Dynamics of a spherical particle near a flat liquid boundary under acoustic radiation forces

The effect of radiation forces on a spherical particle near a flat liquid boundary is studied. The force is established to depend on the density ratio, the distance to the boundary, and the acoustic field parameters. The motion of a spherical particle under the action of radiation forces is described Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 30–41, November 2008.     

Dynamics of a small bubble in a compressible fluid

An efficient (simplified) method for solving problems of spherically symmetric dynamics of a small gas bubble in a compressible fluid is proposed. The method is based on the joint use of the full problem statement (the gas dynamics equations for the gas and the fluid) and its relevant simplifications. Some approximate statements are discussed. In the proposed method, the rarefaction and compression of the gas during the slow motion of the bubble surface is assumed to be uniform over the bubble volume. At the same time the fluid in the thin zone adjacent to the bubble is considered to be slightly compressible. Otherwise the gas dynamics equations are used for the gas and the fluid. The dynamics of the fluid in the thick external zone are described by the linear acoustics only. The proposed simplified method and two others used in literature are estimated by comparison of their numerical results with those obtained in full statement. Copyright © 2000 John Wiley & Sons, Ltd.     

Dynamics of a cavitation bubble near a solid surface and the induced damage

Numerical and experimental studies of the dynamics of a cavitating bubble near a resilient metal surface were performed. To augment the experimental flow visualizations of a collapsing bubble, numerical simulations were conducted to more thoroughly identify the collapse dynamics and analyze the flow. A bubble collapse was captured using a high-speed camera and back illumination. The metal sample was made of pure aluminum placed near a collapsing cavitation bubble at various distances from the metal surface. Width, depth, and volume of the induced material deformations were measured using an optical microscope and a three-dimensional profilometer and then compared against existing experimental data from the literature. The cavitating bubble’s dynamics and the related flow were simulated numerically using the open source finite volume based flow solver CavitatingFOAM. This code solved the Navier–Stokes equations for compressible two-phase flows using an Euler–Euler approach, including the barotropic equations of state. Bubble shapes, collapse times, and obtained damage parameters were compared to experimental observations. Impact velocities, pressures, shear rates, and various flow phenomena were discussed, providing broad insight into bubble dynamics and the induced damage.     

Numerical study of bubble rise and interaction in a viscous liquid

In this article, the flow instabilities during the rise of a single bubble in a narrow vertical tube are studied using a transient two-dimensional/axisymmetric model. To predict the shape of the bubble deformation, the Navier-Stokes equations in addition to an advection equation for liquid volume fraction are solved. A modified volume-of-fluid technique based on Youngs' algorithm is used to track the bubble deformation. To validate the model, the results of simulations for terminal rise velocity and bubble shape are compared with those of the experiments. The effect of different parameters such as initial bubble radius, channel height, liquid viscosity and surface tension on the shape and rise velocity of the bubble is investigated.     

Dynamics of a bubble in a liquid under laser pulse action

Simulation was performed of the behavior of a vapor bubble in a liquid under laser irradiation in laboratory experiments. A mathematical model was developed to analyze the effect of heat conduction, diffusion, and mass transfer on the bubble dynamics under compression and expansion. It is found that at the stage of collapse, intense condensation occurs on the bubble wall, which results in a significant (more than 15fold) decrease in bubble mass and an increase in pressure (to 10⁵ atm) and temperature (to 10⁴ K(. Results of numerical calculations of the radius of the first rebound and the amplitude of the divergent shock wave in water are compared with experimental data. It is shown that small (:about 1%) additives of an incondensable gas lead to a considerable decrease in mass transfer on the bubble wall.     

nfluence of exciting parameters on the vibration of single cavitation bubble driven by intensive sound

根据考虑了液体可压缩性的改进的微气泡动力学方程,采用改进的初始半径对单泡超声空化现象进行了数值计算研究. 结果表明,微气泡振动对一些参量很敏感：微气泡振动半径与初始半径的比值随振动频率的增大而减小;提高声场声压会加剧气泡崩塌程度,但过高的声压又不能使微气泡崩塌;微气泡崩塌速率随气泡初始半径的增加而增大,在一定范围内能保证空化泡稳定振动,在初始半径为1.6\,$\mu$m 处空化程度最强,如果继续增大初始半径则空化程度减弱、甚至消失;微气泡崩塌程度随黏滞系数和表面张力的增大而减弱,过大的黏滞系数和表面张力会使微气泡崩塌难以发生. 计算结果与他人的实验数据相比,发现液体的可压缩性使单泡空化强度增强, 对最佳空化区域范围的确定有较大的影响.     

Wake properties of a single gas bubble in three-dimensional liquid-solid fluidized bed

Experiments were performed to investigate the wake properties of a single gas bubble in a three-dimensional liquid-solid fluidized bed via a video camera moving at the same speed as the bubble. The solids holdup in the fluidized bed varied up to around 10%. The bubble size varied from 5 to 20 mm with corresponding bubble Reynolds numbers ranging from 1000 to 6500. The bubble was observed to have two types of wake configurations depending on the bubble size: the asymmetric/helical vortex wake for small bubbles and the symmetric wake for large bubbles. The bubble shape and relative rise velocity in the fluidized bed can be well-represented by correlations developed for single bubbles in liquid media, although the bubble shape in liquid-solid media is slightly more flattened compared to that in liquid media. The bubble rocking frequency was found to be independent of particle properties and to correspond in magnitude to the vortex shedding frequency in a two-dimensional liquid-solid fluidized bed. The average primary wake size in three dimensions is comparable to that in two dimensions.     

气泡射流载荷作用下圆柱壳动态响应

为了解药包在距离结构较近时水下爆炸气泡对水中结构冲击的影响,假设圆柱壳结构附近气泡的位移为自由场中气泡由于浮力产生位移和圆柱壳对气泡吸引产生位移的和,并建立了简化射流模型,对射流冲击下圆柱壳板架所产生的毁伤效应进行研究,分析了破坏形式,拟为水下爆炸气泡射流对船体的毁伤提供参考。     

Numerical simulation of shock propagation in a polydisperse bubbly liquid

The effect of distributed bubble nuclei sizes on shock propagation in a bubbly liquid is numerically investigated. An ensemble-averaged technique is employed to derive the statistically averaged conservation laws for polydisperse bubbly flows. A finite-volume method is developed to solve the continuum bubbly flow equations coupled to a single-bubble-dynamic equation that incorporates the effects of heat transfer, liquid viscosity and compressibility. The one-dimensional shock computations reveal that the distribution of equilibrium bubble sizes leads to an apparent damping of the averaged shock dynamics due to phase cancellations in oscillations of the different-sized bubbles. If the distribution is sufficiently broad, the phase cancellation effect can dominate over the single-bubble-dynamic dissipation and the averaged shock profile is smoothed out.     

Dynamics of a vapor shell around a heated particle in a liquid

The dynamics and heat and mass exchange of a vapor bubble containing a heated particle is studied in relation to the problem of vapor explosions. It is shown that the process involves two stages: dynamic stage and thermal stage. The dynamic stage is characterized by pressure fluctuations and a rapid increase in the thickness of the vapor layer. It is shown that the simplifying assumptions of the constancy of assumptions of constant heat conductivity of the vapor and linear temperature profile in the vapor layer lead to qualitatively incorrect results. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 69–78, July–August, 2007     

Domain perturbation method and shape of a bubble in a uniform flow of an inviscid liquid

In many problems with a free boundary there is defined a small parameter, , for which the solution is sometimes known for a particular value, =0, and the general solution is obtained as a series in the parameter. To find this solution, the equations can be written on a reference configuration and solved in a fixed domain. The purpose of this study is to show that this method of domain perturbation is a good one. The range of validity of this method will be studied on the model example of the irrotational flow of a perfect fluid around a bubble. The radius of convergence of the series solution will be determined, as will the nature of the solution in the neighbourhood of the first real singularity.     

柱形装药自由场水中爆炸气泡的射流特性

为研究柱形装药水中爆炸气泡射流特性,采用高速摄影方法在实验水箱中对PETN药柱进行水中爆炸实验,初步获得了有关柱形装药自由场水中爆炸气泡运动的数据资料.研究结果表明:柱形装药自由场水中爆炸形成气泡的运动与球形装药的存在差别,药柱放置方式的变化也会导致水中爆炸气泡产生性质迥异的运动.当药柱水平放置时,气泡表面的运动呈非对...     

Dynamics of a single bubble in a liquid in the presence of chemical reactions and interphase heat and mass exchange

The influence of inert and chemically reactive additives in the form of microdrops on the dynamics of a single bubble filled with an active gas mixture and collapsing under the action of a shock wave is considered. The development of a reaction during formation of the mixture is analyzed for instantaneous and dynamic evaporation of drops with allowance for various phases of their injection t _inj . It is shown that in instantaneous evaporation, an increase in the fraction of gaseous argon in the H₂+O₂ system raises the final temperature of the system under cryogenic conditions, lowers it under ordinary conditions, and causes appreciable oscillations of the values of γ, heat release, and molecular weight. It is noted that there are values of t _inj and D₀ at which the final temperature of the mixture decreases practically to the initial temperature. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 119–127, March–April. 1999.     

Numerical simulation of a single bubble by compressible two‐phase fluids

The present work deals with the numerical investigation of a collapsing bubble in a liquid–gas fluid, which is modeled as a single compressible medium. The medium is characterized by the stiffened gas law using different material parameters for the two phases. For the discretization of the stiffened gas model, the approach of Saurel and Abgrall is employed where the flow equations, here the Euler equations, for the conserved quantities are approximated by a finite volume scheme, and an upwind discretization is used for the non‐conservative transport equations of the pressure law coefficients. The original first‐order discretization is extended to higher order applying second‐order ENO reconstruction to the primitive variables. The derivation of the non‐conservative upwind discretization for the phase indicator, here the gas fraction, is presented for arbitrary unstructured grids. The efficiency of the numerical scheme is significantly improved by employing local grid adaptation. For this purpose, multiscale‐based grid adaptation is used in combination with a multilevel time stepping strategy to avoid small time steps for coarse cells. The resulting numerical scheme is then applied to the numerical investigation of the 2‐D axisymmetric collapse of a gas bubble in a free flow field and near to a rigid wall. The numerical investigation predicts physical features such as bubble collapse, bubble splitting and the formation of a liquid jet that can be observed in experiments with laser‐induced cavitation bubbles. Opposite to the experiments, the computations reveal insight to the state inside the bubble clearly indicating that these features are caused by the acceleration of the gas due to shock wave focusing and reflection as well as wave interaction processes. While incompressible models have been used to provide useful predictions on the change of the bubble shape of a collapsing bubble near a solid boundary, we wish to study the effects of shock wave emissions into the ambient liquid on the bubble collapse, a phenomenon that may not be captured using an incompressible fluid model. Copyright © 2009 John Wiley & Sons, Ltd.     

The drainage and rupture of a non-foaming liquid film formed upon bubble impact with a free surface

Experiments are performed to measure the thickness of a thin liquid film formed between a free surface and the apex of a bubble which is approaching at its terminal velocity. Measurements are made using bubbles of < 1 mm dia both in distilled water and alcoholic solutions (methanol, ethanol). The results of the experiments show that the models based on the lubrication approximation fail to predict the initial stage of drainage. A better agreement is obtained by modifying the model proposed by Chesters.     

Dynamics of a Taylor bubble in steady and pulsatile co-current flow of Newtonian and shear-thinning liquids in a vertical tube

A computational analysis is carried out to ascertain the effects of steady and pulsatile co-current flow, on the dynamics of an air bubble rising in a vertical tube containing water or a solution of Carboxymethylcellulose (CMC) in water. The mass fraction (m_f) of CMC in the solution is varied in the range 0.1% ⩽ m_f ⩽ 1% to accommodate zero-shear dynamic viscosities in the range 0.009–2.99 Pa-s. It was found that the transient and time-averaged velocities of Taylor bubbles are independent of the bubble size under both steady as well as pulsatile co-current flows. The lengths of the Taylor bubbles under the Newtonian conditions are found to be consistently greater than the corresponding shear-thinning non-Newtonian conditions for any given zero-shear dynamic viscosity of the liquid. In contrast to observations in stagnant liquid columns, an increase in the dynamic viscosity of the liquid (under Newtonian conditions) results in a concomitant increase in the bubble velocity, for any given co-current liquid velocity. In shear-thinning liquids, the change in the bubble velocity with an increase in m_f is found to be relatively greater at higher co-current liquid velocities. During pulsatile shear-thinning flows, distinct ripples are observed to occur on the bubble surface at higher values of m_f, the locations of which remain stationary with reference to the tube for any given pulsatile flow frequency, while the bubble propagated upwards. In such a pulsatile shear-thinning flow, a localised increase in dynamic viscosity is accompanied near each ripple, which results in a localised re-circulation region inside the bubble, unlike a single re-circulation region that occurs in Newtonian liquids, or shear-thinning liquids with low values of m_f. It is also seen that as compared to frequency, the amplitude of pulsatile flow has a greater influence on the oscillating characteristics of the rising Taylor bubble. The amplitude of oscillation in the bubble velocity increases with an increase in the CMC mass fraction, for any given value of pulsatile flow amplitude.     

Numerical simulation of motion and deformation of ring bubble along body surface

Numerical simulation for fluid flow over an attached rigid body with a deformable ring bubble is analyzed based on the velocity potential theory together with the boundary element method （BEM）. The analysis is focused on the axisymmetric case. The bubble surface is treated as a well defined air-liquid interface and is tracked by a mixed Eulerian-Lagrangian method. The points of intersection between the bubble and body are treated, specially in the numerical procedure. The auxiliary function method is adopted to calculate the pressure on the body surface and in the flow field. The convergence study is undertaken to assess the developed numerical method and the computation code. Some case studies are undertaken in which the interactions between the bubble/body and the incoming flow field are simulated. The effects of various physical parameters on the interactions are investigated.     

Free nonlinear oscillations of a thermally relaxing spherical gas bubble in an incompressible liquid

The quasi-adiabatic regime of free oscillation of a bubble in the presence of irreversible interphase heat transfer between the bubble and the ambient liquid is studied. On the basis of simplified model equations of a rarefield bubble mixture, a nonlinear-oscillation equation of the relaxation type is obtained. In constructing an exact particular solution of this equation, the heat transfer law associated with bubble compression is established. For studying the harmonic oscillations, the Krylov-Bogolyubov-Mitropol’skii asymptotic method is used. It is shown that, for a small bubble, the viscosity and heat transfer effects are of the same order. For a small bubble, the influence of these effects on the formation of the natural-oscillation frequency, which is small in the linear approximation, may be significant in the nonlinear formulation. For a large bubble, the influence of these effects is negligible in both approximations. For the approximate solution of the nonlinear equation, a uniformly valid second-order expansion is constructed.     

Characteristics of developing vertical bubbly flow under normal and microgravity conditions

The axial development of the void fraction profile, interfacial area concentration and Sauter mean bubble diameter of adiabatic nitrogen-water bubbly flows in a 9 mm-diameter pipe were measured using stereo image processing under normal and microgravity conditions. The flow measurements were performed at four axial locations (axial distance from the inlet, z normalized by the pipe diameter, D, z/D = 5, 20, 40 and 60) and with various flows: superficial gas velocity of 0.00840-0.0298 m/s, and superficial liquid velocity of 0.138-0.914 m/s. The effect of gravity on radial distribution of bubbles and the axial development of two-phase flow parameters is discussed in detail based on the obtained database and visual observation. Following Serizawa-Kataoka’s phase distribution pattern criteria under normal gravity conditions, the phase distribution pattern map was developed. Similar to normal gravity two-phase flows, wall, core and intermediate void peak patterns are observed under microgravity conditions but a transition void distribution pattern is not observed in the current experimental conditions. The data obtained in the current experiment are expected to contribute to the benchmarking of CFD simulation of phase distribution pattern and interfacial area concentration in forced convective pipe flow under microgravity conditions.     

Numerical simulation of a single rising bubble by VOF with surface compression

The capability of the direct volume of fluid method for describing the surface dynamics of a free two‐dimensional rising bubble is evaluated using quantities of a recently published benchmark. The model equations are implemented in the open source computational fluid dynamics library OpenFOAM®. Here, a main ingredient of the numerical method is the so‐called surface compression that corrects the fluxes near the interface between two phases. The application of this method with respect to two test cases of a benchmark is considered in the main part. The test cases differ in physical properties, thus in different surface tension effects. The quantities centre of mass position, circularity and rise velocity are tracked over time and compared with the ones given in the benchmark. For test case one, where surface tension effects are more pre‐eminent, deviations from the benchmark results become more obvious. However, the flow features are still within reasonable range. Nevertheless, for test case two, which has higher density and viscosity ratios and above all a lower influence of the surface tension force, good agreement compared with the benchmark reference results is achieved. This paper demonstrates the good capabilities of the direct volume of fluid method with surface compression with regard to the preservation of sharp interfaces, boundedness, mass conservation and low computational time. Some limitation regarding the occurrence of parasitic currents, bad pressure jump prediction and bad grid convergence have been observed. With these restrictions in mind, the method is suitable for the simulation of similar two‐phase flow configurations. Copyright © 2012 John Wiley & Sons, Ltd.