Vortex sound under the influence of a piecewise porous material on an infinite rigid plane

Abstract

The vortex dynamics and the sound generation by an inviscid vortex in the presence of a finite length porous material on an otherwise rigid plane are studied numerically in the present study in an attempt to understand the sound generation near the surface of a wall lining in a lined duct. The combined effects of the effective fluid density and flow resistance inside the porous material, and the length and thickness of the porous material on the sound generation process are examined in detail. Results obtained demonstrate the sound pressure is longitudinal dipole and show how seriously the above-mentioned parameters are affecting the vortex sound pressure under the influence of the porous material.

Two-dimensional model of low Mach number vortex sound generation in a lined duct

“…Therefore, only the cases where the initial height of the vortex y oi is smaller than 0.5 will be considered as the vortex is stationary if y oi = 0.5 and will move further upstream if y oi Ͼ 0.5 in the absence of a mean flow with nearly constant speed and thus radiates no sound. One can also notice that many equations involved infinite summations which have to be truncated in the computation as in many previous studies ͑for instance, Lau and Tang 18 ͒. It is found that the difference of the far field pressure amplitudes for y oi = 0.2, L =2, h = 0.2, and = 3 with various R f computed with five-term summation and ten-term summation is within 1%-2%.…”

“…As in the previous studies of the authors, [15][16][17][18] the air density inside the duct is denoted by while the properties of the porous materials are characterized using the effective density e and the flow resistance R f inside its lattice. 19 The flow resistance is normalized by ⌫ / d 2 .…”

“…The position of the vortex as well as the mode magnitudes can then be estimated using standard Runge-Kutta method as in the previous study of the authors. 18 The flow potential due to the presence of the vortex can be found by applying the Cauchy-Rieman principle, 21 which states that…”

“…The more recent work of the authors examines the vortex sound radiation under the influence of a porous lining in an opened space. 18 In the present investigation, the vortex sound generation inside an infinitely long two-dimensional rigid wall duct with porous linings of finite length on both sides of the duct is studied. This configuration is analogous to the situation of a lined duct in the air conditioning and ventilation ductwork.…”

“…Using the technique of Lau and Tang, 18 the rates of change in the mode magnitudes and the vortex velocities can be estimated from their instantaneous values by solving the simultaneous equations ͓Eqs. ͑14͒, ͑15͒, ͑17͒, and ͑18͔͒ with the initial condition Ȧ n = Ḃ n =0, ẏ o = 0, and ẋ o = cot͑y o ͒ / 4.…”