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

• Published in: Physics of fluids (1994) Vol. 33; no. 5
• Main Authors: Kanagawa, Tetsuya, Ayukai, Takahiro, Maeda, Taiki, Yatabe, Takahiro
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 01.05.2021
• Subjects: Bubbles; Compressibility; Drag; Elastic waves; Fluid dynamics; Multiscale analysis; Physics; Radiation; Sound waves; Viscous damping; Wave propagation
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/5.0042625

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.