神经网络，发展拓扑映射方法，构建了尖点突变模型的突变边界与压气机在部分工况下失速点集合的拓扑映射关系，从而利用已知的尖点突变模型的突变边界去预测未知的压气机失速边界，形成了压气机失速的边界预测方法；（4）边界预测方法的实验验证：针对某台低速轴流压气机，通过发展的边界预测方法和实验方法分别获取压气机在不同转速工况下的失速边界，并将二者进行对比，发现模型的预测精度均在3%以内，由此证明了所发展的边界预测方法的可靠性。.通过上述工作的开展，较为系统的完成了理论分析、模型方法探索和模型的实验验证，形成了一种新的压气机失速边界预测方法，其有望为传统的数值模拟方法提供失速点的判据，以及在压气机设计阶段有效的预估压气机的稳定裕度，指导压气机的设计。