Analysis of pressure fluctuation in transonic cavity flows using modal decomposition

Turbulent flows at a free stream Mach number of 1.19 over an open cavity with L/D ratio of 5.0 are numerically investigated using improved delayed detached-eddy simulation based on two-equation shear stress transport model. Modal decompositions including proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are applied to analyze the pressure fluctuations. The extracted first six POD modes possess more than 75% of the total energy and contain multiple frequencies. Their spatial structures exhibit well regular and periodic behaviors along the cavity lip line. The DMD algorithm identifies the flow structures associated with single frequencies. Major distribution areas of high intensity pressure fluctuations move upstream as the mode frequency increases, and the structures with high frequencies are prone to break down near the trailing edge. The alternating pressure patterns convection process is clearly presented, and the propagation of acoustic waves validates that the acoustic waves share the same sound source but are radiated following two different paths, consistent with the feedback mechanism. In addition, the effects of free stream Reynolds number on sound pressure spectrum levels are investigated at a fixed pressure and temperature. Results show that free stream Reynolds number has no effect on the non-dimensional frequencies of the dominant modes, while the main recirculation area shrinks as Reynolds number increases. Furthermore, variations of sound pressure levels as a function of Reynolds numbers exhibit significant discrepancies for a fixed free stream pressure or temperature, indicating that the Reynolds number is not critical to the feedback tone amplitude. The enhancement of sound pressure levels mainly attributes to the increment of free flow pressure or the impingement of enlarged fluid velocity due to higher free stream temperature.