Vortex convection in the flow-excited Helmholtz resonator

Vorticity convection as well as its excitation to a Helmholtz resonator is studied numerically. Convection velocities of both the concentrated vortical structure and the total distributed vorticity in the orifice region are calculated. Results indicate that the vortex convection velocity is the more useful one in controlling the oscillation frequency. The excitation pressure from the vortical flow is found almost in phase with the fluctuation of the total circulation in the orifice region. This helps us to deduce that vorticity accumulation in the opening region and its relatively simultaneous efflux, due to the shear layer rolling-up into a vortex, are responsible for the pressure fluctuation that excites the acoustic mode of the cavity. It is found that the frequency characteristics can be significantly varied by the system damping. Increasing the damping leads to a reduction in the range of the Strouhal number of oscillation, which is associated with the disappearing lock-in effect in frequency. The dependence of the vortex convection velocity and the critical Strouhal number for the maximum oscillation on damping is also shown.