An evaluation of a 3D free‐energy‐based lattice Boltzmann model for multiphase flows with large density ratio

In this paper, the 3D Navier–Stokes (N–S) equation and Cahn–Hilliard (C–H) equations were solved using a free‐energy‐based lattice Boltzmann (LB) model. In this model, a LB equation with a D3Q19 velocity model is used to recover continuity and N–S equations while another LB equation with D3Q7 velocity model for solving C–H equation (Int. J. Numer. Meth. Fluids, 2008; 56 :1653–1671) is applied to solve the 3D C–H equation. To avoid the excessive use of computational resources, a moving reference frame is adopted to allow long‐time simulation of a bubble rising. How to handle the inlet/outlet and moving‐wall boundary conditions are suggested. These boundary conditions are simple and easy for implementation. This model's performance on two‐phase flows was investigated and the mass conservation of this model was evaluated. The model is validated by its application to simulate the 3D air bubble rising in viscous liquid (density ratio is 1000). Good agreement was obtained between the present numerical results and experimental results when Re is small. However, for high‐Re cases, the mass conservation seems not so good as the low‐Re case. Copyright © 2009 John Wiley & Sons, Ltd.     

Non-adiabatic gravitational collapse of charged radiating fluid spheres

Dynamical equations governing the non-adiabatic collapse of a shear-free spherical distribution of unisotropic matter in the presence of charge are obtained. A brief outline of constructing a model describing collapse of a charged radiating fluid sphere in the set up developed is given.     

考虑利率因素的保险破产模型研究

本文首先介绍了在一般化破产模型基础上够造的保险费收取次数为Poisson过程的破产模型,并进一步在此模型上考虑了利率因素,使得相应的破产概率更具有实际意义。     

The virtual mass of an oblate-ellipsoidal bubble

A semi-analytical solution is presented for the virtual mass coefficient of an oblate-ellipsoidal bubble rising in liquid. The solution was found to be a function of Weber number. The present solution compared well with the numerical solution of the lattice Boltzmann method and the analytical solutions of other investigators.     

Relationships between distributions of chord lengths and distributions of bubble sizes including their statistical parameters

The performance of fluidized beds is strongly influenced by bubble behavior. Among various hydrodynamic properties, bubble size distributions are of prime concern, but in practice, bubble size is not readily measured. When a probe is used to determine bubble size, it intersects a bubble with a chord length other than the largest vertical dimension. The relationships between the size distribution of bubbles in the bed, the size distribution of bubbles touching the probe and the distribution of chord lengths must be resolved for correct interpretation of probe signals. A method for translating statistical parameters, namely mean and standard deviation of chord lengths to mean and standard deviation of bubble sizes, and an approach to infer the size distribution of bubbles touching the probe and the size distribution of bubbles in the bed system by using the distribution of chord lengths measured by a probe in closed form are proposed for the first time.     

The effect of noise on the Chafee-Infante equation: A nonlinear case study

We investigate the effect of perturbing the Chafee-Infante scalar reaction diffusion equation, , by noise. While a single multiplicative Itô noise of sufficient intensity will stabilise the origin, its Stratonovich counterpart leaves the dimension of the attractor essentially unchanged. We then show that a collection of multiplicative Stratonovich terms can make the origin exponentially stable, while an additive noise of sufficient richness reduces the random attractor to a single point.

     

The Peculiar Dynamics of Cavitation Bubbles

Details from cavitation bubble dynamics are reported: jet formation, counterjet formation, shock wave radiation and light emission. Multiple shock wave radiation from single bubble collapse with jet formation could be time resolved by high speed photography with 20 million frames per second. An explanation of counterjet formation is given. Pictures of the light emission (sonoluminescence) in acoustic cavitation are presented.     

三维气泡与自由表面相互作用的直接数值模拟

采用VOF中的PLIC界面重构方法数值模拟了三维气泡在液流中上升并与自由表面相互作用的运动.分别考察了不同初始高度,有无来流及有无再生气泡对气泡上升高度、上升速度、压力及与自由表面相互作用等的影响.结果表明:气泡初始位置越低,顶端上升的高度越大,自由面隆起的范围更广.越靠近自由表面,底部射流横向发展越窄,而向上的压力梯度,气泡上升速度,底部射流上升高度越大,反之则反;但如果底部射流均在接近自由表面以前已横向发展充分,则差别不大.气泡外形、上升高度、破裂时间以及上升速度与来流无关.产生再生气泡后,原生气泡与再生气泡相吸,相互加速对方的上升;自由表面抬升的高度增幅较大,范围拓宽,上升速度也大大增加,且再生气泡越多,自由表面隆起的范围越大.     

Motion of inviscid fluid tongues and bubbles in a Hele-Shaw cell occupied by a viscoelastic fluid

Problems of steady-state motion of an inviscid fluid tongue or bubble in a Hele-Shaw cell occupied by a viscoelastic fluid are considered. The problems generalize the well-known Saffman-Taylor problems [1, 2] in the approximation in which the pressure jump on the interface between the two fluids depends on the normal velocity of the interface [4]. In the zero approximation the results obtained by means of an iteration technique are in good agreement with the analytic solutions obtained by Saffman and Taylor [1, 2].__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 117–123. Original Russian Text Copyright © 2005 by Entov, Kolganov, and Kolganova.