We have been working on the problem of supersonic cavity flows, which are characterized by violent self-sustaining flow oscillations generating strong vortical motions, hoping that such vortical motions can be used as a powerful means for supersonic mixing/combustion enhancement, a key technology for developing scramjet engines. In our previous study we proposed a new formula for the oscillation frequency that simply expresses a resonance condition for the self-sustaining oscillation. In the present study we conducted experiments of supersonic cavity flows particularly for laminar oncoming boundary layers at M_∞=1.85, 2.5 for various values of L/D (length to depth ratio of rectangular cavity). This is because there has been no such supersonic laminar flow data for examining the validity of the oscillation frequency formula. Through hot-wire measurements and linear stability calculations we found that the growth of small-amplitude shear-layer disturbance governing the oscillation is well described by the linear stability theory and that the flow inside the cavity can work to broaden the unstable frequency band significantly. The present paper discusses these important new findings for the mechanism of supersonic cavity oscillation and verifies the validity of the proposed formula for laminar and turbulent boundary layer cases.

View full abstract

We have been working on the problem of supersonic cavity flows, which are characterized by violent self-sustaining flow oscillations generating strong vortical motions, hoping that such vortical motions can be used as a powerful means for supersonic mixing/combustion enhancement, a key technology for developing scramjet engines. In the present study we have made theoretical efforts to clarify the mechanism of supersonic cavity oscillations for the case of two-dimensional rectangular cavity. In particular we have tried to understand the feedback-loop mechanism for the self-sustaining oscillations theoretically by relating the acoustic radiation at the trailing edge to the shear layer instability. Our flow model assumes (1) that shear layer may be approximated by a vortex sheet, (2) that the shear layer is disturbed by a periodic pressure pulse only in the vicinity of the leading edge, and the subsequent downstream growth of the wave motion of the shear layer is described by the linear stability theory, (3) that the pressure pulse is radiated by a single acoustic monopole located at the trailing edge, and propagates inside the cavity to reach the leading edge, almost without disturbing the shear layer, (4) that the frequency of oscillation is determined by the resonance condition that the positive maximum of the pressure fluctuation at the source occurs when the shear layer displacement becomes positive maximum at the trailing edge. Good agreement is obtained between the oscillation frequencies predicted from the present theory and experimental measurements for a wide range of the cavity lenght-to-depth ratio, L/D at a freestream Mach number 1.85. It is also noted that our new formula for the oscillation frequency, that expresses the resonance condition for the feedback-loop mechanism, is found to be in good agreement with the present theoretical results.

View full abstract