Large Eddy Simulation of cross-flow around a square rod at incidence with application to tonal noise prediction

We consider the prediction of the flow around a square rod as a generic bluff body at low Mach number (below 0.3) and high Reynolds number (above 5000) and the corresponding tonal noise. Instability of such flow is crucial for potential mechanical vibrations and noise production. Due to the presence of sharp edges the flow separation along a square rod is relatively easy to predict. The flow remains however quite complex as it involves re-attachment and secondary vortex shedding. Depending on the angle of attack, between the main flow direction and the bottom side wall of the rod, three flow types are observed. Firstly at low angles of attack the flow separating from both upstream edges forms a periodic vortex street in the wake. Secondly above a critical angle of attack around 13o, the flow re-attaches to the bottom side wall. The wake is dominated by vortex shedding from the upper front edge and the lower downstream edge. At 45o the stagnation point is on the front edge and flow separation occurs from the two lateral edges. In the literature the wake is reported to display a von K`arm`an vortex street corresponding to a whistling mode. For angle of attack between 25o and 45o, we observe experimentally a second mode in which the wake is stable and the rod does not whistle. We call this the silent mode. One can switch from one mode to the other by perturbing the flow in front or behind the rod. Direct Numerical Simulation of the radiated sound is extremely difficult and certainly not feasible for industrial applications. We assess the potential of a hybrid method in which the flow is modelled by means of an incompressible Large Eddy Simulation (LES). The flow data is then used to estimate the sound radiation by using the Lighthill-Curle aeroacoustical analogy. Incompressible resolved LES obtained with a commercial code provides a fair prediction of the flow if the full length of the rod is taken into account including the side walls used to support the rod in the experiments. Combining the LES results with the aero-acoustical analogy provides a prediction of observed tonal noise within 2 dB. The prediction of broad band noise was not considered. The use of quasi two-dimensional LES calculations or two-dimensional Unsteady-Reynolds Averaged Navier Stokes (URANS) models appears to be much less accurate. These LES calculations are unfortunately still much too demanding to allow a systematic parametric study. They also do not capture the observed silent mode