Interactions between a cavitation bubble and solidification front under the effects of ultrasound: Experiments and lattice Boltzmann modeling

The phenomena of melting and dendritic fragmentation are captured by using an in-situ device during the ultrasound-assisted solidification of a succinonitrile-acetone (SCN-ACE) alloy. The experimental results show that the dendrite arms detach from primary trunk due to the melting of the solid phase, which is caused by a moving ultrasound cavitation bubble. To quantify the interactions between the ultrasound cavitation bubble and the solidification front, a coupled lattice Boltzmann (LB) model is developed for describing the fields of temperature, flow, and solid fraction, and their interactions. The multi-relaxation-time (MRT) scheme is applied in the LB model to calculate the liquid-gas flow field, while the Bhatnagar–Gross–Krook (BGK) equation is executed to simulate the evolution of temperature. The kinetics of solidification and melting are calculated according to the lever rule based on the SCN-ACE phase diagram. After the validation of the LB model by an analytical model, the morphologies of the cavitation bubble and solidification front are simulated. It is revealed that the solidification interface melts due to the increase of the temperature nearby the cavitation bubble in ultrasonic field. The simulated morphologies of the cavitation bubble and solidification front are compared well with the experimental micrograph. Quantitative investigations are carried out for analyzing the melting rate of the solidification front under different conditions. The simulated data obtained from LB modeling and theoretical predictions reasonably accord with the experimental results, demonstrating that the larger the ultrasonic intensity, the faster the melting rate. The present study not only reveals the evolution of the solidification front shape caused by the cavitation bubbles, which is invisible in the ultrasound-assisted solidification process of practical alloys, but also reproduces the complex interactions among the temperature field, acoustic streaming, and multi-phase flows.     

An Inverse Finite Element Method for Pure and Binary Solidification Problems

A 2D axisymmetric formulation for the solution of a directional solidification problem using an inverse finite-element method (IFEM) is presented. An algorithm developed by A. N. Alexandrou (Int. J. Numer. Methods Eng.28, 2383, 1989) has been modified and extended to include more general boundary conditions. The latter includes the explicit presence of an ampoule (with a complex shape) that contains the solid and the melt from which it is growing. Heat transfer between the ampoule and the external environment, time-dependent thermal boundary conditions, nonmonotonic temperature distributions, and species diffusion in the melt and crystal are also taken into account. Thus, our extended formulation encompasses a wider class of solidification problems than previous IFEM methods. Numerical experiments that illustrate the suitability of the extended IFEM are presented. In particular, we present a simulation of the directional solidification of zinc cadmium telluride using boundary conditions corresponding to an actual experiment scenario.     

The Adjoint Method for an Inverse Design Problem in the Directional Solidification of Binary Alloys

This paper presents a systematic procedure based on the adjoint method for solving a class of inverse directional alloy solidification design problems in which a desired growth velocityv_fis achieved under stable growth conditions. To the best of our knowledge, this is the first time that a continuum adjoint formulation is proposed for the solution of an inverse problem with simultaneous heat and mass transfer, thermo-solutal convection, and phase change. In this paper, the interfacial stability is considered to imply a sharp solid–liquid freezing interface. This condition is enforced using the constitutional undercooling criterion in the form of an inequality constraint between the thermal and solute concentration gradients,GandG_c, respectively, at the freezing front. The main unknowns of the design problem are the heating and/or cooling boundary conditions on the mold walls. The inverse design problem is formulated as a functional optimization problem. The cost functional is defined by the square of theL₂norm of the deviation of the freezing interface temperature from the temperature corresponding to thermodynamic equilibrium. A continuum adjoint system is derived to calculate the adjoint temperature, concentration, and velocity fields such that the gradient of the cost functional can be expressed analytically. The cost functional minimization process is realized by the conjugate gradient method via the finite element method solutions of the continuum direct, sensitivity, and adjoint problems. The developed formulation is demonstrated with an example of designing the directional solidification of a binary aqueous solution in a rectangular mold such that a stable vertical interface advances from left to right with a desired growth velocity.     

Numerical Simulation of Dendritic Solidification with Convection: Two-Dimensional Geometry

A front tracking method is presented for simulations of dendritic growth of pure substances in the presence of flow. The liquid–solid interface is explicitly tracked and the latent heat released during solidification is calculated using the normal temperature gradient near the interface. A projection method is used to solve the Navier–Stokes equations. The no-slip condition on the interface is enforced by setting the velocities in the solid phase to zero. The method is validated through a comparison with an exact solution for a Stefan problem, a grid refinement test, and a comparison with a solution obtained by a boundary integral method. Three sets of two-dimensional simulations are presented: a comparison with the simulations of Beckermann et al. (J. Comput. Phys.154, 468, 1999); a study of the effect of different flow velocities; and a study of the effect of the Prandtl number on the growth of a group of dendrites growing together. The simulations show that on the upstream side the dendrite tip velocity is increased due to the increase in the temperature gradient and the formation of side branches is promoted. The flow has the opposite effect on the downstream side. The results are in good qualitative agreement with published experimental results, even though only the two-dimensional aspects are examined here.     

声悬浮条件下环己烷液滴的蒸发凝固

采用单轴式声悬浮方法研究了环己烷液滴的蒸发过程,发现环己烷液滴的蒸发可以使自身温度降至熔点以下并发生凝固.高速摄像实时观测表明,环己烷晶核开始形成于液滴赤道附近,并以枝晶方式长大,平均生长速度为12.5-160.4 mm/s.进一步研究发现,声悬浮条件下平均Sherwood数与平均Nusselt数的比值Sh/Nu是在自然对流条件下的1.3倍,这表明声流边界层有效提高了环己烷液滴的蒸发速率而对传热的促进作用相对较小,因而可以使液滴降至更低温度,进而发生凝固.据此,提出了挥发性液体在声悬浮条件下发生蒸发凝固的必要条件. 关键词： 声悬浮 声流 环己烷 蒸发凝固     

The melting and solidification of nanowires

A mathematical model is developed to describe the melting of nanowires. The first section of the paper deals with a standard theoretical situation, where the wire melts due to a fixed boundary temperature. This analysis allows us to compare with existing results for the phase change of nanospheres. The equivalent solidification problem is also examined. This shows that solidification is a faster process than melting; this is because the energy transfer occurs primarily through the solid rather than the liquid which is a poorer conductor of heat. This effect competes with the energy required to create new solid surface which acts to slow down the process, but overall conduction dominates. In the second section, we consider a more physically realistic boundary condition, where the phase change occurs due to a heat flux from surrounding material. This removes the singularity in initial melt velocity predicted in previous models of nanoparticle melting. It is shown that even with the highest possible flux the melting time is significantly slower than with a fixed boundary temperature condition.     

A hybrid level set method for modelling detonation and combustion problems in complex geometries

We present an accurate and fast wave tracking method that uses parametric representations of tracked fronts, combined with modifications of level set methods that use narrow bands. Our strategy generates accurate computations of the front curvature and other geometric properties of the front. We introduce data structures that can store discrete representations of the location of the moving fronts and boundaries, as well as the corresponding level set fields, that are designed to reduce computational overhead and memory storage. We present an algorithm we call stack sweeping to efficiently sort and store data that is used to represent orientable fronts. Our implementation features two reciprocal procedures, a forward ‘front parameterization’ that constructs a parameterization of a front given a level set field and a backward ‘field construction’ that constructs an approximation of the signed normal distance to the front, given a parameterized representation of the front. These reciprocal procedures are used to achieve and maintain high spatial accuracy. Close to the front, precise computation of the normal distance is carried out by requiring that displacement vectors from grid points to the front be along a normal direction. For front curves in two dimensions, a cubic interpolation scheme is used, and G ¹ surface parameterization based on triangular patches is used for the three-dimensional implementation to compute the distances from grid points near the front. To demonstrate this new, high accuracy method we present validations and show examples of combustion-like applications that include detonation shock dynamics, material interface motions in a compressible multi-material simulation and the Stephan problem associated with dendrite solidification.     

Calculation of laser-induced temperature field on moving thin metal foils in consideration of Stefan problem

A temperature field on a moving thin sheet heated by a high-quality laser beam (TEM₀₀) is calculated. Effects of melting and solidification of sheet material is taken into account. Convective and radiation cooling is included into a mathematical model. Nonlinear effects connected with temperature dependencies of material properties are considered. An explicit finite-difference numerical method was used to calculate the non-steady-state 2D and 3D Stefan problems. A surface, on which the melting occur, is replaced by a zone of finite thickness. All physical properties in this zone are smoothed and considered as continuous values. Evaporation of liquid metal begins when temperature reaches some critical value. This effect is also included in the developed model. As a result, the geometry of the melting zone can be derived and is compared with a cross section of real laser welding seem.     

Decreasing electrical resistivity of gold along the melting boundary up to 5 GPa

ABSTRACT

The electrical resistivity of gold was experimentally measured at high pressures from 2 to 5?GPa and temperatures ～300?K above melting. The resistivity decreased as a function of pressure and increased as a function of temperature as expected. The temperature dependence of resistivity in the solid and liquid phases are comparable to 1?atm results. The observed melting temperatures at each pressure agree well with previous experimental and theoretical studies. The essential result of this study is that resistivity decreases along the pressure-dependent melting boundary, conflicting with a prediction of invariant behavior as reported in the literature. This result is discussed in terms of the interaction between s and d-bands as both pressure and temperature increase along the melting boundary. The thermal conductivity of gold was calculated from the measured electrical resistivity using the Wiedemann-Franz law. The temperature-induced effect on the thermal conductivity at high temperatures is as expected in both the solid and liquid phase while the pressure-effect shows some variability.     

Study of the crystallization morphology of VT3-1 alloy during VAR

In this paper, we consider the crystallization morphology formation of VT3-1 titanium alloy in the process of vacuum arc remelting (VAR). Based on experimental data obtained by the method of autoradiography, we numerically determine remelting parameters such as the temperature gradient G at the solidification front and its velocity V. Since practically all kinds of morphology of the crystallization microstructure of metal systems are present in an ingot (planar front, cellular, cellular-dendritic, and dendritic structures), we consider two simple models of transition from one structure to another. The models greatly depend on the parameters G and V. In this paper, the liquidus curve slopes for the alloying elements of VT3-1 alloy are determined and a morphology map is constructed. Also, the results are compared with those obtained earlier by other authors.     

Solidification microstructure selection of the peritectic Nd-Fe-B alloys

Bridgman directional solidification and laser remelting experiments were carried out on Nd_11.76Fe_82.36B_5.88 and Nd_13.5Fe_79.75B_6.75 alloys. Microstructure evolutions along with solidification parameters (temperature gradient G, growth velocity V and initial alloy composition C ₀) were investigated. A solidification microstructure selection map was established, based on the consideration of solidification characteristics of peritectic T₁ phase. In Bridgman directional solidification experiments, with the increasing growth velocities, the morphology of T₁ phase changed from plane front or faceted plane front to dendrites. In laser remelting experiments, a transition from primary γ-Fe dendrites to T₁ dendrites was found. Theoretical predictions are in good agreement with experimental results. Supported by the National Natural Science Foundation of China (Grant No. 50395100)     

Molecular dynamics simulation of the melting of a twist Σ=5 grain boundary

The existence of a possible grain boundary disordering transition of the melting type in a =5 (001) twist boundary of aluminium bicrystal below the melting temperature was investigated using a constant pressure molecular dynamics simulation. The calculated melting temperature T _cm of the bulk Al is about 960 K. The total internal energy, the structure factor, and the pair distribution function were calculated at different layers across the grain boundary. The mean atomic volume, the grain boundary energy, and the thermal expansion coefficients were also calculated using the same simulation method. This simulation also allows us to image the grain boundary structure at different temperatures. The equilibrium grain boundary structure at 300 K retains the periodicity of the coincident site lattice, so that the lowest energy structure corresponds to the coincident site arrangement of the two ideal crystals. With increasing temperature, the total internal energy of the atoms for both the perfect crystal and the grain boundary increases, as do the number of layers in the grain boundary. The grain boundary core exists and the perfect crystal structure still exists outside the grain boundary at 0.9375 T _cm. However, two atomic layers of the equilibrium grain boundary structure at 0.9375 T _cm lose the coincident site lattice periodicity and attain a structure with liquid-like disorder. Therefore, partial melting of the grain boundary has occurred at the temperature above 0.9375 T _cm which is in agreement with the experimental results.     

Solidification mechanism transition of liquid Co–Cu–Ni ternary alloy

We report a solidification mechanism transition of liquid ternary Co₄₅Cu₄₅Ni₁₀ alloy when it solidifies at a critical undercooling of about 344 K. When undercooling at ΔT<344 K, the solidification process is characterized by primary S (Co) dendritic growth and a subsequent peritectic transition. The dendritic growth velocity of S (Co) dendrite increases with the rise of undercooling. However, once ΔT>344 K, the solidification velocity decreases with the increase of undercooling. In this case, liquid/liquid phase separation takes place prior to solidification. The minor L₂ (Cu) droplets hinder the motion of the solidification front, and a monotectic transition may occur in the major L₁ phase. These facts caused by metastable phase separation are responsible for the slow growth at high undercoolings.     

Equilibrium melting temperature as a result of induction time measurements: Isotactic polypropylene

A method for the determination of equilibrium melting temperature from induction time measurements is suggested. Theory of the induction time, t _i (most probable period from the beginning of isothermal crystallization to the instant when a stable crystal nucleus starts growing) involves parameters that influence the nucleation-crystallization process, such as specific interfacial free-energy parameter, specific surface energies of a growing nucleus, enthalpy of crystal melting, diffusion activation energy, undercooling and the equilibrium melting temperature, T_m°. An extrapolation method exploiting the aspect of the induction time that it increases to infinity, that is, 1/t _i decreases to zero at the equilibrium melting temperature, cannot be used to calculate the equilibrium melting temperature. High- or low-temperature approximations of the basic equation yield some simplifications that make it possible to find its parameters via the best fit of the equation with experimental data. This procedure can yield also the value of the equilibrium melting temperature if the measured data are sufficiently precise. Applying that procedure to crystallization data of isotactic polypropylene, we obtained the values of the equilibrium melting temperatures 199.5°C (high-temperature approximation) and 212.7°C (low-temperature approximation). A more detailed discussion of the procedure suggests that from both these reasonable values, the higher one is more justified. This result agrees well with higher T_m° data reported in the literature.     

Influence of local nonequilibrium on the rapid solidification of binary alloys

A local-nonequilibrium model of the diffusion of a solute during the rapid solidification of a binary alloy is considered. The model has two characteristic parameters: the diffusion velocity through the interface V _Di and the diffusion velocity in the bulk of the liquid phase V _D. The influence of local nonequilibrium on the separation of an impurity, the stability of the interface, and the dependence of the temperature of the interface on the velocity of the solidification front is investigated. A comparison with experiment is made. Zh. Tekh. Fiz. 68, 45–52 (March 1998)     

Single domain generation in YBCO textured samples

This paper discusses the partial melting technique applied to texture cylindrical YBa₂Cu₃O_6+x samples with Y₂BaCuO₅ additions and the experimental procedures developed for obtaining large single domains. The thermal texturing methods produce liquid migration which hinders the stable and continuous solidification process. In the present work different methodologies for avoiding capillary liquid absorption are discussed. The mechanism of single domain selection is studied and an interpretation proposed explaining the oblique angle that the (001) plane of the single domain forms with the sample axis. This mechanism is also compatible with the shape of the recrystallization front shown by the samples studied. In order to impose axial orientation of the (001) crystallographic planes, solidification experiments with textured YBCO seeds are carried out.     

Heat transfer and diffusion-controlled kinetics of liquid–solid phase in titanium matrix composite during selective laser melting

This study describes a self-consistent theoretical model of simulating diffusion-controlled kinetics on the liquid–solid phase boundary during high-speed solidification in the melt pool after the selective laser melting (SLM) process for titanium matrix composite based on Ti–TiC system. The model includes the heat transfer equation to estimate the temperature distribution in the melt pool and during crystallization process for some deposited layers. The temperature field is used in a micro region next to solid–liquid boundary, where solute micro segregation and dendrite growth are calculated by special approach based on transient liquid phase bonding. The effect of the SLM process parameters (laser power, scanning velocity, layer thickness and substrate size) on the microstructure solidification is being discussed.     

The liquid phase ENDOR spectrum of the 1,2,3,6,7,8-hexahydropyrene anion radical

Neutron diffraction measurements have been made on bulk samples of liquid D₂O below the melting point. A first order difference function has been used to determine the structural changes which are found to follow the trends previously observed in the liquid above the melting point but the displacement of the main peak to lower Q values becomes more pronounced as the temperature is reduced. The data suggest that there is an enhanced local order through the effects of hydrogen bonding and that the system progressively evolves towards the continuous random hydrogen-bonded network similar to that exhibited by amorphous ice.     

温度梯度区域熔化作用下熔池迁移的元胞自动机模拟

本文采用耦合凝固和熔化效应的二维元胞自动机(cellular automaton, CA)模型,对温度梯度区域熔化(temperature gradient zone melting, TGZM)效应引起的熔池在固液两相区中的迁移现象进行模拟研究.模拟分析了抽拉速度、熔池初始位置、温度梯度和合金成分等因素对TGZM动力学的影响,并将模拟结果与解析模型的预测结果进行比较验证.通过模拟发现,在温度梯度作用下,熔池总是向着高温方向迁移;当抽拉速度低于或高于临界抽拉速度时,熔池朝向移动的液相线或固相线迁移;对于给定的抽拉速度,位于糊状区内临界位置以上的熔池会迁移进入液相,而位于临界位置以下的熔池会逐步靠近固相线.此外,温度梯度越高,合金成分越低,熔池的迁移速度越快.