轴向温差对不可压BEK边界层线性稳定性的影响

Linear stability analysis of incompressible BEK boundary layers subject to axial temperature gradients

  • 摘要: 涡轮轮盘腔内部流动普遍存在明显轴向温差,温差引起的流动特性与稳定性变化直接关系到高速飞行器涡轮轮盘的工作可靠性。本研究将盘腔流动简化为具有轴向温差的BEK(Bodonyi-Emanuel-Kleiser)边界层,基于Boussinesq假设,研究了轴向温差对基本流剖面及线性稳定性特征的影响。研究结果表明:轴向温差对盘腔边界层基本流及线性稳定性具有显著影响,且对稳定性的影响主要是通过温差对基本流剖面的改变起作用;冷壁使得基本流的拐点特征变得显著,从而增强了横流失稳特性,进而使无黏横流效应主导的Type I模态变得不稳定;对于黏性-科里奥利耦合效应主导的Type II模态,冷壁会使其变得稳定,热壁则产生相反的影响;温差对Type I模态的影响幅度远大于对Type II模态的影响;三类BEK边界层的稳定性对温差的敏感性存在显著差异:von Kármán流响应最强,旋转坐标系Ekman流次之,Bödewadt流响应最弱。本研究明确了轴向温差对BEK边界层稳定性的影响机制,为发动机涡轮轮盘腔的优化设计及流动稳定性控制提供了理论依据与工程参考。

     

    Abstract: Significant axial temperature differences are ubiquitous in the internal flows of turbine disk cavities, and their impact directly affects the operational reliability of turbine disks in high-speed aircraft. In this study, the cavity flow was modeled as an incompressible BEK boundary layer subject to an axial temperature difference. Based on the Boussinesq approximation, the influence of the axial temperature difference on the base flow profile and linear stability characteristics was investigated. The results demonstrated that the axial temperature difference exerted a significant modulation effect on both the base flow and the linear stability of the cavity boundary layer, and this effect is primarily achieved through the modification of the base flow profile by the temperature difference. A cold wall enhances the inflection point characteristics of the base flow profile, thereby intensifying the cross-flow instability. Consequently, the inviscid cross-flow dominated Type I mode becomes unstable, whereas the viscous–Coriolis coupled Type II mode is stabilized by a cold wall, and a hot wall has the opposite effect. The modulating effect of the temperature difference on the inviscid-dominated Type I mode is much stronger than that on the viscous–Coriolis coupled Type II mode. Furthermore, the three types of BEK flows exhibit distinct sensitivities to the temperature difference: the von Kármán flow on the rotating disk side shows the strongest response, followed by the Ekman flow in the intermediate layer, and the Bödewadt flow on the stationary disk side shows the weakest response. This study clarified the mechanism by which axial temperature differences affect the stability of BEK boundary layers, providing a theoretical foundation and engineering reference for the optimal design and flow stability control of turbine disk cavities in high-speed aircraft.

     

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