Filling-box process during solidification of a liquid hypoeutectic binary solution

Solidification of binary solutions often occurs in many industrial applications, including the casting of binary alloys. In this study we consider the effect of a side cooling wall on the development of double-diffusive convection during solidification of a hypoeutectic aqueous ammonium chloride (NH₄Cl–H₂O) solution. To study flow development during solidification of this solution, we used the shadowgraph technique, particle image velocimetry, and a thermochromic-liquid-crystal slurry. In addition, the transient temperature distribution within the test cell was measured by type-T thermocouples. The results of these experiments revealed that the filling-box process originated from the bottom of the test cell to the top. This process induced several double-diffusive layers and counterclockwise roll cells in the melt, mainly caused by double-diffusive convection. Consequently, the filling-box process may cause serious V-segregates and material defects in solidified ingots.     

Study of double-diffusive velocity during the solidification process using particle image velocimetry

This paper reports the velocity distribution of double-diffusive convection of a binary mixture in a rectangular enclosure during the solidification process. The mixture was a NH₄Cl–H₂O solution. The advanced technique, particle image velocimetry (PIV), was used to measure the velocity distribution in the liquid region during solidification. For the purpose of comparison, the solidification of pure water was studied with the same technique. The temperature of the cooling walls in the test chamber and the temperature of the test solution during solidification were also measured. The double-diffusive flow was found to be stronger at the beginning of solidification; the flow decays as solidification proceeds. The velocity distribution of the hypereutectic solution of NH₄Cl–H₂O has evident difference in comparison with hypoeutectic solution.     

In-situ measurements of concentration and temperature during transient solidification of aqueous solution of ammonium chloride using laser interferometry

The variation in temperature and concentration plays a crucial role in predicting the final microstructure during solidification of a binary alloy. Most of the experimental techniques used to measure concentration and temperature are intrusive in nature and affect the flow field. In this paper, the main focus is laid on in-situ, non-intrusive, transient measurement of concentration and temperature during the solidification of a binary mixture of aqueous ammonium chloride solution (a metal-analog system) in a top cooled cavity using laser based Mach–Zehnder Interferometric technique. It was found from the interferogram, that the angular deviation of fringe pattern and the total number of fringes exhibit significant sensitivity to refractive index and hence are functions of the local temperature and concentration of the NH₄Cl solution inside the cavity. Using the fringe characteristics, calibration curves were established for the range of temperature and concentration levels expected during the solidification process. In the actual solidification experiment, two hypoeutectic solutions (5% and 15% NH₄Cl) were chosen. The calibration curves were used to determine the temperature and concentration of the solution inside the cavity during solidification of 5% and 15% NH₄Cl solution at different instants of time. The measurement was carried out at a fixed point in the cavity, and the concentration variation with time was recorded as the solid–liquid interface approached the measurement point. The measurement exhibited distinct zones of concentration distribution caused by solute rejection and Rayleigh Benard convection. Further studies involving flow visualization with laser scattering confirmed the Rayleigh Benard convection. Computational modeling was also performed, which corroborated the experimental findings.     

Effects of Solutal Undercooling on Three-Dimensional Double-Diffusive Convection and Macrosegregation during Solidification of a Binary Alloy

ABSTRACT

A three-dimensional transient numerical model is developed for simulation of double-diffusive convection during binary alloy solidification processes, taking into account nonequilibrium effects due to solutal undercooling. Such an effect arising from microscopic convection near the diffusion boundary layer adjacent to the mushy region is captured by devising a macroscopic model based on a fixed-grid, enthalpy-based, control-volume approach. Microscopic features pertaining to solutal undercooling are incorporated through a modification of the partition coefficient by means of a number of macroscopically observable parameters. Numerical simulations are performed for solidification of a metallic alloy system kept in a side-cooled cubic enclosure. Typical curvatures of the streamlines and their nonequidistant characteristics, as projected on various cross-sectional planes, show an element of three-dimensionality in the double-diffusive convection (originating from the solidification process itself) and its interaction with the progressing solidification front. The three-dimensional transport leads to a global macrosegregation, with significant composition variations across the longitudinal planes, as dictated by the modified partition coefficient and thermosolutal convection mechanisms.     

The structure of plumes generated in the unidirectional solidification process for a binary system

The present article describes the structure of plumes generated during solidification of a binary system. A transparent aqueous ammonium chloride solution is employed for super-eutectic growth in a Hele-Shaw cell. The velocities of plume convection in the melt layer and interstitial fluid flow within the mushy layer are measured by the particle tracking and dye tracing methods, respectively. Several important features are identified for each convective flow. In particular, the plume convection is found to consist of the upward flow enveloped in the downward flow, i.e., double flow structure. The downward flow enhances the solidification in the neighborhood of the exit of the channel emanating the plume, like a volcano. Interstitial fluid within the mushy layer is observed to move downward uniformly, which is induced by the plume convection.     

Experimental and numerical investigation of double-diffusive convection induced by a discrete heat source

Various engineering systems, such as those associated with crystal growth techniques or solar ponds, may be characterized by double-diffusive behavior induced by discrete heat sources. Due to the relevance of such systems, the objective of this study is to investigate double-diffusive convection induced by bottom heating with a finite, heated strip placed beneath a salt-stratified layer. Attention is focused on the formation and growth of converting regions in the salt-stratified fluid. Experimental and numerical results reveal that development of convective conditions is characterized by an interaction between Rayleigh-Bénard-type convection and longitudinal convective rolls formed by horizontal temperature gradients. Secondary flow is visualized and predicted to occur above the bottom convection cell. For relatively unstable combinations of the salt stratification and applied heat flux, a complicated interaction between chaotic, double-diffusive convection and a three-dimensional, gravity wave distribution are observed.     

Three-dimensional double-diffusive convection and macrosegregation during non-equilibrium solidification of binary mixtures

A three-dimensional transient mathematical model (following a fixed-grid enthalpy-based continuum formulation) is used to study the interaction of double-diffusive natural convection and non-equilibrium solidification of a binary mixture in a cubic enclosure cooled from a side. Investigations are carried out for two separate test systems, one corresponding to a typical model “metal-alloy analogue” system and other corresponding to a real metal-alloy system. Due to stronger effects of solutal buoyancy in actual metal-alloy systems than in corresponding analogues, the convective transport mechanisms for the two cases are quite different. However, in both cases, similar elements of three-dimensionality are observed in the curvature and spacing of the projected streamlines. As a result of three-dimensional convective flow patterns, a significant solute macrosegregation is observed across the transverse sections of the cavity, which cannot be captured by two-dimensional simulations.     

Call for contributions to a numerical benchmark problem for 2D columnar solidification of binary alloys

This call describes a numerical comparison exercise for the simulation of ingot solidification of binary metallic alloys. Two main steps are proposed, which may be treated independently: 1. The simulation of the full solidification process. First a specified ‘minimal’ solidification model is used and the contributors are provided with the corresponding sets of equations. The objective is to verify the agreement of the numerical solutions obtained by different contributors. Then different physical solidification models may be compared to check the features that allow for the best possible prediction of the physical phenomena. 2. A separate preliminary exercise is also proposed to the contributors, only concerned with the convective problem in the absence of solidification, in conditions close to those met in solidification processes. Two problems are considered for the case of laminar natural convection: transient thermal convection for a pure liquid metal with a Prandtl number on the order of 10^?2, and double-diffusive convection in an enclosure for a liquid binary metallic mixture with a Prandtl number on the order of 10^?2 and a Lewis number on the order of 10⁴.     

NUMERICAL EXPERIMENTS ON NATURAL CONVECTION IN A STABLY STRATIFIED FLUID DUE TO SIDE-WALL HEATING

Numerical experiments were conducted to study the natural convection in a stably stratified salt water solution with lateral heating in a square rectangular enclosure. The method of investigation employed is the finite-difference solution of the basic conservation equations for a two-dimensional, laminar, unsteady double-diffusive convection, and calculation is made for 1.0 × 10⁵ ≤ Ra_T ≤ 1.0 × l0⁶ and ≤ N ≤ 15. Four distinct flow regimes are observed depending on the magnitude of solutal stratification relative to thermal buoyancy N; unicell flow regime for N - 1, fully developed flow regime for N - 3, layered flow regime with the stagnant core for N - 5, and stagnant flow regime for N - 7. Formation of layered flow structure with time and the corresponding temperature and concentration distributions are examined. Due to the double-diffusive nature of heat and salt, interesting temperature and concentration profiles are obtained in each flow regime.     

MAGNETIC DAMPING OF g-JITTER INDUCED DOUBLE-DIFFUSIVE CONVECTION

This article describes a numerical study of g-jitter driven double-diffusive convective flows and thermal and concentration distributions in binary alloy melt systems subject to an external magnetic field. The study is based on the finite element solution of transient magnetohydrodynamic equations governing the momentum, thermal, and solutal transport in the melt pool. Numerical simulations are conducted using synthesized single- and multi-frequency g-jitter as well as real g-jitter data taken during space flights with or without an applied magnetic field. It is found that for the conditions studied, the main melt flow follows approximately a linear superposition of velocity components induced by individual g-jitter components, regardless of whether a magnetic field exists or not. The flow field is characterized by a recirculating double-diffusive convection loop oscillating in time with a defined frequency equal to that of the driving g-jitter force. An applied magnetic field has little effect on the oscillating recirculating pattern, except around the moment when the flow reverses its direction. The field has no effect on the oscillation period, but it changes the phase angle. It is very effective in suppressing the flow intensity and produces a notable reduction of solute striations and time fluctuations in the melt. For a given magnetic field strength, the magnetic damping effect is more pronounced on the velocity associated with the largest g-jitter component present and/or the g-jitter spiking peaks. A stronger magnetic field is more effective in suppressing the melt convection and also is more helpful in bringing the convection in phase with the g-jitter driving force. The applied field is particularly useful in suppressing the effect of real g-jitter spikes on both flow and solutal distributions. With appropriately selected magnetic fields, the convective flows caused by g-jitter can be reduced sufficiently, and it is possible that diffusion dominates the solutal transport in the melt.     

Solidification of aqueous ammonium chloride in a rectangular cell under constant wall temperature - an experimental study

The effect of a binary alloy solidification process was investigated for four different initial ammonium chloride concentrations (5%, 10%, 15% and 25%) and for four different constant wall temperature conditions (−13°C, −20°C, −25°C and −30°C). The solidification process inside the test cell was interrupted at various time steps to capture the phase front profile. Results show that a higher initial concentration and a lower constant wall temperature tend to increase the strength of thermal-driven buoyancy flow and solute-driven buoyancy flow respectively. The shape of both the solid and mushy phase front profiles are affected by the strength of these two flows. Isotherm plots and superimposed images are used to determine the location of solid-must interface and must-liquid interface respectively, inside the test cell at any time interval.     

Proper orthogonal decomposition (POD) analysis of flow structure in volatile binary droplets

In the present study we perform an in-depth analysis of the internal flow induced by concentration gradients in an evaporating binary ethanol–water droplet. The flow structure during the first stage of evaporation is characterised using micro particle image velocimetry (PIV) to investigate the flow field and analyse various modes of convection. Although PIV shows convection vortices, it does not help in identifying the various superimposed convection modes present. The proper orthogonal decomposition (POD) method is hence used in conjunction with PIV data to identify and characterise prevailing convection modes. During the first stage of evaporation many modes i.e. flow structures are found to co-exist, however the analysis reveals one dominant mode. In addition to the identification of this new mode of convection, the analysis quantifies the energetic contribution of each of these convection modes. The dominant mode is found to contribute to more than half of the total kinetic energy.     

Transient double-diffusive convection in an enclosure with large density variations

An extension of a slightly compressible flow model to double-diffusive convection of binary mixtures of ideal gases enclosed in a cavity is presented. The problem formulation is based on a low-Mach number approximation and the impermeable surface assumption is not invoked. The main objectives of this work are the statement of the mathematical model used, and the analysis of some significant results showing the influence of density variation on transient solutions for pure thermal or pure solutal convection as well as for thermosolutal convection in the special case where the thermal and solutal buoyancy forces are equal in intensity either for aiding or for opposing cases.     

埋地原油管道停输期间温降及原油凝固传热模型及数值模拟

假设原油凝固区域为一固相和液相组成的动态多孔介质区域,建立了土壤、管道能量方程与原油质量、动量和能量方程相互耦合的传热模型,并对埋地原油管道停输温降过程进行了数值模拟.数值模拟结果能够合理解释停输期间温度场、凝固界面和自然对流规律.     

Effect of the Buoyancy Ratio on Oscillatory Double-Diffusive Convection in Binary Mixture

In this work, a numerical study of double-diffusive convection in binary mixture has been presented. A square cavity filled with a binary mixture and exposed to opposition solute and thermal gradients has been considered. The following flow parameters were considered: Prandtl number Pr = 10, Lewis number Le = 10, and buoyancy ratio varies 0 ≤ N ≤ 2. The finite volume method with SIMPLER algorithm was used to solving numerically the mathematical model. Our computer code is validated and shows a good agreement with literature available results. The obtained results show a strongest dependence of the thermal structure and solute effect with the buoyancy ratio. The oscillatory double-diffusive flow appeared from periodic time-evolution where the phenomena retuned in each period time. A critical thermal Rayleigh number Ra_Tcr and corresponding dominated frequency for the onset of oscillatory double-diffusive convection were determined for each buoyancy ratio N, and the results show a strongest dependence between the buoyancy ratio and critical Rayleigh number. Also, the dominance of solute force increases the intensity of the flow better than the case of the dominance of thermal force.     

Transient natural convective heat transfer in porous medium with solidification of binary mixture

In this paper an enthalpy porosity method associated with finite control volume scheme and SIMPLE iteration was employed to solve Navier–Stokes equation coupled with energy equation through Ergun equation and Boussinesq approximation for studying the effect of two-dimensional transient natural convective heat transfer from a closed region of porous medium with the different porosity on solidification in carbon–iron system. As shown in the results, it is fund that the thickness of solidification layer is increased with time due to thermal coupled flow induced by natural convection; and the wall temperature is faster changed in porous medium with larger porosity, which corresponds to slow the growth of the solidification layer in binary system.     

PIV measurements of velocity of water in the presence of ice and comparison with calculated values

Particle imaging velocimetry (PIV) has been used to measure the laminar natural convection resulting from buoyancy attendant on the freezing of water in a small rectangular cavity with transparent walls. The measured velocities show the “unusual” flow resulting from water having a density maximum at 277 K. The PIV images also permitted the accurate determination of the shape and position of the solidification front in these quasi-steady experiments. The CFD software FLUENT® was used to simulate the flow and the position/shape of the solidification front with satisfactory results.     

合金枝晶生长及微细界面热质传递模拟

利用元胞自动机法(CA)耦合对流和热质传递模型模拟了Al-Cu二元合金微观组织在多种影响因素下的二维生长过程,分析了枝晶凝固、微界面热质传递以及微流动等微细现象之间的相互作用,得到了单枝晶以及多个枝晶在微流作用下的生长规律。模拟结果表明:(1)枝晶凝固过程中溶质富集于生长前沿。随着枝晶生长,凝固前沿远离冷源,枝晶尖端温度逐渐增大,而浓度逐渐变小;(2)流动对于枝晶的生长有着重要影响。流动破坏了枝晶生长的对称性,下游溶质浓度大于上游,枝晶在上游方向优先生长,而在下游方向有所抑止;(3)多个枝晶生长时,枝晶彼此间有阻碍生长的作用,二次枝晶臂的形成相对减少,枝晶间几乎不存在微流动。     

Studies on turbulent momentum, heat and species transport during binary alloy solidification in a top-cooled rectangular cavity

A two-dimensional transient fixed-grid enthalpy-based numerical method is developed to analyze the effects of turbulent transport during a binary alloy solidification process. Turbulence effects are introduced through standard k-ε equations, where coefficients are appropriately modified to account for phase-change. Microscopically-consistent estimates are made regarding temperature-solute coupling in a non-equilibrium solidification situation. The model is tested against laboratory experiments performed using an NH₄Cl-H₂O system in a rectangular cavity cooled and solidified from the top. Particular emphasis is laid on studying the interaction between Rayleigh-Benard type convection and directional solidification in the presence of turbulent transport. Numerical predictions are subsequently compared with experimental results regarding flow patterns, interface growth and evolution of the temperature field, and the agreement is found to be good.