溶质运移中多孔介质弥散度影响因素的SPH模拟研究
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摘要
借助光滑粒子流体动力学(SPH)方法,本文从流体质点运动和溶质扩散的物理本质出发,设计并进行孔隙尺度下多孔介质中溶质运移的仿真实验,进而分析多孔介质弥散度影响因素,并讨论弥散度与多孔介质结构参数的关系。通过离散化N-S方程和Fick扩散方程,建立描述孔隙水流动的SPH水动力模型和描述溶质分子扩散的扩散模型,求解出在低Pe数下对流扩散方程的一维定解问题,检验了模型的准确性。在高Pe数流场中,进行了恒定流速的黏性流体穿透多孔介质薄层的仿真实验,计算结果可准确模拟出过水断面上各流体质点的流速差异、流体质点在多孔介质中的弥散过程以及流体质点的迂曲绕流过程;通过建立三段理想化的孔隙通道模型,发现在迂曲路径相同时,速度差对机械弥散度仍有显著影响。最后,为探究弥散度与多孔介质结构参数的关系,生成了多组随机粒径的二维多孔介质进行溶质穿透仿真实验。计算结果表明,弥散度与流速变异系数、迂曲度、迂曲路径差以及不均匀系数大致呈正相关,与孔隙率呈负相关。
Smoothed particle hydrodynamics(SPH) method is used to simulate the dispersion process of saturated porous media from the physical nature of fluid particle movement in pore scale. On the basis of simulation experiments, the influencing factors of dispersity are discussed. By discretizing the Navier-Stokes equations, the SPH flow model is built to describe the pore water flow. Similarly, the solute diffusion model is built to describe molecular dispersion based on Fick's law. When solving the diffusion-convection case of low Peclet number, the numerical results coincide with analytical solutions well, which verifies the accuracy of the models. Adopting the models, a 2-D simulation experiment is achieved for viscous fluid at a constant velocity to penetrate a thin layer of porous medium at high Peclet number. The features depicted by velocity contour plot agree with the real behavior of viscous fluid. To evaluate the effect of velocity differences on dispersity, three ideal micro winding tubes are established with the tortuous pathways controlled the same. The results show the difference between fluid particles' velocity has a close relationship with dispersity. Then the relationships between dispersity and the structure parameters of porous media are discussed based on the results of simulation experiments with random grain-size porous media. The conclusion proves that the increase of tortuosity and nonuniform coefficient tend to result in the enhancement of the dispersion effect. And there is a negative correlation between porosity and dispersity.
Smoothed particle hydrodynamics(SPH) method is used to simulate the dispersion process of saturated porous media from the physical nature of fluid particle movement in pore scale. On the basis of simulation experiments, the influencing factors of dispersity are discussed. By discretizing the Navier-Stokes equations, the SPH flow model is built to describe the pore water flow. Similarly, the solute diffusion model is built to describe molecular dispersion based on Fick's law. When solving the diffusion-convection case of low Peclet number, the numerical results coincide with analytical solutions well, which verifies the accuracy of the models. Adopting the models, a 2-D simulation experiment is achieved for viscous fluid at a constant velocity to penetrate a thin layer of porous medium at high Peclet number. The features depicted by velocity contour plot agree with the real behavior of viscous fluid. To evaluate the effect of velocity differences on dispersity, three ideal micro winding tubes are established with the tortuous pathways controlled the same. The results show the difference between fluid particles' velocity has a close relationship with dispersity. Then the relationships between dispersity and the structure parameters of porous media are discussed based on the results of simulation experiments with random grain-size porous media. The conclusion proves that the increase of tortuosity and nonuniform coefficient tend to result in the enhancement of the dispersion effect. And there is a negative correlation between porosity and dispersity.
引文
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[14]饶登宇,白冰,陈佩佩.基于SPH方法的非饱和多孔介质相变耦合研究[J].岩土力学,2018,39(12):4527-4536.
[15] RANDLES P W,LIBERSKY L D. Smoothed particle hydrodynamics:some recent improvements and applications[J]. Computer Methods in Applied Mechanics&Engineering,1996,139(1/4):375-408.
[16] BAI Bing,RAO Dengyu,XU Tao,et al. SPH-FDM boundary for the analysis of thermal process in homogeneous media with a discontinuous interface[J]. International Journal of Heat and Mass Transfer,2018,117:517-526.
[17] CLEARY P W,MONAGHAN J J. Conduction modeling using smoothed particle hydrodynamics[J]. Journal of Computational Physica,1999,148(1):227-264.
[18] MONAGHAN J J. On the problem of penetration in particle methods[J]. Journal of Computational Physics,1989,82(1):1-15.
[19] SQUIRES T. Microfluidics:Fluid physics at the nanoliter scale[J]. Reviews of Modern Physics,2005,77(3):977-1026.
[20] PERKINS T K. A review of diffusion and dispersion in porous media[J]. Soc. Petrol. Eng.,1963,3(3):70-84.
[21] BAI Bing,LONG Fei,RAO Dengyu,et al. The effect of temperature on the seepage transport of suspended particles in a porous medium[J]. Hydrological Processes,2017,31(2):382-393.
[22]高光耀,冯绍元,马英,等.考虑弥散尺度效应的一维反应性溶质运移两区模型及应用[J].水利学报,2011,42(6):631-640.
[23] GHANBARIAN B,HUNT A G,EWING R P,et al. Tortuosity in porous media:A critical review[J]. Soil Science Society of America Journal,2013,77(5):1461.
[24] NIYA S M R,SELVADURAI A P S. A statistical correlation between permeability,porosity,tortuosity and conductance[J]. Transport in Porous Media,2018,121:741-752.
[2]李维仲,赵月帅,宋永臣.多孔介质孔隙尺度下不可压缩流体流动特性SPH模拟[J].大连理工大学学报,2013,53(2):189-193.
[3] ZHAO Y,ZHAO J,SHI D,et al. Micro-CT analysis of structural characteristics of natural gas hydrate in porous media during decomposition[J]. Journal of Natural Gas Science&Engineering,2016,31:139-148.
[4] BERG C F,HELD R. Fundamental transport property relations in porous media incorporating detailed pore structure description[J]. Transport in Porous Media,2016,112(2):467-487.
[5] MONAGHAN J J. Simulating free surface flows with SPH[J]. Journal of Computational Physics,1994,110(2):399-406.
[6] LIU M B,LIU G R. Smoothed particle hydrodynamics(SPH):an overview and recent developments[J]. Archives of Computational Methods in Engineering,2010,17(1):25-76.
[7]李静,陈健云,徐强,等.滑坡涌浪对坝面冲击压力的影响因素研究[J].水利学报,2018,49(2):232-240.
[8] MORRIS J P,FOX P J,ZHU Y. Modeling low reynolds number incompressible flows using SPH[J]. Journal of Computational Physics,1997,136(1):214-226.
[9] ZHU Y,FOX P J. Simulation of pore-scale dispersion in periodic porous media using smoothed particle hydrodynamics[J]. Journal of Computational Physics,2002,182(2):622-645.
[10] 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.
[11] RYAN E M,TARTAKOVSKY A M,AMON C. Pore-scale modeling of competitive adsorption in porous media.[J]. Journal of Contaminant Hydrology,2011,120(3):56-78.
[12] YANG P,WEN Z,DOU R,et al. Permeability in multi-sized structures of random packed porous media using three-dimensional lattice Boltzmann method[J]. International Journal of Heat&Mass Transfer,2017,106:1368-1375.
[13]陈佩佩,白冰.内含圆柱域热源的非饱和土介质水热耦合作用的SPH数值模拟[J].岩土工程学报,2015,37(6):1025-1030.
[14]饶登宇,白冰,陈佩佩.基于SPH方法的非饱和多孔介质相变耦合研究[J].岩土力学,2018,39(12):4527-4536.
[15] RANDLES P W,LIBERSKY L D. Smoothed particle hydrodynamics:some recent improvements and applications[J]. Computer Methods in Applied Mechanics&Engineering,1996,139(1/4):375-408.
[16] BAI Bing,RAO Dengyu,XU Tao,et al. SPH-FDM boundary for the analysis of thermal process in homogeneous media with a discontinuous interface[J]. International Journal of Heat and Mass Transfer,2018,117:517-526.
[17] CLEARY P W,MONAGHAN J J. Conduction modeling using smoothed particle hydrodynamics[J]. Journal of Computational Physica,1999,148(1):227-264.
[18] MONAGHAN J J. On the problem of penetration in particle methods[J]. Journal of Computational Physics,1989,82(1):1-15.
[19] SQUIRES T. Microfluidics:Fluid physics at the nanoliter scale[J]. Reviews of Modern Physics,2005,77(3):977-1026.
[20] PERKINS T K. A review of diffusion and dispersion in porous media[J]. Soc. Petrol. Eng.,1963,3(3):70-84.
[21] BAI Bing,LONG Fei,RAO Dengyu,et al. The effect of temperature on the seepage transport of suspended particles in a porous medium[J]. Hydrological Processes,2017,31(2):382-393.
[22]高光耀,冯绍元,马英,等.考虑弥散尺度效应的一维反应性溶质运移两区模型及应用[J].水利学报,2011,42(6):631-640.
[23] GHANBARIAN B,HUNT A G,EWING R P,et al. Tortuosity in porous media:A critical review[J]. Soil Science Society of America Journal,2013,77(5):1461.
[24] NIYA S M R,SELVADURAI A P S. A statistical correlation between permeability,porosity,tortuosity and conductance[J]. Transport in Porous Media,2018,121:741-752.