1. A 2D1/2 model for natural convection and solidification in a narrow enclosure
- Author
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Valéry Botton, L. Hachani, Ahmed Benzaoui, Séverine Millet, R. Boussaa, Yves Fautrelle, I. Hamzaoui, Kader Zaidat, Daniel Henry, Laboratoire de Thermodynamique et des Systèmes Energétiques, Université des Sciences et de la Technologie Houari Boumediene [Alger] (USTHB), INSA Euro-Méditerranée, Institut National des Sciences Appliquées (INSA), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA), Laboratoire de Mecanique des Fluides et d'Acoustique (LMFA), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Physique des Matériaux (LPM), Université Amar Telidji - Laghouat, Science et Ingénierie des Matériaux et Procédés (SIMaP ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Laboratoire d'Etudes des Transferts d'Energie et de Matière (LETEM), Université Paris-Est Marne-la-Vallée (UPEM), Université Amar Telidji - Laghouat (ALGERIA), Science et Ingénierie des Matériaux et Procédés (SIMaP), and Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)
- Subjects
Physics ,Natural convection ,[PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph] ,020209 energy ,Thermal resistance ,Prandtl number ,General Engineering ,Grashof number ,02 engineering and technology ,Mechanics ,Parameter space ,Condensed Matter Physics ,Boundary layer thickness ,Hagen–Poiseuille equation ,01 natural sciences ,010305 fluids & plasmas ,Physics::Fluid Dynamics ,symbols.namesake ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Boundary value problem ,[PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] ,ComputingMilieux_MISCELLANEOUS - Abstract
Efficient numerical models are derived for problems of natural convection and material solidification in a horizontal differentially heated slender cavity. These 2D1/2 models are obtained by averaging the equations of momentum, heat, and mass conservation along the transverse direction assuming both a constant temperature and a well defined velocity profile in this direction. Based on our former works, the transverse velocity profile is assumed to be either a Poiseuille profile ( 2 D p 1 / 2 model), or Hartmann-type profiles featuring two boundary layers on the sides of a uniform bulk ( 2 D H 1 / 2 model). For this 2 D H 1 / 2 model, however, a parameter δ (giving the boundary layer thickness) has to be adjusted: optimal values have been found in a large range of the control parameters and expressed as a reliable fitted function of G r . The ability of the model to reproduce 3D results in a 2D framework is investigated in a large range of the control parameters (Prandtl number P r and Grashof number G r ); the validity domain of the model in this parameter space is also clarified and rigorously defined. A good precision is obtained for natural convection problems (intensity of the flow, temperature field) as well as for solid-liquid phase change problems (shape, position, and evolution of the front). A comparison with unpublished experimental data of solidification of pure tin is also conducted. The boundary conditions for the simulation are first defined after a post-treatment of the time-dependent experimental data in order for them to be representative of the experimental process despite a significant and time dependent thermal resistance between the walls of the crucible and the liquid. A very good agreement is observed between the 2 D H 1 / 2 model and the experimental measurements for this pure tin solidification experiment in the AFRODITE setup.
- Published
- 2019