A Formula for Prediction of Frequency of Tonal Sound in Cavity Flows With Acoustic Resonance

Self-sustained oscillations with tonal sound in flows over a cavity are investigated by experiments using a wind tunnel and direct numerical simulation of flow and acoustic fields. The effects of the length-to-depth ratio of the cavity and the ratio of the cavity length L to the momentum thickness of the incoming boundary layer on the mode of the oscillations are clarified. The simultaneous measurements of flow pattern and sound pressure are also performed. The results show that a time lag between the generation of an expansion wave due to the collision of a vortex with the downstream edge and the radiation of the expansion wave from the cavity becomes larger for the cavity flow with the acoustic resonance. The computational results explain why the delay becomes larger. Moreover, considering this delay, a new formula for the frequency of the tonal sound in cavity flows with the acoustic resonance is proposed. The frequencies predicted by this formula agree well with those measured.