Modeling of Cavitation Bubble Cloud with Discrete Lagrangian Tracking

In this paper, a Lagrangian-Eulerian (LE) two-way coupling model is developed to numerically study the cavitation bubble cloud. In this model, the gas-liquid mixture is treated directly as a continuous and compressible fluid and the governing equations are solved by methods in Eulerian descriptions. An isobaric closure exhibiting better consistency properties is applied to evaluate the pressure of gas-liquid mixture. The dispersed gas/vapor bubbles are tracked in a Lagrangian fashion, and their compression and expansion are described by a modified Rayleigh-Plesset equation, which considers the close-by flow properties other than these of the infinity for each bubble. The performance of the present method is validated by a number of benchmark tests. Then, this model is applied to study how the bubble cloud affects the shape and propagation of a pressure wave when the pressure pulse travels through. In the end, a three-dimensional simulation of a vapor cloud’s Rayleigh collapse is carried out, and the induced extreme pressure is discussed in detail. The total bubble number’s influence on the extreme collapse pressure and the size distribution of bubbles during the collapse are also analyzed.

Clouds of bubbles in a viscoplastic fluid

Viscoplastic fluids can hold bubbles/particles stationary by balancing the buoyancy stress with the yield stress – the key parameter here is the yield number $Y$ , the ratio of the yield stress to the buoyancy stress. In the present study, we investigate a suspension of bubbles in a yield-stress fluid. More precisely, we compute how much is the gas fraction $\phi$ that could be held trapped in a yield-stress fluid without motion. Here the goal is to shed light on how the bubbles feel their neighbours through the stress field and to compute the critical yield number for a bubble cloud beyond which the flow is suppressed. We perform two-dimensional computations in a full periodic box with randomized positions of the monosized circular bubbles. A large number of configurations are investigated to obtain statistically converged results. We intuitively expect that for higher volume fractions, the critical yield number is larger. Not only here do we establish that this is the case, but also we show that short-range interactions of bubbles increase the critical yield number even more dramatically for bubble clouds. The results show that the critical yield number is a linear function of volume fraction in the dilute regime. An algebraic expression model is given to approximate the critical yield number (semi-empirically) based on the numerical experiment in the studied range of $0\le \phi \le 0.31$ , together with lower and upper estimates.

Numerical Study of Bubble Cloud and Thermal Lesion Evolution During Acoustic Droplet Vaporization Enhanced Hifu Treatment

Acoustic droplet vaporization (ADV) has proven to enhance high intensity focused ultrasound (HIFU) thermal ablation of tumor. It has also been demonstrated that triggering droplets before HIFU exposure could be a potential way to control both the size and the shape of the thermal lesion. In this paper, a numerical model is proposed to predict the thermal lesion created in ADV enhanced HIFU treatment. Bubble oscillation was coupled into a viscoelastic medium in the model to more closely represent real applications in tissues. Several physical processes caused by continuous wave ultrasound and elevated temperature during the HIFU exposure were considered, including rectified diffusion, gas solubility variation with temperature in the medium, boiling, etc. Four droplet concentrations spanning two orders of magnitude were calculated. The bubble cloud formed from triggering of the droplets by the pulse wave ultrasound, along with the evolution of the shape and location of the bubble cloud and thermal lesion during the following continuous wave exposure were obtained. The increase of bubble void fraction caused by continuous wave exposure were found to be consistent with the experimental observation. With the increase of droplet concentration, the predicted bubble cloud shapes vary from tadpole to triangular and double triangular, while the thermal lesions move toward the transducer. The results show that the assumptions used in this model increased the accuracy of the results. This model may be used for parametrical study of ADV enhanced HIFU treatment and be further used for treatment planning and optimization in the future.

Cavitation Bubble Cloud Break-Off Mechanisms at Micro-Channels

This paper provides new physical insight into the coupling between flow dynamics and cavitation bubble cloud behaviour at conditions relevant to both cavitation inception and the more complex phenomenon of flow “choking” using a multiphase compressible framework. Understanding the cavitation bubble cloud process and the parameters that determine its break-off frequency is important for control of phenomena such as structure vibration and erosion. Initially, the role of the pressure waves in the flow development is investigated. We highlight the differences between “physical” and “artificial” numerical waves by comparing cases with different boundary and differencing schemes. We analyse in detail the prediction of the coupling of flow and cavitation dynamics in a micro-channel 20 m high containing Diesel at pressure differences 7 MPa and 8.5 MPa, corresponding to cavitation inception and "choking" conditions respectively. The results have a very good agreement with experimental data and demonstrate that pressure wave dynamics, rather than the “re-entrant jet dynamics” suggested by previous studies, determine the characteristics of the bubble cloud dynamics under “choking” conditions.