open access

https://hdl.handle.net/2115/51719

Nonlinear Wave Equations for Pressure Wave Propagation in Liquids Containing Gas Bubbles : Comparison between Two-Fluid Model and Mixture Model

日本語

Bubble-Liquid Mixture Model

2010-11-25

Japan Society of Mechanical Engineers

Transactions of the Japan Society of Mechanical Engineers. B

76(771)

1802-1810

Based on the unified theory by the present authors (T. Kanagawa, et al., J. Fluid Sci. Tech., 5, 2010), the Korteweg-de Vries-Burgers (KdVB) equation and the nonlinear Schrödinger (NLS) equation with an attenuation term for weakly nonlinear waves in bubbly liquids are re-derived from a system of bubble-liquid mixture model equations composed of the conservation equations of mass and momentum, the Keller equation for bubble dynamics, and supplementary equations. We show that the re-derived KdVB equation and NLS equation are essentially the same as those derived from a system of two-fluid model equations except for the coefficients of nonlinear, dissipation, and dispersion terms. The differences in these coefficients are studied in detail, and we find that for the case of KdVB equation, the mixture model is valid only for sufficiently small initial void fractions. On the other hand, for the case of NLS equation, the range of validity of the mixture model depends on not only the initial void fraction but also the wavenumber concerned.

学術雑誌論文

Accepted Manuscript

© 2010 日本機械学会

0387-5016