Elucidation of pressure wave attenuation due to cross-sectional area change in bubbly flow

Abstract

Pressure waves in bubbly flows are attenuated by various factors such as liquid viscosity and compressibility. However, existing studies have not elucidated the attenuation mechanism and lack quantitative comparisons. This study investigates the weakly nonlinear propagation of pressure waves in liquids containing spherical bubbles with varying cross-sectional areas. The Korteweg–de Vries–Burgers equation describing the wave propagation was derived using the singular perturbation method for averaged equations based on a two-fluid model. The study revealed that the attenuation is influenced by the cross-sectional area change, liquid viscosity and compressibility, and wall friction force. Second, the effects of the cross-sectional area change contribute to the amplification and attenuation of the wave amplitude when the cross-sectional area is converging and diverging, respectively. Furthermore, using the converging–diverging tube (i.e., Venturi tube) as the primary example, the study found that for large cross-sectional area change, the contribution to attenuation was the most significant, followed by liquid viscosity, compressibility, and wall friction force. This underscores the importance of the rate of change as a key parameter in cross-sectional area. This study established a new attenuation term for cross-sectional area change, which is useful in both basic and practical viewpoints.