Self-sustained oscillations with tonal sound around a backward-facing step with a small upstream step

Self-sustained oscillations with acoustic feedback take place in a flow over a two-dimensional two-step configuration: a small forward-backward facing step, which we hereafter call "a bump", and a relatively large backward-facing step (backstep). These oscillations can radiate intense tonal sound and fatigue nearby components of industrial products. We clarify the mechanism of these oscillations by directly solving the compressible Navier-Stokes equations. The results show that vortices are shed from the leading edge of the bump and acoustic waves are radiated when these vortices pass the trailing edge of the backstep. The propagated acoustic waves shed new vortices by stretching the vortex formed by the flow separation at the leading edge of the bump, and a feedback loop is formed. Moreover, we propose a formula for predicting the frequencies of the tonal sound based on the detailed investigation of the phase relationship between the vortices and the acoustic waves. Also, we investigate the flow conditions for these oscillations by changing the bump configurations. The results show that the oscillations strongly occur when the bump is sufficiently high and the trailing edge of the bump is sufficiently distant from the backstep.