NUMERICAL SIMULATION OF FULL PHASES OF COLLAPSE OF THREE-DIMENSIONAL CYLINDRICAL GRANULAR PILE
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摘要: 静态颗粒堆在重力作用下的坍塌问题, 是认识和理解许多人为过程和自然现象的基础. 采用传统方法进行模拟存在单颗粒追踪数量大、宏观模拟流变特性明显和相态演变复杂等计算难点. 本文从颗粒介质表现出不同相态的物理机理出发, 对全相态概念进行了定义并进行了区域划分. 根据颗粒介质的应力-应变关系及体积分数的不同, 通过确定不同相态之间的耦合关系和转化准则, 将描述各相态的现有理论有效结合起来, 建立了描述颗粒介质经历全部相态的耦合模型理论. 采用光滑离散颗粒流体动力学方法和离散单元法相耦合的策略, 对颗粒介质物理模型求解, 实现了对不同长径比下的三维圆柱型颗粒堆坍塌过程的数值模拟. 计算结果与实验结果吻合较好, 同时与离散单元法相比, 计算量得到了控制. 不仅捕捉到了不同参数影响下颗粒堆坍塌后沉积的不同现象, 同时获得了不同条件参数对颗粒堆坍塌后铺展特性的影响规律, 为揭示工业和自然界中广泛存在的颗粒介质复杂运动机理提供有效的支撑.Abstract: The collapse of static granular pile under gravity is the basis for understanding many human processes and natural phenomena. There are some difficulties for the traditional simulation methods, such as large number of single particle tracking, obvious rheological characteristics, and complex phase evolution of macro simulation. Based on the physical mechanism of different phases in granular media, the concept of full phases is defined and divided into three regions. According to the stress-strain relationship and volume fraction of granular media, the existing theories describing each phase are effectively combined by determining the coupling relationship and transformation criteria between different phases, and the coupling model theory describing all phase states of granular media is established. Then the physical model of granular media is solved with the strategy of coupling smoothed discrete particle hydrodynamics and discrete element method. The coupling and transformation algorithm between different phase particles is clarified and the particle size independence of the diameter selection of the initial SDPH particles is tested. The numerical simulation of collapse process of granular pile under different aspect ratio is realized. The calculated results are in good agreement with the experimental results. At the same time, compared with the discrete element method, the amount of calculation is controlled. It not only captures the different phenomena of deposition after granular pile collapse under the influence of different parameters, but also obtains the effects of different conditions and parameters on the spreading characteristics of granular pile after collapse are obtained, which provides effective support for revealing the complex motion mechanism of granular media widely existing in industry and nature.
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Key words:
- granular pile /
- collapse /
- all phases /
- numerical simulation
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图 16
$ a = 16.7 $ 三维圆柱型颗粒堆坍塌过程不同相态演变(黑色表示颗粒处于浓密态, 红色表示颗粒处于稀疏态, 白色表示颗粒处于超稀疏态)Figure 16. The evolution of different phases during the collapse of cylindrical granular pile (Black indicates that the particles are in dense state, red indicates that the particles are in dilute state, and white indicates that the particles are in ultra-dilute state)
表 1 本文方法与DEM方法计算耗时对比
Table 1. Comparison of calculation time between this method and DEM method
Method Total number of particles Computing platform Time step Calculation time method in this paper 182484 i9-9900 16 thread parallelism 1 × 10−5 s 4 h 32 min DEM method 182484 i9-9900 16 thread parallelism 2 × 10−6 s 23 h 15 min -
[1] Kim S, Kamrin K. Power-law scaling in granular rheology across flow geometries. Physical Review Letters, 2020, 125: 088002 [2] 孙其诚. 颗粒介质的结构及热力学. 物理学报, 2015, 64(7): 076101 (Sun Qicheng. Granular structure and the nonequilibrium thermodynamics. Acta Physica Sinica, 2015, 64(7): 076101 (in Chinese) doi: 10.7498/aps.64.076101Sun Qicheng. Granular structure and the nonequilibrium thermodynamics. Acta Physica Sinica, 2015, 64(7): 076101 (in Chinese)) doi: 10.7498/aps.64.076101 [3] 黄德财, 孙刚, 厚美瑛等. 颗粒速度在颗粒流稀疏流-密集流转变中的作用. 物理学报, 2006, 55(9): 4754-4759 (Huang Decai, Sun Gang, Hou Meiying, et al. The effect of the granule velocity on the dilute-dense flow transition in granular system. Acta Physica Sinica, 2006, 55(9): 4754-4759 (in Chinese) doi: 10.3321/j.issn:1000-3290.2006.09.062Huang Decai, Sun Gang, Hou Meiying, Lu Kunquan, et al. The effect of the granule velocity on the dilute-dense flow transition in granular system. Acta Physica Sinica, 2006, 55(9): 4754-4759 (in Chinese)) doi: 10.3321/j.issn:1000-3290.2006.09.062 [4] Jaeger H, Nagel S, Behringer R. Granular solids, liquids, and gases. Reviews of Modern Physics, 1996, 68(4): 1259-1273 doi: 10.1103/RevModPhys.68.1259 [5] Chialvo S, Sun J, Sundaresan S. Bridging the rheology of granular flows in three regimes. Physical Review E, 2012, 85: 021305 [6] Lube G, Huppert HE, Sparks RSJ, et al. Axisymmetric collapses of granular columns. Journal of Fluid Mechanics, 2004, 508: 175-199 doi: 10.1017/S0022112004009036 [7] Lube G, Huppert HE, Sparks R, et al. Collapses of two-dimensional granular columns. Physical Review E, 2005, 72(4): 041301 [8] Lajeunesse E, Mangeney-Castelnau A, Vilotte JP. Spreading of a granular mass on a horizontal plane. Physics of Fluids, 2004, 16(7): 2371-2381 doi: 10.1063/1.1736611 [9] Lajeunesse E, Monnier JB, Homsy GM. Granular slumping on a horizontal surface. Physics of Fluids, 2005, 17(10): 177 [10] Roche O, Attali M, Mangeney A, et al. On the run-out distance of geophysical gravitational flows: Insight from fluidized granular collapse experiments. Earth and Planetary Science Letters, 2011, 311(3-4): 375-385 doi: 10.1016/j.jpgl.2011.09.023 [11] Artoni R, Santomaso AC, Gabrieli F, et al. Collapse of quasi-two-dimensional wet granular columns. Physical Review E, 2013, 87(3): 032205 doi: 10.1103/PhysRevE.87.032205 [12] Farin M, Mangeney A, Roche O. Fundamental changes of granular flow dynamics, deposition, and erosion processes at high slope angles: Insights from laboratory experiments. Journal of Geophysical Research Earth Surface, 2014, 119(3): 504-532 doi: 10.1002/2013JF002750 [13] Hungr O. Simplified models of spreading flow of dry granular material. Canadian Geotechnical Journal, 2008, 45(8): 1156-1168 [14] Pouliquen, O. Scaling laws in granular flows down rough inclined planes. Physics of Fluids, 1999, 11(3): 542-548 doi: 10.1063/1.869928 [15] Mangeney A, Roche O, Hungr O, et al. Erosion and mobility in granular collapse over sloping beds. Journal of Geophysical Research:Earth Surface, 2010, 115: 03040 doi: 10.1029/2009JF001462 [16] 张昱, 韦艳芳, 彭政等. 倾斜沙漏流与颗粒休止角研究. 物理学报, 2016, 65(8): 084502 (Zhang Yu, Wei Yanfang, Peng Zheng, et al. Inclined glass-sand flow and the angle of repose. Acta Physica Sinica, 2016, 65(8): 084502 (in Chinese) doi: 10.7498/aps.65.084502Zhang Yu, Wei Yanfang, Peng Zheng, et al. Inclined glass-sand flow and the angle of repose. Acta Physica Sinica, 2016, 65(8): 084502 (in Chinese)) doi: 10.7498/aps.65.084502 [17] Staron L, Hinch EJ. Study of the collapse of granular columns using DEM numerical simulation. Journal of Fluid Mechanics, 2005, 545(1): 1-27 [18] Lacaze L, Phillips JC, Kerswell RR. Planar collapse of a granular column: experiments and discrete element simulations. Physics of Fluids, 2008, 20(6): 144302 [19] Utili S, Zhao T, Houlsby GT. 3D DEM investigation of granular column collapse: Evaluation of debris motion and its destructive power. Engineering Geology, 2015, 186: 3-16 [20] 孙其诚, 王光谦. 静态堆积颗粒中的力链分布. 物理学报, 2008, 57(8): 4667-4674 (Sun Qicheng, Wang Guangqian. Force distribution in static granular matter in two dimensions. Acta Physica Sinica, 2008, 57(8): 4667-4674 (in Chinese) doi: 10.3321/j.issn:1000-3290.2008.08.007Sun Qicheng, Wang Guangqian. Force distribution in static granular matter in two dimensions. Acta Physica Sinica, 2008, 57(8): 4667-4674 (in Chinese)) doi: 10.3321/j.issn:1000-3290.2008.08.007 [21] 成浩, 韩培锋, 苏有文. 基于离散元方法的松散体滑动堆积特性及影响因素分析. 物理学报, 2020, 69(16): 164501 (Cheng Hao, Han Peifeng, Su Youwen. Sliding and accumulation characteristics of loose materials and its influencing factors based on discrete element method. Acta Physica Sinica, 2020, 69(16): 164501 (in Chinese) doi: 10.7498/aps.69.20200223Cheng Hao, Han Peifeng, Su Youwen. Sliding and accumulation characteristics of loose materials and its influencing factors based on discrete element method. Acta Physica Sinica, 2020, 69(16): 164501 (in Chinese)) doi: 10.7498/aps.69.20200223 [22] Zhang R, Su D, Lei G, et al. Three-dimensional granular column collapse: Impact of column thickness. Powder Technology, 2021, 389: 328-338 doi: 10.1016/j.powtec.2021.05.043 [23] Klein ML, Shinoda W. Large-scale molecular dynamics simulations of self-assembling systems. Science, 2008, 321(5890): 798-800 doi: 10.1126/science.1157834 [24] Chu K, Chen J, Yu A. Applicability of a coarse-grained CFD–DEM model on dense medium cyclone. Minerals Engineering, 2016: 43-54 [25] Kamrin K. Nonlinear elasto-plastic model for dense granular flow. International Journal of Plasticity, 2010, 26(2): 167-188 doi: 10.1016/j.ijplas.2009.06.007 [26] 杨肃, 张会琴, 余王昕等. 基于沿程坐标积分模式颗粒流与结构物阵列相互作用的数值模拟. 力学学报, 2021, 53(12): 3401-3414 (Yang Su, Zhang Huiqin, Yu Wangxin, et al. Numerical study of interaction between granular flow and an array of obstacles by a bed-fitted depth-averaged model. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(12): 3401-3414 (in Chinese)Yang Su, Zhang Huiqin, Yu Wangxin, et al. Numerical study of interaction between granular flow and an array of obstacles by a bed-fitted depth-averaged model. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(12): 3401-3414 (in Chinese)) [27] Chauchat J, Medale M. A three-dimensional numerical model for dense granular flows based on the μ(I) rheology. Journal of Computational Physics, 2014, 256: 696-712 [28] Gesenhues L, José J, Camata Crtes AMA, et al. Finite element simulation of complex dense granular flows using a well-posed regularization of the μ(I)-rheology. Computers & Fluids, 2019, 188(30): 102-113 [29] Henann DL, Kamrin K. A finite element implementation of the nonlocal granular rheology. International Journal for Numerical Methods in Engineering, 2016, 108: 273-302 [30] Lagrée PY, Staron L, Popinet S. The granular column collapse as a continuum: Validity of a two-dimensional Navier-Stokes model with a μ (I)-rheology. Journal of Fluid Mechanics, 2011, 686: 378-408 doi: 10.1017/jfm.2011.335 [31] Staron L, Lagrée PY, Popinet S. Continuum simulation of the discharge of the granular silo. European Physical Journal E, 2014, 37(1): 1-12 doi: 10.1140/epje/i2014-14001-x [32] Staron L, Lagrée PY, Popinet S. The granular silo as a continuum plastic flow: The hour-glass vs the clepsydra. Physics of Fluids, 2012, 24(10): 103301 doi: 10.1063/1.4757390 [33] Andersen S, Andersen L. Analysis of stress updates in the material-point method//Proceedings of the Twenty Second Nordic Seminar on Computational Mechanics, 2009, 129-134. [34] Wieckowski Z. The material point method in large strain engineering problems. Computer Methods in Applied Mechanics & Engineering, 2004, 193: 4417-4438 [35] Abe K, Soga K, Bandara S. Material point method for coupled hydromechanical problems. Journal of Geotechnical & Geoenvironmental Engineering, 2014, 140(3): 04013033 [36] Bandara S, Soga K. Coupling of soil deformation and pore fluid flow using material point method. Computers & Geotechnics, 2015, 63: 199-214 [37] Fern EJ, Soga K. The role of constitutive models in MPM simulations of granular column collapses. Acta Geotechnica, 2016, 11(3): 659-678 doi: 10.1007/s11440-016-0436-x [38] Dunatunga S, Kamrin K. Continuum modelling and simulation of granular flows through their many phases. Journal of Fluid Mechanics, 2015, 779: 483-513 doi: 10.1017/jfm.2015.383 [39] Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 1977, 181(3): 375-389 doi: 10.1093/mnras/181.3.375 [40] Lucy LB. A numerical approach to the testing of the fission hypothesis. Astronomical Journal, 1977, 82: 1013-1024 doi: 10.1086/112164 [41] Bui HH, Fukagawa R, Sako K, et al. Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic-plastic soil constitutive model. International Journal for Numerical & Analytical Methods in Geomechanics, 2010, 32(12): 1537-1570 [42] Nguyen CT, Chi TN, Bui HH, et al. A new SPH-based approach to simulation of granular flows using viscous damping and stress regularisation. Landslides, 2017, 14: 69-81 doi: 10.1007/s10346-016-0681-y [43] Ikari H, Gotoh H. SPH-based simulation of granular collapse on an inclined bed. Mechanics Research Communications, 2016, 73: 12-18 doi: 10.1016/j.mechrescom.2016.01.014 [44] Minatti L, Paris E. A SPH model for the simulation of free surface granular flows in a dense regime. Applied Mathematical Modelling, 2015, 39(1): 363-382 [45] Liang DF, He XZ. A comparison of conventional and shear-rate dependent Mohr-Coulomb models for simulating landslides. Journal of Mountain Science, 2011, 11(6): 1478-1490 [46] Chambon G, Bouvarel R, Laigle D, et al. Numerical simulations of granular free-surface flows using smoothed particle hydrodynamics. Journal of Non-Newtonian Fluid Mechanics, 2011, 166(12-13): 698-712 doi: 10.1016/j.jnnfm.2011.03.007 [47] Chen FZ, Qiang HF, Gao WR. A coupled SDPH-FVM method for gas-particle multiphase flows: Methodology. International Journal for Numerical Methods in Engineering, 2016, 109(1): 73-101 [48] Chen FZ, Qiang HF, Gao WR. Coupling of smoothed particle hydrodynamics and finite volume method for two-dimensional spouted beds. Computer & Chemical Engineering, 2015, 77: 135-146 [49] 陈福振, 强洪夫, 高巍然. 风沙运动问题的SPH-FVM耦合方法数值模拟研究. 物理学报, 2014, 63(13): 130202 (Chen Fuzhen, Qiang Hongfu, Gao Weiran. Simulation of aerolian sand transport with SPH-FVM coupled method. Acta Physica Sinica, 2014, 63(13): 130202 (in Chinese) doi: 10.7498/aps.63.130202Chen Fuzhen, Qiang Hongfu, Gao Weiran. Simulation of aerolian sand transport with SPH-FVM coupled method. Acta Physica Sinica, 2014, 63(13): 130202 (in Chinese)) doi: 10.7498/aps.63.130202 [50] 陈福振, 强洪夫, 高巍然. 气粒两相流传热问题的光滑离散颗粒流体动力学方法数值模拟. 物理学报, 2014, 63(23): 230206 (Chen Fuzhen, Qiang Hongfu, Gao Weiran. Numerical simulation of heat transfer in gas-particle two-phase flow with smoothed discrete particle hydrodynamics. Acta Physica Sinica, 2014, 63(23): 230206 (in Chinese) doi: 10.7498/aps.63.230206Chen Fuzhen, Qiang Hongfu, Gao Weiran. Numerical simulation of heat transfer in gas-particle two-phase flow with smoothed discrete particle hydrodynamics. Acta Physica Sinica, 2014, 63(23): 230206 (in Chinese)) doi: 10.7498/aps.63.230206 [51] 陈福振, 强洪夫, 苗刚等. 燃料抛撒成雾及其燃烧爆炸的光滑离散颗粒流体动力学方法数值模拟研究. 物理学报, 2015, 64(11): 110202 (Chen Fuzhen, Qiang Hongfu, Miao Gang, et al. Numerical simulation of fuel dispersal into cloud and its combustion and explosion with smoothed discrete particle hydrodynamics. Acta Physica Sinica, 2015, 64(11): 110202 (in Chinese) doi: 10.7498/aps.64.110202Chen Fuzhen, Qiang Hongfu, Miao Gang, et al. Numerical simulation of fuel dispersal into cloud and its combustion and explosion with smoothed discrete particle hydrodynamics. Acta Physica Sinica, 2015, 64(11), 110202 (in Chinese)) doi: 10.7498/aps.64.110202 [52] Chen FZ, Yan H. Elastic-viscoplastic constitutive theory of dense granular flow and its three-dimensional numerical realization. Physics of Fluids, 2021, 33(12): 123310 doi: 10.1063/5.0068458 [53] Chen FZ, Yan H. Constitutive model for solid-like, liquid-like, and gas-like phases of granular media and their numerical implementation. Powder Technology, 2021, 390: 369-386 doi: 10.1016/j.powtec.2021.05.023 [54] Lun CKK, Savage SB, Jeffrey DJ, et al. Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield. Journal of Fluid Mechanics, 1984, 140: 223-256 doi: 10.1017/S0022112084000586 [55] Jenkins JT, Savage SB. A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. Journal of Fluid Mechanics, 1983, 130: 187-202 doi: 10.1017/S0022112083001044 [56] Srivastava A, Sundaresan S. Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology, 2003, 129(1-3): 72-85 doi: 10.1016/S0032-5910(02)00132-8 [57] Savage SB. Analyses of slow high-concentration flows of granular materials. Journal of Fluid Mechanics, 1998, 377: 1-26 doi: 10.1017/S0022112098002936 [58] Johnson PC, Nott P, Jackson R. Frictional-collisional equations of motion for participate flows and their application to chutes. Journal of Fluid Mechanics, 1990, 210: 501-535 doi: 10.1017/S0022112090001380 [59] Johnson PC, Jackson R. Frictional-collisional constitutive relations for granular materials, with application to plane shearing. Journal of Fluid Mechanics, 1987, 176: 67-93 doi: 10.1017/S0022112087000570 [60] Schaeffer DG. Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations, 1987, 66(1): 19-50 doi: 10.1016/0022-0396(87)90038-6 [61] Forterre Y, Pouliquen O. Long-surface-wave instability in dense granular flows. Journal of Fluid Mechanics, 2003, 486: 21-50 doi: 10.1017/S0022112003004555 [62] MiDi GDR. On dense granular flows. European Physical Journal E, 2004, 14: 341-365 [63] Chen JK, Beraun JE, Carney TC. A corrective smoothed particle method for boundary value problems in heat conduction. International Journal for Numerical Methods in Engineering, 1999, 46(2): 231-252 doi: 10.1002/(SICI)1097-0207(19990920)46:2<231::AID-NME672>3.0.CO;2-K [64] Bonet J, Lok T. Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Computer Methods in Applied Mechanics & Engineering, 1999, 180(1-2): 97-115 [65] Hertz H. On the contact of elastic solids. Journal für die reine und angewandte Mathematik, 1882, 92: 156-171 [66] Coulomb CA. Sur une application des regles maximis et minimis a quelques problems de statique, relatives a l’architecture. Acad. Sci. Paris Mem. Math. Phys., 1776, 7: 343-382 [67] Li S, Liu WK. Meshfree and particle methods and their applications. Applied Mechanics Reviews, 2002, 55(1): 1-34 doi: 10.1115/1.1431547 -