Pressure and kinetic energy transport across the cavity mouth in resonating cavities

Basic properties of the incompressible fluid motion in a rectangular cavity located along one wall of a plane channel are considered. For Mach numbers of the order of 1 × 10−3 and using the incompressible formulation, we look for observable properties that can be associated with acoustic emission, which is normally observed in this kind of flow beyond a critical value of Reynolds number. The focus is put on the energy dynamics, in particular on the accumulation of energy in the cavity which takes place in the form of pressure and kinetic energy. By increasing the external forcing, we observe that the pressure flow into the cavity increases very rapidly, then peaks. However, the flow of kinetic energy, which is many orders of magnitude lower than that of the pressure, slowly but continuously grows. This leads to the pressure–kinetic energy flows ratio reaching an asymptotic state around the value 1000 for the channel bulk speed Reynolds number. It is interesting to note that beyond this threshold when the channel flow is highly unsteady—a sort of coarse turbulent flow—a sequence of high and low pressure spots is seen to depart from the downward cavity step in the statistically averaged field. The set of spots forms a steady spatial structure, a sort of damped standing wave stretching along the spanwise direction. The line joining the centers of the spots has an inclination similar to the normal to the fronts of density or pressure waves, which are observed to propagate from the downstream cavity edge in compressible cavity flows (at Mach numbers of 1 × 102 to 1 × 103, larger than those considered here). The wavelength of the standing wave is of the order of 1/8 the cavity depth and observed at the channel bulk Reynolds number, Re ∼ 2900. In this condition, the measure of the maximum pressure differences in the cavity field shows values of the order of 1 × 10−1 Pa.We interpret the presence of this sort of wave as the fingerprint of the noise emission spots which could be observed in simulations where the full compressible formulation is used. The flow is studied by means of a sequence of direct numerical simulations in the Reynolds number range 25–2900. This allows the study to span across the steady laminar regime up to a first coarse turbulent regime. These results are confirmed by the good agreement with a set of laboratory results obtained at a Reynolds number one order of magnitude larger in a different cavity geometry [M. Gharib and A. Roshko, J. Fluid Mech. 177, 501 (1987)]. This leaves room for a certain degree of qualitative universality to be associated with the present findings. DOI: 10.1103/PhysRevE.87.013013