High fidelity simulation and spectral proper orthogonal decomposition-based wave packet parameterization of wall pressure fluctuations in backward facing step flow

Abstract

Separated flows generate intense unsteady wall pressure fluctuations that are critical sources of aerodynamic noise and structural fatigue. Although reduced-order models (ROMs) have been widely used to represent such dynamics, many existing approaches remain largely data-driven and offer limited physical interpretability of the underlying instability mechanisms. The present study aims to develop a highly compact and interpretable ROM framework for representing wall-pressure spectral dynamics using a sparse set of physical parameters. To generate a reliable high-fidelity database, a modified delayed detached eddy simulation (DDES) model incorporating a Vortex Tilting Measure-based subgrid-scale definition is employed for a backward-facing step flow at ReH = 3.7 × 104. Spectral proper orthogonal decomposition (SPOD) is then applied to disentangle the multiscale dynamics, followed by the introduction of a Gabor wave packet model to analytically parameterize the leading SPOD modes. The modified DDES successfully mitigates the gray-area issue, accurately predicting the rapid shear-layer transition and a reattachment length of Xr/H ≈ 6.2. SPOD analysis demonstrates that the wall-pressure field is dominated by coherent structures associated with the Kelvin–Helmholtz instability, with the leading mode capturing 40%–60% of the local fluctuation energy. The proposed SPOD-Gabor ROM achieves extreme analytical compression, maintaining a high spatial reconstruction accuracy (R2 > 0.9) for the dominant fluctuations using only nine scalar parameters per frequency. Furthermore, the identified parameters exhibit consistent physical trends, explicitly capturing the asymmetric growth-decay behavior of the wave packets and recovering a convection velocity of Uc ≈ 0.55U0, in excellent agreement with classical free shear layer theory.