Marangoni效应下气泡上升过程的FTM模拟
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摘要
采用界面跟踪法FTM(Front-Tracking Method),并结合CSF(continuum surface force)模型,研究了在垂直方向上温度分布不均匀的对称流场中由Marangoni效应引起的气泡上升运动问题。模拟了在不同的M a数和Pr数下单气泡及同轴双气泡的运动。研究结果表明,在不同的M a数下气泡的运动差异较大,M a数越大,气泡运动至稳态时的速度越大,且气泡运动的最大速度值与M a数呈正相关关系;增大Pr数所造成的粘度增大或热扩散率减小将削弱气泡的迁移运动;Marangoni对流中双气泡的局部运动证实了温度梯度和气泡运动速度紧密相关。
Using front tracking method combined with the continuum surface force model,the bubble rising motion caused by the Marangoni effect in the symmetric flow field with non-uniform temperature distribution in the vertical direction was studied.The motion of a single bubble and a coaxial double bubble under different Ma and Pr numbers were simulated.The results show that the motion of bubbles is different under different Ma numbers.The larger the Ma number,the faster the bubble moves to a steady state,and there is a positive correlation between the maximum velocity of bubble motion and the Ma number;increasing the viscosity or decreasing the thermal diffusivity caused by increasing the Pr number will weaken the migration motion of the bubble;the local motion of the double bubbles in the Marangoni convection confirms that the temperature gradient is closely related to the bubble motion velocity.
Using front tracking method combined with the continuum surface force model,the bubble rising motion caused by the Marangoni effect in the symmetric flow field with non-uniform temperature distribution in the vertical direction was studied.The motion of a single bubble and a coaxial double bubble under different Ma and Pr numbers were simulated.The results show that the motion of bubbles is different under different Ma numbers.The larger the Ma number,the faster the bubble moves to a steady state,and there is a positive correlation between the maximum velocity of bubble motion and the Ma number;increasing the viscosity or decreasing the thermal diffusivity caused by increasing the Pr number will weaken the migration motion of the bubble;the local motion of the double bubbles in the Marangoni convection confirms that the temperature gradient is closely related to the bubble motion velocity.
引文
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[3] 张锋,耿皎,马少玲,等.Marangoni效应对降膜加热流动的影响[J].化工学报,2005,56(9):1606-1611.(ZHANG Feng,GENG Jiao,MA Shao -ling,et al.Influence of Marangoni effect on heated falling films[J].CIESC Journal,2005,56(9):1606-1611.(in Chinese))
[4] 王松岭,李春曦,叶学民.温度和活性剂浓度梯度协同驱动的液滴铺展特性[J].化工学报,2011,62(9):2512-2519.(WANG Song-ling,LI Chun-xi,YE Xue -min.Drop spreading characteristics driven by gradients of temperature and surfactant concentration[J].CIESC Journal,2011,62(9):2512-2519.(in Chinese))
[5] 沙勇,李樟云,江桂仙,等.竖直流动皂膜中解吸导致的Marangoni对流观察[J].化工学报,2010,61(5):1123-1126.(SHA Yong,LI Zhang-yun,JIANG Gui-xian,et al.Observation on Marangoni convection induced by desorption in falling soap film[J].CIESC Journal,2010,61(5):1123-1126.(in Chinese))
[6] 周乐平,李媛园,魏龙亭,等.自润湿液体过冷核态沸腾射液流现象分析[J].化工学报,2014,65(s1):79-84.(ZHOU Le -ping,LI Yuan-yuan,WEI Long-ting,et al.Jet flow phenomenon during subcooled nucleate boiling of self-rewetting fluid[J].CIESC Journal,2014,65(s1):79-84.(in Chinese))
[7] 汪洋,陈杰,王智慧,等.多相传质过程中的Marangoni效应[J].化工学报,2013,64(1):124-132.(WANG Yang,CHEN Jie,WANG Zhi-hui,et al.Marangoni effect accompanying mass transfer processes in multiphase systems[J].CIESC Journal,2013,64(1):124-132.(in Chinese))
[8] 沙勇,成弘,袁希钢,等.伴有Marangoni效应的传质动力学[J].化工学报,2003,54(11):1518-1523.(SHA Yong,CHENG Hong,YUAN Xi-gang,et al.Kinetics of mass transfer accompanied by Marangoni effect[J].CIESC Journal,2003,54(11):1518-1523.(in Chinese))
[9] Treuner M,Galindo V,Gerbeth G,et al.Thermocapi-llary bubble migration at high Reynolds and Marangoni numbers under low gravity[J].Journal of Colloid and Interface Science,1996,179:114-127.
[10] Bozzano G,Dente M.Single bubble and drop motion modeling[J].Chemical Engineering Transactions,2009,17:60-66.
[11] Charoensawan P,Khandekar S,Groll M,et al.Closed loop pulsating heat pipes.Part A:Parametric experimental investigations[J].Applied Thermal Engineering,2003,23(16):2009-2020.
[12] Wu Z B.Terminal states of thermocapillary migration of a planar droplet at moderate and large Marangoni numbers[J].International Journal of Heat and Mass Transfer,2017,105:704-711.
[13] Yin Z H,Li Q H.Thermocapillary migration and interaction of drops:Two non-merging drops in an aligned arrangement[J].Journal of Fluid Mecha-nics,2015,766:436-467.
[14] Xie H Q,Zeng Z,Zhang L Q,et al.Simulation on thermocapillary-driven drop coalescence by hybrid lattice Boltzmann method[J].Microgravity Science and Technology,2016,28(1):67-77.
[15] Brackbill J U,Kothe D B,Zemach C.A continuum method for modeling surface tension[J].Journal of Computational Physics,1992,100(2):335-354.
[16] Ma M,Lu J C,Tryggvason G.Using statistical lear-ning to close two-fluid multiphase flow equations for a simple bubbly system[J].Physics of Fluids,2015,27(9):97-110.
[17] Ma M,Lu J C,Tryggvason G.Using statistical lear-ning to close two-fluid multiphase flow equations for bubbly flows in vertical channels[J].International Journal of Multiphase Flow,2016,85:336-347.
[18] Lieutenant Commer H H,Curry U S Coast Guard.On-board experimental study of bubble thermocapi-llary migration in a recoverable satellite[J].Microgravity Science and Technology,2008,20(2):67-71.
[19] Alhendal Y,Turan A,Hollingsworth P.Thermocapillary simulation of single bubble dynamics in zero gravity[J].Acta Astronautica,2013,88(88):108-115.
[20] Subramanian R S,Balasubramaniam R,Wozniak G.Fluid mechanics of bubbles and drops[J].Physics of Fluids in Microgravity,2002:149-177.
[21] Young N O,Goldstein J S,Block M J.The motion of bubbles in a vertical temperature gradient[J].Journal of Fluid Mechanics,1959,6(3):350-356.