Numerical analysis shows critical reynolds number decreases in laminar flows with a helmholtz resonator, indicating instability effects.
The linear stability of steady-state laminar parallel flows is investigated when the flow is coupled with a Helmholtz resonator imbedded in the solid wall. The governing equations for the disturbances are derived which form an eigenvalue problem with appropriate boundary conditions that reflect the effects of Helmholtz resonator. It is assumed that the presence of the Helmholtz resonator has no effect on the basic flow, which can be achieved by placing a permeable membrane that separates the cavity and the external boundary-layer flow. The flow across the membrane is modeled by Darcy’s law for porous medium. The objective is to investigate the destabilizing effects of the Helmholtz resonator on parallel flows. It is shown that with the presence of Helmholtz resonator, the condition for inviscid instability that the basic flow profile possesses a inflection point becomes unnecessary. Numerical solutions show that the critical Reynolds number can be decreased by this coupling mechanism.
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Dou et al. (1995) studied this question.
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