Numerical prediction of fluid-resonant oscillation at low mach number

We have constructed a method (governing equation set and numerical procedure) that is suited for the numerical simulation of the Fluid-Resonant Oscillation at low Mach number. By using the new equation set we have derived under assumption that the compressibility effect is weak, we do not have to worry about the stiffness problem from which we suffer with the usual compressible flow equations. In addition, because the derived equations are essentially the same as the incompressible Navier-Stokes equations except for an additional term, we can apply almost the same numerical procedure as developed for the incompressible flow equations. In order to verify the present method, we apply it to the flows over a three-dimensional open cavity. The results show that strong pressure fluctuations occur at specific flow velocities. Also shown is that the frequency of the pressure fluctuations is locked-in at the Helmholtz resonant frequency of the cavity. Thus, it is confirmed that the present method has the capability of predicting the Fluid-Resonant Oscillation in low-Mach-number flows.