Multi-time delay, multi-point linear stochastic estimation of a cavity shear layer velocity from wall-pressure measurements

In this paper, the recently introduced multi-time-delay linear stochastic estimation technique is thoroughly described, focusing on its fundamental properties and potentialities. In the multi-time-delay approach, the estimate of the temporal evolution of the velocity at a given location in the flow field is obtained from multiple past samples of the unconditional sources. The technique is applied to estimate the velocity in a cavity shear layer flow, based on wall-pressure measurements from multiple sensors. The cavity flow was investigated by performing simultaneous measurements of a single hot-wire probe, traversed on a fine grid in the shear layer, and of multiple wall-mounted condenser microphones in the cavity region. The paper compares classical high-order single-time-delay estimation approaches with the multi-time-delay technique, which is significantly more accurate as it produces a much lower mean-square estimation error, thus providing a faithful reconstruction of the time-evolution of the velocity field. This improved accuracy is strongly dependent on the number n of past wall-pressure samples used in the estimate. In this paper, we also demonstrate that the estimated velocity field only contains the signature of the relevant flow mechanisms which correlate well with the wall-pressure, while incoherent components are filtered out. The multi-time-delay approach successfully captures the spatio-temporal dynamics of the velocity fluctuation distribution in the shear layer, as it clearly resolves the dynamics of the relevant flow structures. The effect of the number of sensors used in the estimate was also considered. In general, it was evident that use of more sensors leads to better accuracy, but as the number n of past values increases, the gain becomes marginal.