Spectral analysis modal methods (SAMMs) using non-time-resolved PIV
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RESEARCH ARTICLE
Spectral analysis modal methods (SAMMs) using non‑time‑resolved PIV Yang Zhang1 · Louis N. Cattafesta III1 · Lawrence Ukeiley2 Received: 13 July 2020 / Revised: 10 September 2020 / Accepted: 16 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. (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. 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. (J Fluid Mech, https://doi. org/10.1017/jfm.2018.283, 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. Graphic abstract
* Louis N. Cattafesta III [email protected] 1
Florida Center for Advanced Aero‑Propulsion (FCAAP), FAMU‑FSU College of Engineering, Florida State University, 2003 Levy Ave, Tallahassee, FL 32310, USA
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
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1 Introduction Modal methods provide powerful tools for fluid dynamics, encompassing proper orthogonal decomposition (POD) (Lumley 1967), dynamic mode decomposition (Schmid
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et al. 2010), and resolvent analysis (McKeon and Sharma 2010). They provide fundamental understanding of turbulent flows, for example, to identify coherent structures (Berkooz et al. 1993), develop reduced-order models (Pinnau 2008), or facilitate flow control. These popular methods are recently reviewed by Taira et al. (2017, 2019). Applications of the POD are associated with the solution of an eigenvalue problem which yields an orthogonal set of basis functions (eigenvect
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