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

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概要

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• Based on the unified theory by the present authors (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.

著者

• Fujikawa Shigeo

  Division Of Mechanical And Space Engineering Hokkaido University

• YANO Takeru

  Department of Mechanical Engineering, Osaka University

• KANAGAWA Tetsuya

  Division of Mechanical and Space Engineering, Hokkaido University, Research Fellow of the Japan Society for the Promotion of Science

• WATANABE Masao

  Division of Mechanical and Space Engineering, Hokkaido University

関連論文

• Linear Analysis of Dispersive Waves in Bubbly Flows Based on Averaged Equations
• Linear wave propagation of fast and slow modes in mixtures of liquid and gas bubbles
• Condensation coefficient of water in a weak condensation state
• Nonlinear Wave Equations for Pressure Wave Propagation in Liquids Containing Gas Bubbles : (Comparison between Two-Fluid Model and Mixture Model)

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