Dominique Gobin

Momentum transport at a fluid-porous interface.

Abstract 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.

Melting driven by natural convection A comparison exercise: first results

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

Moving boundary problem: heat conduction in the solid phase of a phase-change material during melting driven by natural convection in the liquid

Abstract 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.

Average momentum equation for interdendritic flow in a solidifying columnar mushy zone

Abstract 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.

Stability of Natural Convection in Superposed Fluid and Porous Layers Using Integral Transforms

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.

Natural convection in porous media—dual reciprocity boundary element method solution of the Darcy model

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

Dual reciprocity boundary element method solution of natural convection in Darcy -Brinkman porous media

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.

Transient Double Diffusive Convection in a Vertical Enclosure With Asymmetrical Boundary Conditions

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

Passive dispersion in dendritic structures

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.

Heat Diffusion in Solidifying Alumina Splat Deposited on Solid Substrate under Plasma Sprayed Conditions: Application to Coating Formation

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.