Surface tension effects on the behaviour of a rising bubble driven by buoyancy force

In the inviscid and incompressible fluid flow regime,surface tension effects on the behaviour of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by a volume of fluid （VOF） method. The ratio of the gas density to the liquid density is 0.001, which is close to the case of an air bubble rising in water. It is found by numerical experiment that there exist four critical Weber numbers We1,~We2,~We3 and We4, which distinguish five different kinds of bubble behaviours. It is also found that when 1≤We2, the bubble will finally reach a steady shape, and in this case after it rises acceleratedly for a moment, it will rise with an almost constant speed, and the lower the Weber number is, the higher the speed is. When We 〉We2, the bubble will not reach a steady shape, and in this case it will not rise with a constant speed. The mechanism of the above phenomena has been analysed theoretically and numerically.

A model for predicting bubble rise velocity in a pulsed gas solid fluidized bed

Bed stability, and especially the bed density distribution, is affected by the behavior of bubbles in a gas solid fluidized bed. Bubble rise velocity in a pulsed gas-solid fluidized bed was studied using photographic and computational fluid dynamics methods. The variation in bubble rise velocity was investigated as a function of the periodic pulsed air flow. A predictive model of bubble rise velocity was derived: ub=ψ(Ut+Up-Umf)+kp(gdb)(1/2). The software of Origin was used to fit the empirical coefficients to give ψ = 0.4807 and kp = 0.1305. Experimental verification of the simulations shows that the regular change in bubble rise velocity is accurately described by the model. The correlation coefficient was 0.9905 for the simulations and 0.9706 for the experiments.

Optimized Vertical Layers for the Hybrid Terrain-Following Coordinate Minimizing Numerical Errors in a 2D Rising Bubble Experiment near Steep Terrain

The basic terrain-following(BTF)coordinate simplifies the lower boundary conditions of a numerical model but leads to numerical error and instability on steep terrain.Hybrid terrain-following(HTF)coordinates with smooth slopes of vertical layers(slopeVL)generally overcome this difficulty.Therefore,the HTF coordinate becomes very desirable for atmospheric and oceanic numerical models.However,improper vertical layering in HTF coordinates may also increase the incidence of error.Except for the slopeVL of an HTF coordinate,this study further optimizes the HTF coordinate focusing on the thickness of vertical layers(thickVL).Four HTF coordinates(HTF1–HTF4)with similar slopeVL but different vertical transition methods of thickVL are designed,and the relationship between thickVL and numerical errors in each coordinate is compared in the classic idealized thermal convection[two-dimensional(2D)rising bubble]experiment over steep terrain.The errors of potential temperatureθand vertical velocity w are reduced most,by approximately 70%and 40%,respectively,in the HTF1 coordinate,with a monotonic increase in thickVL according to the increasing height;however,the errors ofθincreased in all the other HTF coordinates,with nonmonotonic thickVLs.Furthermore,analyses of the errors of vertical pressure gradient force(VPGF)show that due to the interpolation errors of thickVL,the inflection points in the vertical transition of thickVL induce the initial VPGF errors;therefore,the HTF1 coordinate with a monotonic increase in thickVL has the smallest errors among all the coordinates.More importantly,the temporal evolution of VPGF errors manifests top-type VPGF errors that propagate upward gradually during the time integration.Only the HTF1 and HTF4 coordinates with a monotonic increase in thickVL near the top of the terrain can suppress this propagation.This optimized HTF coordinate(i.e.,HTF1)can be a reference for designing a vertical thickVL in a numerical model.

A LEVEL SET METHOD FOR SIMULATION OF RISING BUBBLE

A level set method, the TVD scheme of second-order upwind procedure coupledwith flux-limiter, and SIMPLE algorithm were incorporated to simulate the flow and interfacialmotion of immiscible two-fluids with large density ratio and viscosity ratios, large topologydistortion and surface tension. As a numerical example axi-symmetric rising bubbles wereinvestigated. It is found that the method is numerically stable and has good convergence propertyand the results are in good agreement with other works.

VISCOSITY EFFECTS ON THE BEHAVIOR OF A RISING BUBBLE

In the incompressible fluid flow regime, without taking consideration of surface tension effects, the viscosity effects on the behavior of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by the Volume Of Fluid （VOF） method. The ratio of the gas density to the liquid density is taken as 0.001, and the gas viscosity to the liquid viscosity is 0.01, which is close to the case of an air bubble rising in water. It is found by numerical experiments that there exist two critical Reynolds numbers Re1 and Re2 , which are in between 30 and 50 and in between 10 and 20, respectively. As Re 〉 Re1 the bubble will have the transition to toroidal form, and the toroidal bubble will break down into two toroidal bubbles. In this case viscosity will damp the development of the liquid jet and delay the formation of the toroidal bubble. As Re〈Re1 the transition will not happen. As Re2 〈 Re 〈 Re1, the bubble will split from its rim into a toroidal bubble and a spherical cap-like bubble, and as Re〈Re2 the splitting will not occur and the bubble can finally reach a stationary shape. With the decrease of the Reynolds number, the stationary shape changes from spherical-cap bubble with skirt to dimpled peach-like bubble. Before the bubble reaches its stationary shape the vortex structure in the flow field varies with time. The vortex structure corresponding to bubble stationary shape varies with the Reynolds number. It is also found that there exists another critical Reynolds number Re^＊ which is in between Re1 and Re2 , and as Re 〈 Re^＊, after the bubble rises in an accelerating manner for a moment, it will rise with an almost constant speed, and the speed increases with increasing Reynolds number. As Re 〉 Re^＊, it will not rise with a constant speed. The mechanism of the above phenomena has been analyzed theoretically and numerically.

Bubble dynamics and its applications

Bubbles have very important applications in many fields such as shipbuilding engineering, ocean engineering, mechanical engineering, environmental engineering, chemical engineering, medical science and so on. In this paper, the research status and the development of the bubble dynamics in terms of theory, numerical simulation and experimental technique are reviewed, which cover the underwater explosion bubble, airgun bubble, spark bubble, laser bubble, rising bubble, propeller cavitation bubble, water entry/exit cavitation bubble and bubble dynamics in other fields. Former researchers have done a lot of researches on bubble dynamics and gained fruitful achievements. However, due to the complexity of the bubble motion, many tough mechanical problems remain to be solved. Based on the research progress of bubble dynamics, this paper gives the future research direction of bubble dynamics, aiming to provide references for researches related to bubble dynamics.

Numerical investigation of gas bubble behavior in tapered fluidized beds

In this article, the behavior of gas bubbles in tapered fluidized beds is investigated with the use of a two- fluid model incorporating kinetic theory of granular flow. The effects of various parameters such as apex angle, particle size, and particle density on the size distribution and the rise velocity of gas bubbles were examined. In addition, the simulation results for the bubble fraction and axial velocity of gas bubbles were compared with experimental data reported in the literature and good agreement was observed. As the apex angle was increased, the fraction of gas bubbles with large sizes increased and the fraction of bubbles with small sizes decreased. As the particle size increased, the fraction of gas bubbles with large diameters decreased; however, the fraction of bubbles with medium diameters increased. The obtained results clearly indicate that an increased solid density increased the bubble rise velocity up to a specified height and reduced the velocity at larger heights, in tapered fluidized beds.

A novel dual-material probe for in situ measurement of particle charge densities in gas-solid fluidized beds

Particle charge density is vitally important for monitoring electrostatic charges and understanding particle charging behavior in fluidized beds. In this paper, a dual-material probe was tested in a gas-solid fluidized bed for measuring the charge density of fluidized particles. The experiments were conducted in a two-dimensional fluidized bed with both single bubble injection and freely bubbling, at various particle charge densities and superficial gas velocities. Uniformly sized glass beads were used to eliminate complicating factors at this early stage of probe development. Peak currents, extracted from dynamic signals, were decoupled to determine charge densities of bed particles, which were found to be qualitatively and quantitatively consistent with charge densities directly measured by Faraday cup from the freely bubbling fluidized bed. The current signals were also decoupled to estimate bubble rise velocities, which were found to be in reasonable agreement with those obtained directly by analyzing video images.