Abstract
Amethod (governing equation set andnumerical procedure) suited to the numerical simulationof uid-resonant oscillation at lowMach 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 ow equations without dif culty. 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 ow equations under low Mach number conditions has been alleviated. To verify the present method, we apply it to the ows over a three-dimensional open cavity. The results show that strong pressure uctuations occur at speci c ow velocities and that the frequency of the pressure uctuations is locked in at the Helmholtz resonant frequency of the cavity. Thus, the present method is con rmed to have the capability of predicting uid-resonant oscillation in low-Mach-number ows.
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