Dissipation of ultrasonic wave propagation in bubbly liquids considering the effect of compressibility to the first order of acoustical Mach number
2013
Jamshidi, Rashid | Brenner, Gunther
In this paper, the energy conservation approach presented by Louisnard (2010) [1] for bubbly liquid is modified by applying the Keller–Miksis Equation (KME) on the radial dynamics of cavitation bubbles. As the sound wave is damped through the liquid due to thermal, viscous and radiation effects, it cannot propagate over long distances. With the use of the Rayleigh–Plesset Equation (RPE) in the energy conservation approach, the part of the damping due to the acoustic radiation is neglected. However, it should be taken into account as noticed in the aforementioned reference. Here, it is shown that this damping is of importance especially above the Blake threshold. Furthermore, the thermal damping is calculated by a new formulation. The method is based on the effect of temperature gradient at the thermal boundary layer around the bubble surface on the gas pressure inside the bubble. Results show that the power dissipated by acoustic radiation has the same order of magnitude as the thermal one and cannot be neglected. Moreover, it is revealed that the rate of change of different energies which contribute in bubble oscillation, can result in damping of the wave as secondary effects. It is observed that the thermal damping has stronger effect on the pressure wave than the viscous one. Considering the compressibility of the liquid to the first order of the acoustical Mach number causes an increase in the thermal damping by a factor of about two to three for acoustic pressure amplitudes higher than the Blake threshold. Besides that, considering the compressibility has negligible effects on viscous damping.
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