Experimental and numerical study on the growth and collapse of a bubble in a narrow tube

The growth, expansion and collapse of a bubble in a narrow tube are studied using both experiments and numerical simulations. In experiment, the bubble is generated by an electric spark in a water tank and recorded by a high-speed camera system. In numerical simulation, the evolution of the bubble is solved by adopting axisymmetric boundary integral equation, considering the surface tension effect. The results of experiments and numerical simulations are compared and good agreements are achieved. Both of them show that a counter-jet forms and penetrates the bubble at the end of the collapse stage, before a ring type bubble forms. Under the attraction of the tube wall due to Bjerknes force, a ring jet is generated, pointing towards the tube. On the basis of this, some physical quantities like the pressure on the tube wall and kinetic energy are calculated in a case study. The effects of tube diameters and tube lengths on the bubble’s behaviors are also investigated.     

A CFD comparative study of bubble break-up models in a turbulent multiphase jet

In this paper several bubble break-up models are compared. They have been implemented in the CFX-4.4 fluid dynamic commercial code, which uses the population balance equations for describing liquid/gas multi-phase flows. The models have been assessed against published experimental data, obtained for air bubble break-up within a turbulent water jet. The model of Martínez-Bazán, based on purely kinematics arguments, has shown better agreement with the experimental data. The capabilities of using these models coupled to a CFD code for multiphase flow prediction in industrial applications have been demonstrated.     

Experimental and numerical study on nucleate bubble deformation in subcooled flow boiling

Experimental and numerical study was conducted to investigate the bubble behaviors in subcooled flow nucleate boiling. The bubble behaviors in subcooled flow boiling in an upward annular channel were investigated in the range of subcooling degree 5–30 K by visualization with high spatial and temporal resolutions using a high speed video camera and Cassegrain tele-microscope. Obvious deformation on the upstream side surface of the bubble during its growth process was frequently observed. This deformation phenomenon was caused by the condensation occurring at the upstream side bottom of the bubble, which results from the Marangoni flow along the bubble surface from the bubble bottom to the top. Since the Marangoni flow cannot be directly observed by the current experiments because it occurs in a very thin interface along the bubble surface, the numerical simulations of bubble growth and departure behaviors in subcooled flow boiling were carried out. As a result, it was confirmed that the bubble deformation was caused by the Marangoni flow along the bubble surface. Moreover, the phenomenon of wave propagation on the bubble surface during the condensation process was observed, and it can enhance the heat transfer between the bubble and the surrounding subcooled liquid.     

Stability of a numerical algorithm for gas bubble modelling

A free-surface-tracking algorithm based on the SOLA-VOF method is analysed for numerical stability when modelling gas bubble evolution in a fluid. It is shown that an instability can arise from the fact that the bubble pressure varies with its volume. A time step stability criterion is introduced which is a function of the natural oscillation period but does not depend on the mesh size. This dependence suggests that the instability is likely to arise in the case of a general motion of a bubble, especially if break-up occurs. The effect is shown using linear Fourier analysis of the discretized equation for radial bubble oscillation and demonstrated numerically using a CFD code FLOW-3D. One- and three-dimensional situations are considered: a bubble in a fluid bounded by two concentric surfaces and a bubble floating in a fluid chamber with and without gravity. In cases where no analytical solution is available, a numerical method for the stability time step limit calculation is suggested based on finding the natural oscillation frequency. The nature of the instability suggests that it can be a feature of any numerical algorithm which models transient fluid flow with a free surface.     

Modeling of bubble coalescence and break-up considering turbulent suppression phenomena in bubbly two-phase flow

New mechanistic bubble coalescence and break-up models considering turbulent suppression phenomena, which can possibly occur in the high liquid velocity condition of turbulent bubbly two-phase flow, are presented. The energy exchange mechanism between a turbulent eddy and interfacial structure was taken into account in the efficiency terms. Numerical simulations of turbulent bubbly flow were conducted in a CFD code to evaluate the newly developed models, in comparison with other advanced models coupled with a bubble-induced turbulent effect for one-group interfacial area transport equation. Local measurements of the bubble characteristics on the bubble size evolution along a vertical pipe flow were performed at KAERI-VAWL test facility using the five-sensor conductivity probe method to provide database for models validation. Results from the calculation clearly show the improvements of the newly developed models.     

近场水下爆炸气泡脉动及水射流的实验与数值模拟研究

海上作战时,近场水下爆炸形成的水射流能造成水面舰船结构的严重局部毁伤。为了研究近场爆炸时舰船底部水射流的形成机理及规律,开展了TNT当量2.5 g的炸药在固支方板底部不同爆距下起爆的水下爆炸实验。结果表明,气泡坍塌形成水射流的过程随着爆距的增加由吸附式向非吸附式转化。接着,基于ABAQUS软件采用CEL方法开展了系列数值模拟,结果表明:爆距在0.821～0.867倍最大气泡半径时,存在吸附式射流向非吸附式射流转化的临界点;固支方板加快了气泡坍塌的进程,炸药与钢板间的距离越小则射流形成的时间越早;射流形成过程中最大速度和射流击中钢板时速度均随着爆距的增大先增大后减小,并在临界点附近达到最大值,射流速度最大可达621 m/s,射流击中钢板时速度最大可达269 m/s。最后,给出了射流开始形成时间、射流最大速度、射流最大速度出现时间、射流击中钢板速度和射流击中钢板时间与距离参数的函数关系式。     

Experimental investigation of the interaction between a pulsating bubble and a rigid cylinder

In this paper, the behavior of a bubble near a rigid cylinder is studied experimentally as the positions of bubble induction change, and several cylinders with different diameters are used in the experiment. The main results are as follows. The behavior of a bubble near a rigid cylinder is distinct from that near a rigid plate. When the cylinders are laid in deep water, there will occur three kinds of typical bubble shapes as the distance between bubble and cylinder increases. And the bubble shapes are different as the diameter of cylinder varies. When the cylinders are laid near a free surface, the behaviors of bubble near cylinders with different diameters are similar. For a certain distance between bubble and free surface, as the distance between bubble and cylinder increases, "double jet", "inclined jet" and "downward jet" will take place successively.     

Robust numerical analysis of the dynamic bubble formation process in a viscous liquid

The dynamics of bubble formation from a submerged nozzle in a highly viscous liquid with relatively fast inflow gas velocity is studied numerically. The numerical simulations are carried out using a sharp interface coupled level set/volume-of-fluid (CLSVOF) method and the governing equations are solved through a hydrodynamic scheme with formal second-order accuracy. Numerical results agree well with experimental results and it is shown that the sharp interface CLSVOF method enables one to reproduce the bubble formation process for a wide range of inflow gas velocities. From numerical results, one can improve their understanding of the mechanisms regarding the dynamics of bubble formation. For example, it is found that for some sets of parameters that the bubble formation process reaches steady state after several bubbles are released from the nozzle. At steady state, bubbles uniformly rise freely in the viscous liquid. It is observed that the fluid flow around a formed bubble has a significant role in determining the overall dynamic process of bubble formation; e.g. the effect of the fluid flow from the preceding bubble can be seen on newly formed bubbles.     

Chaotic behavior of gas bubble in non-Newtonian fluid: a numerical study

In the present paper, the nonlinear behavior of bubble growth under the excitation of an acoustic pressure pulse in non-Newtonian fluid domain has been investigated. Due to the importance of the bubble in the medical applications such as drug, protein or gene delivery, blood is assumed to be the reference fluid. Effects of viscoelasticity term, Deborah number, amplitude and frequency of the acoustic pulse are studied. We have studied the dynamic behavior of the radial response of bubble using Lyapunov exponent spectra, bifurcation diagrams, time series and phase diagram. A period-doubling bifurcation structure is predicted to occur for certain values of the effects of parameters. The results show that by increasing the elasticity of the fluid, the growth phenomenon will be unstable. On the other hand, when the frequency of the external pulse increases the bubble growth experiences more stable condition. It is shown that the results are in good agreement with the previous studies.     

Experimental study of the falling film of liquid around a Taylor bubble

The present work reports an experimental study of the falling liquid film around single Taylor bubbles rising in vertical tubes filled with stagnant liquids by using a pulse-echo ultrasonic technique. The experiments were carried out in acrylic tubes 2.0  m long, with inner diameters of 0.019, 0.024 and 0.034  m, with five water-glycerin mixtures, corresponding to inverse viscosity number ranging from 15 to 22422. The rising bubble and the falling liquid film were measured by using ultrasonic transducers located at the one side of the tube. The velocity and profile of the Taylor bubble, and the development length and equilibrium thickness of the falling liquid film around the bubble were obtained by the ultrasonic signals processing. Based on the experimental results of the present study, several correlations available to estimate the equilibrium thicknesses of liquid films falling around Taylor bubbles were evaluated and new correlations were proposed to estimate the dimensionless equilibrium film thickness and the film development length respectively.     

Direct numerical simulation of a bubble suspension in small amplitude oscillatory shear flow

Bubble suspensions can be found in many different fields and studying their rheology is crucial in order to improve manufacturing processes. When bubbles are added to a liquid, the magnitude of the viscosity changes and the behavior of the material is modified, giving it viscoelastic properties. For the purpose of this work, the suspended bubbles are considered to be monodisperse. It is assumed that Brownian motion and inertia can be neglected and that the fluid of the matrix is Newtonian and incompressible. The suspension is subject to an oscillatory strain while remaining in the linear regime. The resulting equations are solved in 3D with direct numerical simulation using a finite element discretization. Results of an ordered and random distribution of bubbles of volume fractions up to 40% are presented. The presence of bubbles has an opposite effect on the rheology of the suspension depending on the applied frequency. When the frequency is low, bubbles act as rigid fillers giving a rise to viscosity. On the contrary, when the frequency is high, the strain rate is being accommodated by the gaseous phase. Hence, bubbles deform, leading to a decrease of the viscosity.     

Diffusion flux to a distorted gas bubble at large Reynolds numbers

The diffusion flux to a distorted gas bubble situated in a uniform viscous incompressible fluid flow is determined for large Reynolds and Péclet numbers and finite Weber numbers. The bubble has the shape of an ellipsoid of revolution, oblate in the flow direction, making it possible to use the flow field derived by Moore [1] in the form of a two-term expansion with respect to the flow parameter =R^–1/2 (R is the Reynolds number; the zeroth term of the expansion corresponds to potential flow). The dependence of the diffusion flux onto the bubble surface on the Weber and Reynolds numbers is determined. The results of Winnikow [2] and Sy and Lightfoot [3] are thus generalized to the case of finite Weber numbers and a broader range of Reynolds numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 70–76, July–August, 1976.     

The unsteady drag on a spherical bubble at large Reynolds numbers

The flow past a spherical bubble undergoing a rectilinear motion in the unsteady flow of an unbounded liquid medium is investigated. The liquid velocity field at infinity is assumed to be uniform and the Reynolds number to be large. The Strouhal number is taken to be of order unity. The velocity distribution is sought by superposition of a perturbation field on the potential flow past the bubble so that the flow field is divided into four regions, i.e. the external flow field where the potential flow holds, the boundary layer, the rear stagnation point region and the wake. The flow in the rear stagnation point region and the wake is assumed to be essentially inertial. The unsteady drag experienced by the bubble is calculated from the mechanical energy balance of the liquid.     

Slug and bubble flows in a flat sheet ultrafiltration module: Experiments and numerical simulation

In this paper, the effect of gas bubbling including slug and bubble flows on enhancing shear force in an ultrafiltration (UF) process in a flat sheet module is investigated experimentally by image processing and numerically using the OpenFOAM software. In order to study characteristics of bubbles in the slug and bubble flows, the flat sheet module is analyzed by a video system facilitated with a high speed camera. The experimental results show that the average diameter of the slug flow is much larger than that of the bubble flow. The permeate flux for the slug and bubble flows is increased by 78% and 30%, respectively, compared to the case with no gas bubbling. The numerical results are shown to be in good agreement with those of the measurements both qualitatively and quantitatively. The results of simulations also demonstrate that although both flow patterns increase the shear stress by increasing the velocity gradient and/or vorticity, the shear stress induced by the slug flow is considerably larger. Therefore, the slug flow with a higher induced shear stress is more effective on the enhancement of the permeate flux in a UF process.     

Experimental and asymptotic study of nonspherical bubble collapse

Observations of the behavior of spark-generated bubbles in the vicinity of solid and free boundaries are described. In all cases, the formation of a reentering region (microjet or constriction) occurs on the part of the bubble which has the most freedom of motion. Drag-reducing polymer additives are seen to significantly affect bubble departure from sphericity. Their presence weakens the influence of nearby solid boundaries, and seems to enhance that of a free surface. The relative importance of the acoustic pulses emitted during successive implosions and rebounds of the bubble is seen to be modified by the proximity of a solid wall. When the radius of the bubble is small compared to its distance from the closest boundary, a theoretical approach, using matched asymptotic expansion, is applied successfully to describe the nonspherical bubble behavior and the pressure field. This method is extended to the case of a multi-bubble system. It is very useful in determining the limiting distances of interaction. In the case of a free surface this distance is less than two bubble diameters. When applied to a solid wall covered with an elastic coating of finite thickness, or to a two-liquid interface this technique shows a selection process: bubbles closer than a limiting distance to the boundary are repelled during their collapse. The collapse is toward the boundary only for bubbles beyond this distance and is therefore less damaging.     

Experimental and numerical investigation of the shock-induced fluidization of a particles bed

An experimental study on unsteady two phase flow is conducted in a vertical shock tube. Shock Mach numbers range from 1.3 to 1.5 in 1 bar. The particles are initially positioned in horizontal beds of various thicknesses. Our research covers a large domain of void fraction from 1 (single particles) to 0.35 (compact beds). The experiments provide shadowgraph images for the recording of particle trajectories (effect of the gas on the particles) and side-wall pressures (action of the particles on the gas). A dense two phase flow model has been elaborated and numerically solved using a finite difference scheme with pseudoviscosity. The simulated shock-induced fluidization of a 2 cm thick bed of 1.5 mm diameter glass particles is compared to the experiment. Received 10 September 1996 / Accepted 4 January 1997     

Experimental and numerical modeling of the turbulent wake of a self-propelled body

The development of the turbulent axisymmetric wake of a self-propelled body is modeled experimentally and numerically. Experimentally, the self-propulsion regime was implemented in the wake of a body of revolution whose hydrodynamic resistance was completely compensated by the pulse of a swirling jet rejected from its trailing part, and the jet-induced swirling was counterbalanced by the rotation of a part of the body surface in the opposite direction. The second-order semiempirical turbulence model that includes the differential equation of motion. the transfer of the normal Reynolds stresses, and the dissipation rate was used to describe this wake mathematically, and the nonequilibrium algebraic relations were used to determine the tangential stresses. A satisfactory agreement between the calculation results and the experimental data is shown. Degeneration of the distant turbulent wake is investigated numerically. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 49–58, July–August, 2000.     

Experimental study of the gravity influence on the periodic thermocapillary convection around a bubble

The 3D periodic state, following the steady thermocapillary convection state, around an air bubble immersed in a low-Prandtl-number silicone oil layer under a heated wall was experimentally investigated on the ground and during parabolic flights. This oscillation was observed under reduced gravity conditions for the first time. Consequently, the initiation of this oscillation seems to be independent of gravity and so of buoyancy convection. The reduced and increased gravity conditions showed that the gravity level modifies the oscillation. Its frequency increases with the gravity level. The comparison with the results obtained on the ground shows the bubble aspect ratio is not a relevant parameter when the gravity varies. Received: 27 November 2000/Accepted: 25 May 2001     

Experimental characterization of the spreading and break-up of liquid flat-fan sheets discharging in a low-density atmosphere and application to BrLi solutions

This work presents and characterizes the existence of two different regimes in the spreading and break-up of liquid flat-fan sheets when discharging in low-density atmospheres. The motivation of the study is the improvement on the absorption phenomena of lithium bromide aqueous solution when discharging in a 600–1,500 Pa water vapor environment. This corresponds to the absorber conditions in current absorption closed-cycle cooling machines. Despite this, the dimensionless characterization obtained has universal validity. The conditions that define the change in the break-up regime, the dimensionless sheet break-up length and the break-up time are given as a function of the parameters involved. Digital particle tracking velocimetry (PTV) has been applied to measure the velocity field and additional visualization techniques have been used to further characterize the break-up process. The experiments verify the existence of critical gas-to-liquid density and viscosity ratios below which gas to liquid interaction becomes negligible. The article also offers expressions that define their values as a function of the other dimensionless parameters.