Dynamics of a bubble rising in gravitational field

IF 0.3 Q4 MATHEMATICS

Communications in Applied and Industrial Mathematics Pub Date : 2016-03-01 DOI:10.1515/caim-2016-0018

Enrico De Bernardis, G. Riccardi

引用次数: 4

Abstract

Abstract The rising motion in free space of a pulsating spherical bubble of gas and vapour driven by the gravitational force, in an isochoric, inviscid liquid is investigated. The liquid is at rest at the initial time, so that the subsequent flow is irrotational. For this reason, the velocity field due to the bubble motion is described by means of a potential, which is represented through an expansion based on Legendre polynomials. A system of two coupled, ordinary and nonlinear differential equations is derived for the vertical position of the bubble center of mass and for its radius. This latter equation is a modified form of the Rayleigh-Plesset equation, including a term proportional to the kinetic energy associated to the translational motion of the bubble.

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引力场中气泡上升的动力学

摘要研究了在等时无粘性液体中，由重力驱动的脉动球形气泡在自由空间中的上升运动。液体在初始时刻处于静止状态，因此随后的流动是无旋的。因此，气泡运动引起的速度场用势来描述，势通过基于勒让德多项式的展开来表示。导出了气泡质心的垂直位置及其半径的两个耦合的常非线性微分方程组。后一种方程是瑞利-普莱塞特方程的改进形式，其中包括一个与气泡平移运动相关的动能成比例的项。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Applied and Industrial Mathematics Mathematics-Applied Mathematics

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.