基于VOF方法的大水滴袋状破碎的仿真研究
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摘要
为研究大水滴(d>50μm)运动和袋状破碎的复杂特性,以便于进一步研究大水滴破碎在飞机结冰方面独特的危害性,本文应用VOF(Volume of Fluid)方法对不同韦伯数(Weber number,We数)下的水滴进行数值模拟,观察到了水滴的典型袋状破碎形态,并将袋状破碎划分为五个特征阶段。本文还应用瑞利-泰勒不稳定性(Rayleigh-Taylor Instability,R-T不稳定性)和瑞利-普拉特不稳定性(Rayleigh-Plateau Instability,R-P不稳定性)解释破碎的形态特征。此外,本文统计了水滴的迎风直径、破碎时间和沿程的阻力系数,并与实验数据和本课题组创立的BTB(Bag Type Breakup)理论模型加以对比,验证了破碎时间与形变量、阻力系数的无量纲关系,即形变量在初期与时间呈线性关系,后期为二次函数关系;而破碎时间随着We数增长逐渐减小,水滴阻力系数随形变先迅速增大后减小。本文所用方法可用于进一步的液滴破碎机理研究。
For the purpose of studying the properties of large droplets(d>50μm)in the bag breakup regime and the unique harmfulness of large droplets breakup in aircraft icing process,the VOF method has been introduced to track the gas-liquid interfaces of droplets at different Weber numbers(16-22).The simulation has been conducted with Ohnesorge number of 0.00473 and Reynold numbers of 1662-1948.In this work,the typical deformation and fragmentation processes of large droplets in the bag breakup regime have been observed,and the processes are divided into 5 phases.Furthermore,the morphological characteristics have been analyzed with Rayleigh-Taylor instability and Rayleigh-Plateau instability.In addition,the calculation has been performed regarding the parent drop cross-stream diameter,the drop breakup time,and the drag coefficient.The validation has been carried out for the dimensionless functions representing the relation between breakup time,drop cross-stream diameter,and drag coefficient.The simulation results are in good agreement with the experimental observations and the results of the bag-type breakup theoretical model(BTB theoretical model).It is showed that the VOF method is effective to capture the breakup properties and can be applied in further studying the mechanism of drop atomization.
For the purpose of studying the properties of large droplets(d>50μm)in the bag breakup regime and the unique harmfulness of large droplets breakup in aircraft icing process,the VOF method has been introduced to track the gas-liquid interfaces of droplets at different Weber numbers(16-22).The simulation has been conducted with Ohnesorge number of 0.00473 and Reynold numbers of 1662-1948.In this work,the typical deformation and fragmentation processes of large droplets in the bag breakup regime have been observed,and the processes are divided into 5 phases.Furthermore,the morphological characteristics have been analyzed with Rayleigh-Taylor instability and Rayleigh-Plateau instability.In addition,the calculation has been performed regarding the parent drop cross-stream diameter,the drop breakup time,and the drag coefficient.The validation has been carried out for the dimensionless functions representing the relation between breakup time,drop cross-stream diameter,and drag coefficient.The simulation results are in good agreement with the experimental observations and the results of the bag-type breakup theoretical model(BTB theoretical model).It is showed that the VOF method is effective to capture the breakup properties and can be applied in further studying the mechanism of drop atomization.
引文
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[14] Wang C,Chang S,Wu H,et al.Theoretical modeling of spray drop deformation and breakup in the multimode regime[J].Atomization and Sprays,2014,25(10):857-869.
[15] Wright W B,Potapczuk M G.Semi-empirical modelling of SLD physics[R].AIAA,2004-412.
[16]Gordon G D.Mechanism and speed of breakup of drops[J].Journal of Applied Physics,1959,30(11):1759-1761.
[17]O’Rourke P J,Amsden A A.The TAB method for numerical calculation of spary droplet breakup[R].SAE 1987,87209.
[18]Jain M,Prakash R S,Tomar G,et al.Secondary breakup of a drop at moderate Weber numbers[C]//Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences:The Royal Society,2015,471(2177):20140930.
[19]Van Doormaal J P,Raithby G D.Enhancements of the simple method for predicting incompressible fluid flows[J].Numerical Heat Transfer Applications,1984,7(2):147-163.
[20]Chandrasekhar S.Hydrodynamic and hydromagnetic stability[J].Physics Today,1961,15(15):109-154.
[21]Joseph D D,Belanger J,Beavers G S.Breakup of a liquid drop suddenly exposed to a high-speed airstream[J].International Journal of Multiphase Flow,1999,25(6-7):1263-1303.
[22]Joseph D D,Beavers G S,Funada T.Rayleigh-Taylor instability of viscoelastic drops at high Weber numbers[J].Journal of Fluid Mechanics,1999,453(6):109-132.
[23]Ng C L,Sankarakrishnan R,Sallam K A.Bag breakup of nonturbulent liquid jets in crossflow[J].International Journal of Multiphase Flow,2008,34(3):241-259.
[24]Pilch M,Erdman C A.Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop[J].International Journal of Multiphase Flow,1987,13(6):741-757.
[2] Hinze J.Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes[J].Aiche Journal,1955,1(3):289-295.
[3] Krzeczkowski S A.Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes[J].Multiphase Flow,1980,6(3):227-239.
[4] Chou W H,Faeth G.Temporal properties of secondary drop breakup in the bag breakup regime[J].Multiphase Flow,1998,24(6):889-912.
[5] Rimbert N,Castanet G.Crossover between Rayleigh-Taylor instability and turbulent cascading atomization mechanism in the bag-breakup regime[J].Phys Rev E,2011,84(1):016318.
[6] Guildenbecher D,Lopez-Rivera C,Sojka P.Secondary atomization[J].Exp Fluids,2009,46:371-402.
[7] Zaleski S,Li J,Succi S.Two-dimensional Navier-Stokes simulation of deformation and breakup of liquid patches[J].Phys Rev Lett,1995,75(2):244-247.
[8] Desjardins O,McCaslin J O,Owkes M,et al.Direct numerical and large-eddy simulation of primary atomization in complex geometries[J].Atomization Sprays,2013,23(11):1001-1048.
[9] Lebas R,Menard T,Beau P,et al.Numerical simulation of primary break-up and atomization:DNS and modelling study[J].Multiphase Flow,2009,35(3):247-260.
[10]Sander W,Weigand B.Direct numerical simulation and analysis of instability enhancing parameters in liquid sheets at moderate Reynolds numbers[J].Phys Fluids,2008,20(5):053301-053308.
[11] Hu J P,Liu Z X,Zhang L F.Supercooled large droplet impact behaviors on an aero-engine strut[J].Acta Aeronautica ET Astronautica Sinica,2011,32(10):1778-1785.(in Chinese)胡剑平,刘振侠,张丽芬.发动机整流支板大尺寸过冷水滴撞击特性[J].航空学报,2011,32(10):1778-1785.
[12]Luo H,Kong W L,Liu H.The influence of SLD crushing effect on parallel study[J].Mechanics Quarterly Publication,2011,32(4):597-604.罗辉,孔维梁,刘洪.SLD破碎效应对并行的影响研究[J].力学季刊,2011,32(4):597-604.
[13] Wang C,Chang S,Wu H,et al.Modeling of drop breakup in the bag breakup regime[J].Applied Physics Letters,2014,104(15):154-107.
[14] Wang C,Chang S,Wu H,et al.Theoretical modeling of spray drop deformation and breakup in the multimode regime[J].Atomization and Sprays,2014,25(10):857-869.
[15] Wright W B,Potapczuk M G.Semi-empirical modelling of SLD physics[R].AIAA,2004-412.
[16]Gordon G D.Mechanism and speed of breakup of drops[J].Journal of Applied Physics,1959,30(11):1759-1761.
[17]O’Rourke P J,Amsden A A.The TAB method for numerical calculation of spary droplet breakup[R].SAE 1987,87209.
[18]Jain M,Prakash R S,Tomar G,et al.Secondary breakup of a drop at moderate Weber numbers[C]//Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences:The Royal Society,2015,471(2177):20140930.
[19]Van Doormaal J P,Raithby G D.Enhancements of the simple method for predicting incompressible fluid flows[J].Numerical Heat Transfer Applications,1984,7(2):147-163.
[20]Chandrasekhar S.Hydrodynamic and hydromagnetic stability[J].Physics Today,1961,15(15):109-154.
[21]Joseph D D,Belanger J,Beavers G S.Breakup of a liquid drop suddenly exposed to a high-speed airstream[J].International Journal of Multiphase Flow,1999,25(6-7):1263-1303.
[22]Joseph D D,Beavers G S,Funada T.Rayleigh-Taylor instability of viscoelastic drops at high Weber numbers[J].Journal of Fluid Mechanics,1999,453(6):109-132.
[23]Ng C L,Sankarakrishnan R,Sallam K A.Bag breakup of nonturbulent liquid jets in crossflow[J].International Journal of Multiphase Flow,2008,34(3):241-259.
[24]Pilch M,Erdman C A.Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop[J].International Journal of Multiphase Flow,1987,13(6):741-757.