Evaluation of Aeroacoustic Performance of a Helmholtz Resonator System with Different Resonator Cavity Shapes in the Presence of a Grazing Flow

In this paper, the effect of the resonator cavity shape on a constant volume is investigated for the aeroacoustics performance of a Helmholtz resonator system. This scrutiny is performed for various Mach numbers of the grazing flow in the range of 0–0.4. In this regard, a three-dimensional numerical approach was used. In the work, the resonator shape of sphere, cubic, cone, triangular prisms and cylinders were considered. The numerical approach was first verified with the experimental measurements available in the literature. The assessment of the numerical approach by comparing the numerical results with the available experimental data indicated good accordance, which, in turn, affirmed the validity and competency of the method. The simulation results show that by changing the resonator cavity shape, a maximum change of 24% occurred in ${\mathrm{TL}}_{\max }$. For all cavity shapes, increasing the grazing flow Mach number $M_a$ from 0 to 0.4 led to about a 90% reduction in ${\mathrm{TL}}_{\max }$. Furthermore, a 30% change in the resonant frequency happened with changing the resonator cavity shape. In addition, in $M_a\le 0.1$ and $M_a\ge 0.2$, for all the resonator cavity shapes, the increment trend occurred for the resonant frequency, and in $M_a=0.15$, all cavity shapes had a span for the resonant frequency except cubic. Overall, spheres and cylinders as the resonator cavity had better performance with respect to other considered resonator cavity shapes.