A flow-resonant model of transonic laminar open cavity instability

A transonic air stream flowing over a rectangular cavity or enclosure is unsteady. At certain flow conditions, large scale oscillations develop in the shear layer which, for an open cavity, spans across the whole enclosure. The convected shear layer instabilities interact with the cavity geometry, they generate resonance, and induce large amplitude wall pressure fluctuations, aerodynamic pressure drag and noise radiation. A numerical method has been developed to analyse the physics of the cavity flow instability. A specific interest of this study is to investigate the nature of the feed-back loop in the transonic laminar regime, where a flow-resonant feed-back may be complementing the flow-acoustic resonance documented in past work. A Mach 1.5 laminar cavity flow is modelled in which the selected numerical method gives low dispersion and dissipation. Discrete solutions of the short-time averaged laminar Navier-Stokes equations, the flow governing equations, are obtained by a finite volume integral approach. A monotone upwind flux interpolation method by Mensink is used to obtain second order accurate solutions in space. This is based on the Roe approximate Riemann solver. A fourth order Dispersion Relation Preserving scheme time-advances the flow history; this is a multi-step Runge-Kutta type integration method. The available results indicate that the method is able to reproduce the unsteady self-sustained character of the flow. A dominant cavity mode characterises the instability. The dominant mode frequency is determined by (i) the cavity streamwise length, (ii) the shear layer convection speed, (iii) the feed-back pressure and momentum wave phase speeds in the enclosure, and (iv) the shear layer receptivity phase delay at the upstream cavity edge. A comparison of phase matched ‘instantaneous’ density fields from uniform (baseline) and uniform refined computational grid models shows a similar shear layer motion and wave pattern outside the enclosure. Inside the enclosure, similar waveforms of wall pressure history are predicted by both models, indicating stationarity. A slightly higher amplitude in the refined grid case is due to the sharper feed-back pressure wave being captured in the enclosure. The major physics of supersonic cavity flow instability is resolved on the uniform baseline computational grid. Different levels of resolution of the upstream pressure wave, propagating inside in the cavity, lead to overall similar shear layer mode shapes. This is evidence of a flow resonant feed-back being present in the modelled flow, in which the unsteady vorticity and momentum fields in the cavity combine with the up-stream propagating pressure wave, complementing the flow-acoustic resonance.