Organized self-sustained oscillations of turbulent flows over an open cavity

Abstract

Direct numerical and large eddy simulations of incompressible turbulent flows over deep and shallow cavities were performed in the range of $600 \leq Re_D \leq 12000$ to investigate the influence of incoming turbulent boundary layer on self-sustained oscillations of separated shear layer. The turbulent boundary layer was imposed at the inlet with realistic velocity fluctuations of $Re_\theta = 300$. When the turbulent boundary layer approached the open cavity with $Re_D = 3000$, the energy spectra of pressure fluctuations showed energetic frequencies in the range of $0.15 \leq \omega_\theta \leq 0.3$. Conditionally averaged flow fields disclosed that the energetic frequencies arise from the separation of high speed streaky structures rather than from a geometric peculiarity of the cavity. The high speed streaky structures of the incoming turbulent boundary layer were little disturbed by the presence of cavity, and the undisturbed high speed streaky structures generated the pressure fluctuations with the energetic frequencies. The same energetic frequencies were observed in a backward-facing step flow as well as in deep and shallow cavity flows, despite the different geometries of these systems. In the turbulent cavity flow of $Re_D = 12000$, however, the peak frequencies of the energy spectra at cavity lengths of L/D=1 and 2 were found to correspond to the Nth modes with N=2 and 3 respectively. These Nth modes were very similar to the frequency characteristics of self-sustained oscillations reported for laminar cavity flows. Inspection of instantaneous pressure fluctuations as well as spanwise-averaged pressure fluctuations revealed that regular shedding of quasi two-dimensional vortical structures was responsible for the peak frequency in the energy spectra. Examination of spanwise-averaged vector fields of the velocity fluctuations showed that when the vortical structures impinged on the trailing edge of the cavity, they split into a small part entrained into...