Liquid compressibility effects during the collapse of a single cavitating bubble

Abstract

The effect of liquid compressibility on the dynamics of a single, spherical cavitating bubble is studied. While it is known that compressibility damps the amplitude of bubble rebounds, the extent to which this effect is accurately captured by weakly compressible versions of the Rayleigh-Plesset equation is unclear. To clarify this issue, partial differential equations governing conservation of mass, momentum, and energy are numerically solved both inside the bubble and in the surrounding compressible liquid. Radiated pressure waves originating at the unsteady bubble interface are directly captured. Results obtained with Rayleigh-Plesset type equations accounting for compressibility effects, proposed by Keller and Miksis [J. Acoust. Soc. Am. 68, 628-633 (1980)], Gilmore, and Tomita and Shima [Bull. JSME 20, 1453-1460], are compared with those resulting from the full model. For strong collapses, the solution of the latter reveals that an important part of the energy concentrated during the collapse is used to generate an outgoing pressure wave. For the examples considered in this research, peak pressures are larger than those predicted by Rayleigh-Plesset type equations, whereas the amplitudes of the rebounds are smaller.

Delay differential equations for single-bubble dynamics in a compressible liquid

“…Comparison with previous results presented by [50] suggests that the new model is more accurate. Fuster et al based on direct integration of the Navier-Stokes equations for bubbles undergoing violent collapse.…”

“…As the amplitude increases, the models begin to diverge. Fuster et al [50] showed that the Keller-Miksis, Gilmore-Akulichev, and Tomita-Shima models underpredict the damping due to liquid compressibility by comparing to the results of numerical integration of the fluid equations of motion. Our new model predicts more damping for high amplitude motion than the other discrete bubble models and is qualitatively closer to the predictions of the direct numerical simulation, thus suggesting that the new model better represents the physical system.…”

Growth-and-collapse dynamics of small bubble clusters near a wall

“…Similarly, Delale & Tunc (2004) developed a modified Rayleigh-Plesset model to account for fission losses during rebound. The other mechanisms are expected to become relatively more important in more intense collapses (Fuster, Dopazo & Hauke 2011), particularly for vapour-filled cavities (Akhatov et al 2001). In strong collapses of relatively weakly interacting bubbles, they would behave more as individual units, and the energy loss to kinetic energy via jetting or similar mechanisms could be much smaller compared to the dominant damping for spherical collapses.…”

An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics

“…The radial bubble-wall evolution and convergence results for the larger pressure ratio p ∞ /p b = 1427 are shown in Figure 7. In Figure 7 (a), we only show the Keller-Miksis solution (a) < l a t e x i t s h a 1 _ b a s e 6 4 = " ( n u l l ) " > ( n u l l ) < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " ( n u l l ) " > ( n u l l ) < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " ( n u l l ) " > ( n u l l ) < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " ( n u l l ) " > ( n u l l ) < / l a t e x i t > (b) < l a t e x i t s h a 1 _ b a s e 6 4 = " ( n u l l ) " > ( n u l l ) < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " ( n u l l ) " > ( n u l l ) < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " ( n u l l ) " > ( n u l l ) < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = " ( n u l l ) " > ( n u l l ) < / l a t e x i t > until t = 1.05t c , just after the minimum bubble radius is achieved, since the subsequent rebounds for large pressure ratios are well-known to be physically inaccurate [62]. We see that MUSCL2 is marginally more accurate at predicting the minimum bubble radius and collapse time than the WENO5 method.…”