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

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.