A numerical study of the early-stage dynamics of a bubble cluster
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A numerical study of the early-stage dynamics of a bubble cluster * Ya-zhen Shi1, Kai Luo1, Xiao-peng Chen1, 2, Dai-jin Li1 1. School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China 2. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710129, China (Received April 24, 2019, Revised July 22, 2019, Accepted August 5, 2019, Published online September 23, 2020) ©China Ship Scientific Research Center 2020 Abstract: The dynamics of multiple cavitating bubbles is numerically simulated, with the ambient pressure lower than the saturated vapor pressure, using a pseudopotential lattice Boltzmann method (LBM) coupled with the Carnahan-Starling equation of state. Dual-bubble and multi-bubble systems are tested, and the method for the bubble cluster is validated. It is found that the bubble can either grow or collapse in the early stage, depending on the configuration of the bubble cluster, characterized by the bubble number, the inter-bubble distance and the initial radii. In the induced flow, the bubbles are mutually interacted. Scaling relations of the interaction are proposed according to the numerical results. With consideration of the interactions, the simplified Rayleigh-Plesset equations (RPEs) for multiple bubbles can describe the evolution of the bubbles approximately. The results may serve as the basis for improved cavitation models. Key words: Cavitation, bubble dynamics, interaction, lattice Boltzmann method (LBM), Rayleigh-Plesset equation (RPE)
Introduction The cavitation involves a liquid-to-vapor phase transition due to the low ambient pressure to form small vapor cavities. It occurs in various hydraulic machineries, such as pump, propeller, artificial heart and ultrasonic cleaner[1]. It is found that the snapping shrimp can induce cavitation for predation, the maximum swimming speed of the dolphin is limited by the occurrence of cavitation[2], and the coastal erosion has a special cavitating mechanism. The pioneering work dates back to Besant and Lord Rayleigh, who explored the dynamics of a bubble in the fluidic environment. The analyses were further extended with considering the effects of the surface tension by Plesset. Hitherto, the Rayleigh-Plesset equation (RPE) is one of the most widely used equations in hydrodynamics. The theories provide support for the development of modern technologies, including HIFU[3], sonochemical reactions[4] and so forth. * Project supported by the National Natural Science Foundation of China (Grant Nos. 11872315, 51679202 and 51579209). Biography: Ya-zhen Shi (1992-), Male, Ph. D., E-mail: [email protected] Corresponding author: Xiao-peng Chen, E-mail: [email protected]
In real constitutions, large or huge number of bubbles may exist in the liquid phase. The bubbles are in sophisticated motions, such as expanding, oscillation and translation. The motions are coupled with the flow field, to induce extra influences on the behaviors of the bubbles[5]. Mettin et al.[
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