Detecting and classifying interfacial defects by inverse ultrasound scattering analysis

We formulate and solve a time-harmonic inverse scattering problem to estimate the interfacial stiffness distribution at an interface between two elastic solid half-spaces. We assume prior knowledge of the material properties of both solid half-spaces, as well as the ultrasound incident field. The interfacial stiffness distribution is then estimated from the reflected signal. We use the Quasi-Static-Approximation for the interface, where it is modelled by a set of tangential and normal springs, and allow the interfacial stiffness to depend upon the position along the interface. In addition, we use the Particle Swarm Optimization Technique to solve the formulated inverse problem. We validate our implementation and evaluate the presented method’s performance for noisy input data and different measurement scenarios with the aid of numerical simulations. From the obtained numerical results, we may say that the proposed method is robust to the presence of noise and has the potential to detect and classify interfacial defects.     

Bubble dynamics: a review and some recent results

Several aspects of small-amplitude oscillations of bubbles containing gas, vapor, or a gas-vapor mixture are discussed. An application to pressure-wave propagation in a bubbly liquid is described. Nonlinear forced oscillations are considered in the light of recent research on forced oscillations of nonlinear systems. The growth of vapor bubbles, an extension of the Rayleigh-Plesset equation to non-Newtonian liquids and appreciable mass transfer at the interface, and a boundary integral numerical method for nonspherical cavitation bubble dynamics are also briefly discussed.     

水平均流中细管排放气泡的三维数值模拟

在液体为无粘不可压，流动有势和气体遵循完全气体绝热关系的假定下，本文应用边界积分方程方法数值模拟了水平均流中垂直细管排放气泡的三维动力学问题，边界采用高阶有限元表达。文中介绍了有关泡面法向矢量、切向速度、曲率和接触线等的计算技术。与已知解的比较，表明了这一数值方法的高精度和优越性。算例显示了水平均流对于气泡形状和体积的影响     

Numerical prediction of turbulent thermocapillary convection in superposed fluid layers with a free interface

The present paper introduces a new numerical method for predicting the characteristics of thermocapillary turbulent convection in a differentially-heated rectangular cavity with two superposed and immiscible fluid layers. The unsteady Reynolds form of the Navier–Stokes equations and energy equation are solved by using the control volume approach on a staggered grid system using SIMPLE algorithm. The turbulence quantities are predicted by applying the standard k–ε turbulence model. The level set formulation is applied for predicting the topological changes of the interface separating the two fluid layers and to provide an accurate and robust modeling of the interfacial normal and tangential stresses. The computational results obtained showed good agreement when compared with the previous experimental, numerical and analytical benchmark data for different validation cases in both laminar and turbulent regimes. The present numerical method is then applied to predict the velocity and temperature distribution in two immiscible liquid layers with undeformable interface for a wide range of Marangoni numbers. The laminar-turbulent transition is demonstrated by obtaining the turbulence features at high interfacial temperature gradient which is characterized by high Marangoni number. The effect of increasing Marangoni number on the interface dynamics in turbulent regime is also investigated.     

Numerical prediction of turbulent thermocapillary convection in superposed fluid layers with a free interface

The present paper introduces a new numerical method for predicting the characteristics of thermocapillary turbulent convection in a differentially-heated rectangular cavity with two superposed and immiscible fluid layers. The unsteady Reynolds form of the Navier–Stokes equations and energy equation are solved by using the control volume approach on a staggered grid system using SIMPLE algorithm. The turbulence quantities are predicted by applying the standard k–ε turbulence model. The level set formulation is applied for predicting the topological changes of the interface separating the two fluid layers and to provide an accurate and robust modeling of the interfacial normal and tangential stresses. The computational results obtained showed good agreement when compared with the previous experimental, numerical and analytical benchmark data for different validation cases in both laminar and turbulent regimes. The present numerical method is then applied to predict the velocity and temperature distribution in two immiscible liquid layers with undeformable interface for a wide range of Marangoni numbers. The laminar-turbulent transition is demonstrated by obtaining the turbulence features at high interfacial temperature gradient which is characterized by high Marangoni number. The effect of increasing Marangoni number on the interface dynamics in turbulent regime is also investigated.     

A coupled level set and volume-of-fluid method for sharp interface simulation of plunging breaking waves

A coupled level set and volume-of-fluid (CLSVOF) method is implemented for the numerical simulations of interfacial flows in ship hydrodynamics. The interface is reconstructed via a piecewise linear interface construction scheme and is advected using a Lagrangian method with a second-order Runge–Kutta scheme for time integration. The level set function is re-distanced based on the reconstructed interface with an efficient re-distance algorithm. This level set re-distance algorithm significantly simplifies the complicated geometric procedure and is especially efficient for three-dimensional (3D) cases. The CLSVOF scheme is incorporated into CFDShip-Iowa version 6, a sharp interface Cartesian grid solver for two-phase incompressible flows with the interface represented by the level set method and the interface jump conditions handled using a ghost fluid methodology. The performance of the CLSVOF method is first evaluated through the numerical benchmark tests with prescribed velocity fields, which shows superior mass conservation property over the level set method. With combination of the flow solver, a gas bubble rising in a viscous liquid and a water drop impact onto a deep water pool are modeled. The computed results are compared with the available numerical and experimental results, and good agreement is obtained. Wave breaking of a steep Stokes wave is also modeled and the results are very close to the available numerical results. Finally, plunging wave breaking over a submerged bump is simulated. The overall wave breaking process and major events are identified from the wave profiles of the simulations, which are qualitatively validated by the complementary experimental data. The flow structures are also compared with the experimental data, and similar flow trends have been observed.     

A numerical study of the behaviour of a gas–liquid interface subjected to periodic vertical motion

A numerical study has been undertaken to examine the behaviour of a gas liquid interface in a vertical cylindrical vessel subjected to a sinusoidal vertical motion. The computational method used is based on the simplified marker‐and‐cell method and includes a continuum surface model for the incorporation of surface tension. The numerical results indicate that the surface tension has very little effect on the period and amplitude of oscillations of the interfacial waves. The stability of the interfacial waves has been found to depend on the initial pressure pulse disturbance, and exponential growth of the interfacial wave has been observed in some cases. The influence of the amplitude and frequency of the forcing oscillations has also been investigated. The results are in good agreement with available experimental and analytical solutions. Copyright © 2002 John Wiley & Sons, Ltd.     

Liquid vorticity computation in non‐spherical bubble dynamics

The purpose of this work is to compare efficiency of a number of numerical techniques of computation of liquid vorticity from non‐spherical bubble oscillations. The techniques based on the finite‐difference method (FDM), the collocation method (one with differentiating (CMd) the integral boundary condition and another without it (CM)) and the Galerkin method (GM) have been considered. The central‐difference approximations are used in FDM. Sinus functions are chosen as the basis in GM. Problems of decaying a small distortion of the spherical shape of a bubble and dynamics of a bubble under harmonic liquid pressure variation with various parameters are used for comparison. The FDM technique has been found to be most efficient in all the cases. Copyright © 2004 John Wiley & Sons, Ltd.     

An initially spherical bubble rising near a vertical wall

The dynamics of a single rising bubble in the vicinity of a vertical wall is explored via three-dimensional numerical simulations. A finite volume method is used to solve the incompressible Navier–Stokes equations. The gas–liquid interface is reconstructed by volume-of-fraction (VOF) method. The trajectory, velocity, shape and vorticity of the bubble are analyzed in detail. The numerical results show that the presence of the wall imposes a repulsion on the bubble and that the bubble migrates away from the wall upon release. The onset of bubble path oscillation is found to occur earlier than for a freely rise counterpart and also at a lower Galilei number. Interestingly, we find that the vertical wall serves as a destabilizing factor in the wall-normal direction but a stabilizing factor in the spanwise direction. The increase of bubble inertia is discovered to enhance the influence of the wall. Furthermore, the bubble oscillations seem insensitive to the variation of the initial bubble-wall distance.     

Interception of two spheroidal particles in shear flow

A numerical method is developed for simulating the motion of particles with arbitrary shape in an effectively infinite or bounded viscous flow. The particle translational and angular velocities are computed directly by solving an integral equation of the second kind arising from the double-layer representation for Stokes flow, subject to a specified force and torque. The deflated integral equation is solved by the method successive substitutions using a spectral boundary-element method. In the case of force- and torque-free particles, the contribution of the particles to the effective viscosity of the suspension is expressed in terms of the distribution density of the double-layer potential over the particle surfaces. The method is applied to investigate the interception of two spheroidal particles in simple shear flow, with emphasis on the net particle displacement and shift in the phase of rotation after separation, and on the transient signature of the interception on the effective viscosity of the suspension. The net particle displacement normal to the streamlines of the shear flow is found to have both positive and negative values depending on the relative particle configuration before interception. For moderate particle separations, the phase of rotation is shifted only slightly with respect to the Jeffery orbit executed by a particle in isolation.     

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.     

A control volume finite element method for three-dimensional three-phase flows

A novel control volume finite element method with adaptive anisotropic unstructured meshes is presented for three-dimensional three-phase flows with interfacial tension. The numerical framework consists of a mixed control volume and finite element formulation with a new P₁DG-P₂ elements (linear discontinuous velocity between elements and quadratic continuous pressure between elements). A “volume of fluid” type method is used for the interface capturing, which is based on compressive control volume advection and second-order finite element methods. A force-balanced continuum surface force model is employed for the interfacial tension on unstructured meshes. The interfacial tension coefficient decomposition method is also used to deal with interfacial tension pairings between different phases. Numerical examples of benchmark tests and the dynamics of three-dimensional three-phase rising bubble, and droplet impact are presented. The results are compared with the analytical solutions and previously published experimental data, demonstrating the capability of the present method.     

Ellipsoidal Oscillations of a Gas Bubble with Periodic Variation of the Surrounding Fluid Pressure

Ellipsoidal linear and nonlinear oscillations of a gas bubble under harmonic variation of the surrounding fluid pressure are studied. The system is considered under conditions in which periodic sonoluminescence of the individual bubble in a standing acoustic wave is observable. A mathematical model of the bubble dynamics is suggested; in this model, the variation of the gas/fluid interface shape is described correct to the square of the amplitude of the deformation of the spherical shape of the bubble. The character of the air bubble oscillations in water is investigated in relation to the initial bubble radius and the fluid pressure variation amplitude. It is shown that nonspherical oscillations of limited amplitude can occur outside the range of linearly stable spherical oscillations. In this case, both oscillations with a period equal to one or two periods of the fluid pressure variation and aperiodic oscillations can be observed.     

Numerical Simulation of the Buoyancy-Driven Bouncing of a 2-D Bubble at a Horizontal Wall

The rise of a buoyant bubble and its interaction with a target horizontal wall is simulated with a 2-D numerical code based on the Boundary Element Method (BEM). Developed from a viscous potential flow approximation, the BEM takes into account only the part of the energy dissipation related to the normal viscous stresses. Hence, a simple analytical model based on lubrication approximation is coupled to the BEM in order to compute the drainage of the interstitial liquid film filling the gap between the bubble and the near wall. In this way the bubble–wall interaction is fully computed: the approach stage, the bubble deformation stage and, depending on the values of the Reynolds number and the Weber number, the rebound and the bubble oscillations. From computation of both the bubble interface motion and the liquid velocity field, a physical analysis in terms of energy budget is proposed. Though, in the present study, the bubble under consideration is basically supposed to be a 2-D gaseous cylinder, a comparison between our numerical results and the experiments of Tsao and Koch (1997) enlightens interestingly the physics of bouncing.     

NUMERICAL PREDICTION OF TWO-PHASE FLOW IN BUBBLE COLUMNS

A numerical model is described for the prediction of turbulent continuum equations for two-phase gas–liquid flows in bubble columns. The mathematical formulation is based on the solution of each phase. The two-phase model incorporates interfacial models of momentum transfer to account for the effects of virtual mass, lift, drag and pressure discontinuities at the gas–liquid interface. Turbulence is represented by means of a two-equation k–ϵ model modified to account for bubble-induced turbulence production. The numerical discretization is based on a staggered finite-volume approach, and the coupled equations are solved in a segregated manner using the IPSA method. The model is implemented generally in the multipurpose PHOENICS computer code, although the present appllications are restricted to two-dimensional flows. The model is applied to simulate two bubble column geometries and the predictions are compared with the measured circulation patterns and void fraction distributions.     

An improved diffuse interface method for three-dimensional multiphase flows with complex interface deformation

An improved diffuse interface (DI) method is proposed for accurately capturing complex interface deformation in simulations of three-dimensional (3D) multiphase flows. In original DI methods, the unphysical phenomenon of interface thickening or blurring can affect the accuracy of numerical simulations, especially for flows with large density ratio and high Reynolds number. To remove this drawback, in this article, an interface-compression term is introduced into the Cahn-Hilliard equation to suppress the interface dispersion. The additional term only takes effect in the interface region and works normal to the interface. The difference of the current method from the previous work is that the compression rate can be adjusted synchronously according to the magnitude of local vorticity, which is strongly correlated to the interface dispersion and changes with the computational time and interface position. Numerical validations of the proposed method are implemented by simulating problems of Laplace law, Rayleigh-Taylor instability, bubble rising in a channel, and binary droplet collision. The obtained results agree well with the analytical solutions and published data. The numerical results show that the phenomenon of interface dispersion is suppressed effectively and the tiny interfacial structures in flow field can be captured accurately.     

Level set方法在自适应Cartesian网格上的应用

采用基于自适应Cartesian网格的level set方法对多介质流动问题进行数值模拟。采用基于四叉树的方法来生成自适应Cartesian网格。采用有限体积法求解Euler方程,控制面通量的计算采用HLLC（Hartern, Lax, van Leer, Contact）近似黎曼解方法。level set方程也采用有限体积法求解,采用Lax-Friedchs方法计算通量,通过窄带方法来减少计算量,界面的处理采用ghost fluid方法。Runge-Kutta显式时间推进,时间、空间都是二阶精度。对两种不同比热比介质激波管问题进行数值模拟,其结果和精确解吻合;对空气/氦气泡相互作用等问题进行模拟,取得令人满意的结果。     

Separation phenomena at the interface of a finitely deformed composite sphere

The problem of the finite deformation of a composite sphere subjected to a spherically symmetric dead load traction is revisited focusing on the formation of a cavity at the interface between a hyperelastic, incompressible matrix shell and a rigid inhomogeneity. Separation phenomena are assumed to be governed by a vanishingly thin interfacial cohesive zone characterized by uniform normal and tangential interface force–separation constitutive relations. Spherically symmetric cavity shapes (spheres) are shown to be solutions of an interfacial integral equation depending on the strain energy density of the matrix, the interface force constitutive relation, the dead loading and the volume concentration of inhomogeneity. Spherically symmetric and non-symmetric bifurcations initiating from spherically symmetric equilibrium states are analyzed within the framework of infinitesimal strain superimposed on a given finite deformation. A simple formula for the dead load required to initiate the non-symmetrical rigid body mode is obtained and a detailed examination of a few special cases is provided. Explicit results are presented for the Mooney–Rivlin strain energy density and for an interface force–separation relation which allows for complete decohesion in normal separation.     

一种预测颗粒增强复合材料界面力学性能的新方法

界面在颗粒增强复合材料中起到传递载荷的关键作用,界面性能对复合材料整体力学行为产生重要影响.然而由于复合材料内部结构较为复杂,颗粒与基体间的界面强度和界面断裂韧性难以确定,尤其是法向与切向界面强度的分别预测缺乏有效方法.本文以氧化锆颗粒增强聚二甲基硅氧烷(PDMS)复合材料为研究对象,提出一种预测颗粒增强复合材料界面力...     

A conservative local interface sharpening scheme for the constrained interpolation profile method

A conservative local interface sharpening scheme has been developed for the constrained interpolation profile method with the conservative semi‐Lagrangian scheme, because the conservative semi‐Lagrangian scheme does not feature a mechanism to control the interface thickness, thus causing an increase of numerical error with the advance of the time step. The proposed sharpening scheme is based on the conservative level set method proposed by Olsson and Kreiss. However, because their method can cause excessive deformation of the free‐surface in certain circumstances, we propose an improvement of the method by developing a local sharpening technique. Several advection tests are presented to assess the correctness of the advection and the improved interface sharpening scheme. This is followed by the validations of dam‐breaking flow and the rising bubble flows. The mass of the fluid is exactly conserved and the computed terminal velocity of the rising bubble agrees well with the experiments compared with other numerical methods such as the volume of fluid method (VOF), the front tracking method, and the level set method. Copyright © 2011 John Wiley & Sons, Ltd.