Numerical analysis of the interaction of 3D compressible bubble clusters

Based on the bubble dynamic theory and the compressible two-phase flow solver of the open source software Open FOAM, a numerical simulation study is carried out on the interactions of bubble clusters in a closed volume. The bubble dynamics and interactions of a single bubble, two bubbles, and four bubbles are investigated under the working conditions without and with the presence of a free surface. Through a parametric study, the qualitative patterns of the variations of the bubble collapse period,the volume compressibility, the bubble pressure peak value, and the breakdown, fusion,and separation phenomena with the parameters such as the bubble pressure, the radius size, the bubble spacing, and the distance from the free surface are obtained. The main factors affecting the bubble morphology and the dynamic characteristics are summarized from numerous parameter experiments. It is shown that, in the absence of a free surface,the main factors are the relative size of the bubbles, the pressure of the liquid, and the pressure differences among the bubbles, while in the presence of a free surface, the main factor is the pressure of the liquid between the upper surface of the bubble and the free surface.     

Strong interaction between a buoyancy bubble and a free surface

The growth and collapse of buoyant vapor bubbles close to a free surface in an inviscid incompressible fluid is investigated in this paper. The strong interaction between the deforming bubble and the free surface is simulated numerically by a boundary-integral method (Taib 1985; Blake et al., 1987). Improvements are made in the calculation of the singular integrals, the use of nonuniform boundary elements, and the choice of time-step size. The present numerical results agree better with the experimental observations of Blake and Gibson (1981) than previous numerical predictions for bubbles initiated at one maximum radius from the free surface. There is also concurrence of flow features with the experiments for a bubble initiated as close as half maximum radius from the free surface, where other numerical efforts have failed. The effects of buoyancy on bubbles initiated close to a free surface are also investigated. Vastly different features, depending on the distance of the bubble to the free surface and the buoyancy-force parameter, have been observed.     

The effect of rigid-body motions on the whipping response of a ship hull subjected to an underwater bubble

The dynamic elastic response of a floating ship hull girder to an underwater explosion bubble is normally composed of two parts: rigid-body motion and elastic deformation. However, the effects of rigid-body motion have consistently been neglected in the current literature based on the assumption that they are small. In this paper, our focus is on the study of rigid-body motion effects on the hull girder's elastic deformation, also known as the ‘whipping response’. A theory of interaction between a gas bubble and a hull girder is presented. The bubble dynamic equations combined with the bubble migration, free surface effect and drag force considerations are solved numerically using the Runge–Kutta method. The rigid-body and elastic responses of the hull that are induced by the impulsive pressure of a bubble are calculated using the methods presented herein. Two different examples of real ships are given to demonstrate the effect of rigid-body motion on whipping responses. The numerical results show that rigid-body motions reduce the amplitudes and vibration natural periods of the bending moments of the hull girder. These effects can be ignored for slender hulls, but must be taken into consideration for shorter/wider hulls so as not to underestimate the longitudinal strength.     

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.     

近自由面的多个水下爆炸气泡相互作用研究

将气泡运动阶段周围的流场假设为无黏、无旋、不可压缩的理想流体,运用边界积分法模拟流场中气泡的运动,并开发了三维计算程序,计算值与实验值吻合较好.用该方法模拟了近自由面多气泡之间的相互作用,包括同相气泡和异相气泡. 通过计算发现,气泡的周期随两气泡中心的距离减小而增大,这是由于多气泡之间存在抑制作用,特别是对异相气泡,这种抑制作用更加明显,称之为多气泡之间的抑制效应. 无论有、无自由面存在,多气泡之间均存在抑制效应,由于抑制效应导致同相与异相气泡相互耦合作用的动态特性存在巨大的差异,这些现象可为将来研究多个同时或延时产生的水下爆炸气泡的威力提供参考.      

Seed bubbles stabilize flow and heat transfer in parallel microchannels

Seed bubbles are generated on microheaters located at the microchannel upstream and driven by a pulse voltage signal, to improve flow and heat transfer performance in microchannels. The present study investigates how seed bubbles stabilize flow and heat transfer in micro-boiling systems. For the forced convection flow, when heat flux at the wall surface is continuously increased, flow instability is self-sustained in microchannels with large oscillation amplitudes and long periods. Introduction of seed bubbles in time sequence improves flow and heat transfer performance significantly. Low frequency (∼10 Hz) seed bubbles not only decrease oscillation amplitudes of pressure drops, fluid inlet and outlet temperatures and heating surface temperatures, but also shorten oscillation cycle periods. High frequency (∼100 Hz or high) seed bubbles completely suppress the flow instability and the heat transfer system displays stable parameters of pressure drops, fluid inlet and outlet temperatures and heating surface temperatures. Flow visualizations show that a quasi-stable boundary interface from spheric bubble to elongated bubble is maintained in a very narrow distance range at any time. The seed bubble technique almost does not increase the pressure drop across microsystems, which is thoroughly different from those reported in the literature. The higher the seed bubble frequency, the more decreased heating surface temperatures are. A saturation seed bubble frequency of 1000–2000 Hz can be reached, at which heat transfer enhancement attains the maximum degree, inferring a complete thermal equilibrium of vapor and liquid phases in microchannels. Benefits of the seed bubble technique are the stabilization of flow and heat transfer, decreasing heating surface temperatures and improving temperature uniformity of the heating surface.     

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.     

Simulating air entrainment and vortex dynamics in a hydraulic jump

The air entrainment characteristics of three separate Froude number hydraulic jumps are investigated numerically using an unsteady RANS, realizable k–ε turbulence model, with a Volume of Fluid treatment for the free surface. Mean velocity profiles, average void fraction, and Sauter mean diameter compare favorably with experimental data reported in literature. In all simulations, time-averaged void fraction profiles show good agreement with experimental values in the turbulent shear layer and an accurate representation of interfacial aeration at the free surface. Sauter mean diameter is well represented in the shear layer, and free surface entrainment results indicate bubble size remains relatively unchanged throughout the depth of the jump. Several different grid resolutions are tested in the simulations. Significant improvements in void fraction and bubble size comparison are seen when the diameter to grid size ratio of the largest bubbles in the shear layer surpasses eight. A three-dimensional simulation is carried out for one Froude number jump, showing an improvement in the prediction of entrained air and bubble size compared with two-dimensional results at a substantial increase in computation time. An analysis of three-dimensional vorticity shows a complex interaction between spanwise and streamwise vortical structures and entrained air bubbles. The jump is similar to a turbulent mixing layer, constrained by the free surface, with vortex pairing and subsequent fluctuations in free surface elevation. Downstream fluctuations of the toe are associated with a roll up of the primary spanwise vortex, fluctuations of the free surface, and counter-rotating streamwise vortex pairs. The action of these flow structures is likely responsible for the improvement in three-dimensional results.     

Interaction of two spark-generated bubbles near a confined free surface

In this paper, the oscillation of two spark-generated bubbles placed on a vertical column in close proximity to a confined free surface is considered. The confined free surface is accorded by the top opening of different configurations. These configurations include (i) a centrally perforated horizontal flat plate (\({\theta=90^{\circ})}\), (ii) vertically placed cylinder (\({\theta=0^{\circ})}\) and (iii) nozzle (\({\theta >0^{\circ})}\). The main objective of the present work is to study the effects of key parameters such as the nozzle geometry, the locations of the energy input (i.e., initial position of the bubbles with respect to each other and relative to the free surface) on the dynamics of the two bubbles and the free surface. It was found that the lifetime of the upper bubble decreases from the vertical cylinder to the flat plate case. In addition, by reducing the inter-bubble distance, the lifetime of the upper bubble becomes longer and the repulsion between two bubbles during the expansion phase is stronger. Finally, by reducing the upper bubble-free surface distance, the repulsion between two bubbles during expansion phase increases, the tendency of the upper bubble to rebound and initiate another oscillation cycle decreases, and the amplitude of elevation of the free surface increases.     

On the modeling and simulation of a laser‐induced cavitation bubble

Single cavitation bubbles exhibit severe modeling and simulation difficulties. This is due to the small scales of time and space as well as due to the involvement of different phenomena in the dynamics of the bubble. For example, the compressibility, phase transition, and the existence of a noncondensable gas inside the bubble have strong effects on the dynamics of the bubble. Moreover, the collapse of the bubble involves the occurrence of critical conditions for the pressure and temperature. This adds extra difficulties to the choice of equations of state. Even though several models and simulations have been used to study the dynamics of the cavitation bubbles, many details are still not clearly accounted for. Here, we present a numerical investigation for the collapse and rebound of a laser‐induced cavitation bubble in liquid water. The compressibility of the liquid and vapor are involved. In addition, great focus is devoted to study the effects of phase transition and the existence of a noncondensable gas on the dynamics of the collapsing bubble. If the bubble contains vapor only, we use the six‐equation model for two‐phase flows that was modified in our previous work [A. Zein, M. Hantke, and G. Warnecke, J. Comput. Phys., 229(8):2964‐2998, 2010]. This model is an extension to the six‐equation model with a single velocity of Kapila et al. (Phys. Fluid, 13:3002‐3024, 2001) taking into account the heat and mass transfer. To study the effect of a noncondensable gas inside the bubble, we add a third phase to the original model. In this case, the phase transition is considered only at interfaces that separate the liquid and its vapor. The stiffened gas equations of state are used as closure relations. We use our own method to determine the parameters to obtain reasonable equations of state for a wide range of temperatures and make them suitable for the phase transition effects. We compare our results with experimental ones. Also our results confirm some expected physical phenomena. Copyright © 2013 John Wiley & Sons, Ltd.     

Shock structure in bubbly liquids: comparison of direct numerical simulations and model equations

Shock wave structure in a bubbly mixture composed of a cluster of gas bubbles in a quiescent liquid with initial void fractions around 10% inside a 3D rectangular domain excited by a sudden increase in the pressure at one boundary is investigated using the front tracking/finite volume method. The effects of bubble/bubble interactions and bubble deformations are, therefore, investigated for further modeling. The liquid is taken to be incompressible while the bubbles are assumed to be compressible. The gas pressure inside the bubbles is taken uniform and is assumed to vary isothermally. Results obtained for the pressure distribution at different locations along the direction of propagation show the characteristics of one-dimensional unsteady shock propagation evolving towards steady-state. The steady-state shock structures obtained by the present direct numerical simulations, which show a transition from A-type to C-type steady-state shock structures, are compared with those obtained by the classical Rayleigh–Plesset equation and by a modified Rayleigh–Plesset equation accounting for bubble/bubble interactions in the mean-field theory.      

The interaction of background ocean air bubbles with a surface ship

A two-fluid model suitable for the calculation of the two-phase flow field around a naval surface ship is presented. This model couples the Reynolds-averaged Navier–Stokes (RANS) equations with equations for the evolution of the gas-phase momentum, volume fraction and bubble number density, thereby allowing the multidimensional calculation of the two-phase flow for monodisperse variable size bubbles. The bubble field modifies the liquid solution through changes in the liquid mass and momentum conservation equations. The model is applied to the case of the scavenging of wind-induced sea-background bubbles by an unpropelled US Navy frigate under non-zero Froude number boundary conditions at the free surface. This is an important test case, because it can be simulated experimentally with a model-scale ship in a towing tank. A significant modification of the background bubble field is predicted in the wake of the ship, where bubble depletion occurs along with a reduction in the bubble size due to dissolution. This effect is due to lateral phase distribution phenomena and the generation of an upwelling plume in the near wake that brings smaller bubbles up to the surface. © 1998 John Wiley & Sons, Ltd.     

基于气泡形态影响的水下气幕对冲击波衰减效果分析

气泡帷幕是水下爆炸冲击波防护的重要手段,对其作用机理及技术参数的深入研究对水下爆破安全与应用具有重要意义。采用高速摄影技术对室内小型水下气泡帷幕模型拍摄发现气幕在形成过程和与水下爆炸冲击波相互作用过程中均具有高度非连续性和非均匀性,且气幕区域内气体与液体混杂,界面轮廓复杂多样。在此基础上,考虑气泡形状及界面影响下,通过LS-DYNA有限元软件自带的APDL语言进行编程,实现了在设定的气幕区域内,通过设定气泡直径变化范围及气泡直径之间的最小差异值随机投放一定数量不同直径的气泡来模拟真实气幕中气泡的分布,并通过改变固定区域内气泡个数来模拟不同气压值工况下的气幕效果。分析发现该方法能够更加真实反映气幕在冲击波防护过程中的防护机理,随着单位区域内气泡数量的增大,防护效果越明显,但当气泡数量达到一定数量后气幕整体连续性及稳定性基本固定,防护效果也趋于稳定。     

垂直壁面附近上升单气泡的弹跳动力学研究

采用高速摄影技术结合阴影法,对静止水中垂直壁面附近上升单气泡运动进行实验研究,对比气泡尺度及气泡喷嘴与壁面之间的初始无量纲距离 ($S^{\ast}$)对气泡上升运动特性的影响,分析气泡与壁面碰撞前后,壁面效应与气泡动力学机制及能量变化规律.结果表明,对于雷诺数$Re \approx 580 \sim 1100$,无量纲距离$S^{\ast } <2 \sim3$时,气泡与壁面碰撞且气泡轨迹由无约束条件下的三维螺旋转变成二维之字形周期运动;当$S^{\ast } >2 \sim3$时,壁面效应减弱,有壁面约束的气泡运动与无约束气泡运动特性趋于一致.气泡与壁面碰撞前后,壁面效应导致横向速度峰值下降为原峰值的70%,垂直速度下降50%;气泡与壁面碰撞前,通过气泡中心与壁面距离($x/R$)和修正的斯托克斯数相关式可预测垂直速度的变化规律.上升气泡与壁面碰撞过程中,气泡表面变形能量单向传输给气泡横向动能,使得可变形气泡能够保持相对恒定的弹跳运动.提出了气泡在与壁面反复弹跳时的平均阻力系数的预测模型,能够很好地描述实验数据反映出的对雷诺数${Re}$、韦伯数${We}$和奥特沃斯数${Eo}$等各无量纲参数的标度规律.      

瞬态空化泡演变过程的数值模拟

采用边界积分方程方法，对无粘流体中三个空化泡以及自由面附近二个空化泡相互作用的演变过程进行了数值模拟。计算中边界用二阶有限元离散，影响系数矩阵非对角线元素用六点高斯数值积分方法计算，对第一类、第二类完全椭圆积分用高次多项式近似，对计算系数矩阵对角线元素中遇到的奇异积分进行了特殊处理。结果表明，在不同的给定参数下，空化泡的溃灭形态各异，柱状射流和环形射流都有可能发生，使空化泡演变成双泡或环形泡。     

Parametric Analysis for a Single Collapsing Bubble

This work presents a sensitivity analysis for cavitation processes, studying in detail the effect of various model parameters on the bubble collapse. A complete model (Hauke et al. Phys Rev E 75:1–14, 2007) is used to obtain how different parameters influence the collapse in SBSL experiments, providing some clues on how to enhance the bubble implosion in real systems. The initial bubble radius, the frequency and the amplitude of the pressure wave are the most important parameters determining under which conditions cavitation occurs. The range of bubble sizes inducing strong implosions for different frequencies is computed; the initial radius is the most important parameter characterized the intensity of the cavitation processes. However, other parameters like the gas and liquid conductivity or the liquid viscosity can have an important effect under certain conditions. It is shown that mass transfer processes play an important role in order to correctly predict the trends related with the effect of the liquid temperature, which translates into the bubble dynamics. Moreover, under some particular circumstances, evaporation can be encountered during the bubble collapse; this can be profitably exploited in order to feed reactants when the most extreme conditions inside the bubbles are reached. Thus, this paper aims at providing a global assessment of the effect of the different parameters on the entire cycle of a single cavitating spherical bubble immersed in an ultrasonic field. This work has been partially supported by Ministerio de Ciencia y Tecnologia, under grant number CTM2004-06184-C02-02.     

同相气泡耦合特性实验研究

设计实验, 利用电火花打火生成气泡来研究两个气泡之间以及两个气泡与自由面的相互作用, 在实验过程中, 精确控制打火电路, 使两个电火花气泡的生成时间间隔控制在67\mus以内, 实现了气泡的同相生成. 大量实验后发现, 两气泡相互作用过程中可能会出现融合、蘑菇状气泡、对射流、射流方向逆转、反向射流等现象, 自由面附近不同安置方式的两同相气泡会出现不同的脉动形式. 通过系列实验提出了气泡之间的无量纲距离、无量纲周期差等参数来描述气泡耦合特性, 为气泡群的相互作用提供实验依据.}      

波浪作用下直立结构物附近强湍动掺气流体运动的数值模拟

波浪破碎卷入气体易对建筑物受力产生压力振荡, 了解波浪作用下建筑物附近掺气水流的运动特性是精确计算建筑物受力的前提. 基于OpenFOAM开源程序包和修正速度入口造波方法建立三维数值波浪水槽, 模型采用S-A IDDES湍流模型进行湍流封闭, 并采用修正的VOF 方法捕捉自由液面, 数值模拟了规则波在1:10的光滑斜坡上与直立结构物的相互作用过程, 重点分析了结构物附近的水动力和掺气水流运动特性. 结果表明, 建立的数值模型能精确地捕捉波浪作用下直立结构物附近的自由液面的变化以及气泡输运过程, 较好地描述气体卷入所形成的气腔形态以及多气腔之间的融合、分裂等过程; 波浪与直立结构物相互作用产生强湍动掺气水流, 其运动过程十分复杂; 掺气流体输运过程中水气界面周围一直伴随着涡的存在, 其中, 气泡的分裂与周围正负涡量剪切作用密切相关, 且其输运轨迹主要受周围流场的影响; 研究揭示了结构物附近湍动能与掺气特性的关系, 发现波浪作用下直立结构物附近湍动能的分布与掺气水流特征参数(气泡数量、空隙率)整体呈现一定的线性关系.      

Artificial boiling heat transfer in the free convection to carbonic acid solution

Free convection phenomenon has been experimentally investigated around a horizontal rod heater in carbonic acid solution. Because of the tendency of the solution to desorb carbon dioxide gas when temperature is increased, bubbles appear when cylinder surface is heated. The bubbles consists mainly carbon dioxide and also a negligible amount of water vapor. The results present that dissolved carbon dioxide in water significantly enhances the heat transfer coefficient in compare to pure free convection regime. This is mainly due to the microscale mixing on the heat transfer surface, which is induced by bubble formation. In this investigation, experiments are performed at different bulk temperatures between 288 and 333 K and heat fluxes up to 400 kW m⁻² at atmospheric pressure. Bubble departure diameter, nucleation site density and heat transfer coefficient have been experimentally measured. A model has been proposed to predict the heat transfer coefficient.     

An improved three-dimensional model for interface pressure calculations in free-surface flows

A three-dimensional method for the calculation of interface pressure in the computational modeling of free surfaces and interfaces is developed. The methodology is based on the calculation of the pressure force at the interfacial cell faces and is mainly designed for volume of fluid (VOF) interface capturing approach. The pressure forces at the interfacial cell faces are calculated according to the pressure imposed by each fluid on the portion of the cell face that is occupied by that fluid. Special formulations for the pressure in the interfacial cells are derived for different orientations of an interface. The present method, referred to as pressure calculation based on the interface location (PCIL), is applied to both static and dynamic cases. First, a three-dimensional motionless drop of liquid in an initially stagnant fluid with no gravity force is simulated as the static case and then two different small air bubbles in water are simulated as dynamic cases. A two-fluid, piecewise linear interface calculation VOF method is used for numerical simulation of the interfacial flow. For the static case, both the continuum surface force (CSF) and the continuum surface stress (CSS) methods are used for surface tension calculations. A wide range of Ohnesorge numbers and density and viscosity ratios of the two fluids are tested. It is shown that the presence of spurious currents (artificial velocities present in case of considerable capillary forces) is mainly due to the inaccurate calculation of pressure forces in the interfacial computational cells. The PCIL model reduces the spurious currents up to more than two orders of magnitude for the cases tested.

Also for the dynamic bubble rise case, it is shown that using the numerical solver employed here, without PCIL, the magnitude of spurious currents is so high that it is not possible to simulate this type of surface tension dominated flows, while using PCIL, we are able to simulate bubble rise and obtain results in close agreement with the experimental data.