On the Self-Similarity in an Annular Isolator under Rotating Feedback Pressure Perturbations

Abstract

In this paper, the transient flow simulation in an annular isolator under rotating feedback pressure perturbations simplified from the rotating denotation wave (RDW) is performed. The instantaneous flow characteristics and the self-similarity of the isolator flow-field are investigated in detail. It is found that a helical moving shock wave (MSW) and a quasi-toroidal terminal shock wave (TSW) are induced in the isolator. Hence, the flow-fields on the meridian planes could be classified into three zones, i.e., the undisturbed zone, the terminal shock wave/moving shock wave/boundary layer interaction (TSW/MSW/BLI) zone and the moving shock wave/boundary layer interaction (MSW/BLI) zone. The TSW/MSW/BLI zone is characterized by the coupling of the TSW/BLI and the MSW/BLI due to their small axial distance, which intensifies the adverse pressure gradient on the meridian planes, thus rolling up large separation bubbles developing along the MSW driven by the circular pressure gradient. In the MSW/BLI zone, the shock induces the boundary layer to separate, forming a helical vortex located at the foot of the MSW. During the upstream propagation process, the pattern of the MSWs transforms from a moving normal shock wave to a moving oblique shock wave with decreased strength. Moreover, after the collision with the MSWs, P, Temp and S of the flow elevate with the prompt decrease of va, while vθ increases to a higher level. Despite the deflection effect of the MSWs on the streamlines, the flow direction of the air still maintains an almost axial position at the exit, except in the adjacent region of the MSW. Likewise, three types of zones can be determined in the flow pattern at the exit: the rotating detonation wave/boundary layer interaction (RDW/BLI) zone, the expansion zone, and the vortices discharge zone. Comparing the transient flow patterns at different moments in one cycle and between adjacent cycles, an interesting discovery is that the self-similarity property is observed in the flow-field of the annular isolator under rotating feedback pressure perturbations. The global flow structure of the isolator at different moments shows good agreement despite its rotation with the RDW, and the surface pressure profiles of the corresponding meridian planes all match perfectly. Such a characteristic indicates that the rotation angular velocity of the TSW and the MSW are equal and hold invariant, and the isolator flow could be regarded as a quasi-steady flow. On this basis, the theoretical model of the inclination angles of the MSW by the coordinate transformation and velocity decomposition is developed and validated. The relative errors of the inclination angles between the predicted and measured results are below 3%, which offers a rapid method to predict the shape of the MSW, along with a perspective to better understand the physical meaning of the shape of the MSW.