Computational prediction of pressure wave propagation in bubbly liquid via KdV-Burgers equation based on a two-fluid model

The Korteweg–de Vries–Burgers (KdVB) equation describes the weakly nonlinear propagation of pressure waves in bubbly liquids. We numerically calculated the KdVB equation via a split-step Fourier method and investigated evolved waveform for the initially shock waveform and the dependency of an evolved waveform on an initial void fraction and initial bubble radius. In the range that the initial void fraction were form 0.001 to 0.05 and the initial bubble radius were form 0.2 mm to 0.8 mm, the evolved waveform became the oscillatory shock waveform for all the cases. The initial void fraction affected only the propagation speed of the pressure waves and the initial bubble radius affected only the frequency of oscillation of the oscillatory shock waveform.