Identification of whistling ability of a single hole orifice from an incompressible flow simulation

Pure tone noise from orifices in pipe result from vortex shedding with lock-in. Acoustic amplification at the orifice is coupled to resonant condition to create self-sustained oscillations. One key feature of this phenomenon is hence the ability of an orifice to amplify acoustic waves in a given range of frequencies. Here a numerical investigation of the linear response of an orifice is undertaken, with the support of experimental data for validation. The study deals with a sharp edge orifice. Its diameter equals to 0.015 m and its thickness to 0.005 m. The pipe diameter is 0.030 m. An air flow with a Mach number 0.026 and a Reynolds number 18000 in the main pipe is present. At such a low Mach number, the fluid behavior can reasonably be described as locally incompressible. The incompressible Unsteady Reynolds Averaged Navier-Stokes (URANS) equations are solved with the help of a finite volume fluid mechanics software. The orifice is submitted to an average flow velocity, with superimposed small harmonic perturbations. The harmonic response of the orifice is the difference between the upstream and downstream pressures, and a straightforward calculation brings out the acoustic impedance of the orifice. Comparison with experiments shows that the main physical features of the whistling phenomenon are reasonably reproduced.