Interaction of Interdendritic Convection and Dendritic Primary Spacing: Phase-Field Simulation and Analytical Modeling
Interaction of Interdendritic Convection and Dendritic Primary Spacing: Phase-Field Simulation and Analytical Modeling
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DOI：
10.4028/www.scientific.net/msf.508.145
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发表时间：
2006-01
期刊：
影响因子：
--
通讯作者：
H. Diepers;I. Steinbach
中科院分区：
文献类型：
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作者：
H. Diepers;I. Steinbach
定向凝固的实验研究表明，枝晶初生间距λ取决于重力水平。尽管主要的理论和实践兴趣，目前的模型未能预测枝晶间流动和间距选择之间的相互依赖关系。我们推导出a）描述这种依赖关系的标度关系为λ λ0 <$Ra −1/8 0，其中λ0是无流的间距，瑞利数Ra 0基于λ0。这个关系符合实验数据。我们通过B）与流体流动相耦合的枝晶演化的相场模拟来更详细地研究这种相互依赖性。我们的模型匹配的流动和微观结构形成的相关自由边界条件。初步的数值计算结果表明，在AlCu 4中，流动模式和微观结构关键取决于g的方向：与生长方向相反的浮力使流动模式几乎保持在枝晶间，λ增加。生长方向上的浮力形成羽流，与固体演化不稳定地相互作用，λ减小。
Experimental work on directional solidification has shown, that the dendrite primary spacing λ depends on the gravity level. Despite the major theoretical and practial interests present models fail to predict the interdependence between interdendritic flow and spacing selection. We derive a) a scaling relation describing this dependence as λ λ0 ∼ Ra −1/8 0 , where λ0 is the spacing without flow and the Rayleigh number Ra0 bases on λ0. This relation fits in experimental data. We study this interdependence in more detail by b) phase-field modeling of the dendrite evolution coupled to fluid flow. Our model matches the relevant free boundary conditions for flow and microstructure formation. Preliminary numerical results in AlCu4 show, that flow pattern and microstructure crucially depend on the direction of g: buoyancy opposed to growth direction keeps the flow pattern almost interdendritic and λ increases. Buoyancy in growth direction forms plumes instably interacting with solid evolution and λ decreases.