Sound generation in impinging vortex on the chamfered step

To investigate the effects of various chamfered lengths and angles on the noise emission, a numerical study was conducted for a forward step problem in two-dimensional low Mach number flow. The vortical flow field approaching to the forward step was modeled by using point vortex. Matched asymptotic expansion theory and Schwarz-Christoffel transformation were used to obtain the outer noise field and inner flow field. It is well known that while rectangular forward step has an explicit analytic mapping form, the chamfered forward step has an implicit integral one. The integral mapping function was calculated through Simpson's integral rule. Both far field acoustic pressure and sound intensity were calculated with variations of chamfered step lengths and angles, vortex strengths and initial vortex positions. It was found that the amplitude of the acoustic peaks was decreased exponentially as increasing the chamfering length, decreasing the vortex strength, and increasing the initial vortex height. The amplitude of acoustic pressure was decreased until the chamfering angle decreased up to between 15° and 30° and anew increased below 15°. The calculated sound intensity depends to a significant degree on the chamfering length, chamfering angle, impinging vortex strength, and initial vertical vortex position.