Numerical prediction of fluid-resonant oscillation at low Mach number

A method (governing equation set and numerical procedure) suited to the numerical simulation of fluid-resonant oscillation at low Mach numbers is constructed. The new equation set has been derived under the assumption that the compressibility effect is weak. 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 developed for incompressible flow equations without difficulty. With application of a pressure-based method that treats the continuity equation as a constraint equation for pressure, the stiffness problem that arises in solving the usual compressible flow equations under low Mach number conditions has been alleviated. 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 and that the frequency of the pressure fluctuations is locked in at the Helmholtz resonant frequency of the cavity. Thus, the present method is confirmed to have the capability of predicting fluid-resonant oscillation in low-Mach-number flows.