Mechanisms of noise reduction by corner rounding in turbulent flow over forward-facing steps

The aeroacoustic effects of rounding a forward-facing step in a low-Mach-number turbulent boundary layer are investigated using large-eddy simulation and Lighthill’s theory. The step height is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>26</mml:mn> <mml:mi>%</mml:mi> </mml:math> of the thickness of the unperturbed boundary layer at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>R</mml:mi> <mml:msub> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>θ</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>4755</mml:mn> </mml:math> , and the rounding radius relative to the step height ranges from 0 to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>100</mml:mn> <mml:mi>%</mml:mi> </mml:math> . Consistent with previous experimental findings, step rounding is shown to cause reduced flow separation and increased peak pressure fluctuations on the step upper-surface except in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>100</mml:mn> <mml:mi>%</mml:mi> </mml:math> rounding case. The acoustic radiation is significantly weakened by step rounding, and the noise reduction increases with increasing rounding radius and frequency. The acoustic source fields for different rounding radii are analyzed in conjunction with tailored, acoustically compact Green’s functions to investigate the mechanisms for noise reduction. It is found that while step rounding affects both turbulence production and acoustic diffraction by the step, noise reduction is primarily due to the reduced surface diffraction effect. Additionally, a boundary-element analysis shows that the effect of step rounding on the acoustic directivity is insignificant for acoustically compact steps, but grows with increasing acoustic noncompactness of the step height.