Acoustic Analogy for Multiphase or Multicomponent Flow

Abstract

The Ffowcs Williams and Hawkings (FW-H) equation is widely used to predict sound generated from flow and its interaction with impermeable or permeable surfaces. Owing to the Heaviside function used, this equation assumes that sound only propagates outside the surface. In this paper, we develop a generalized acoustic analogy to account for sound generation and propagation both inside and outside the surface. The developed wave equation provides an efficient mathematical approach to predict sound generated from multiphase or multicomponent flow (MMF) and its interaction with solid boundaries. The developed wave equation also clearly interprets the physical mechanisms of sound generation, emphasizing that the monopole and dipole sources are dependent on the jump in physical quantities across the interface of MMF rather than the physical quantities on one-side surface expressed in the FW-H equation. The sound generated from gas bubbles in water is analyzed by the newly developed wave equation to investigate parameters affecting the acoustic power output, showing that the acoustic power feature concluded from the Crighton and Ffowcs Williams (C-FW) equation is only valid in a specific case of all bubbles oscillating in phase.