.552 北京科技大学学报 第30卷 0.55 界Rm范围(200~250)一致. 3结论 0.50 (1)羽毛状自然对流与糊状区微通道形成的临 e0.45 界雷诺数为247 (2)微通道内不仅有流体向下流,同时也有流 体向上流.32~40min时间段内,通道宽度为0.76 0.40 通道形成 mm,向上的流体速率为0.086mms1,向下的流体 速率为0.017mms1,在通道出口出的液体速率为 0350 30 4050 60 70 t/min 0.461mms1 (3)微通道形成后,液相区的热流体向下流入 图9糊状区平均固相体积分数 通道内,糊状区内稀冷液体向上流动,向上流的稀 Fig.9 Change of mean solid volume fraction in mushy layer 冷流体有利于热量迁移,向下流的浓热流体有利于 动力学黏度,cm2s1. 溶质迁移,促进液体凝固,微通道内溶液再结晶, 对NH4CI一Hz0溶液,ks/kr≈10-2,故Rr与 (4)糊状区平均固相体积分数先急剧下降,随 s相比很小,可以忽略 着微通道的出现和发展而下降至最小值;而后由于 微通道出现溶液再结晶和凝固的继续,平均固相体积 采用Kozeny-Carman方程计算糊状区渗透率K: 3 分数开始增大;后期随凝固速率的下降又再次减小. K=180(1-e)2 (3) 参考文献 取一个细长锥体代表枝晶,其底部直径即为d. [1]Min N B.Physical Fundamentals of Crystal Growth.Shanghai: Poirier基于一系列实验结果,曾对Kozeny一Carman Shanghai Scientific and Technical Publishers.1982:5. 方程进行了修正,但最终形式很接近,本文与Chen (闵乃本.晶体生长的物理基础.上海:上海科学技术出版社, 的实验条件相同,取e=0.625,d=0.05cm,计算得 1982:5) K=2.41×10-5cm2.其他参数值分别为B= [2]Zhang K C.Zhang L H.Science and Technology of Crystal 0.282,ks=1.12×10-5cm2s-1,v=1.2×10-2 Growth.2nd Ed.Beijing:Science Press,1997:147 (张克从,张乐惠,晶体生长科学与技术.2版北京:科学出版 cm2 s-[5] 社,1997:147) 计算得糊状区当量雷诺数R的变化曲线见图 [3]Rosenberger F,Muller G.Interfacial transport in crystal growth, 10.凝固初期,流动充分发展,R剧增;后期流动趋 a parametric comparison of convective effects.J Cryst Growth, 1983,65:91 于稳定,Rg递增速度变缓,其中,通道出现时(33 [4]Chen C F.Experimental study of convection in a mushy layer min),Rm值为247,这与文献[5]通过实验确定的临 during directional solidification.J Fluid Mech.1995,293:81 360 [5]Chen C F,Chen F.Experimental study of directional solidifica- 340 tion of aqueous ammonium chloride solution.J Fluid Mech, 320 1991,227:567 [6]Tait S,Jaupart C.Compositional convection in a reactive crys 300- talline mush and melt differentiation.Geophys Res.1992.97: 280 6735 260 [7]Worster M G.Natural convection in a mushy layer.J Fluid Mech,1991,224:335 240 [8]Nishimura T.Sasaki J,Htoo T T,et al.The structure of plumes 220 generated in the unidirectional solidification process for a binary 200 通道形成 system.Int J Heat Mass Transfer,2003.46:4489 180 [9]Huppert H E.Hallworth M A.Solidification of NH4Cl and 40 50 60 70 NHiBr from aqueous solutions contaminated by CuSO:the ex- t/min tinction of chimneys.JCryst Growth,1993.130:495 图10糊状区当量雷诺数R变化曲线 [10]Nishimura T,Wakamatsu M.Natural convection suppression and erystal growth during unidirectional solidification of a binary Fig.10 Change of equivalent Reynolds number in mushy layer system.Heat Transfer Asian Res.2000.29(2):120图9 糊状区平均固相体积分数 Fig.9 Change of mean solid volume fraction in mushy layer 动力学黏度cm 2·s -1. 对 NH4Cl-H2O 溶液kS/kT ≈10-2故 RT 与 RS 相比很小可以忽略. 采用 Kozeny-Carman 方程计算糊状区渗透率 K: K= ε3d 2 180(1-ε) 2 (3) 图10 糊状区当量雷诺数 Req变化曲线 Fig.10 Change of equivalent Reynolds number in mushy layer 取一个细长锥体代表枝晶其底部直径即为 d. Poirier 基于一系列实验结果曾对 Kozeny-Carman 方程进行了修正但最终形式很接近.本文与 Chen 的实验条件相同取ε=0∙625d=0∙05cm计算得 K =2∙41×10-5 cm 2.其他参数值分别为 β= 0∙282kS =1∙12×10-5 cm 2·s -1υ=1∙2×10-2 cm 2·s -1[5]. 计算得糊状区当量雷诺数 Req的变化曲线见图 10.凝固初期流动充分发展Req剧增;后期流动趋 于稳定Req递增速度变缓.其中通道出现时(33 min)Req值为247这与文献[5]通过实验确定的临 界 Req范围(200~250)一致. 3 结论 (1) 羽毛状自然对流与糊状区微通道形成的临 界雷诺数为247. (2) 微通道内不仅有流体向下流同时也有流 体向上流.32~40min 时间段内通道宽度为0∙76 mm向上的流体速率为0∙086mm·s -1向下的流体 速率为0∙017mm·s -1在通道出口出的液体速率为 0∙461mm·s -1. (3) 微通道形成后液相区的热流体向下流入 通道内糊状区内稀冷液体向上流动.向上流的稀 冷流体有利于热量迁移向下流的浓热流体有利于 溶质迁移促进液体凝固微通道内溶液再结晶. (4) 糊状区平均固相体积分数先急剧下降随 着微通道的出现和发展而下降至最小值;而后由于 微通道出现溶液再结晶和凝固的继续平均固相体积 分数开始增大;后期随凝固速率的下降又再次减小. 参 考 文 献 [1] Min N B.Physical Fundamentals of Crystal Growth.Shanghai: Shanghai Scientific and Technical Publishers1982:5. (闵乃本.晶体生长的物理基础.上海:上海科学技术出版社 1982:5) [2] Zhang K CZhang L H. Science and Technology of Crystal Growth.2nd Ed.Beijing:Science Press1997:147 (张克从张乐惠.晶体生长科学与技术.2版.北京:科学出版 社1997:147) [3] Rosenberger FMuller G.Interfacial transport in crystal growth a parametric comparison of convective effects.J Cryst Growth 198365:91 [4] Chen C F.Experimental study of convection in a mushy layer during directional solidification.J Fluid Mech1995293:81 [5] Chen C FChen F.Experimental study of directional solidification of aqueous ammonium chloride solution. J Fluid Mech 1991227:567 [6] Tait SJaupart C.Compositional convection in a reactive crystalline mush and melt differentiation.Geophys Res199297: 6735 [7] Worster M G.Natural convection in a mushy layer. J Fluid Mech1991224:335 [8] Nishimura TSasaki JHtoo T Tet al.The structure of plumes generated in the unidirectional solidification process for a binary system.Int J Heat Mass T ransfer200346:4489 [9] Huppert H EHallworth M A.Solidification of NH4Cl and NH4Br from aqueous solutions contaminated by CuSO4:the extinction of chimneys.J Cryst Growth1993130:495 [10] Nishimura TWakamatsu M.Natural convection suppression and crystal growth during unidirectional solidification of a binary system.Heat T ransfer Asian Res200029(2):120 ·552· 北 京 科 技 大 学 学 报 第30卷