POD analysis and prediction of cavity flow instability

Aircraft with internal store bays are subject to large amplitude pressure oscillations that, at certain flow conditions, may damage both the bay and the stores. To control these oscillations, a method is required to predict in real-time the store bay flow conditions and use these predictions as feed-back to a control device. This study addresses the design of such a flow predictor, based on a Proper Orthogonal Decomposition (POD) approach. A time dependent numerical model has been developed to investigate the instability of a Mach 1.5 cavity flow. The numerically generated flow history is analysed through the use of POD. Using the methods of snapshots, the large-scale features of the cavity flow can be captured in only a few eigenmodes. A novel method is presented whereby the flow can be accurately predicted, beyond the initial flow history, by decomposing the coefficients applied to the eigenmodes into a short discrete Fourier series. Results are presented for the flow state predicted 10 fundamental instability mode periods beyond the end of the initial flow history. The method is shown to be very effective and predicted pressures at the downstream edge of the cavity are in excellent agreement with a comparative CFD computation. The accuracy of the prediction is shown to be dependent on the number of snapshots taken for the POD analysis. When a small non-optimal number of snapshots is used, the pressure fluctuation amplitude is not adequately predicted. Even so, the error in phase is small and the general structure of the pressure trace is still captured, making the current method a good candidate for active flow control.