包含叶尖间隙影响的多级压气机流动稳定性理论模型研究

In order to predict the stall inception point, considerable progress has been made by two different types of research approach, which are numerical method and analytical models. Numerical method, which is to solve an initial boundary problem, is dependent on numerous computation consumptions which are unsustainable for industrial application. Most analytical models, which can result in an unambiguous judgment as to the stall onset point, require a plenty of simplification and empirical correlations, and cannot consider the effects of complex configuration on flow stability. Although much emphasis is placed on how the blade tip clearance affects the compressor characteristics, nowadays a rigorous and convenient parameter study on the causal connections between the stall prediction result and the tip clearance flow remains some way off. Meanwhile, the tip clearance flow with a great loss of kinetic energy plays a crucial role in setting the stall onset point of multistage compressor. Therefore, how to connect stall inception models with the tip clearance is still a problem of great concern in both industry and academic study. In the present investigation, a stall inception model of multistage compressor with the nontrivial effects of tip clearance will be developed on the basis of a body force approach and a recently proposed general theory of flow stability in turbomachinery. After a parallel computation program of high performance will be developed to calculate the eigenvalues of a large scale matrix involved in the established eigenvalue equation, this model can be adopted to solve the eigen frequencies of the whole compression system, and the flow instability inception boundary can be predicted. The above theoretical model can be straightly computed, and give a deeper insight into the significant feature of the tip gap related to the stall prediction over a broad range of the parameters of interest. This work could provide a reasonable technical approach to assess the stall margin during the design phase of future multistage compressors of high loading and performance.

为了预测旋转失速起始位置，国内外学者开展了数值计算和解析模型两类工作。数值计算方法求解初边值问题，依赖大量的计算资源，难以用于工程实际；大部分解析模型虽能给出清晰的稳定性判据，但应用大量简化和经验关系，难以考虑复杂几何结构影响。同时，多级压气机中的叶尖流动损失大，是影响压气机稳定性的关键因素之一。因此，如何将多级压气机稳定性模型与叶尖间隙模型相关联，并快速给出间隙流动对于失速起始预测的参数分析，是当前一个亟待解决的科学和工程实践问题。本项目将在已建立的叶轮机流动稳定性通用理论的基础上，应用体积力方法，发展考虑叶尖间隙流动影响的多级压气机失稳边界预测模型，开发用于大型矩阵特征值求解的高效并行算法程序，求解压缩系统的特征频率，开展稳定边界预测工作。这种新颖的模型理论既可以在数值解法上快速实现，又能够包含丰富的几何结构影响，有可能在未来多级高负荷压气机设计阶段提供有意义的稳定性预估。

旋转失速问题制约了航空压气机的性能，可能给整个压缩系统带来灾难性的后果。过去几十年来，国内外学者对此现象开展了大量的研究工作。目前有两类方法研究失速预测：一方面，大部分稳定性模型采用了大量的简化，应用很多实验数据或者经验关系，制约了自身的发展；另一方面，非定常数值模拟方法虽然能够包含复杂流动与几何因素的影响，但是巨大的计算量也使其不能在型号设计中发挥作用。因此，发展包含复杂几何与流场因素影响的快速的失速判据方法是当前叶轮机流动稳定性领域的重点问题之一。. 本项目围绕开发包含叶尖间隙影响的多级压气机稳定性模型为目标，基于体积力方法，发展了适合单排、单级、多排叶片的低速、高速轴流压气机失速模型，应用了谱方法高精度数值离散格式，建立了特征值方程问题，通过特征频率的虚部可以清晰的判断系统稳定边界。通过发展带体积力尖部修正系数的方法，定性的考虑了叶尖间隙大小对于失速裕度预测的影响。算例结果表明：模型计算的失速裕度对于端壁体积力系数并不敏感，但是较大的系数情况下会使得失速先兆波的传播速度增大。同时，本项目中还对扰动压缩性对于失速预测的影响做出了进一步定量分析。结果表明：扰动压缩性对于低速压气机失稳边界预测的影响较小，但是考虑扰动压缩性会明显提高高亚音压气机的失稳流量和失速扰动频率的计算精度。通过算例验证，本项目发展的稳定性模型对于低速、高亚音压气机失稳点流量的计算精度较高，与试验失速点流量的相对误差小于1.0%。相比于非定常数值模拟，这一方法的计算效率较高。. 总之，该模型不依赖于大量经验关系与试验数据，考虑了三维定常主流流场，包含了更多的流动细节，考虑了叶片展向位置基元级的造型影响，并且能够快速清晰的给出失速判据。因此，这样一种方法在未来有可能为压气机气动设计中的稳定性设计而服务。这便是本项目的研究意义和未来的应用潜力。.在项目实施过程中，研究成果主要发表在本领域国际一流期刊中，包含2篇ASME Journal of Turbomachinery、1篇ASME Journal of Fluids Engineering、2篇AIAA JOURNAL、1篇AIAA Journal of Propulsion and Power、1篇Chinese Journal of Aeronautics。