Christine Bénard

Melting in Rectangular Enclosures: Experiments and Numerical Simulations

This paper presents a numerical and experimental analysis of the heat transfer process that takes place while melting a solid material, in a rectangular enclosure. Natural convection is present in the melt layer, and the solid phase is assumed to be isothermal. Very detailed and precise experimental results are given that are used to validate a particularly rapid numerical code. Some insights into the kinetics of the melting process lead to a deeper understanding of the coupling between convection and phase change and allow us to propose a simple algebraic correlation that predicts the time evolution of the melting front to within 5 percent.

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.

Wavy secondary instability of longitudinal rolls in Rayleigh–Bénard–Poiseuille flows

An experimental investigation of the stability of longitudinal rolls in a horizontal layer heated from below in the presence of a Poiseuille flow is carried out. This study follows on from the theoretical work of Clever & Busse ( J. Fluid Mech. , vol. 229, 1991, p. 517) who detected a wavy instability for a range of relatively low Rayleigh and Reynolds numbers depending on the Prandtl number. In the present study, an air flow is circulating in a rectangular channel of transverse aspect ratio 10 for Rayleigh numbers of 6300 and 9000 and Reynolds numbers from 100 to 174. The system exhibits a wavy pattern only if the flow is continuously excited. The amplitude of the waves grows as they propagate downstream and the frequency of the oscillations is equal to the frequency of the imposed disturbance. The bifurcation from steady longitudinal rolls to unsteady wavy rolls is thus a convective instability. A mode by mode study is performed by measuring the wave velocity and the spatial growth of the instability along the channel for a large range of the imposed frequency. The phase velocity is found to depend only on the Reynolds number, and is nearly equal to the bulk velocity of the flow for all the modes in the range of parameters under study. The maximum spatial growth rate corresponding to the most unstable mode as well as the corresponding frequency decrease with decreasing Reynolds number or Rayleigh number, providing a decrease in the wavelength. This feature is in agreement with the theoretical results of Clever & Busse (1991).

Ice Block Melting Into a Binary Solution: Coupling of the Interfacial Equilibrium and the Flow Structures

Melting of a vertical ice block in a cavity filled with an aqueous solution is studied experimentally. Local interfacial temperatures and front velocities are measured allowing for a quantitative study of the coupling of the fluid motion, thermal equilibrium and the local heat transfers at the melting front. It is found that the front equilibrium shift is correlated to the classical parameter of the phase change process, that is the Stefan number, while the local heat transfer at the interface is correlated to the parameters characterizing thermosolutal natural convection. Quantitative results about the time evolution of the double-diffusive multi-layers structure in the fluid phase are obtained. The formation of the first thermosolutal layer is analyzed with the help of numerical simulations. It is found that the mechanism responsible for the onset of this layer is due to a well known double-diffusive instability.

Linear Stability Analysis for the Wall Temperature Feedback Control of Planar Poiseuille Flows

Active control of a planar Poiseuille flow can be performed by increasing or decreasing the wall temperature in proportion to the observed wall shear stress perturbation. In continuation with the work of H. H. Hu and H. H. Bau (1994, Feedback Control to Delay or Advance Linear Loss of Stability in Planar Poiseuille Flow, Proc. R. Soc. London A, 447, pp. 299-312), a linear stability analysis of such a feedback control is developed in this paper The Poiseuille flow control problem is reduced to a modified Orr-Sommerfeld equation coupled with a heat equation. By solving numerically the coupled equations with a finite element method, many numerical results about the stability of the flow control are obtained. We focus our attention on the interpretation of the numerical results. In particular, the role of two essential parameters-the Prandtl number Pr and the control gain K-is investigated in detail. When Pr>1.31, stabilizing K is negative; while, when Pr <1.31, stabilizing K is positive. And when Pr =1.31, the flow cannot be stabilized by a real K. A comparison between symmetric two-wall control and non-symmetric one-wall control is also made.

Experimental Study of Heat and Mass Transfers at the Interface of Solidification of a Binary Solution

This paper deals with the experimental analysis of the influence of thermohaline natural convection on phase change liquid-solid of multicomponent mixtures. We present solidification experiments (dendritic front) from a horizontal plane heat exchanger placed in a cavity filled with a binary NH4 Cl-H2 O mixture. The solid grows simultaneously on the upper and lower faces of the exchanger and permits the study of two simultaneous configurations. We qualitatively study phenomena met in the presence of thermohaline convection in the liquid phase (cooling from the top) and we analyze in detail the case of the growth without convective movement in the liquid phase (cooling from the bottom). Thus, coupled effects of salt rejection and solid fraction on the front kinetics are examined by measurements of the front temperature and solid fraction. A simple model confirms the weak role played by these two phenomena for the range of characteristic parameters studied. Two conflicting effects of the solid fraction are nevertheless put in evidence.Copyright