Numerical modeling of submicron particles for acoustic concentration in gaseous flow.

This paper intends to explore the rationality and feasibility of modeling dispersed submicron particles in air by a kinetic-based method called the unified gas-kinetic scheme (UGKS) and apply it to the simulation of particle concentration under a transverse standing wave. A gas-particle coupling scheme is proposed where the gas phase is modeled by the two-dimensional linearized Euler equations (LEE) and, through the analogous behavior between the rarefied gas molecules and the air-suspended particles, a modified UGKS is adopted to estimate the particle dynamics. The Stokes' drag force and the acoustic radiation force applied on particles are accounted for by introducing a velocity-dependent acceleration term in the UGKS formulation. To validate this methodology, the computed concentration patterns are compared with experimental results in the literature. The comparison shows that the adopted LEE-UGKS coupling scheme could well capture the concentration pattern of suspended submicron particles in a channel. In addition, numerical simulations with varying standing wave amplitudes, different acoustic radiation force to drag force ratios, and mean flow velocities are conducted. Their respective influences on the particle concentration pattern and efficiency are analyzed.

On a time domain boundary integral equation formulation for acoustic scattering by rigid bodies in uniform mean flow.

It has been well-known that under the assumption of a uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation. However, the constant mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the assumed uniform flow. A customary boundary condition for rigid surfaces is that the normal acoustic velocity be zero. In this paper, a careful study of the acoustic energy conservation equation is presented that shows such a boundary condition would in fact lead to source or sink points on solid surfaces. An alternative solid wall boundary condition, termed zero energy flux boundary condition, is proposed that conserves the acoustic energy and a time domain boundary integral equation is derived. Furthermore, stabilization of the integral equation by Burton-Miller type reformulation is presented. The stability is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the current formulation.