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International audience; This paper describes the first step of a study dedicated to the development of a macroscopic model of casting of a metal foam by infiltration and solidification of a liquid metal in a porous mould. The first stage presented here describes a local model of injection of the metallic melt in a capillary tube and subsequent solidification of the metal by heat transfer to the duct walls.The model is intended to account for the air/liquid interface displacement during the infiltration phase, for the heat transfer to the wall and for the growth of the solid phase in the presence of the fluid flow. The objective is to determine the influence of the operating conditions on the penetration depth and on the solidification time in a simplified geometry before using this local information in a macroscopic homogenized model presently under development.

International audience; A macroscopic model for solidification of pure metal in porous media is derived using the volume averaging method. Solidification starts when the infiltration of the porous mould is completed and therefore the phase change problem involving three phases (liquid and solid metal, mould) is governed by diffusion. The upscaled model is first characterized by the local thermal equilibrium assumption (LTE) between the liquid and the solid metallic phases leading to one energy conservation equation for the equivalent metallic phase. On the other hand, local thermal non-equilibrium (LTNE) between the equivalent continuous metallic phase and the mould is considered, giving rise to two coupled energy conservation equations. The associated closure problems are derived and numerically solved allowing for the determination of the effective transport properties. Numerical solutions of the macroscopic model are qualitatively compared with available experiments.

Corrigendum to this publication: http://hal.archives-ouvertes.fr/hal-00528029; International audience; 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 10(4).

International audience; Stability analyses of thermal and/or solutal natural convection in a configuration composed by a fluid layer overlying a homogeneous porous medium have been performed using different modeling approaches, especially for the treatment of the interfacial region. Comparisons between the one-domain approach and the two-domain formulation have shown important discrepancies of the marginal stability curves. This note shows that, according to Kataoka [I. Kataoka, Local instant formulation of two-phase flow, Int. J. Multiphase Flow 12(5) (1986) 745–758.], the differentiation of the macroscopic properties of the porous layer at the interface (porosity, permeability, thermal effective diffusivity) must be considered in the meaning of distributions. In that case, the one- and the two-domain approaches are shown to be equivalent and very good agreement is indeed found when comparing the results obtained with both approaches.

This study deals with the onset of thermal natural convection in a system consisting of a fluid layer overlying a homogeneous porous medium. A linear stability analysis is carried out, using the so-called two-domain approach and including the Brinkman term in the porous region (2ΩDB). Results are systematically compared to those obtained using the one-domain approach (1Ω) and the classical Darcy formulation of the two-domain approach (2ΩD). A better agreement is found between the 2 Ω DB and 2ΩD neutral curves, than with the 1Ω curves, indicating that the inclusion of the Brinkman term plays a secondary role on the stability results. The different treatment of the interfacial region is discussed on the basis of these results.

A stability analysis of thermal natural convection in superposed fluid and porous layers is carried out. The two-layer system is described using a one-domain formulation, and the eigenvalue problem resulting from the stability analysis is solved using the generalized integral transform technique (GITT). The numerical results confirm that the onset of convection can have a bimodal nature depending on the depth ratio. The influence of the dimensionless permeability and thermal diffusivity ratio are investigated.

In this paper we rely on the constructal law of maximization of flow access in order to construct a theory of geometry generation (selection, evolution) during molten droplet impact. We show that immediately after impact the liquid spreads inviscidly as a ring with a radial velocity that scales with the initial impact velocity. If the initial droplet is small and slow enough, the ‘splat’ comes to rest (dies) viscously, as a disc. If the droplet is large and fast enough, the ring splashes and is continued outward by needles that grow radially until they are arrested by viscous effects. We optimized the number of needles such that the total splash time is minimum. The theoretical dimensionless group that governs the selection of geometry (G) is the ratio of two lengths, the final radius of the disc that dies viscously, divided by the radius of the still inviscid ring that just wrinkles. Splats form when G ⩽ O(1) and splashes are favored when G ⩾ O(1). Experimental measurements reported in the literature confirm several of the features of the constructal development of splat vs. splash flow architecture.

This paper deals with natural convection driven by combined thermal and solutal buoyancy forces in a binary fluid. The configuration under study is a confined enclosure partially filled with a vertical porous layer. The mathematical description of the problem is based on a one-domain formulation of the conservation equations. The set of numerical results presented here quantitatively shows the influence of the porous layer on the flow structure and on heat and species transfer in the enclosure. The paper is focused on the analysis of the influence of the characteristic parameters governing double diffusive convection, namely the ratios of solutal and thermal parameters: the diffusivities and the buoyancy forces. Heat and mass transfer is analyzed as a function of the permeability of the porous layer. It is shown that the coupling of the flow penetration in the porous layer with the combined buoyancy forces induces a specific behavior of the flow structure and average heat transfer in the enclosure.

This study deals with the experimental analysis of double diffusive effects on the solidification process of a binary mixture. Solidification experiments from a horizontal plate heat exchanger are performed in a cavity filled with a hypoeutectic NH4Cl–H2O solution. Solute redistribution at the interface creates concentration gradients in the fluid phase and a dendritic front growth is expected. We analyze the influence of solute rejection on the equilibrium conditions at the solid–liquid interface, on the solidification front kinetics and on the solid structure. Local front temperature measurements and estimation of the solid fraction of the growing solid allow us to quantitatively analyze the coupled influence of solute rejection and solid fraction on the front growth. A simplified numerical analysis shows that the role played by these two phenomena is very weak in the range of parameters under study.

This paper describes the solution of a steady natural convection problem in porous media by the dual reciprocity boundary element method. The boundary element method for the coupled set of mass, momentum, and energy equations in two-dimensions is structured by the fundamental solution of the Laplace equation. The dual reciprocity method is based on augmented scaled thin plate splines. Numerical examples include convergence studies with different mesh size, uniform and non-uniform mesh arrangement, and constant, linear, and quadratic boundary field discretisations for differentially heated rectangular cavity problems at filtration with Rayleigh number of Ra p ¼ 25; 50, and 100, Darcy numbers Da ¼ 10 23 ; and 10 25 , and aspect ratios A ¼ 1=2; 1, and 2. The solution is assessed by comparison with reference results of the fine-mesh finite volume method. q 2003 Elsevier Ltd. All rights reserved.

The momentum balance at the interface between a liquid and a porous substrate is investigated for a configuration with forced flow parallel to the interface. An heterogeneous continuously varying transition layer between the two outer bulk regions is introduced. The stress jump coefficient earlier introduced in the jump interface condition is here derived as an explicit function of the variations of the velocity and effective properties of the transition layer. Agreement is found between our numerical results based on the single-domain approach and the existing ad hoc estimates in the literature. Further advantages of this non-homogeneous analysis are also provided.

This paper deals with the derivation of the macroscopic momentum transport equation in a non-homogeneous solidifying columnar dendritic mushy zone using the method of volume averaging. One of the originalities of this study lies in the derivation of an associated closure problem for the determination of the spatial evolution of the effective transport properties in such a complex situation. In this analysis—where the phase change has been included at the different stages of the derivation—all the terms arising from the averaging procedure (geometrical moments, phase interactions, interfacial momentum transport due to phase change, porosity gradients, etc.) are systematically estimated and compared on the basis of the characteristic length-scale constraints associated with the porous structures presenting evolving heterogeneities. For dendritic structures with “moderate” (but not small) evolving heterogeneities, we show that phase change and non local effects could hardly affect the determination of the permeability and inertia tensors. Finally, a closed form of the macroscopic momentum equation is proposed and a discussion is presented about the need to consider inertia terms and the second Brinkman correction (explicitly involving gradients of the liquid volume fraction) in such non-homogeneous systems.

In order to improve mass transport description in solidification modeling, this study deals with the determination of the solute dispersion tensor in columnar dendritic mushy zone. The closure problem associated with the derivation of the macroscopic species conservation equation, using the volume averaging method, is solved numerically. Using schematic structures and digitized images of real dendritic structures observed experimentally during solidification of succinonitrile-4 wt.% acetone, the influence of tortuosity and microscopic dispersion on the determination of the effective solute dispersion coefficients is represented in terms of the Peclet number.

This paper describes the solution of a steady state natural convection problem in porous media by the dual reciprocity boundary element method (DRBEM). The boundary element method (BEM) for the coupled set of mass, momentum, and energy equations in two dimensions is structured by the fundamental solution of the Laplace equation. The dual reciprocity method is based on augmented scaled thin plate splines. Numerical examples include convergence studies with different mesh size, uniform and non-uniform mesh arrangement, and constant and linear boundary field discretizations for differentially heated rectangular cavity problems at filtration with Rayleigh numbers of Ra*=25, 50, and 100 and aspect ratios of A=1/2, 1, and 2. The solution is assessed by comparison with reference results of the fine mesh finite volume method (FVM). Copyright © 2000 John Wiley & Sons, Ltd.

This study deals with the numerical analysis of transient heat and species transfer by natural convection in a binary fluid vertical layer. The cavity is differentially heated and a solutal buoyancy force is created by imposing a concentration step at one vertical wall: This refers to the experimental situation where the composition gradient inducing the solutal buoyancy force is created by melting of pure ice in a salty solution. The constitution of the flow structure and the time evolution of the heat and mass transfer characteristics are studied for opposing body forces over a range of thermal and solutal Rayleigh numbers. The numerical results allow to provide a better insight into the mechanisms driving the heat and species transfer at high Lewis number thermohaline convection. [S0022-1481(00)00303-0]

This paper presents a scale analysis of the parameters for which flow instabilities can be expected in coupled phase change - natural convection in cavities heated from the side. The results are in agreement with what was observed numerically for very low Prandtl number fluids, where multiple cells were found to appear early on as a result of the instability of the conduction regime. For very large Prandtl number flow instabilities, multiple cells, if any, would only occur at very large nominal Rayleigh number.

This paper presents the first results of a benchmark problem concerning the simulation of coupled natural convection and melting from an isothermal vertical wall. The exercise is restricted to the simulation of phase change of pure substances, driven by laminar natural convection in 2D enclosures. The comparison covers two ranges of Prandtl numbers, corresponding to the melting of metals or organic materials. The results of the test cases are presented in detail and show that, while qualitative agreement is obtained in most situations, it is still relevant to proceed to thorough numerical comparisons before assessing the accuracy of the different algorithms. The dispersion of the results is a strong motivation to extend the exercise to a second stage incorporating a larger number of contributions. ~) Elsevier, Paris

This study presents some Computer Vision techniques to analyze a phase change problem with natural convection. The analysis and interpretation of images are important to understand the phenomenon under study. Methods of image processing and analysis are used to validate the mathematical model and to automate the process of extracting information from the experimental model. The images produced by the experiment show the melting of a vertical ice layer into a heated rectangular cavity in the presence of natural convection and maximum density.

This paper addresses the derivation of the macroscopic momentum equation for flow through a nonhomogeneous porous matrix, with reference to dendritic structures characterized by evolving heterogeneities. A weighted averaging procedure, applied to the local Stokes' equations, shows that the heterogeneous form of the Darcy's law explicitly involves the porosity gradients. These extra terms have to be considered under particular conditions, depending on the rate of geometry variations. In these cases, the local closure problem becomes extremely complex and the full solution is still out of reach. Using a simplified two-phase system with continuous porosity variations, we numerically analyze the limits where the usual closure problem can be retained to estimate the permeability of the structure.

International audience; We investigate the role of the inertia of the flow through the dendritic mushy zone in the numerical prediction of channel segregations during columnar solidification. The contribution of inertia is included in the momentum transport equation through the quadratic Forchheimer correction term. The study reveals a significant influence of the Forchheimer term in the vicinity of the liquidus front, i.e. at high liquid fractions. The natural convective flow field in this region is modified due to the additional inertial drag. This strongly influences the convective transport of solute and thereby incurs a modification of the dynamics of the advancement of the mushy zone. The most notable consequence is a significant decrease in the predicted channel segregation.

Thermosolutal natural convection is considered in binary fluids presenting a density maximum. The situation under study concerns an aqueous solution in an enclosure with a temperature and concentration difference applied between the vertical walls. The fluid presents a density maximum in the temperature range of interest, and the temperature of the maximum depends on the local solute concentration. Numerical results are provided which show the complex influence on the flow structure and on the heat transfer at the walls of the contra-rotative rolls due to the density maximum competing with the corotative cells created by double diffusive effects.

This paper reports the numerical simulations of double diffusive natural convection flows in a binary fluid contained in a two-dimensional enclosure, with imposed horizontal temperature and concentration differences between the vertical walls. The analysis concerns the influence of the different parameters governing the problem in the heat transfer characteristics and on the flow structure. The study is focused on steady-state solutions in the cooperating situation. At high Lewis numbers, numerical simulations show that heat transfer decreases with increasing buoyancy ratios. This phenemenon is analysed on the basis of the flow structure, and a scale analysis is provided to estimate the decrease in heat transfer. Then, the influence of the parameters on the formation of a multicellular flow structure is discussed.

This paper reports the analytical and numerical results on double diffusive natural convection in a binary fluid contained in a two-dimensional enclosure where horizontal temperature and concentration differences are specified. A numerical code, based on a finite volume procedure, and a scaling law approach are used to analyse the influence of the different parameters which characterize those thermosolutal flows: in this first paper, the mass transfer problem is studied in the steady-state. A general mass transfer correlation is proposed, which is valid over a wide range of parameters.

This paper deals with natural convection in confined porous media, driven by cooperating thermal and solutal buoyancy forces. The physical model for the momentum conservation equation makes use of the B:rinkman extension of the classical Darcy equation, and the set of coupled equations is solved using a finite volume approach. The numerical simulations presented here span a wide range of the main parameters (the Rayleigh and Darcy numbers) in the domain of positive buoyancy numbers and for Le > 1. When possible, the results are compared with previous numerical data or existing scaling laws. The results are mainly analyzed in terms of the average heat and mass transfers at the walls of the enclosure. Although the mass transfer characteristics are fairly well predicted by the scale analysis, it is shown that convective heat transfer has a specific behavior in given ranges of the governing parameters.

This study is concerned with the experimental and numerical analysis of thermohaline natural convection in an aqueous solution, driven by melting of a block of pure ice into the liquid mixture. Experimentally, the flow structure evolution and the heat transfer characteristics are studied for a binary H2O–Na2CO3 mixture in the domain of negative buoyancy ratios and for a wide range of solutal and thermal Rayleigh numbers. The observations are analyzed with the help of the classical results about cell formation in a stratified fluid due to sideways heating. The comparison with the numerical results shows that the mechanisms that define the flow structure are essentially due to thermohaline convection and not to the melting process. Finally, the fusion kinetics is analyzed, and the melting rate is correlated to the governing parameters of natural convection in the liquid.

A measurement system consisting of two high- speed two- color pyrometers was used to monitor the flattening degree and cooling rate of zirconia particles on a smooth steel substrate at 75 or 150 °C during plasma spray deposition. This instrument provided data on the deformation behavior and freezing of a particle when it impinged on the surface, in connection with its velocity, size, and molten state at impact. The results emphasized the influence of temperature and surface conditions on particle spreading and cooling. When the substrate temperature was 150 °C, the splats had a perfect lenticular shape, and the thermal interface resistance between the lamella and the substrate ranged from 10− 7 to 10− 8 W/m2 · K. The dependence of the flattening degree on the Reynolds number was investigated.

International audience; During the solidification of metal alloys, chemical heterogeneities at the scale of the product develop. It is referred to as "macrosegregation". Numerical simulation tools exist in the industry. However, their predictive capabilities are not validated and are still limited. A 2D numerical benchmark is presented, based on the solidification of metallic Pb-Sn alloys. Concerning the numerical benchmark, a "minimal" common model of solidification is assumed, including columnar growth without undercooling, fixed solid, isotropic permeability of the mushy region, local thermodynamic equilibrium, lever-rule assumption for the local average composition. We focus our attention on the numerical method used to solve the average conservation equations: Finite Volume, Finite Element, Velocity-Pressure coupling treatment, scheme for convective terms, etc. At this stage of the work, we cannot exhibit a reference solution. However we draw some conclusions on the effects of the grid dependency, in particular on the location and sizes of the segregate channels. The development of both thermally and solutal driven convections in the first stage of the process (cf. low Prandtl and high Lewis numbers) and the relative independency of the convective scheme are also discussed. This presentation also have the goal to call other contributors to join this benchmark [1] in order to enrich the exercise and to reach a reference solution for this important problem in metallurgy.

International audience; The numerical prediction of channel segregations during two-dimensional columnar solidification of Sn-Pb alloy is analyzed when inertia is considered in the dendritic mushy zone. This contribution is included in the momentum transport equation through the quadratic Forchheimer correction term. A significant influence of the Forchheimer term in the vicinity of the liquidus region is found. The natural convective flow field and therefore the global shape of the mushy zone are modified giving rise to significant decrease of channel segregation, due to additional drag in these regions.

International audience; The onset of double-diffusive natural convection in under-ice melt ponds is investigated through a linear stability analysis. The three-layer configuration is composed by a fluid layer (melt pond) overlying a saturated porous medium (ice matrix), which in turn overlies another fluid layer (under-ice melt pond). Water density inversion is taken into account by adopting a density profile with a quadratic temperature dependence and a linear concentration dependence. We show that the key parameter affecting stability is the depth of the ice matrix, while the depths of the upper and lower fluid layers play a marginal role. A Hopf bifurcation is observed in the whole range of parameters studied, and the size of the convection cells depends on ice permeability. The influence of the external temperature gradient is investigated by means of the definition of an extra thermal parameter accounting for the relative position of the density maximum. It is shown that convection is favored by larger temperature gradients, which occur during Arctic summer.

In many industrial processes or natural phenomena coupled heat and mass transfer and fluid flow take place in configurations combining a clear fluid and a porous medium. Since the pioneering work by Beavers and Joseph (1967), the modelling of such systems has been a controversial issue, essentially due to the description of the interface between the fluid and the porous domains. The validity of the so-called one-domain approach — more intuitive and numerically simpler to implement — compared to a two-domain description where the interface is explicitly accounted for, is now clearly assessed. This paper reports recent developments and the current state of the art on this topic, concerning the numerical simulation of such flows as well as the stability studies. The continuity of the conservation equations between a fluid and a porous medium are examined and the conditions for a correct handling of the discontinuity of the macroscopic properties are analyzed. A particular class of problems dealing with thermal and double diffusive natural convection mechanisms in partially porous enclosures is presented, and it is shown that this configuration exhibits specific features in terms of the heat and mass transfer characteristics, depending on the properties of the porous domain. From the viewpoint of the stability of convection in a horizontal layer where a fluid layer lies on top of a porous medium, the analysis shows that the onset of convection is strongly influenced by the presence of the porous medium. The case of thermal convection is fully detailed and many open problems arise in the field of double diffusive convection.Copyright © 2010 by ASME

This paper considers the onset of double diffusive natural convection in a vertical layer of a binary fluid submitted to horizontal thermal and compositional gradients. The analysis deals with the particular situation where the resulting buoyancy forces (the Grashof numbers corresponding to the thermal and solutal effects) are opposing and of equal intensity. The stability analysis for the infinite layer shows that the purely diffusive (motionless) solution prevails at moderate Grashof numbers, and an analytical expression of the critical Rayleigh number as a function of the Lewis number is obtained. These results are then compared to the critical values which are determined from numerical simulations in an enclosure. Numerical calculations in the transient regime are used to give an interpretation of the stability of the steady state diffusive regime when the buoyancy forces are below the critical value.

International audience; During the solidification of metal alloys, chemical heterogeneities at the product scale (macrosegregation) develop. Numerical simulation tools are beginning to appear in the industry, however their predictive capabilities are still limited. We present a numerical benchmark exercise treating the performance of models in the prediction of macrosegregation. In a first stage we defined a "minimal" (i.e. maximally simplified) solidification model, describing the coupling of the solidification of a binary alloy and of the transport phenomena (heat, solute transport and fluid flow) that lead to macrosegregation in a fully columnar ingot with a fixed solid phase. This model is solved by four different numerical codes, employing different numerical methods (FVM and FEM) and various solution schemes. We compare the predictions of the evolution of macrosegregation in a small (10×6 cm) ingot of Sn-10wt%Pb alloys. Further, we present the sensitivities concerning the prediction of instabilities leading to banded channel mesosegregations.

International audience; Refers to: Call for contributions to a numerical benchmark problem for 2D columnar solidification of binary alloys International Journal of Thermal Sciences, Volume 48, Issue 11, November 2009, Pages 2013-2016, M. Bellet, H. Combeau, Y. Fautrelle, D. Gobin, M. Rady, E. Arquis, O. Budenkova, B. Dussoubs, Y. Duterrail, A. Kumar, C.A. Gandin, B. Goyeau, S. Mosbah, M. Založnik

PurposeThis paper aims to tackle the problem of thermo‐solutal convection and macrosegregation during ingot solidification of metal alloys. Complex flow structures associated with the development of channels segregate and sharp gradients in the solutal field call for the implementation of accurate methods for numerical modeling of alloy solidification. In particular, the solute transport equation is convection dominated and requires special non‐oscillarity type high‐order schemes to handle the regions of channels segregates.Design/methodology/approachIn the present study, a time‐splitting approach has been adopted to separately handle solute advection and diffusion. This splitting technique allows the application of accurate total variation dimensioning (TVD) schemes for solution of solute advection. Applications of second‐order Lax‐Wendroff TVD SUPERBEE and fifth‐order weighted essentially non‐oscillatory (WENO) schemes are described in the present article. Classical numerical solution of solute transport using hybrid and central‐difference schemes are also employed for the purpose of comparisons. Numerical simulations for solidification of Pb‐18%Sn in a two‐dimensional rectangular cavity have been carried out using different numerical schemes.FindingsNumerical results show the difficulty of obtaining grid‐independent solutions with respect to local details in the region of channels. Grid convergence patterns and numerical uncertainty are found to be dependent on the applied scheme. In general, the first‐order hybrid scheme is diffusive and under predicts the formation of channels. The second‐order central‐difference scheme brings about oscillations with possible non‐physical extremes of solute composition in the region of channel segregates due to sharp gradients in the solutal field. The results obtained using TVD and WENO schemes contain no oscillations and show an excellent capture of channels formation and resolution of the interface between solute‐rich and depleted bands. Different stages of channels formation are followed by analyzing thermo‐solutal convection and macrosegregation at different times during solidification.Research limitations/implicationsAccurate prediction of local variation in the solutal and flow fields in the channels regions requires grid refinement up to scales in the order of microscopic dendrite arm spacing. This imposes limitations in terms of large computational time and applicability of available macroscopic models based on classical volume‐averaging techniques.Practical implicationsThe present study is very useful for numerical simulation of macrosegregation during ingot casting of metal alloys.Originality/valueThe paper provides the methodology and application of TVD schemes to predict channel segregates during columnar solidification of metal alloys. It also demonstrates the limitations of classical schemes for simulation of alloy solidification.

International audience; A one-dimensional model has been developed to address the non-equilibrium heat transfer between an alumina lamella deposited by plasma spraying, and a steel or alumina substrate. The model includes under-cooling phenomenon, heterogeneous nucleation and crystal growth kinetics, allowing for the prediction of the temperature evolution in the lamella and substrate and of the nucleation temperature, grain density and size distribution. The effect on the nucleation process of the contact angle between the nucleus and substrate surface and of the quality of the contact at the splat–substrate interface is emphasized. The influence of the splat thickness, substrate material and substrate oxidation on the grain size distribution is also discussed.

International audience; A plasma-sprayed coating is built up by the layering of individual splats. The latter are formed by spreading and solidification of molten particles sprayed onto a solid substrate. The coating properties depend on its microstructure and the quality of contact between the splats and the underlying layer and between the piled-up splats. This work deals with a 1D model of heat transfer between plasma-sprayed alumina splat and smooth substrate. The model is based on heat diffusion in the solidifying splat and substrate and includes undercooling phenomenon, heterogeneous nucleation and crystal growth kinetics. It assumes that splat spreading and solidification are two independent processes. The model predicts splat cooling and solidification taking into account, as far as possible, the in-flight particle properties drawn from the literature in order to study their effect on splat thermal history. The effect of the quality of contact between the splats as well as the already-deposited and solidified layer thickness on the grain size distribution and front solidification velocity is investigated.

The analysis of the melting process of a pure material from an isothermal vertical wall has motivated a significant number of experimental and numerical studies in the last ten years. When the only external field is gravity and if no capillary or solutal effects have to be taken into account, the melting process is controlled by thermally induced natural convection in the liquid phase. Most of the available experimental and numerical results have been obtained for the melting of phase-change materials (PCMs) with a high Prandtl number liquid phase. Detailed experimental results concerning melting of PCMs with a low Prandtl number (metals) have appeared only recently and comparisons with numerical solutions show qualitative agreement, but the influence of the governing parameters on the kinetics of the melting process has not been clearly analyzed. The purpose of this paper is to provide results on the heat transfer characteristics of the system over a wide range of Rayleigh and Prandtl numbers in the low Prandtl domain.

This article deals with the onset of thermosolutal natural convection in horizontal superposed fluid and porous layers. A linear stability analysis is performed using the one-domain approach. As in the thermal convection case, the results show a bimodal nature of the marginal stability curves where each mode corresponds to a different convective instability. At small wave numbers, the convective flow occurs in the whole cavity (“porous mode”) while perturbations of large wave numbers lead to a convective flow mainly confined in the fluid layer (“fluid mode”). Furthermore, it is shown that the onset of thermosolutal natural convection is characterized by a multi-cellular flow in the fluid region for negative thermal Rayleigh numbers. For positive thermal Rayleigh numbers, the convective flow takes place both in the fluid and porous regions. The influence of the depth ratio and thermal diffusivity ratio is also investigated for a wide range of the thermal Rayleigh numbers.

International audience; A recent development in thermal spraying is to design the microstructure of coatings by controlling the sizes of the structural features within the coating so that they exhibit dimensions at the nanoscale. Improvements in performance can be in mechanical properties as well as functional properties. The size of these nano-structured features depend both on the form of the starting material (agglomerates of nanoparticles, liquid precursors) and the process conditions employed during production. Narrowing the crystal size distribution can be obtained from a carefully-controlled nucleation and growth process. This study presents a one-dimensional heat transfer model of splat cooling and solidification under plasma spray conditions. The model involves melt undercooling, nucleation and crystal growth kinetics. It intends to investigate the effect of the oxidation of various steel substrates, on the size and density of the nucleated grains.

Cet article a pour objectif de fournir les bases pour une analyse des situations de convection naturelle rencontrees le plus couramment. L’attention est attiree sur les aspects fondamentaux afin d’aider a la formulation d’un probleme. Sont presentees d’une part des configurations de convection naturelle externe (le long d'une paroi ou en panache), ainsi que des cas de convection mixte, ou convection naturelle et forcee sont associees. D'autre part, la convection naturelle interne est abordee par le traitement de ses trois grandes classes de problemes : dans une conduite verticale, dans une couche horizontale, ou en cavite. Les cas presentes de convection naturelle presentes sont les plus frequents, c’est-a-dire qu’ils possedent des solutions analytiques accessibles ou des resultats de simulation numerique bien etablis.

Large particle transport in porous media plays an important role in chemical and mechanical engineering but also in the medical field, especially in cancer treatment. The major difficulty in large particle transport results from the fact that the particles themselves influence the effective transport properties by pore plugging due to particle entrapment. In this study, we used a random walk model describing the particle transport inside the pores. The effective macroscopic transport properties are determined using the results of the random walk model. It is shown that the permeability tensor strongly depends on the particle size and the injection point location, whereas the dispersion coefficients remain independent. We also determined the maximal particle radius for which particle transport can be described by the convection-diffusion equation. Another important point in the chemical and medical field is the final particle distribution, and particularly the distribution of the quantity of liquid transported by the particles. Our results show that large particles do not lead to a homogeneous liquid distribution. Hence when a large quantity of liquid should be homogeneously distributed in the porous medium, the use of smaller particles is recommended.

On parle de transfert de chaleur (ou de masse) par convection lorsque la chaleur (ou le constituant) est transmise a, ou par, un fluide en ecoulement. Par opposition a la convection forcee, ou un ecoulement est cree par une force exterieure (gradient de pression), la convection est dite libre ou naturelle si le mouvement du fluide n'est du qu'a des variations de masse volumique. Ces variations sont, en general, causees par une distribution non uniforme de la temperature et/ou de la concentration des especes dans un melange. La difference entre ces deux modes de convection est essentielle dans la mesure ou, dans le cas de la convection forcee, la temperature ou la concentration peuvent etre des scalaires passifs, advectes par un ecoulement impose par ailleurs. Dans la convection naturelle au contraire, les gradients de masse volumique sont le terme moteur de l'ecoulement du fluide, qui transfere par ailleurs chaleur ou solute avec son environnement. Il y a donc fondamentalement couplage entre le champ de vitesse et les differents champs scalaires. La comprehension des mecanismes de convection naturelle constitue un enjeu scientifique important afin de pouvoir les modeliser et predire leurs effets dans l'environnement ou dans les equipements. On concoit que l'ingenieur doive faire face a une tres grande variete de situations due a la taille du domaine d'etude, a sa geometrie, a la nature des fluides concernes et leurs proprietes thermophysiques, aux conditions limites et a l'importance des gradients de masse volumique mis en jeu, etc. L'objet de cet article n'est evidemment pas de pretendre aborder toutes les configurations possibles, mais de poser les principes physiques qui regissent ce type d'ecoulement et de montrer comment ceux-ci interviennent dans les transferts de chaleur ou de masse. On se limitera donc aux aspects plus fondamentaux, en ne considerant que des configurations simples, parfois academiques. Nous tenterons de renvoyer le lecteur aux principales references s'il souhaite approfondir des points plus particuliers ou des situations plus complexes, ou s'il recherche des correlations specifiques pour resoudre des problemes pratiques (voir a ce sujet les articles « Convection thermique et massique » [BE 8 205] [BE 8 206] (BE 8 207]). Enfin, dans la plupart des cas, on ne peut pas obtenir de solution suffisamment detaillee par des calculs simples: on doit alors faire appel a la simulation numerique pour resoudre ce type de probleme. La plupart des nombreux logiciels de mecanique des fluides numerique (MFN, ou CFD pour computational fluid dynamics) commercialises permettent de resoudre des problemes de convection naturelle dans des geometries complexes et de prendre en compte des couplages multiples. L'objectif de cet article et du suivant [AF 4 081] est de fournir quelques elements pour comprendre les principales hypotheses sur lesquelles reposent les modeles implantes dans ces codes de calcul et de donner quelques cles pour orienter l'interpretation des resultats. Ce premier article introduit les aspects theoriques de la convection naturelle. Dans la suite [AF 4 081] sont abordes les cas pratiques courants pour lesquels des solutions (analytiques ou simulees) sont connues.

This paper deals with the macroscopic modeling and numerical simulation of columnar dendritic solidification of binary alloys. The macroscopic governing equations and associated effective transport properties were previously derived using a volume averaging technique with local closure. The macroscopic model takes into account the spatial variation of the pore-scale geometry within the mushy zone, which leads to additional terms involving porosity gradients. The second important feature concerns solute mass conservation, which is described by considering a macro-scale non-equilibrium accounting for chemical exchanges at the solid–liquid interface. A simplified version of the model is validated through a comparison of the numerical solution to three experiments available in the literature. Porosity extra terms are systematically estimated on the basis of these numerical simulations, and the influence on solidification of effective transport properties such as permeability and interfacial solute exchange coefficients is investigated.

International audience; This paper deals with the derivation of a macroscopic model for columnar dendritic solidification of binary mixtures using the volume averaging method with closure. The main originalities of the model are first related to the explicit description of evolving heterogeneities of the dendritic structures and their consequences on the derivation of averaged conservation equations, where additional terms involving porosity gradients are present, and on the determination of effective transport properties. These average properties are defined by the associated closure problems taking into account the geometry of the dendrites and the local intensity of the flow. The macroscopic solute transport is obtained by considering macroscale non-equilibrium giving rise to macroscopic dispersion and interfacial exchange phenomena. Mass exchange coefficients are accurately explicited as a function of the local geometry. © 2004 SBMAC.