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.658 北京科技大学学报 第30卷 过冷度|T©|与初始液相浓度决定.对于纯熔体中 [3]Horvay G,Cahn J W.Dendritic and spheroidal growth.Acta 枝晶的生长，当Sc→oo时，枝晶生长的Peclet数与 Metall,1961,9:695 [4]Emsellem V,Tabeling P.Experimental study of dendritic growth Ivantsov结果相一致： with an external flow.JCryst Growth,1995.156:285 3结论 [5]Emsellem V,Tabeling P.On the role of convection in free den- dritic growth:experimental measurement of the concentration 研究了二元系中枝晶在远场来流作用下的定常 field.JCryst Grotth,1996,166:251 生长，通过应用渐近分析方法获得了温度场、浓度场 [6]Benamar M.Bouissou P.Pelce P.An exact solution for the shape 一致有效的渐近解.在来流作用下枝晶界面形状已 of a erystal growing in a forced flow.JCryst Growth.1988.92: 91 不再是完全的旋转抛物面，而是界面上有细微波动 [7]Ananth R,Gill W N.Self-consistent theory of dendritic growth 的近似抛物面，这些细微波动的具体形态还需在进 with convection.JCryst Growth.1991.108:173 一步求解中得到， [8]Levin P.Quasi-steady "state modeling of dendritic growth.Phys 远场来流的强弱影响枝晶生长的Peclet数，进 Let A,2003.310:383 而影响着枝晶的尖端半径与生长速度.当Sc→∞ [9]Saville D A,Beaghton P J.Growth of needle-shaped crystals in the presence of convection.Phys Rev A.1988.37:3423 时，温度场与浓度场存在相似性解，枝晶生长的 [10]Huang S C.Glicksman M E.Fundamentals of dendritic solidifi- Peclet数为常数.在求解过程中假定表面张力系数 cation:(i)steady-state tip growth:(ii)development of side- 为零，枝晶的尖端半径与生长速度仍没有被唯一确 branch structure.Acta Metall,1981,29:701 定，对于有强加来流的枝晶生长速度的选择性问 [11]Lee Y W.Pattern Formation and Convective Heat Transfer 题，按照界面波理论，需要考虑表面张力系数，在对 during Dendritic Crystal Growth [Dissertation ]New York: Rensselaer Polytechnic Institute,1991 枝晶稳定性分析中确定， [12]Glicksman M E.Lupulescu A 0.Dendritic crystal growth in 参考文献 pure materials.J Cryst Growth.2004.264:541. [13]Lee Y W,Gill W,Ananth R.Forced convection heat transfer [1]Ivantsov G P.Temperature field around a spheroidal.cylindrical during dendritic crystal growth:local solution of Navier Stokes and acicular crystal growing in supercooled melt.Dokl Akad equations.Chem Eng Commun,1992.116:193 Nauk USSR,1947,58(4):567 [14]Xu J.Dynamical Theory of Dendritie Growth in Convective [2]Bouissou P.Pelce P.Effect of a forced flow on dendritic growth Flow.Berlin:Springer,2004 Phys Rev A,1989,40:6673过冷度｜T ∞｜与初始液相浓度决定．对于纯熔体中 枝晶的生长当 SC→∞时枝晶生长的 Peclet 数与 Ivantsov 结果相一致． 3 结论 研究了二元系中枝晶在远场来流作用下的定常 生长通过应用渐近分析方法获得了温度场、浓度场 一致有效的渐近解．在来流作用下枝晶界面形状已 不再是完全的旋转抛物面而是界面上有细微波动 的近似抛物面这些细微波动的具体形态还需在进 一步求解中得到． 远场来流的强弱影响枝晶生长的 Peclet 数进 而影响着枝晶的尖端半径与生长速度．当 SC→∞ 时温度场与浓度场存在相似性解枝晶生长的 Peclet 数为常数．在求解过程中假定表面张力系数 为零枝晶的尖端半径与生长速度仍没有被唯一确 定．对于有强加来流的枝晶生长速度的选择性问 题按照界面波理论需要考虑表面张力系数在对 枝晶稳定性分析中确定． 参 考 文 献 ［1］ Ivantsov G P．Temperature field around a spheroidalcylindrical and acicular crystal growing in supercooled melt． Dokl Akad Nauk USSR194758（4）：567 ［2］ Bouissou PPelce P．Effect of a forced flow on dendritic growth． Phys Rev A198940：6673 ［3］ Horvay GCahn J W．Dendritic and spheroidal growth． Acta Metall19619：695 ［4］ Emsellem VTabeling P．Experimental study of dendritic growth with an external flow．J Cryst Growth1995156：285 ［5］ Emsellem VTabeling P．On the role of convection in free dendritic growth：experimental measurement of the concentration field．J Cryst Growth1996166：251 ［6］ Benamar MBouissou PPelce P．An exact solution for the shape of a crystal growing in a forced flow．J Cryst Growth198892： 97 ［7］ Ananth RGill W N．Self-consistent theory of dendritic growth with convection．J Cryst Growth1991108：173 ［8］ Levin P．Quas-i steady-state modeling of dendritic growth．Phys Lett A2003310：383 ［9］ Saville D ABeaghton P J．Growth of needle-shaped crystals in the presence of convection．Phys Rev A198837：3423 ［10］ Huang S CGlicksman M E．Fundamentals of dendritic solidification：（i） steady-state tip growth；（ii） development of sidebranch structure．Acta Metall198129：701 ［11］ Lee Y W．Pattern Formation and Convective Heat T ransfer during Dendritic Crystal Growth ［Dissertation ］．New York： Rensselaer Polytechnic Institute1991 ［12］ Glicksman M ELupulescu A O．Dendritic crystal growth in pure materials．J Cryst Growth2004264：541． ［13］ Lee Y WGill WAnanth R．Forced convection heat transfer during dendritic crystal growth：local solution of Navier-Stokes equations．Chem Eng Commun1992116：193 ［14］ Xu J J．Dynamical Theory of Dendritic Growth in Convective Flow．Berlin：Springer2004 ·658· 北 京 科 技 大 学 学 报 第30卷