改进的泡泡布点方法研究

泡泡布点方法能够在复杂区域内生成高质量的节点集，但是其计算效率仍有待提高，为此本文做了两方面的改进。一是种子填充算法思想应用于节点的初始布置中，从而生成数目合适的节点集，省去了原布点方法中的节点增删过程，有效地节约模拟时间；二是简化了泡泡运动模拟的控制方程，使得运动模拟更加简单。数值算例表明，改进的泡泡布点方法生成的网格平均质量均高于0.94,且计算效率相比原布点方法提高90%以上。因此，改进的泡泡布点方法是一种高质量、高效率且适宜求解大规模问题的节点布置方法。     

Three-dimensional desingularized boundary integral methods for potential problems

The concept of desingularization in three-dimensional boundary integral computations is re-examined. The boundary integral equation is desingularized by moving the singular points away from the boundary and outside the problem domain. We show that the desingularization gives better solutions to several problems. As a result of desingularization, the surface integrals can be evaluated by simpler techniques, speeding up the computation. The effects of the desingularization distance on the solution and the condition of the resulting system of algebraic equations are studied for both direct and indirect versions of the boundary integral method. Computations show that a broad range of desingularization distances gives accurate solutions with significant savings in the computation time. The desingularization distance must be carefully linked to the mesh size to avoid problems with uniqueness and ill-conditioning. As an example, the desingularized indirect approach is tested on unsteady non-linear three-dimensional gravity waves generated by a moving submerged disturbance; minimal computational difficulties are encountered at the truncated boundary.     

The shape and position of bubbles at horizontal liquid surfaces

The scope of this investigation comprises the determination of the shape and position of a gas bubble floating at the horizontal surface of a liquid. — A starting point towards the solution of this problem is provided by Laplace's law, but this equation is soluble analytically in very few cases only. It is shown that the most useful parameters can be obtained from Princen's table which is a modified version of Bashford and Adams table and other dimensions can be evaluated from the equations as proposed in the context. It is suggested that r√c should be used as the fundamental dimensionless shape parameter and further the radius r of the equivalent sphere can be related to original radius r₀ of the bubble by means of a correction factor. — This system has also been studied experimentally. A photographic technique has been used, both the length x_c and the height h of upper part of the bubble at the surface have been measured on photographs thus allowing a sensitive test of the theory.     

Controlled foam generation using cyclic diphasic flows through a constriction

Numerous industrial and academic applications of liquid foams require a fine control over their bubble size distribution and their liquid content. A particular challenge remains the generation of foams with very small bubbles and low liquid content. A simple technique which fulfils these different criteria, the “double-syringe technique”, has been exploited for decades in hospital applications. In this technique, the foaming liquid and gas are pushed repeatedly back and forth through the constriction that connects two syringes. After having motorised the technique we investigate here the influence of the different processing conditions on the obtained foam properties in a quantitative manner. We show that this technique is unique in producing foams with the same characteristic bubble size distributions over a wide range of processing conditions (tubing, fluid velocities,...), making it an ideal tool for controlled foam generation. In contrast to other techniques, the liquid fraction in the double-syringe technique can be varied without impacting the bubble size distribution. Using high-speed imaging we show that bubbles are dispersed in the aqueous phase at two different places in the device via a hitherto unreported fragmentation mechanism. We put in evidence that the obtained bubble size distributions are largely independent of most processing parameters with the exception of the geometry of the constriction and the foam formulation. We put forward a first analysis of the non-dimensional numbers of the flow and compare our results with bubbles size distributions obtained from fragmentation processes. Future work on simplified model systems is required to explain the observed mechanisms.     

岩石节理粗糙面的分形几何特性与剪切强度关系的实验研究

自然形成的岩石节理面的表面形状具有分形特性，利用分形理论来描述岩石节理的粗糙特性，并确立与岩石节理面的剪切力学特性间的关系对于指导岩体工程设计，和管理具有重要一研究利用开发设计的三维激光测距仪在精确测定岩石节理面的表面形状４ 基础上，依据变量图法建立了 岩石节理面的     

Filtration in a Porous Granular Medium: 2. Application of Bubble Model to 1-D Column Experiments

This paper describes the formulation of a quasi-1-D network model, referred to as the ‘bubble model’, and its application for simulating particle transport and filtration through a granular filter bed. The model comprises a series of homogeneous sites linked through bundles of cylindrical bonds that represent flow pathways through distributions of pores and pore throats. This model incorporates pore scale processes of particle sieving and infiltration are based on numerical simulations described in a companion paper. The modeling of infiltration is further refined based on detailed experimental observations and measurements of the filtration of a dilute suspension of acrylic particles through a column of glass beads reported by Yoon et al. (2005 Water Resour. Res., to appear). Their data distinguish (a) between the collection of particles on grain surfaces and at grain-to-grain contact points, and (b) between particles that are fully entrapped and those that are hindered (temporarily collected) and can later become detached. These effects are represented by two parameters that characterize the probability of attachment and are linked to the surface roughness of the grains; one that describes the minimum particle size that can be fully entrapped, and one that describes the detachment rate. These parameters can be readily calibrated from conventional measurements of effluent concentration and effluent particle size distribution. Detailed comparisons with the data reported by Yoon et al. show that the proposed bubble model is able to achieve reliable predictions of the spatial distribution of particles within the filter bed following phases of particle injection and washing.     

柱状含铝炸药水下爆炸近场的特征线法研究

基于之前提出的一种含熵变项的特征线法,通过控制非等熵流中的能量释放来刻画铝粉燃烧的影响,结合简单Chapman-Jouguet模型和JWL-Miller状态方程,计算了柱形含铝炸药水下爆炸的近场参数。对比模拟结果与实验数据,发现这种特征线法可以较好地预测近场冲击波的传播迹线、爆轰产物的膨胀轨迹以及内部压缩波的反射过程。结果表明,这种特征线法可用于含铝炸药水下爆炸的近场计算,进一步可用于评估含铝炸药性能或计算水下能量输出。     

Simulating gas–liquid multiphase flow using meshless Lagrangian method

A multiphase flow model has been established based on a moving particle semi‐implicit method. A surface tension model is introduced to the particle method to improve the numerical accuracy and stability. Several computational techniques are employed to simplify the numerical procedure and further improve the accuracy. A particle fraction multiphase flow model is developed and verified by a two‐phase Poiseuille flow. The multiphase surface tension model is discussed in detail, and an ethanol drop case is introduced to verify the surface tension model. A simple dam break is simulated to demonstrate the improvements with various modifications in particle method along with a new boundary condition. Finally, we simulate several bubble rising cases to show the capacity of this new model in simulating gas–liquid multiphase flow with large density ratio difference between phases. The comparisons among numerical results of mesh‐based model, experimental data, and the present model, indicate that the new multiphase particle method is acceptable in gas–liquid multiphase fluids simulation. Copyright © 2014 John Wiley & Sons, Ltd.     

Nonconforming local projection stabilization for generalized Oseen equations

A new method of nonconforming local projection stabilization for the gen- eralized Oseen equations is proposed by a nonconforming inf-sup stable element pair for approximating the velocity and the pressure. The method has several attractive features. It adds a local projection term only on the sub-scale （H ≥ h）. The stabilized term is simple compared with the residual-free bubble element method. The method can handle the influence of strong convection. The numerical results agree with the theoretical expectations very well.     

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.     

A framework to perform high-order deconvolution for finite-volume method on simplicial meshes

In this article, a new framework to design high-order approximations in the context of node-centered finite volumes on simplicial meshes is proposed. The major novelty of this method is that it relies on very simple and compact differential operators, which is a critical point to achieve good performances in the High-performance computing context. This method is based on deconvolution between nodal and volume-average values, which can be conducted to any order. The interest of the new method is illustrated through three different applications: mesh-to-mesh interpolation, levelset curvature computation, and numerical scheme for convection. Higher order can also be achieved within the present framework by introducing high-rank tensors. Although these tensors feature much symmetries, their manipulation can quickly become an overwhelming task. For this reason and without loss of generality, the present articles are limited to third-order expansion. This method, although tightly connected to the k-exact schemes theory, does not rely on successive corrections: the high-order property is obtained in a single operation, which makes them more attractive in terms of performances.     

A boundary element method for the simulation of non-spherical bubbles and their interactions near a free surface

The basic principle and numerical technique for simulating two three-dimensional bubbles near a free surface are studied in detail by using boundary element method. The singularities of influence coefficient matrix are eliminated using coordinate transformation and so-called 4 π rule. The solid angle for the open surface is treated in direct method based on its definition. Several kinds of configurations for the bubbles and free surface have been investigated. The pressure contours during the evolution of bubbles are obtained in our model and can better illuminate the mechanism underlying the motions of bubbles and free surface. The bubble dynamics and their interactions have close relation with the standoff distances, buoyancy parameters and initial sizes of bubbles. Completely different bubble shapes, free surface motions, jetting patterns and pressure distributions under different parameters can be observed in our model, as demonstrated in our calculation results.     

基于固定网格和拓扑导数的结构拓扑优化自适应泡泡法

为继承传统拓扑优化泡泡法变量少、精度高等优点,并克服其网格重划频繁、孔洞合并操作繁琐等不足,提出了一种基于固定网格和拓扑导数的自适应泡泡方法.该方法的主要特点是:(1)采用有限胞元固定网格分析方法计算结构力学响应,在优化过程中无需网格更新和重划分,就能保证较高的分析精度;(2)根据拓扑导数信息指导结构区域中孔洞的引入,不仅消除了优化结果对孔洞初始布局的依赖性,还能有效控制设计变量的数量;(3)引入拓扑导数阈值和孔洞影响区域新概念,实现了孔洞引入频次和位置的自适应调节,保证了拓扑优化过程的数值计算稳定性;(4)采用光滑变形隐式曲线描述孔洞边界,不仅设计参数少、变形能力强,而且便于处理孔洞间的融合/分离操作以及与固定网格分析方法的有机结合.理论分析和数值算例表明,改进后的自适应泡泡法能够消除传统泡泡法因采用拉格朗日网格和参数化B样条曲线模型而存在的实施困难,采用很少的设计变量就可获得边界光滑清晰的优化结果.      

静水中气泡上升运动及阻力系数研究

采用模型计算法与实验法结合的方式对静水中气泡上升运动行为进行研究。通过牛顿运动定律,基于不同物理模型,建立气泡在水中运动的微分方程;假设气泡在运动过程中的关键参数取值,推导小气泡在水中浮升过程中的气泡行为预测公式;针对不同流态下的气泡上升关键参数进行适应性分析和算例计算。通过设计气泡上升运动实验,对气泡上升运动公式进行适应性分析,修正关键参数的取值。据此提出一种小气泡上升运动规律的计算方法以及关键参数取值方式及参考区间。     

Interactions of multiple spark-generated bubbles with phase differences

This paper aims to study the complex interaction between multiple bubbles, and to provide a summary and physical explanation of the phenomena observed during the interaction of two bubbles. High-speed photography is utilized to observe the experiments involving multiple spark-generated bubbles. Numerical simulations corresponding to the experiments are performed using the Boundary Element Method (BEM). The bubbles are typically between 3 and 5 mm in radius and are generated either in-phase (at the same time) or with phase differences. Complex phenomena are observed such as bubble splitting, and high-speed jetting inside a bubble caused by another collapsing bubble nearby (termed the ‘catapult’ effect). The two-bubble interactions are broadly classified in a graph according to two parameters: the relative inter-bubble distance and the phase difference (a new parameter introduced). The BEM simulations provide insight into the physics, such as bubble shape changes in detail, and jet velocities. Also presented in this paper are the experimental results of three bubble interactions. The interesting and complex observations of multiple bubble interaction are important for a better understanding of real life applications in medical ultrasonic treatment and ultrasonic cleaning. Many of the three bubble interactions can be explained by isolating bubble pairs and classifying their interaction according to the graph for the two bubble case. This graph can be a useful tool to predict the behavior of multiple bubble interactions.     

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.     

An efficient method for the prediction of the motion of individual bubbles

We present a method for the simulation of two-phase flows which can be applied to problems characterised by the presence of up to several hundreds of gas bubbles. The bubble model is kept simple, requiring only six parameters to describe the shape of a single bubble. The model is coupled to a conventional time discrete finite-volume scheme for the solution of the Navier–Stokes equations by the density field which is calculated on basis of the information on the positions and the shapes of the bubbles before each time step. The motion of the bubbles is in turn calculated from an analysis of the computed flow field. Systematical errors due to simplifications are eliminated by the introduction of correction factors. For a selection of fluid dynamical problems, the results of simulations using the method are compared to experimental data. Good quantitative agreement could be found.     

Numerical study on the hydrodynamic behavior of the dielectric fluid around an electrical discharge generated bubble in EDM

In the process of EDM, due to the electrical current, very small bubbles are created within the gap. These bubbles are connected to each other and generate a single bubble. The vapor bubble continues to grow until it finally collapses to small bubbles. The bubble behavior can be ascertained on the distribution of the pressure in the dielectric fluid around the bubble. In this paper, velocity fields and pressure distribution in the dielectric fluid around the bubble that is generated in the process of EDM are investigated numerically. The tool and the workpiece are assumed as two parallel rigid boundaries with dielectric liquid between them. The boundary integral equation method is applied for the numerical solution of the problem. This study can lead to better understanding of the bubble importance in the performance of the electrical discharge machining process.     

Computation of internal high-speed separated flow with modified B–L and J–K models

The existence of shock–turbulent boundary layer interactions lead to very complicated flow phenomena and pose a challenge for numerical simulation. In this paper, two turbulence models, the Baldwin–Lomax (B–L) model and the Johnson–King (J–K) model, which were originally developed for simple external flow simulation, are modified to model complex high-speed internal separated flows. The full Navier–Stokes solver used in this paper is based on a cell-centered finite volume method and multistepping time marching scheme. Both implicit residual smoothing and local time stepping techniques are incorporated to accelerate the convergence rate. To ensure the numerical stability with the present explicit scheme, a point-implicit treatment to the source term in the ordinary differential equation (ODE) of the J–K model has been developed and has proved to be very effective in modeling such a complex flow. An arc-bump channel flow case has been studied. Comparisons of computed results with experimental data show that the present solver, with the modified turbulence models, predicts the shock and the flow separation very well. The J–K model is found to predict the size of the separation bubble with a higher accuracy. © 1998 John Wiley & Sons, Ltd.     

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.