Applications of Conditional Spectral Analysis to Fluid Dynamics

Abstract

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This presentation describes applications of conditional spectral analysis to fluid dynamics. In the first part, we describe a general noise-removal technique via a multiple-input, multiple-output (MIMO) framework capable of removing an arbitrary number of possibly coherent contaminating noise measurements, regardless of their order, from multiple sensor measurements. An application example to unsteady surface pressure measurements in an air wind tunnel is provided to demonstrate the technique. In the second part, we present spectral analysis modal methods (SAMMs) to perform POD in the frequency domain using non-time-resolved particle image velocity (PIV) data combined with unsteady surface pressure measurements. Here, time-resolved unsteady surface pressure measurements are synchronized with non-time-resolved planar PIV measurements acquired at 15 Hz in a Mach 0.6 cavity flow. Leveraging the spectral linear stochastic estimation (LSE) method of Tinney et al. (Exp Fluids 41:763–775, 2006), we first estimate the cross-correlations between the velocity field and the unsteady pressure sensors via sequential time shifts, followed by a Fast Fourier transform to obtain the pressure–velocity cross spectral density matrix. This leads to a linear multiple-input/multiple-output (MIMO) model that determines the optimal transfer functions between the input cavity wall pressure and the output velocity field.