Coupled CFD-DEM method for soils incorporating equation of state for liquid
JIANG Ming-jing1, 2, ZHANG Wang-cheng1, 3
1. Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China; 2. Key Laboratory of Geotechnical & Underground Engineering, Ministry of Education, Shanghai 200092, China; 3. Centre for Offshore Foundation Systems, University of Western Australia, Perth WA6009, Australia
Abstract：The Tait equation of state for liquid is implemented into the N-S equations-based computational fluid dynamics (CFD). This method is then coupled with the distinct element method (DEM) so as to establish CFD-DEM codes to simulate the porous media with weakly compressive fluid. Firstly, the governing equations for the coupled CFD-DEM method are introduced, including equations for fluid-particle interaction forces, N-S equations, Tait equation of state for liquid and motion equations for particle system. Then, a coupled CFD-DEM scheme is implemented into the DEM commercial software PFC2D. Finally, two benchmarking examples, namely, single particle free settling and one-dimensional consolidation, are used to validate the coupled CFD-DEM method. The results show that in the CFD-DEM simulations the free settling velocity of single particle meets the Stokes's solution, and the excess pore pressure and degree of consolidation at different values of Tv are close to those of the Terzaghi's consolidation theory.
蒋明镜, 张望城. 一种考虑流体状态方程的土体CFD-DEM耦合数值方法[J]. 岩土工程学报, 2014, 36(5): 793-801.
JIANG Ming-jing, ZHANG Wang-cheng. Coupled CFD-DEM method for soils incorporating equation of state for liquid. Chinese J. Geot. Eng., 2014, 36(5): 793-801.
[1] CUNDALL P A, STRACK O D L. The discrete numerical model for granular assemblies[J]. Géotechnique, 1979, 29(1): 47-65. [2] ANDERSON J D. Computational fluid dynamics[M]. New York: McGraw-Hill, 1995. [3] TSUJI Y, KAWAGUCHI T, TANAKA T. Discrete particle simulation of two-dimensional fluidized bed[J]. Powder Technology, 1993, 77(1): 79-87. [4] XU B, YU A. Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics[J]. Chemical Engineering Science, 1997, 52(16): 2785-2809. [5] XU B, YU A, CHEW S, et al. Numerical simulation of the gas-solid flow in a bed with lateral gas blasting[J]. Powder Technology, 2000, 109(1): 13-26. [6] YU A B, XU B H. Particle-scale modelling of gas-solid flow in fluidisation[J]. Journal of Chemical Technology and Biotechnology, 2003, 78(2‐3): 111-121. [7] CHU K, YU A. Numerical simulation of complex particle-fluid flows[J]. Powder Technology, 2008, 179(3): 104-114. [8] EL SHAMY U, ZEGHAL M. Coupled continuum-discrete model for saturated granular soils[J]. Journal of Engineering Mechanics, 2005, 131(4): 413-426. [9] KAFUI K, THORNTON C, ADAMS M. Discrete particle-continuum fluid modelling of gas-solid fluidised beds[J]. Chemical Engineering Science, 2002, 57(13): 2395-2410. [10] ZHAO J, SHAN T. Coupled CFD-DEM simulation of fluid-particle interaction in geomechanics[J]. Powder Technology, 2013, 239: 248-258. [11] ERGUN S. Fluid flow through packed columns[J]. Chemical Engineering Progress, 1952, 48(2): 89-94. [12] WEN C Y, YU Y H. Mechanics of fluidization[J]. Chemical Engineering Progress Symposium Series, 1966, 62(67): 100-111. [13] ANDERSON T B, JACKSON R. Fluid mechanical description of fluidized beds. Equations of motion[J]. Industrial & Engineering Chemistry Fundamentals, 1967, 6(4): 527-539. [14] TAIT P G. Report on some of the physical properties of fresh water and of sea-water[M]. Johnson Reprint Corp, 1965. [15] LI Y H. Equation of state of water and sea water[J]. Journal of Geophysical Research, 1967, 72(10): 2665-2678. [16] JIANG M, YU H-S, HARRIS D. A novel discrete model for granular material incorporating rolling resistance[J]. Computers and Geotechnics, 2005, 32(5): 340-357. [17] ISSA R I. Solution of the implicitly discretised fluid flow equations by operator-splitting[J]. Journal of Computational Physics, 1986, 62(1): 40-65. [18] Itasca Consulting Group Inc. Particle Flow Code in 2 Dimensions, version3.1[M]. USA: Minnesota, 2004. [19] MCCABE W L, SMITH J C, HARRIOTT P. Unit operations of chemical engineering[M]. New York: McGraw-Hill, 1956.
