Effect of drag force and translation of bubbles on nonlinear pressure waves with a short wavelength in bubbly flows

Abstract

To clarify the effect of the drag force acting on bubbles and translation of bubbles on pressure waves, the weakly nonlinear (i.e., finite but small-amplitude) propagation of plane pressure waves with a thermal conduction in compressible water flows containing many spherical bubbles is theoretically investigated for moderately high-frequency and short-wavelength case. This work is an extension of our previous report [Yatabe et al., Phys. Fluids, 33, 033315 (2021)], wherein we elucidated the same for low-frequency and long-wavelength case. Based on our assumptions, the main results of this study are as follows: (i) using the method of multiple scales, the nonlinear Schrödinger type equation was derived; (ii) as in the previous long wave case, the translation of bubbles increased the nonlinear effect of waves, and the drag force acting on the bubbles resulted in the dissipation effect of waves; (iii) the increase in the nonlinear effect of the waves owing to the translation in the present short wavelength case is larger than that in the previous long wavelength case; (iv) the dissipation effect caused by the drag force was smaller than that caused by the liquid viscosity, acoustic radiation (i.e., liquid compressibility), and thermal conduction; (v) we then succeeded the comparison of the four dissipation factors (i.e., liquid viscous damping, thermal conduction, acoustic radiation, and drag force) on pressure waves.