A 2D1/2 model for natural convection and solidification in a narrow enclosure

Autor: Valéry Botton, L. Hachani, Ahmed Benzaoui, Séverine Millet, R. Boussaa, Yves Fautrelle, I. Hamzaoui, Kader Zaidat, Daniel Henry
Přispěvatelé: 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), 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)
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: International Journal of Thermal Sciences
International Journal of Thermal Sciences, Elsevier, 2019, 140, pp.167-183. ⟨10.1016/j.ijthermalsci.2019.02.028⟩
ISSN: 1290-0729
DOI: 10.1016/j.ijthermalsci.2019.02.028⟩
Popis: 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.
Databáze: OpenAIRE
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