Investigation on flow–acoustic resonance behaviors inside ducts with tandem cavities using a high-order spectral/hp element method

This study numerically investigates the flow–acoustic resonance behaviors inside ducts with tandem cavities, containing the flow-excited acoustic eigenmodes and elevated flow dynamics under self-sustained acoustic forcing. An advanced high-order spectral/hp element method integrated with implicit large-eddy simulations was utilized to solve the nonlinear compressible Navier–Stokes equations, which effectively identified the fully coupled self-sustained flow–acoustic resonance fields. The benchmark shallow cavity configuration with a length-to-depth (L/D) ratios of 2 was motivated by the experimental findings from Shaaban and Ziada [“Fully developed building unit cavity source for long multiple shallow cavity configurations,” Phys. Fluids 30, 086105 (2018)], in which the intensive flow–acoustic resonance was occurred at a Reynolds number of 1.3×105, and we further investigated three deeper cavity configurations with L/D of 1, 2/3, and 1/2 for numerical validation and further comparison. Subsequently, aeroacoustic characteristics were assessed by analyzing the wall pressure fluctuations, indicating broader resonance regions and augmented pressure pulsation amplitudes extending from main duct to local cavity volumes with larger cavity depths. As feedback, the intensified acoustic forcing can modulate the cavity flow dynamics into stronger fluctuation levels. Furthermore, the spectral proper orthogonal decomposition analysis was conducted on the pressure fields and velocity fields, respectively. The significant fluctuations in acoustic pressure were linked to transitional acoustic modes that were present as global modes in the main duct and local modes in tandem cavities. As for velocity analysis, coherent vortex structures were extracted along the cavity entrances. These vortex structures caused progressively amplified velocity fluctuations and classified the shear layers into two dynamic motions, i.e., a flapping motion in shallow cavities and a rolling-up motion in deep cavities.