宋彦坡等：基于数值模拟的气液相界面积计算方法 ·1097· B3]Cents A HG,Brilman D W F,Versteeg G F.Gas absorption in 1013 agitated gas-iquid-liquid system.Chem Eng Sci,2001,56(3): (张勤，陈泽敬，李志信.PLC方法在浮法成型模拟中的应 1075 用.工程热物理学报，2010,31(6)：1013) 4]Liang Y C,Zhou Z,Zhang Z B.Interfacial area on valve trays. 02] Liu CL,Wu S Z,Zhang J M,et al.Numerical simulation on Chem Ind Eng,2007,58(5):1232 the surface fluctuation of molten steel in a wide slab continuous (粱银春，周政，张志炳.浮阀塔板气液相界面积.化工学报， casting mold.J Univ Sci Technol Beijing,2009,31 (2):229 2007,58(5):1232) (刘国林，吴苏州，张炯明，等.宽板坯连铸结品器内液面波 5]Danckwerts PV,Lannus A.Gas-iquid reactions.Electrochem 动的数值模拟.北京科技大学学报，2009,31(2)：229) Soc,1970,117(10):369C [13]Maurya R S,Sundararajan T,Das S K.Development of a PLIC- 6]Ma D,Liu M Y,Zu Y G,et al.Two-dimensional volume of fluid -VOF method for the dynamic simulation of entry region flow in a simulation studies on single bubble formation and dynamics in laminar falling film.Int J Comput Fluid Dyn,2009,23 (5): bubble columns.Chem Eng Sci,2012,72(16):61 391 7]Zhang Y J,Liu M Y,Xu Y G,et al.Three-dimensional volume [14]Yang J Y,Jia Y X,Ding YY,et al.Numerical simulation of of fluid simulations on bubble formation and dynamics in bubble mold filling stage in resin transfer molding processes based on columns.Chem Eng Sci,2012,73 (7):55 VOF/PLIC method.Chin J Mater Res,2009,23(6):622 [8]Xu L J,Chen G,Shao J B.Numerical simulation of bubble be- (杨俊英，贾玉玺，丁妍羽，等.基于VOF/PLIC界面追踪方 havior using VOF method.Electr Technol Cir Eng,2011,22 法的RTM工艺充模过程数值模拟.材料研究学报，2009,23 (24):2408 (6):622) 9]Mencinger J,Zun I.A PLIC-VOF method suited for adaptive [15]Ashman D W,Mckelliget J W,Brimacombe J K.Mathematical moving grids.J Comput Phys,2011,230(3):644 model of bubble formation at the tuyeres of a copper converter. [10]Lopez J,Hernandez J,Gomez P,et al.An improved PLIC-VOF Can Metall,1981,20(4):387 method for tracking thin fluid structures in incompressible two- [16]Zhu ZZ.He J Q.Modern Copper Metallurgy.Beijing:Science phase flows.J Comput Phys,2005,208 (1):51 Pres5,2003 [11]Zhang Q.ChenZJ,LiZ X.Application of PLIC method in sim- (朱祖泽，贺家齐.现代铜治金学.北京：科学出版社， ulation of float glass forming.J Eng Thermophys,2010,31(6): 2003)宋彦坡等: 基于数值模拟的气液相界面积计算方法 ［3］ Cents A H G，Brilman D W F，Versteeg G F． Gas absorption in agitated gas-liquid-liquid system． Chem Eng Sci，2001，56 ( 3) : 1075 ［4］ Liang Y C，Zhou Z，Zhang Z B． Interfacial area on valve trays． J Chem Ind Eng，2007，58( 5) : 1232 ( 梁银春，周政，张志炳． 浮阀塔板气液相界面积． 化工学报， 2007，58( 5) : 1232) ［5］ Danckwerts P V，Lannus A． Gas-liquid reactions． J Electrochem Soc，1970，117( 10) : 369C ［6］ Ma D，Liu M Y，Zu Y G，et al． Two-dimensional volume of fluid simulation studies on single bubble formation and dynamics in bubble columns． Chem Eng Sci，2012，72( 16) : 61 ［7］ Zhang Y J，Liu M Y，Xu Y G，et al． Three-dimensional volume of fluid simulations on bubble formation and dynamics in bubble columns． Chem Eng Sci，2012，73( 7) : 55 ［8］ Xu L J，Chen G，Shao J B． Numerical simulation of bubble be￾havior using VOF method． Electr Technol Civ Eng，2011，22 ( 24) : 2408 ［9］ Mencinger J，Zun I． A PLIC-VOF method suited for adaptive moving grids． J Comput Phys，2011，230( 3) : 644 ［10］ Lopez J，Hernandez J，Gomez P，et al． An improved PLIC--VOF method for tracking thin fluid structures in incompressible two￾phase flows． J Comput Phys，2005，208( 1) : 51 ［11］ Zhang Q，Chen Z J，Li Z X． Application of PLIC method in sim￾ulation of float glass forming． J Eng Thermophys，2010，31( 6) : 1013 ( 张勤，陈泽敬，李志信． PLIC 方法在浮法成型模拟中的应 用． 工程热物理学报，2010，31( 6) : 1013) ［12］ Liu G L，Wu S Z，Zhang J M，et al． Numerical simulation on the surface fluctuation of molten steel in a wide slab continuous casting mold． J Univ Sci Technol Beijing，2009，31( 2) : 229 ( 刘国林，吴苏州，张炯明，等． 宽板坯连铸结晶器内液面波 动的数值模拟． 北京科技大学学报，2009，31( 2) : 229) ［13］ Maurya Ｒ S，Sundararajan T，Das S K． Development of a PLIC- -VOF method for the dynamic simulation of entry region flow in a laminar falling film． Int J Comput Fluid Dyn，2009，23 ( 5 ) : 391 ［14］ Yang J Y，Jia Y X，Ding Y Y，et al． Numerical simulation of mold filling stage in resin transfer molding processes based on VOF /PLIC method． Chin J Mater Ｒes，2009，23( 6) : 622 ( 杨俊英，贾玉玺，丁妍羽，等． 基于 VOF /PLIC 界面追踪方 法的 ＲTM 工艺充模过程数值模拟． 材料研究学报，2009，23 ( 6) : 622) ［15］ Ashman D W，Mckelliget J W，Brimacombe J K． Mathematical model of bubble formation at the tuyeres of a copper converter． Can Metall Q，1981，20( 4) : 387 ［16］ Zhu Z Z，He J Q． Modern Copper Metallurgy． Beijing: Science Press，2003 ( 朱祖泽，贺 家 齐． 现 代 铜 冶 金 学． 北 京: 科 学 出 版 社， 2003) · 7901 ·