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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.

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 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

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.

The purpose of this paper is to present an analysis of the melting process in a rectangular enclosure, driven by the coupling of heat conduction in the solid phase and natural convection in the melt of the phase-change material (PCM). The numerical solution of the problem which is presented here is validated by comparison with precise experimental results. Heat conduction in the solid phase is shown to significantly modify the kinetics of the melting process compared with previous studies on phase change with isothermal solid phase.