Numerical modelling and theoretical analysis of the acoustic attenuation in bubbly liquids

Abstract

The propagations of acoustic waves in bubbly liquids have been extensively investigated through experimental and theoretical methods, a computational fluid dynamics (CFD) method was introduced to investigate the acoustic attenuation through bubbles in this study. Numerical ‘measurements’ of attenuation coefficient (α) and phase velocity (V) were conducted using a homogeneous cavitation model, which were modeled from experimental schemes and compared with the theoretical results. At extremely small bubble volume fraction (β around 10−11), new formulas of the theoretical α (αtheo) were proposed respectively for linear and transient oscillations, and a new formula of the numerical α (αnum) was proposed for transient oscillations. Results showed that αnum matched precisely with αtheo for linear, nonlinear and transient oscillations. At medium β (around 10−4), the relative difference of αnum between the VOF and present methods was less than 1.6%, while it reached 15.4% after replacing the bounded Keller-Miksis equation (KME) in the present method with the KME. However, the traditional theoretical α and V matched precisely with the predictions by the present method with the KME. Thus new theoretical α and V were proposed based on the bounded KME, and the relative differences between αtheo and αnum were less than 1%. It can be concluded that the bounded KME should be used in both numerical and theoretical predictions.

Keywords

• Ultrasonic cavitation
• numerical modelling
• attenuation
• phase velocity
• transient analysis