Modified quadratic stochastic estimation of resonating subsonic cavity flow

Quadratic stochastic estimation of far‐field acoustic pressure with coherent structure events in a 2D compressible plane mixing layer

“…The inclusion of non-linear terms in the SE model may be viewed as recognition that real distributions of turbulent data and event vectors are not jointly normal. Moreover, when dealing with two variables (velocity and pressure fields), the use of QSE leads to quantitatively more accurate results than those deduced from LSE [19,38]. Based on these preliminary works and also on the fact that the far-field pressure is correlated with the square of the velocity amplitude fluctuations [41], QSE is used in the present work to estimate the far-field acoustic pressure from the knowledge of selected aerodynamic coherent events.…”

“…The condition of joint normalcy between turbulent data and event measures is not generally satisfied (see Section 4). Therefore, many works have provided a physical rationale for preferentially using the QSE procedure instead of LSE [19,35,38]. The inclusion of non-linear terms in the SE model may be viewed as recognition that real distributions of turbulent data and event vectors are not jointly normal.…”

“…The aim of such a complementary method is to extract coherent structures of the turbulent flow, using POD decomposition and to access their dynamical evolution, thanks to LSE. More recently, several applications using similar combinations (POD and SE) have been performed to investigate the time evolution of the large-scale flow structures from the knowledge of wall pressure signals [18][19][20]. Then, these works led to propose a mechanism for the wall pressure generation process within the shear layer flow.…”

Nonlinear Multi-Time-Delay Stochastic Estimation: Application to Cavity Flow and Turbulent Channel Flow

“…Hence, it would be of interest to investigate this speculation further on other datasets. In fact, several other researchers which investigated estimation of cavity flows from wall-pressure measurements have shown that nonlinear techniques produce a significant improvement in accuracy, e.g Murray et al, [19]. A nonlinear estimator, and more precisely the quadratic stochastic estimation, was also successfully employed by Samimy et al, [31], to estimate the amplitudes of Proper Orthogonal Decomposition modes in a feedback control experiment on subsonic cavity flows.…”

“…This case has been the subject of numerous investigations concerning stochastic estimation, see for example the works of Murray and Ukeiley [19] and Zhang and Naguib [20], and can be regarded as a benchmark problem.…”