倾斜壁面中Kelvin-Helmholtz不稳定性演化数值分析
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摘要
基于FTM(Front Tracking Method)对倾斜壁面下的二维不混溶、不可压缩流体的Kelvin-Helmholtz(K-H)不稳定性进行数值模拟.研究壁面倾角,速度梯度层厚度以及理查德森数对K-H不稳定性发展的影响.研究表明,壁面倾角越大,K-H不稳定性发展越快,卷起的液体越多;倾斜壁面下速度梯度层厚度的增加对界面卷起表现出抑制作用.理查德森数重力项越大,界面卷起越缓慢,而理查德森数表面张力项对界面卷起高度的影响较小.
Kelvin-Helmholtz instability of two-dimensional immiscible incompressible fluid in a sloping tube was numerically simulated with front tracking method. Effects of inclined angles of wall, thickness of velocity gradient layer and Richardson number on development of K-H instability were investigated. It shows that the greater the angle of wall inclination is, the faster the K-H instability develops and the more liquid is rolled up. It was also found that increase of thickness of the velocity gradient layer under the inclined wall presented an inhibitory effect on roll-up of the interface. The greater gravity items of Richardson number is, the slower the interface rolls up. However, surface tension items of Richardson number have weak effect on the growth of interface.
Kelvin-Helmholtz instability of two-dimensional immiscible incompressible fluid in a sloping tube was numerically simulated with front tracking method. Effects of inclined angles of wall, thickness of velocity gradient layer and Richardson number on development of K-H instability were investigated. It shows that the greater the angle of wall inclination is, the faster the K-H instability develops and the more liquid is rolled up. It was also found that increase of thickness of the velocity gradient layer under the inclined wall presented an inhibitory effect on roll-up of the interface. The greater gravity items of Richardson number is, the slower the interface rolls up. However, surface tension items of Richardson number have weak effect on the growth of interface.
引文
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[3] SUN J,DU P,LI P,et al.Natural convection heat transfer in a porous medium with partially thermally active walls used LBM[J].Chinese Journal of Computational Physics,2017,34(5):583-592.
[4] LV Y Q,NIE D,LIN J Z.Lattice Boltzmann simulation of gas bubble merging in three dimensions[J].Chinese Journal of Computational Physics,2015,32(5):553-560.
[5] XIE C,ZHANG J,BERTOLA V,et al.Lattice Boltzmann modeling for multiphase viscoplastic fluid flow[J].Journal of Non-Newtonian Fluid Mechanics,2016,234:118-128.
[6] MAZLOOMI M A,CHIKATAMARLA S S,KARLIN I V.Entropic lattice Boltzmann method for multiphase flows[J].Physical Review Letters,2015,114(17):174502.
[7] TARTAKOVSKY A M,TRASK N,PAN K,et al.Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media[J].Computational Geosciences,2016,20(4):807-834.
[8] KRIMI A,REZOUG M,KHELLADI S,et al.Smoothed particle hydrodynamics:A consistent model for interfacial multiphase fluid flow simulations[J].Journal of Computational Physics,2018,358:53-87.
[9] WANG Z B,CHEN R,WANG H,et al.An overview of smoothed particle hydrodynamics for simulating multiphase flow[J].Applied Mathematical Modelling,2016,40(23-24):9625-9655.
[10] TARTAKOVSKY A M,PANCHENKO A.Pairwise force smoothed particle hydrodynamics model for multiphase flow:Surface tension and contact line dynamics[J].Journal of Computational Physics,2016,305:1119-1146.
[11] JUNK V,NAAB F H T.The Kelvin-Helmholtz instability in smoothed-particle hydrodynamics[J].Proceedings of the International Astronomical Union,2007,2(S235):210-210.
[12] OUSAKA A,DEENDARLIANTO,KARIYASAKI A,et al.Prediction of flooding gas velocity in gas-liquid counter-current two-phase flow in inclined pipes[J].Nuclear Engineering & Design,2006,236(12):1282-1292.
[13] CHEN J,WANG Y,WEI Z,et al.Theoretical prediction of flooding velocity in an inclined tube based on viscous Kelvin-Helmholtz instability[J].Chemical Engineering Science,2016,144:395-403.
[14] ZHANG X B,YAO L,CHEN J Y,et al.Prediction of the onset of flooding in an inclined tube at cryogenic temperatures[J].Cryogenics,2014,61(5):98-106.
[15] LU M,DONG B,ZHANG Y,et al.Numerical simulation of free-rising of bubbles in a tube with fins using front tracking method[J].Chinese Journal of Computational Physics,2018,35(1):47-54.
[16] IRFAN M,MURADOGLU M.A front tracking method for direct numerical simulation of evaporation process in a multiphase system[J].Journal of Computational Physics,2017,337(C):132-153.
[17] MA M,LU J,TRYGGVASON G.Using statistical learning to close two-fluid multiphase flow equations for a simple bubbly system[J].Physics of Fluids,2015,27(9):093303-110.
[18] MA M,LU J,TRYGGVASON G.Using statistical learning to close two-fluid multiphase flow equations for bubbly flows in vertical channels[J].International Journal of Multiphase Flow,2016,85:336-347.
[19] HUA J,LOU J.Numerical simulation of bubble rising in viscous liquid[J].Journal of Computational Physics,2007,222(2):769-795.
[20] SHADLOO M S,YILDIZ M.Numerical modeling of Kelvin-Helmholtz instability using smoothed particle hydrodynamics[J].International Journal for Numerical Methods in Engineering,2011,87(10):988-1006.