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

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 (alpha) 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 (beta around 10(-11)), new formulas of the theoretical alpha (alpha (theo)) were proposed respectively for linear and transient oscillations, and a new formula of the numerical alpha (alpha (num)) was proposed for transient oscillations. Results showed that alpha (num) matched precisely with alpha (theo) for linear, nonlinear and transient oscillations. At medium beta (around 10(-4)), the relative difference of alpha (num) 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 alpha and V matched precisely with the predictions by the present method with the KME. Thus new theoretical alpha and V were proposed based on the bounded KME, and the relative differences between alpha (theo) and alpha (num) were less than 1%. It can be concluded that the bounded KME should be used in both numerical and theoretical predictions.