2005
DOI: 10.1002/fld.979
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A reference solution for phase change with convection

Abstract: SUMMARYA reference solutions for phase change involving convection in the melt is currently missing. In the present study, we focus on the problem of melting of pure tin in a square cavity heated from the side, which is used as a benchmark test problem. The mathematical model used for the simulations is based on the enthalpy formulation. Extensive numerical computations are performed with grids as ÿne as 800 × 800. The convergence of the numerical solution is demonstrated and its level assessed. Data values an… Show more

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Cited by 46 publications
(31 citation statements)
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“…The analysis of the past (till very recent) literature on the two-dimensional numerical simulation of this Gau & Viskanta experiment leads to the following significant considerations: i) the multicellular flow structure of the melt convection meets expectations from fluid dynamics (Lee & Korpela [38], Derebail & Koster [17]), and from ad hoc stability analysis of melting from a side (Le Quere & Gobin [39]), ii) the multicellular flow structure of the melt convection appears combined with unphysical wavy shaped phase fronts (Dantzig [14], Stella & Giangi [48], Hannoun et al [27]), iii) certain low order numerical schemes yield one main cell melt flow and produce smoother phase fronts, surprisingly closer to experimental observation (Brent et al [6], Viswanath & Jaluria [55]), iv) some specialists, counting on highly accurate numerical discretizations, have started to explain the inconsistencies by conjecturing that the mathematical models in use for phase change with convection are not adequate for this experiment (Hannoun et al [26], Tenchev et al [51]). …”
Section: Discussionmentioning
confidence: 99%
“…The analysis of the past (till very recent) literature on the two-dimensional numerical simulation of this Gau & Viskanta experiment leads to the following significant considerations: i) the multicellular flow structure of the melt convection meets expectations from fluid dynamics (Lee & Korpela [38], Derebail & Koster [17]), and from ad hoc stability analysis of melting from a side (Le Quere & Gobin [39]), ii) the multicellular flow structure of the melt convection appears combined with unphysical wavy shaped phase fronts (Dantzig [14], Stella & Giangi [48], Hannoun et al [27]), iii) certain low order numerical schemes yield one main cell melt flow and produce smoother phase fronts, surprisingly closer to experimental observation (Brent et al [6], Viswanath & Jaluria [55]), iv) some specialists, counting on highly accurate numerical discretizations, have started to explain the inconsistencies by conjecturing that the mathematical models in use for phase change with convection are not adequate for this experiment (Hannoun et al [26], Tenchev et al [51]). …”
Section: Discussionmentioning
confidence: 99%
“…A Darcy's law type of porous medium treatment is used to account for the effect of phase change on nature convection. The corresponding mathematical model can be found in Hannoun et al's study [17]. Results obtained for the two enclosures are presented together for the purpose of comparison.…”
Section: Numerical Analysismentioning
confidence: 97%
“…The first case is a benchmark problem for melting with natural convection of low-Prandtl-number PCMs. The primary reason for selecting this case is that it has been extensively studied in the literature [87][88][89] and thus provides a quantitative comparison for our numerical methods. The second case involves sodium nitrate subject to alternate melting and solidification controlled by a stepwise-varying boundary temperature.…”
Section: De-fg36-08go18146 Research and Development For Novel Tes Sysmentioning
confidence: 99%