一种基于几何重构的Youngs-VOF耦合水平集追踪方法
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摘要
针对界面追踪方法中拉格朗日方法和欧拉–拉格朗日方法计算效率低、不适用大变形、不能应用于三维数值计算模型等问题,研究了一种效率高、界面清晰、适用于三维模型的计算气液两相界面迁移特性的欧拉运动界面追踪方法,该方法将"米"状相邻单元Youngs方法用于运动界面重构,将Youngs-VOF和水平集通过几何方法耦合,提高运动界面精度,克服了VOF和水平集方法存在的缺陷,避免了利用高阶导数本身的稳定性去求解水平集对流方程和距离函数方程."米"状相邻单元Youngs方法避免了数值耗散、数值色散性以及非线性效应引起的捕捉界面模糊的情况. Youngs-VOF耦合水平集方法既保证了计算界面时的稳定性,与拉格朗日方法相比又提高了计算效率.利用Youngs-VOF耦合水平集方法与VOF方法对单个气泡在水中上升过程数值计算与实验对比并对经典剪切流场中圆形运动界面模型的数值计算,验证了Youngs-VOF耦合水平集方法的有效性并比VOF方法捕捉界面更清晰、锐利;通过对溃坝–自由表面流动过程数值计算并与实验进行对比,验证了Youngs-VOF耦合水平集方法的稳定性以及对三维数值模型的适用性.
The Lagrangian method and the Euler-Lagrangian method in the interface tracking method have low computational efficiency. They are not suitable for large deformation, and can not be applied to three-dimensional numerical calculation models. An Euler motion interface tracking method is applied to calculate the migration characteristics of gas-liquid two-phase interface with high efficiency and clear interface and suitable for three-dimensional models. This method uses the "米" shaped adjacent grid Youngs method for interface reconstruction. The Youngs-VOF and level set are coupled by geometric methods, so it can improve the accuracy of the interface, and overcome the defects of the VOF method and level set method, and avoid to solve the level set convection equation and the distance function equation with its own stability of the high-order derivation. The "米" shaped adjacent grid Youngs method is used to avoid the situation that the captured interface was blurred due to numerical dissipation and numerical dispersion, as well as nonlinear effects.The Youngs-VOF coupled level set method not only ensures the stability of the computing interface, but improves the computational efficiency compared with the Lagrangian method. The Youngs-VOF coupled level set method and VOF method is designed to simulate the rising process of a single bubble in water. After compared, the Youngs-VOF coupled level set method is more efficient and sharper than the VOF method. By using the Youngs-VOF coupled level set method and the VOF method to numerically calculate the circular motion interface model in the classical shear flow field, it is verified that the Youngs-VOF coupled level set method can better calculate the interface curvature compared with the VOF method. Through the numerical calculation of the break dam-free surface flow process and compared with the experiment,the stability of the Youngs-VOF coupled level set method are verified. And the Youngs-VOF coupled level set method can be applied to the three-dimensional numerical models.
The Lagrangian method and the Euler-Lagrangian method in the interface tracking method have low computational efficiency. They are not suitable for large deformation, and can not be applied to three-dimensional numerical calculation models. An Euler motion interface tracking method is applied to calculate the migration characteristics of gas-liquid two-phase interface with high efficiency and clear interface and suitable for three-dimensional models. This method uses the "米" shaped adjacent grid Youngs method for interface reconstruction. The Youngs-VOF and level set are coupled by geometric methods, so it can improve the accuracy of the interface, and overcome the defects of the VOF method and level set method, and avoid to solve the level set convection equation and the distance function equation with its own stability of the high-order derivation. The "米" shaped adjacent grid Youngs method is used to avoid the situation that the captured interface was blurred due to numerical dissipation and numerical dispersion, as well as nonlinear effects.The Youngs-VOF coupled level set method not only ensures the stability of the computing interface, but improves the computational efficiency compared with the Lagrangian method. The Youngs-VOF coupled level set method and VOF method is designed to simulate the rising process of a single bubble in water. After compared, the Youngs-VOF coupled level set method is more efficient and sharper than the VOF method. By using the Youngs-VOF coupled level set method and the VOF method to numerically calculate the circular motion interface model in the classical shear flow field, it is verified that the Youngs-VOF coupled level set method can better calculate the interface curvature compared with the VOF method. Through the numerical calculation of the break dam-free surface flow process and compared with the experiment,the stability of the Youngs-VOF coupled level set method are verified. And the Youngs-VOF coupled level set method can be applied to the three-dimensional numerical models.
引文
1王昭,严红.基于气液相界面捕捉的统一气体动理学格式.力学学报,2018,50(4):711-721(Wang Zhao,Yan Hong.Unified gaskinetic scheme for two phase interface capturing.Chinese Journal of Theoretical and Applied Mechanics,2018,50(4):711-721(in Chinese))
2刘文超,刘曰武.低渗透煤层气藏中气-水两相不稳定渗流动态分析.力学学报,2017,49(4):828-835(Liu Wenchao,Liu Yuewu.Dynamic analysis on gas-water two-phase unsteady seepage flow in low-permeable coalbed gas reservoirs.Chinese Journal of Theoretical and Applied Mechanics,2017,49(4):828-835(in Chinese))
3 Hua J,Stene JF,Lin P.Numerical simulation of 3D bubbles rising in viscous liquids using a Front tracking method.Journal of Computation Physics,2008,227(6):3358-3382
4 Lu H,Ning Z,Wang D.A Front tracking method for the simulation of compressible multimedium flows.Communications in Computational Physics,2016,19(1):124-142
5陈斌,Kawamura T,Kodama Y.静止水中单个上升气泡的直接数值模拟.工程热物理学报,2005,26(6):980-982(Chen Bin,Kawamura T,Kodama Y.Direct numerical simulations of a single bubble rising in still water.Journal of Engineering Thermophysics,2005,26(6):980-982(in Chinese))
6陈斌.倾斜壁面附近上升气泡的直接数值模拟.工程热物理学报,2007,28(6):965-967(Chen Bin.Direct numerical simulations of a single bubble rising along an inclination wall.Journal of Engineering Thermophysics,2007,28(6):965-967(in Chinese))
7张洋,陈科,尤云祥等.壁面约束对裙带气泡动力学的影响.力学学报,2017,49(5):1050-1058(Zhang Yang,Chen Ke,You Yunxiang,et al.Confinement effect on the rising dynamics of a skirted bubble.Chinese Journal of Theoretical and Applied Mechanics,2017,49(5):1050-1058(in Chinese))
8 Yokoi K.Efficient implementation of THINC scheme:A simple and practical smoothed VOF algorithm.Journal of Computational Physics,2007,226(2):1985-2002
9 Nguyen VT,Park WG.A volume-of-fluid(VOF)interfacesharpening method for two-phase incompressible flows.Computers&Fluids,2017,152:104-119
10 Cifani P,Michalek WR,Priems GJM,et al.A comparison between the surface compression method and an interface reconstruction method for the VOF approach.Computers&Fluids,2016,136:421-435
11杨魏,刘树红,吴玉林.基于VOF方法的圆柱箱体中液体晃动阻尼计算.力学学报,2009,41(6):936-940(Yang Wei,Liu Shuhong,Wu Yulin.Liquid sloshing damping computation in cylindrical container based on VOF method.Chinese Journal of Theoretical and Applied Mechanics,2009,41(6):936-940(in Chinese))
12 Ge Z,Loiseau JC,Tammisola O,et al.An efficient mass-preserving interface-correction level set/ghost fluid method for droplet suspensions under depletion forces.Journal of Computational Physics,2018,353:435-459
13袁德奎,陶建华.用水平集方法求解具有自由面的流动问题.力学学报,2000,32(3):264-271(Yuan Dekui,Tao Jianhua.Simulation of the flow with free surface by Level Set method.Chinese Journal of Theoretical and Applied Mechanics,2000,32(3):264-271(in Chinese))
14 Sun Y,Beckermann C.Sharp interface tracking using the phase-field equation.Journal of Computational Physics,2007,220(2):626-653
15 Ryskin G,Leal LG.Numerical simulation of free-boundary problems in fluid mechanics.Part 2.Buoyancy-driven motion of a gas bubble through a quiescent liquid.Journal of Fluid Mechanics,1984,148(148):19-35
16 Hu HH,Patankar NA,Zhu MY.Direct numerical simulation of fluid-solid system using the arbitrary Lagrangian-Eularian technique.Journal of Computational Physics,2001,169(2):427-462
17 Unverdi SO,Tryggvason G.A front-tracking method for viscous,incompressible,multi-fluid flows.Journal of Computational Physics,1992,100(1):25-37
18 Wang Z,Yang J,Stern F.A new volume-of-fluid method with a constructed distance function on general structured grids.Journal of Computational Physics,2012,231(9):3703-3722
19 Haghshenas M,Wilson JA,Kumar R.Algebraic coupled level setvolume of fluid method for surface tension dominant two-phase flows.International Journal of Multiphase Flow,2017,90:13-28
20 Sussman M,Puckett EG.A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible twophase flows.Journal of Computational Physics,2000,162(2):301-337
21 Chakraborty I,Biswas G,Ghoshdastidar PS.A coupled level-set and volume-of-fluid method for the buoyant rise of gas bubbles in liquids.International Journal of Heat&Mass Transfer,2013,58(1-2):240-259
22廖斌,陈善群.基于CLSVOF方法的三维单个上升气泡运动的数值模拟.水动力学研究与进展A辑,2012,27(3):275-283(Liao Bin,Chen Shanqun.Numerical simulation of a three-dimensional rising gas bubble based on CLSVOF method.Chinese Journal of Hydrodynamics,2012,27(3):275-283(in Chinese))
23 Skarysz M,Garmory A,Dianat M.An iterative interface reconstruction method for PLIC in general convex grids as part of a Coupled Level Set Volume of Fluid solver.Journal of Computational Physics,2018,368:254-276
24 Zhao Y,Chen HC.A new coupled Level Set and volume-of-fluid method to capture free surface on an overset grid system.International Journal of Multiphase Flow,2017,90:144-155
25 Ansari MR,Azadi R,Salimi E.Capturing of interface topological changes in two-phase gas-liquid flows using a coupled volume-offluid and level-set method(VOSET).Computers&Fluids,2016,125:82-100
26李康,刘娜,何志伟等.一种基于双界面函数的界面捕捉方法.力学学报,2017,49(6):1290-1300(Li Kang,Liu Na,He Zhiwei,et al.A new interface capturing method based on double interface functions.Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1290-1300(in Chinese))
27贾祖朋,蔚喜军.基于水平集的Eulerian-Lagrangian耦合方法及其应用.力学学报,2010,42(2):177-182(Jia Zupeng,Wei Xijun.A coupled Eulerian-Lagrangian method based on Level Set and its applications.Chinese Journal of Theoretical and Applied Mechanics,2010,42(2):177-182(in Chinese))
28 Ha CT,Kim DH,Park WG,et al.A compressive interface-capturing scheme for computation of compressible multi-fluid flows.Computers&Fluids,2017,152:164-181
29 Youngs DL.Time dependent multimaterial flow with large fluid distortion.Numerical Methods in Fluid Dynamics.New York:Morton KW,Baines MJ,1982:273-285
30 Bhaga D,Weber ME.Bubbles in viscous liquids:Shapes,wakes and velocities.Journal of Fluid Mechanics,1981,105(105):61-85
31 Hirt CW,Nichols BD.Volume of fluid(VOF)method for the dynamics of free boundaries.Journal of Computational Physics,1981,39(1):201-225
32 Rudman M.Volume-tracking methods for interfacial flow calculations.International Journal for Numerical Methods in Fluids,1997,24(7):671-691
33 Fang QJ,HE CJ,Zhang M,et al.Interface calculations in numerical method for Eulerian hydrodynamics.Chinese Journal of Computational Mechanics,2004,21(4):412-418
34 Hua J,Lou J.Numerical simulation of bubble rising in viscous liquid.Journal of Computational Physics,2007,222(2):769-795
35 Brackbill JU,Kothe DB,Zemach C.A continuum method for modeling surface tension.Journal of Computational Physics,1992,100(2):335-354
36 Lobovsk′y L,Botia-Vera E,Castellana F,et al.Experimental investigation of dynamic pressure loads during dam break.Journal of Fluids&Structures,2014,48:407-434
2刘文超,刘曰武.低渗透煤层气藏中气-水两相不稳定渗流动态分析.力学学报,2017,49(4):828-835(Liu Wenchao,Liu Yuewu.Dynamic analysis on gas-water two-phase unsteady seepage flow in low-permeable coalbed gas reservoirs.Chinese Journal of Theoretical and Applied Mechanics,2017,49(4):828-835(in Chinese))
3 Hua J,Stene JF,Lin P.Numerical simulation of 3D bubbles rising in viscous liquids using a Front tracking method.Journal of Computation Physics,2008,227(6):3358-3382
4 Lu H,Ning Z,Wang D.A Front tracking method for the simulation of compressible multimedium flows.Communications in Computational Physics,2016,19(1):124-142
5陈斌,Kawamura T,Kodama Y.静止水中单个上升气泡的直接数值模拟.工程热物理学报,2005,26(6):980-982(Chen Bin,Kawamura T,Kodama Y.Direct numerical simulations of a single bubble rising in still water.Journal of Engineering Thermophysics,2005,26(6):980-982(in Chinese))
6陈斌.倾斜壁面附近上升气泡的直接数值模拟.工程热物理学报,2007,28(6):965-967(Chen Bin.Direct numerical simulations of a single bubble rising along an inclination wall.Journal of Engineering Thermophysics,2007,28(6):965-967(in Chinese))
7张洋,陈科,尤云祥等.壁面约束对裙带气泡动力学的影响.力学学报,2017,49(5):1050-1058(Zhang Yang,Chen Ke,You Yunxiang,et al.Confinement effect on the rising dynamics of a skirted bubble.Chinese Journal of Theoretical and Applied Mechanics,2017,49(5):1050-1058(in Chinese))
8 Yokoi K.Efficient implementation of THINC scheme:A simple and practical smoothed VOF algorithm.Journal of Computational Physics,2007,226(2):1985-2002
9 Nguyen VT,Park WG.A volume-of-fluid(VOF)interfacesharpening method for two-phase incompressible flows.Computers&Fluids,2017,152:104-119
10 Cifani P,Michalek WR,Priems GJM,et al.A comparison between the surface compression method and an interface reconstruction method for the VOF approach.Computers&Fluids,2016,136:421-435
11杨魏,刘树红,吴玉林.基于VOF方法的圆柱箱体中液体晃动阻尼计算.力学学报,2009,41(6):936-940(Yang Wei,Liu Shuhong,Wu Yulin.Liquid sloshing damping computation in cylindrical container based on VOF method.Chinese Journal of Theoretical and Applied Mechanics,2009,41(6):936-940(in Chinese))
12 Ge Z,Loiseau JC,Tammisola O,et al.An efficient mass-preserving interface-correction level set/ghost fluid method for droplet suspensions under depletion forces.Journal of Computational Physics,2018,353:435-459
13袁德奎,陶建华.用水平集方法求解具有自由面的流动问题.力学学报,2000,32(3):264-271(Yuan Dekui,Tao Jianhua.Simulation of the flow with free surface by Level Set method.Chinese Journal of Theoretical and Applied Mechanics,2000,32(3):264-271(in Chinese))
14 Sun Y,Beckermann C.Sharp interface tracking using the phase-field equation.Journal of Computational Physics,2007,220(2):626-653
15 Ryskin G,Leal LG.Numerical simulation of free-boundary problems in fluid mechanics.Part 2.Buoyancy-driven motion of a gas bubble through a quiescent liquid.Journal of Fluid Mechanics,1984,148(148):19-35
16 Hu HH,Patankar NA,Zhu MY.Direct numerical simulation of fluid-solid system using the arbitrary Lagrangian-Eularian technique.Journal of Computational Physics,2001,169(2):427-462
17 Unverdi SO,Tryggvason G.A front-tracking method for viscous,incompressible,multi-fluid flows.Journal of Computational Physics,1992,100(1):25-37
18 Wang Z,Yang J,Stern F.A new volume-of-fluid method with a constructed distance function on general structured grids.Journal of Computational Physics,2012,231(9):3703-3722
19 Haghshenas M,Wilson JA,Kumar R.Algebraic coupled level setvolume of fluid method for surface tension dominant two-phase flows.International Journal of Multiphase Flow,2017,90:13-28
20 Sussman M,Puckett EG.A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible twophase flows.Journal of Computational Physics,2000,162(2):301-337
21 Chakraborty I,Biswas G,Ghoshdastidar PS.A coupled level-set and volume-of-fluid method for the buoyant rise of gas bubbles in liquids.International Journal of Heat&Mass Transfer,2013,58(1-2):240-259
22廖斌,陈善群.基于CLSVOF方法的三维单个上升气泡运动的数值模拟.水动力学研究与进展A辑,2012,27(3):275-283(Liao Bin,Chen Shanqun.Numerical simulation of a three-dimensional rising gas bubble based on CLSVOF method.Chinese Journal of Hydrodynamics,2012,27(3):275-283(in Chinese))
23 Skarysz M,Garmory A,Dianat M.An iterative interface reconstruction method for PLIC in general convex grids as part of a Coupled Level Set Volume of Fluid solver.Journal of Computational Physics,2018,368:254-276
24 Zhao Y,Chen HC.A new coupled Level Set and volume-of-fluid method to capture free surface on an overset grid system.International Journal of Multiphase Flow,2017,90:144-155
25 Ansari MR,Azadi R,Salimi E.Capturing of interface topological changes in two-phase gas-liquid flows using a coupled volume-offluid and level-set method(VOSET).Computers&Fluids,2016,125:82-100
26李康,刘娜,何志伟等.一种基于双界面函数的界面捕捉方法.力学学报,2017,49(6):1290-1300(Li Kang,Liu Na,He Zhiwei,et al.A new interface capturing method based on double interface functions.Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1290-1300(in Chinese))
27贾祖朋,蔚喜军.基于水平集的Eulerian-Lagrangian耦合方法及其应用.力学学报,2010,42(2):177-182(Jia Zupeng,Wei Xijun.A coupled Eulerian-Lagrangian method based on Level Set and its applications.Chinese Journal of Theoretical and Applied Mechanics,2010,42(2):177-182(in Chinese))
28 Ha CT,Kim DH,Park WG,et al.A compressive interface-capturing scheme for computation of compressible multi-fluid flows.Computers&Fluids,2017,152:164-181
29 Youngs DL.Time dependent multimaterial flow with large fluid distortion.Numerical Methods in Fluid Dynamics.New York:Morton KW,Baines MJ,1982:273-285
30 Bhaga D,Weber ME.Bubbles in viscous liquids:Shapes,wakes and velocities.Journal of Fluid Mechanics,1981,105(105):61-85
31 Hirt CW,Nichols BD.Volume of fluid(VOF)method for the dynamics of free boundaries.Journal of Computational Physics,1981,39(1):201-225
32 Rudman M.Volume-tracking methods for interfacial flow calculations.International Journal for Numerical Methods in Fluids,1997,24(7):671-691
33 Fang QJ,HE CJ,Zhang M,et al.Interface calculations in numerical method for Eulerian hydrodynamics.Chinese Journal of Computational Mechanics,2004,21(4):412-418
34 Hua J,Lou J.Numerical simulation of bubble rising in viscous liquid.Journal of Computational Physics,2007,222(2):769-795
35 Brackbill JU,Kothe DB,Zemach C.A continuum method for modeling surface tension.Journal of Computational Physics,1992,100(2):335-354
36 Lobovsk′y L,Botia-Vera E,Castellana F,et al.Experimental investigation of dynamic pressure loads during dam break.Journal of Fluids&Structures,2014,48:407-434