Material forces and phase transitions in elasticity

A computational scheme for the determination of the interface in a strain-induced phase-transition problem for an elastic bar is proposed. The algorithm is based on the material force notion and more specifically on the simultaneous solution of equilibrium equations for the physical and material forces. The weak form of both equations is derived with the aid of a variational principle that accounts for the variations of the dependent and the independent variables. The whole scheme concludes in a nonlinear algebraic system which is numerically solved by the Newton method. The numerical results thus derived seem to be quite encouraging for further application of the concept of material forces in computations related to phase transition problems. The austenite–martensite transformation could be a possible application of the proposed model.     

Level set method for numerical simulation of a cavitation bubble,its growth,collapse and rebound near a rigid wall

A level set method of non-uniform grids is used to simulate the whole evolution of a cavitation bubble, including its growth, collapse and rebound near a rigid wall. Single-phase Navier–Stokes equation in the liquid region is solved by MAC projection algorithm combined with second-order ENO scheme for the advection terms. The moving interface is captured by the level set function, and the interface velocity is resolved by “one-side” velocity extension from the liquid region to the bubble region, complementing the second-order weighted least squares method across the interface and projection inside bubble. The use of non-uniform grid overcomes the difficulty caused by the large computational domain and very small bubble size. The computation is very stable without suffering from large flow-field gradients, and the results are in good agreements with other studies. The bubble interface kinematics, dynamics and its effect on the wall are highlighted, which shows that the code can effectively capture the “shock wave”-like pressure and velocity at jet impact, toroidal bubble, and complicated pressure structure with peak, plateau and valley in the later stage of bubble oscillating. The project supported by the National Natural Science Foundation of China (10272032 and 10672043). The English text was polished by Keren Wang.     

Numerical simulation of the interface molten metal air in the shot sleeve chambre and mold cavity of a die casting machine

The objective of this study relates to the numerical simulation of the free surface during the two-dimensional flow and solidification of aluminum in the horizontal cylinder and mold cavity of the high pressure die casting HPDC machine with cold chamber. The flow is governed by the Navier–Stokes equations (the mass and the momentum conservations) and solved in the two phase’s liquid aluminum and air. The tracking of the free surface is ensured by the VOF method. The equivalent specific heat method is used to solve the phase change heat transfer problem in the solidification process. Considering the displacement of the plunger, the geometry of the problem is variable and the numerical resolution uses a dynamic grid. The study examines the influence of the plunger speed on the evolution of the interface aluminum liquid–air profile, the mass of air imprisoned and the stream function contours versus time. Filling of a mold is an essential part of HPDC process and affects significantly the heat transfer and solidification of the melt. For this reason, accurate prediction of the temperature field in the system can be achieved only by including simulation of filling in the analysis.     

模拟相变问题的精细积分边界元法

将精细积分边界元法和界面追踪法相结合求解相变问题。因为边界元法只需要将待求解空间域的边界离散,方便连续追踪移动界面位置和重构网格,所以边界元法适合应用于移动边界问题的模拟。首先,利用精细积分边界元法在固相区域和液相区域分别求解相应的瞬态热传导控制方程,从而求得温度场和边界热流密度。然后,根据固-液相变界面上的能量平衡方程,利用热流密度求得相变界面的移动速度,再采用界面追踪法预测移动相变界面的位置变化。最后,给出了几个数值算例,并通过与参考解的对比验证本文方法的准确性。     

Numerical Approaches for microscopic modelling of solute redistribution during solidification of binary alloys

In the present study, two numerical approaches for single-domain modelling of microsegregation during solidification of binary alloys are presented. In the first approach, the concentration jump at the moving solid/liquid interface is formulated using a volumetric term and a Boolean function. The governing solute redistribution equation, valid for the whole domain comprising the solid and liquid regions, is derived in terms of the liquid phase composition. The effects of microstructure coarsening on microsegregation has been described and included in the model. In the second approach, the continuum mixture theory is utilized to derive a single domain solute redistribution equation in terms of the mixture composition. The solidification front motion and dendrite arm coarsening effects are accommodated by considering the representative elementary volume to consist of solid, interdendritic, and extradendritic liquid phases. Numerical solutions have been obtained using a control-volume based finite-difference method with a fixed grid. Good agreement has been observed between the predictions of the present fixed-domain models and the exact analytical and experimental results.     

Lattice Gas Analysis of Liquid Front in Non-Crimp Fabrics

The liquid flow front during impregnation of non-crimp fabrics is considered. Irregularities in fibre bundle architecture lead to generation of bubbles at this front. The velocity of this interface is highly influenced by capillary forces mainly caused by the small fibres inside the bundles. In order to better understand which shapes the liquid front takes up at different conditions, a lattice gas model has been applied. First, the macroscopic properties of the solved gas in the liquid are discussed. Next, bubble inclusions are analyzed as to liquid–gas interface position and concentrations of minor component in each phase. The capillary effects at the fluid front are studied for systems both with and without gaps between the bundles. The flow in the interior of the fibre bundles is scrutinized, as well, by also considering the viscous stresses. The flow through unidirectional fabrics is considered by a one-dimensional model, which suggests that the liquid front inside bundles and gaps moves with the same speed when the liquid front inside the bundle has to catch up with the liquid front in the gap.     

Analytical approximation for solidification processes in PCM storage with internal fins: imposed heat flux

Uses of thermal energy storage systems have expanded notably in recent decades. In thermal energy systems, internal heat transfer enhancement techniques such as fins are often used because of the low thermal conductivity of the phase change materials (PCMs). In this paper, solidification of a PCM is studied in a rectangular storage with horizontal internal plate fins and an imposed constant heat flux on the vertical walls. A simplified analytical solution is presented and its results are compared to those for a numerical approach based on an enthalpy method. The fraction of solidified PCM in storage is calculated with the derived analytical model which determines how much of the storage is solidified after a certain time. The results show that the analytical model satisfactorily estimates the solid–liquid interface and the temperature distribution for the fin, which are useful in the design of PCM-based thermal energy storage or cooling systems.     

A double-front structure of detonation wave as the result of phase transitions

Using thermochemical code calculations, we show that the nanographite–nanodiamond phase transition, which may occur in the detonation products of a number of carbon containing explosives, can affect the detonation properties and can cause a specific detonation regime with some unusual peculiarities. Among them, we first note the failure of the Chapman–Jouguet condition and the presence of the sonic plane, where the Mach number is equal to unity, in a detonation product expansion wave at a lower pressure than that at the Chapman–Jouguet point. The peculiarities of this detonation regime are demonstrated by the example of TNT, HNS, and RDX. The computed detonation velocities are in excellent agreement with experiments over a wide range of initial charge densities for all of the investigated explosives. The results of this work allow one to explain, e.g., contradictory experimental data on the detonation pressure and on the length of the reaction zone for TNT. We believe that some other solid–solid, solid–liquid, and liquid–liquid phase transformations in the detonation products may also cause a detonation regime with the same features as shown here for the nanographite–nanodiamond transition. We suggest a computational study that should facilitate proposing detonation experiments strongly arguing in favor of the model presented. PACS 47.40.-x; 47.40.Rs; 64.70.-p; 64.70.Kb; 05.70.-a; 05.70-.CeThis paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003.     

New analysis of contact melting of phase change material around a hot sphere

The process of contact melting of the solid phase change material (PCM) around a hot sphere, which is driven by the temperature difference between the PCM and the sphere, is analyzed in this paper. Considering the difference of the normal angle between the sphere surface and the solid–liquid interface of the melting PCM, the fundamental equations of the melting process are derived with the film theory. The new film thickness and pressure distribution inside the liquid film and the variation law of the normal angle of the solid–liquid interface and the melting velocity of the sphere are also obtained. It is found that (1) while normal angle at sphere surface φ is within a certain value φ₀, which is related to Ste number and the outside force F, it has no obvious effect on the pressure distribution inside the liquid film and the numerical results by the present model are in accordance with the analytical results in the published literature, (2) the film thickness at φ = ±90° is constringent to a certain value and not the infinity, (3) the analytical results can be employed approximately to analyze the contact melting process except for the film thickness at φ = ±90°.     

Calculation of the permeability and apparent permeability of three-dimensional porous media

In this study, creeping and inertial incompressible fluid flows through three-dimensional porous media are considered, and an analytical–numerical approach is employed to calculate the associated permeability and apparent permeability. The multiscale homogenization method for periodic structures is applied to the Stokes and Navier–Stokes equations (aided by a control-volume type argument in the latter case), to derive the appropriate cell problems and effective properties. Numerical solutions are then obtained through Galerkin finite-element formulations. The implementations are validated, and results are presented for flows through cubic lattices of cylinders, and through the dendritic zone found at the solid–liquid interface during solidification of metals. For the interdendritic flow problem, a geometric configuration for the periodic cell is built by the approximate matching of experimental and numerical results for the creeping-flow problem; inertial effects are then quantified upon solution of the inertial-flow problem. Finally, the functional behavior of the apparent permeability results is analyzed in the light of existing macroscopic seepage laws. The findings contribute to the (numerical) verification of the validity of such laws.     

Numerical simulation of 3D free surface flows,with multiple incompressible immiscible phases. Applications to impulse waves

A numerical method for the solution to the density‐dependent incompressible Navier–Stokes equations modeling the flow of N immiscible incompressible liquid phases with a free surface is proposed. It allows to model the flow of an arbitrary number of liquid phases together with an additional vacuum phase separated with a free surface. It is based on a volume‐of‐fluid approach involving N indicator functions (one per phase, identified by its density) that guarantees mass conservation within each phase. An additional indicator function for the whole liquid domain allows to treat boundary conditions at the interface between the liquid domain and a vacuum. The system of partial differential equations is solved by implicit operator splitting at each time step: first, transport equations are solved by a forward characteristics method on a fine Cartesian grid to predict the new location of each liquid phase; second, a generalized Stokes problem with a density‐dependent viscosity is solved with a FEM on a coarser mesh of the liquid domain. A novel algorithm ensuring the maximum principle and limiting the numerical diffusion for the transport of the N phases is validated on benchmark flows. Then, we focus on a novel application and compare the numerical and physical simulations of impulse waves, that is, waves generated at the free surface of a water basin initially at rest after the impact of a denser phase. A particularly useful application in hydraulic engineering is to predict the effects of a landslide‐generated impulse wave in a reservoir. Copyright © 2014 John Wiley & Sons, Ltd.     

Network simulation method for solving phase-change heat transfer problems with variable thermal properties

 The transient heat conduction equation in a finite slab undergoing phase change (two-phase problem of melting and solidification), with isothermal, adiabatic or convective boundary conduction is studied by the network simulation method; solid phase conductivity and specific heat are assumed to be dependent on temperature. Ablation, as a particular case, is also analysed. A network model is established for a cell and boundary conditions are added to complete the whole network model. No restrictions exist, as to the kinds of linear and non-linear boundary conditions, Stefan number values or the initial conditions (when hypotheses concern of the Stefan problem, numerical and exact solutions are compared for a large interval of Stefan numbers; simulation values show good agreement). Movement of the solid–liquid boundary and thermal fields are determined in all cases. Received on 10 May 2000 / Published online: 29 November 2001     

On estimating pressure build-up in severely accelerated,shocked flow

A new approach to the calculation of the high pressures characterizing the flow field in front of a piston undergoing severe acceleration over the short term is presented. In contrast with previous approaches where the computational domain is altered but which stop short of transforming velocities, here the problem is solved in an accelerating non-Euclidean co-ordinate system where the piston is stationary. The method is applied to a study of the problem of premature sabot separation. Through use of Harten's second-order-accurate TVD scheme, flow simulations are performed for both 1D and 3D axisymmetric geometries. The simple 1D model gives pressure profiles surprisingly close to those of the more physical 3D model.     

Some Thermodynamical Aspects of the Solidification of Two-phase Flows

The solidification of a two-phase flow is analyzed. It is shown how fluid-to-fluid phase transformations and kinetic stresses due to relative diffusion between fluid components influence dissipation of energy, friction and heat flux at the interface solid–fluid.     

Numerical study of evaporation by mixed convection of a binary liquid film flowing down the wall of two coaxial cylinders

Evaporation by mixed convection of a binary liquid film flowing down the external wall of a vertical cylinder has been investigated numerically. Two cases were considered: one where the cylinder wall is soaked with a liquid, and another where a liquid film flows along this wall. Heat, mass and momentum transfer in the liquid film and the vapor phase are modelled by mixed convection equations. In order to locate the liquid–vapor interface, a suitable coordinate transformation is carried out with suitable variables. The discretization of the dimensionless equations by an implicit difference scheme leads to a system of algebraic equations, which are solved by using Gauss algorithm for the momentum conservation equations and Thomas algorithm for the energy and diffusion conservation equations. The film thickness is calculated by the Newtons method. Results show, in particular, that the film thickness cannot be neglected and that the latent heat transfers are increasingly significant as the liquid film components become more volatile.     

Fluid Flows past Spheroids at Moderate Reynolds Numbers

Axisymmetric viscous fluid flows past spheroids are considered. The time-independent complete Navier-Stokes equations written in a spherical coordinate system are used for describing the flow. The problem is solved by the stabilization method on the basis of a variable direction scheme. The input coordinate system is transformed in order to construct a regular computational grid. As a result of the numerical investigation, the stream patterns of flow past elongated and oblate spheroids are obtained for various values of the determining parameters. Numerical values of the dimensions of the circulation zone and the drag coefficient are given for various values of the spheroid semi-axis ratio in the domain of moderate Reynolds numbers.     

Large eddy simulation in a fully developed turbulent flow in a channel and comparison of subgrid eddy viscosity models

The accuracy and computational efficiency are compared for a number of models of subgrid eddy viscosity (Smagorinsky model, renormalization group model, and dynamic and one-parameter models). Space-filtered Navier-Stokes equations are solved numerically by the control-volume approach on a nonuniform grid with the use of high-resolution schemes in time and space. The numerical data are compared with the results of a physical experiment and direct numerical simulation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 31–42, May–June, 2006.     

The effect of shock pressures on the inactivation of a marine Vibrio sp.

The effect of shock pressures on the inactivation of a marine Vibrio sp. was studied experimentally and numerically. In the experiment, an aluminum impactor plate accelerated by a gas gun was used to induce shock waves in a sealed aluminum container with cell suspension liquid inside. The shock pressures in the container were measured by a piezofilm gauge. Several 10–100 MPa of pressure were measured at the shock wave front. An FEM simulation, using the Johnson–Cook model for solid aluminum and the Tait equation for the suspension liquid, was carried out in order to know the generation mechanism of shock pressures in the aluminum container. The reflection, diffraction and interaction of shock waves at the solid–liquid boundaries in the aluminum container were reasonably predicted by the numerical simulation. The changes in shock pressures obtained from the computational simulation were in good agreement with those from the experiment. The number of viable cells decreased with the increase of peak pressures of the shock waves. Peak pressures higher than 200 MPa completely inactivated the cells. At this pressure, the cell structures were deformed like the shape of red blood cells, and some proteins leaked from the cells. These results indicate that the positive and negative pressure fluctuations generated by shock waves contribute to the inactivation of the marine Vibrio sp.      

Outward spherical solidification of a superheated melt with time dependent boundary flux

Short-time analytical solutions of solid and liquid temperatures and freezing front have been obtained for the outward radially symmetric spherical solidification of a superheated melt. Although results are presented here only for time dependent boundary flux, the method of solution can be used for other kinds of boundary conditions also. Later, the analytical solution has been compared with the numerical solution obtained with the help of a finite difference numerical scheme in which the grid points change with the freezing front position. An efficient method of execution of the numerical scheme has been discussed in details. Graphs have been drawn for the total solidification times and temperature distributions in the solid.