Spectral Analysis Modal Methods (SAMMs) using Non-Time-Resolved PIV

TL;DR

This paper introduces spectral analysis modal methods (SAMMs) that enable POD analysis in the frequency domain using non-time-resolved PIV data combined with unsteady pressure measurements, avoiding the need for high-speed PIV systems.

Contribution

The paper develops two variants of SAMMs that perform space-time POD in the frequency domain, leveraging spectral LSE and cross-spectral analysis, with validation against time-resolved PIV data.

Findings

SAMMs accurately identify Rossiter frequencies.

SAMMs match results of high-speed PIV in frequency domain.

Method enables POD analysis without high-speed PIV systems.

Abstract

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. In particular, 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. (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. Two variants of SAMMs are developed and applied. The first, termed "SAMM-SPOD", combines the MIMO model with the SPOD algorithm of Towne et al. (2018). The second, called "SAMM-RR'', adds independent sources and uses a sorted eigendecomposition of the input pressure cross-spectral matrix to enable an efficient reduced-rank eigendecomposition of the velocity cross-spectral matrix. In both cases, the resulting rank-1 POD eigenvalues associated with the Rossiter frequencies exhibit very good agreement with those obtained using independent time-resolved PIV measurements. The results demonstrate that SAMMs provide a methodology to perform space-time POD without requiring a high-speed PIV system, while avoiding potential pitfalls associated with traditional time-domain LSE.