非振動成分としての抗力と気泡並進運動が気泡流中の圧力波に及ぼす影響に関する非線形理論

抄録

Weakly nonlinear (i.e., finite but small amplitude) propagation of plane progressive pressure waves in a compressible water flow uniformly containing many spherical gas bubbles is analytically investigated. Gas and liquid phases are flowing with each velocity. Drag force and virtual mass force are incorporated in an interfacial transport term in momentum conservation laws based on a two-fluid model. As bubble dynamics, translation and spherically symmetric oscillation are considered. The bubbles do not coalesce, break up, extinct, and appear. For simplicity, the gas viscosity, the thermal conductivities of the gas and liquid, and the phase change and mass transport across the bubble-liquid interface, are ignored. From theoretical and numerical analyses, the following results are obtained: (i) By the use of the method of multiple scales, two types of Korteweg–de Vries–Burgers (KdVB) equation with a new term without a differentiation due to the drag force are derived from the basic equations for bubbly flows in the two-fluid model. (ii) The translation of bubbles affects the nonlinear effect of waves. (iii) The drag force acting bubbles affects the nonlinear and dissipation effects of waves. (iv) The dissipation effect due to the drag force is strongly dependent on both the initial void fraction and the initial bubble radius.