高气液密度比的传热相变复合模型
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摘要
为研究两相流动中热量传递机制,基于格子Boltzmann热模型及大密度比模型,将相变源项引入到控制两相密度分布函数中,来描述温度场对气液相变的影响,提出了一个可以描述气液密度比达到2778的传热相变复合模型。通过对压力速度分布函数的回归修正克服了气液密度比过大造成的数值不稳定问题。模拟了溴化锂水溶液中双气泡的上升运动过程及周围的温度场分布,研究发现:双气泡上升时,碰撞前上方气泡温度高于下方气泡,碰撞时,两气泡间液桥打开,发生热量传递,气泡内部温度变得均匀;双气泡体积先减小再增大,碰撞时体积达到最大值,在融合成一个气泡后体积逐渐缩小,最终趋于稳定;初始气泡的体积越大,气泡上升过程中的速度越大。
Based on lattice Boltzmann thermal model and large density ratio model, a phase transition source term was introduced into two-phase density distribution control function to describe effect of temperature field on gasliquid phase transition. A composite lattice Boltzmann thermal model, which can describe heat transfer and phase transition at gas-liquid ratio up to 2778, was proposed to study two-phase heat transfer mechanism. Numerical instability caused by extremely large gas-liquid density ratio was resolved by regress correction of pressure velocity distribution function. Double bubble rising movement and the surrounding temperature field distribution in lithium bromide solution was simulated using the model. Upper bubble temperature was higher than that of lower bubble prior to collision during moving up. Upon coalescence, liquid bridge between the two bubbles was open, heat transfer started and temperature inside the bubble became uniform. The volume of the double bubbles decreased first and then increased with maximum at time of two bubbles collision. After bubble coalescence, the volume gradually decreased and eventually stabilized to certain value. The larger the initial bubble volume is, the greater the velocity of the bubble rises.
Based on lattice Boltzmann thermal model and large density ratio model, a phase transition source term was introduced into two-phase density distribution control function to describe effect of temperature field on gasliquid phase transition. A composite lattice Boltzmann thermal model, which can describe heat transfer and phase transition at gas-liquid ratio up to 2778, was proposed to study two-phase heat transfer mechanism. Numerical instability caused by extremely large gas-liquid density ratio was resolved by regress correction of pressure velocity distribution function. Double bubble rising movement and the surrounding temperature field distribution in lithium bromide solution was simulated using the model. Upper bubble temperature was higher than that of lower bubble prior to collision during moving up. Upon coalescence, liquid bridge between the two bubbles was open, heat transfer started and temperature inside the bubble became uniform. The volume of the double bubbles decreased first and then increased with maximum at time of two bubbles collision. After bubble coalescence, the volume gradually decreased and eventually stabilized to certain value. The larger the initial bubble volume is, the greater the velocity of the bubble rises.
引文
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[29]王佐,张家忠,王恒.非正交多松弛系数轴对称热格子Boltzmann方法[J].物理学报,2017,66(4):156-168.WANG Z,ZHANG J Z,WANG H.Non-orthogonal multiple-relaxation time lattice Boltzmann method for axisymmetric thermal flows[J].Acta Phys.Sin.,2017,66(4):156-168.
[30]INAMURO T,YOSHINO M,INOUE H,et al.A lattice Boltzmann method for a binary miscible fluid mixture and its application to a heattransfer problem[J].Journal of Computational Physics,2002,179(1):201-215.
[31]CHORIN A J.Numerical solution of the Navier-Stokes equations[J].Math.Comput.,1968,22(104):745-762.
[2]KHESTANOVA E,GUINEA F,FUMAGALLI L,et al.Universal shape and pressure inside bubbles appearing in van der Waals heterostructures[J].Nature Communications,2016,7:12587.
[3]吴迎亚,彭丽,高金森,等.基于EMMS模型的气固鼓泡床的模拟及气泡特性的分析[J].化工学报,2016,67(8):3259-3267.WU Y Y,PENG L,GAO J S,et al.Numerical simulation of gas-solid bubbling bed and bubble characteristics based on EMMS drag model[J].CIESC Journal,2016,67(8):3259-3267.
[4]吕雅琪,聂德明,林建忠.三维双气泡融合的格子Boltzmann模拟[J].计算物理,2015,(5):553-560.LüY Q,NIE D M,LIN J Z.Lattice Boltzmann simulation of gas bubble merging in three dimensions[J].Chinese Journal of Computational Physics,2015,(5):553-560.
[5]WANG Y,CAI J,LI Q,et al.Diffuse interface simulation of bubble rising process:a comparison of adaptive mesh refinement and arbitrary Lagrange-Euler methods[J].Heat&Mass Transfer,2018,54(6):1767-1778.
[6]ROUDET M,BILLE A,CAZIN S,et al.Experimental investigation of interfacial mass transfer mechanisms for a confined high-Reynolds number bubble rising in a thin gap[J].AICh E Journal,2017,63(6):2394-2408.
[7]HUANG J,SAITO T.Discussion about the differences in mass transfer,bubble motion and surrounding liquid motion between a contaminated system and a clean system based on consideration of three-dimensional wake structure obtained from LIF visualization[J].Chemical Engineering Science,2017,170:105-115.
[8]GUNSTENSEN A K,ROTHMAN D H,ZALESKI S,et al.Lattice Boltzmann model of immiscible fluids[J].Physical Review A,1991,43(8):4320-4327.
[9]SHAN X,CHEN H.Lattice Boltzmann model for simulating flows with multiple phases and components[J].Physical Review E Statistical Physics Plasmas Fluids&Related Interdisciplinary Topics,1993,47(3):1815-1819.
[10]QIAN Y H,CHEN S Y.Finite size effect in lattice-BGK model[J].International Journal of Modern Physics C,1997,8(4):763-771.
[11]SWIFT M,OBSBOME W,YEOMANS J.Lattice Boltzmann simulation of nonideal fluids[J].Physical Review Letter,1995,75(5):830-833.
[12]HE X Y,SHAN X W,DOOLEN G D.Discrete Boltzmann equation model for nonideal gases[J].Physical Review E,1998,57(1):13-16.
[13]GUO Z L,ZHAO T S.Discrete velocity and lattice Boltzmann models for binary mixtures of nonideal fluids[J].Physical Review E,2003,68(3):035302-035312.
[14]张潇丹,雍玉梅,李文军,等.REV尺度多孔介质格子Boltzmann方法的数学模型及应用的研究进展[J].化工进展,2016,35(6):1698-1712.ZHANG X D,YONG Y M,LI W J,et al.Models and application of lattice Boltzmann method at REV-scale in porous media[J].Chemical Industry and Engineering Progress,2016,35(6):1698-1712.
[15]TENG S,CHEN Y,OHASHI H.Lattice Boltzmann simulation of multiphase fluid flows through the total variation diminishing artificial compression scheme[J].International Journal of Heat and Fluid Flow,2000,21(1):112-121.
[16]WERZNER X,MIGUEL A,MENDES A,et al.Numerical investigation on the depth filtration of liquid metals:influence of process conditions and inclusion properties[J].Advanced Engineering Materials,2015,15(12):1037-1314.
[17]LEE T,LIN C L.A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio[J].Journal of Computational Physics,2005,206(1):16-47.
[18]INAMURO T,OGATA T,TAJIMA S,et al.A lattice Boltzmann method for incompressible two-phase flows with large density differences[J].Journal of Computational Physics,2004,198(2):628-644.
[19]KATAOKA T,TSUTAHARA M.Lattice Boltzmann model for the compressible Navier-Stokes equations with flexible specific-heat ratio[J].Physical Review E,2004,69(2):035701.
[20]孙涛,李维仲,杨柏丞,等.气泡群上升过程相互作用的格子Boltzmann三维数值模拟[J].化工学报,2013,64(5):1586-1591.SUN T,LI W Z,YANG B C,et al.Three-dimensional numerical simulation of multiple bubbles rising and interaction with lattice Boltzmann method[J].CIESC Journal,2013,64(5):1586-1591.
[21]CHEN H N,SUN D K,DAI T,et al.Modeling of the interaction between solidification interface and bubble using the lattice Boltzmann method with large density ratio[J].Acta Phys.Sin.,2013,62(12):120502.
[22]ALEXANDER F J,CHEN S,STERLING J D.Lattice Boltzmann thermohydrodynamics[J].Physical Review E Statistical Physics Plasmas Fluids&Related Interdisciplinary Topics,1993,47(4):R2249.
[23]QIAN Y H.Simulating thermohydrodynamics with lattice BGK models[J].Journal of Scientific Computing,1993,8(3):231-242.
[24]CHEN Y,OHASHI H,AKIYAMA M.Two-parameter thermal lattice BGK model with a controllable Prandtl number[J].Journal of Scientific Computing,1997,12(2):169-185.
[25]BARTOLONI A,BATTISTA C,CABASINO S,et al.Lbe simulations of Rayleigh-Bénard convection on the ape100 parallel processor[J].International Journal of Modern Physics C,2011,4(5):993-1006.
[26]SHAN X.Simulation of Rayleigh-Bénard convection using lattice Boltzmann method[J].Physical Review E Statistical Physics Plasmas Fluids&Related Interdisciplinary Topics,1998,55(3):2780-2788.
[27]PALMER B J,RECTOR D R.Lattice-Boltzmann algorithm for simulating thermal two-phase flow[J].Phys.Rev.E Stat.Phys.Plasmas Fluids Relat.Interdiscip.Topics,2000,61(5A):5295-5306.
[28]GUO Z,SHI B,ZHENG C.A coupled lattice BGK model for the Boussinesq equations[J].International Journal for Numerical Methods in Fluids,2002,39(4):325-342.
[29]王佐,张家忠,王恒.非正交多松弛系数轴对称热格子Boltzmann方法[J].物理学报,2017,66(4):156-168.WANG Z,ZHANG J Z,WANG H.Non-orthogonal multiple-relaxation time lattice Boltzmann method for axisymmetric thermal flows[J].Acta Phys.Sin.,2017,66(4):156-168.
[30]INAMURO T,YOSHINO M,INOUE H,et al.A lattice Boltzmann method for a binary miscible fluid mixture and its application to a heattransfer problem[J].Journal of Computational Physics,2002,179(1):201-215.
[31]CHORIN A J.Numerical solution of the Navier-Stokes equations[J].Math.Comput.,1968,22(104):745-762.