Turbulent flow and noise sources on a circular cylinder in the critical regime

The flow around a circular cylinder with long spanwise length has been investigated in the critical regime using a compressible wall-resolved Large Eddy Simulation (LES) for the first time. The flow at such a critical Reynolds number combines complex features: large favorable and adverse pressure gradient, separation and turbulence transition and flow reattachment. The results of the present simulation agree well with previous experimental and incompressible LES data, for the distribution of the mean wall-pressure coefficient that dominates the drag coefficient, and the skin-friction coefficient that illustrates the flow separation and reattachment behaviors. A weak reattachment is observed from the quasi-zero skin-friction in the reattachment region. A detailed study of the boundary-layer and shear-layer development around the cylinder with profiles of mean velocity and turbulence intensities confirms the transition, separation and reattachment behaviors shown by the skin-friction coefficient. The maximum tangential velocity and its location above the wall have also proven to be adequate measures of the edge velocity and associated boundary layer thickness. The Kelvin-Helmholtz instabilities have been observed in the shear layer and the ratio of the frequency of these instabilities and the fundamental vortex shedding frequency matches well with the existing scaling based on experimental data. The far-field noise obtained by both direct computation and acoustic analogy shows a dominant vortex shedding tone, but with additional broadband sources in the cylinder wake. These sound sources are evaluated from maps of filtered pressure signals and cross-correlation analysis of the pressure fluctuations around the cylinder and in the far-field.