Nonlinear Pressure Waves in Bubbly Flows with Drag Force: Theoretical and Numerical Comparison of Acoustic and Thermal and Drag Force Dissipations

Abstract

Weakly nonlinear propagation of plane pressure waves in flowing compressible water containing many spherical microbubbles is theoretically investigated. Special focus is placed on the thermal conduction inside the bubble and drag force acting on translational bubbles. From the method of multiple scales, the Korteweg–de Vries–Burgers equation is derived and two types of dissipation terms appear: a term with a second-order partial derivative owing to the liquid compressibility and a term without differentiation owing to the drag force and thermal conduction. Finally, we numerically found that the dissipation effect due to the thermal conduction is the largest, followed by that due to the acoustic radiation and drag force.