基于不规则钙质砂颗粒发展的拖曳力系数模型及其在细观流固耦合数值模拟中应用
|
摘要
钙质砂广泛分布于我国南海海域,作为岛礁填筑材料,其渗透性很大程度上决定着填筑后土体的固结和沉降。拖曳力系数是表达液体对土体颗粒表面力的参数,也是表征颗粒状土体渗透能力的一个重要指标,目前国内外对具有极不规则形状钙质砂拖曳力系数的研究十分有限。在前期大量钙质砂颗粒沉降试验基础上,建立了能够考虑形状系数的颗粒与液体相互作用拖曳力系数理论公式;在已建立的计算流体动力学-离散元法(CFD-DEM)流固耦合理论框架下,将新发展的拖曳力系数公式嵌入到流固耦合程序中,模拟钙质砂颗粒在液体中沉降过程。通过将模拟结果与室内沉降试验对比,验证了新建立的拖曳力模型及程序实现的准确性。研究结果表明,较CFD-DEM程序中已有的未考虑颗粒形状的拖曳力系数半经验模型,新的拖曳力系数模型能够更准确地模拟不规则颗粒在液体中沉降过程;同时,在数值建模中无需采用异形颗粒即可以反映颗粒形状对拖曳力的影响,这将大大降低数值模拟的计算量,提高计算效率。研究可进一步应用于钙质砂水中堆填后固结沉降以及冲刷等实际工程问题分析中。
Calcareous sand is widely spread in South China Sea. As the sea-filling materials in construction of artificial islands, its permeability has significant influence on the consolidation and settlement of soil mass. The drag coefficient, as the effect of fluid drag force acting on the particle surface, plays an important role on the permeability of calcareous sand, which is not extensively studied by researchers so far. Based on the experimental results of calcareous sand particle settling in various fluids, a new drag coefficient model has been proposed. The new model is now incorporated into the CFD(computational fluid dynamics)-DEM(discrete element method) program and is used to simulate the settling process of calcareous sand particles in fluids. By compared with the experimental results, the CFD-DEM program with new drag coefficient model is validated and it also shows its accuracy in predicting the settling behavior of calcareous sand particles of irregular shape over the existing drag coefficient model without considering the effect of particle shape. On the other hand, the utility of spheres used in CFD-DEM model instead of non-spheres can greatly reduce the computational cost and meanwhile represent the effect of particle shape on the drag force. This CFD-DEM approach is promising and will be applied to the analysis of consolidation, settlement and souring of sea-filling projects with calcareous soils.
Calcareous sand is widely spread in South China Sea. As the sea-filling materials in construction of artificial islands, its permeability has significant influence on the consolidation and settlement of soil mass. The drag coefficient, as the effect of fluid drag force acting on the particle surface, plays an important role on the permeability of calcareous sand, which is not extensively studied by researchers so far. Based on the experimental results of calcareous sand particle settling in various fluids, a new drag coefficient model has been proposed. The new model is now incorporated into the CFD(computational fluid dynamics)-DEM(discrete element method) program and is used to simulate the settling process of calcareous sand particles in fluids. By compared with the experimental results, the CFD-DEM program with new drag coefficient model is validated and it also shows its accuracy in predicting the settling behavior of calcareous sand particles of irregular shape over the existing drag coefficient model without considering the effect of particle shape. On the other hand, the utility of spheres used in CFD-DEM model instead of non-spheres can greatly reduce the computational cost and meanwhile represent the effect of particle shape on the drag force. This CFD-DEM approach is promising and will be applied to the analysis of consolidation, settlement and souring of sea-filling projects with calcareous soils.
引文
[1]H?LZER A,SOMMERFELD M.New simple correlation formula for the drag coefficient of non-spherical particles[J].Powder Technology,2008,184(3):361-365.
[2]BAGHERI G,BONADONNA C.On the drag of freely falling non-spherical particles[J].Powder Technology,2016,301:526-544.
[3]DIOGUARDI F,MELE D.A new shape dependent drag correlation formula for non-spherical rough particles:experiments and results[J].Powder Technology,2015,277:222-230.
[4]DIOGUARDI F,DELLINO P,MELE D.Integration of a new shape-dependent particle-fluid drag coefficient law in the multiphase Eulerian-Lagrangian code MFIX-DEM[J].Powder Technology,2014,260:68-77.
[5]ZEGHAL M,SHAMY U E.Coupled continuum-discrete model for saturated granular soils[J].Journal of Engineering Mechanics,2005,131(4):413-426.
[6]周健,周凯敏,姚志雄,等.砂土管涌-滤层防治的离散元数值模拟[J].水利学报,2010,39(1):17-24.ZHOU Jian,ZHOU Kai-min,YAO Zhi-xiong,et al.Numerical simulation of piping-filter prevention in sandy soil by discrete element method[J].Journal of Hydraulic Engineering,2010,41(1):17-24.
[7]ZHOU J,LI Y X,JIA M C,et al.Numerical simulation of failure behavior of granular debris flows based on flume model tests[J].The Scientific World Journal,2013,2013(ID 603130):1-10.
[8]罗勇,龚晓南,吴瑞潜.颗粒流模拟和流体与颗粒相互作用分析[J].浙江大学学报(工学版),2007,41(11):1932-1936.LUO Yong,GONG Xiao-nan,WU Rui-qian.Analysis and simulation of fluid-particles interaction with particle flow code[J].Journal of Zhejiang University(Engineering Science),2007,41(11):1932-1936.
[9]王胤,艾军,杨庆.考虑粒间滚动阻力的CFD-DEM流固耦合数值模拟方法[J].岩土力学,2017,38(6):1-9.WANG Yin,AI Jun,YANG Qing.A CFD-DEM coupled approach to soil incorporating inter-particle rolling resistance[J].Rock and Soil Mechanics,2017,38(6):1-9.
[10]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,2014,35(5):793-801.JIANG Ming-jing,ZHANG Wang-cheng.Coupled CFD-DEM method for soils incorporating equation of state for liquid[J].Chinses Journal of Geotechnical Engineering,2014,35(5):793-801.
[11]GONIVA C,KLOSS C,HAGER A,et al.An open source CFD-DEM perspective[J].Progress in Computational Fluid Dynamics,2012,12(2):140-152.
[12]WANG Y,ZHOU L,WU Y,et al.New simple correlation formula for the drag coefficient of calcareous sand particles of highly irregular shape[J].Powder Technology,2018,326:379-392.
[13]BROWN P P,LAWLER D F.Sphere drag and settling velocity revisited[J].Journal of Environmental Engineering,2003,129(3):222-231.
[14]吴野,王胤,杨庆.考虑钙质砂细观颗粒形状影响的液体拖曳力系数试验研究[J].岩土力学,2018,39(9):3203-3212.WU Ye,WANG Yin,YANG Qing.Experimental study on the drag force coefficient of calcareous sand in liquid considering the effect of particle shape[J].Rock and Soil Mechanics,2018,39(9):3203-3212.
[15]ANDERSON T B,JACKSON R.Fluid mechanical description of fluidized beds.Equations of motion[J].Industrial&Engineering Chemistry Fundamentals,1967,6(4):527-539.
[16]WEN C Y,YU Y H.A generalized method for predicting the minimum fluidization velocity[J].AICh E Journal,1966,12:610-612.
[2]BAGHERI G,BONADONNA C.On the drag of freely falling non-spherical particles[J].Powder Technology,2016,301:526-544.
[3]DIOGUARDI F,MELE D.A new shape dependent drag correlation formula for non-spherical rough particles:experiments and results[J].Powder Technology,2015,277:222-230.
[4]DIOGUARDI F,DELLINO P,MELE D.Integration of a new shape-dependent particle-fluid drag coefficient law in the multiphase Eulerian-Lagrangian code MFIX-DEM[J].Powder Technology,2014,260:68-77.
[5]ZEGHAL M,SHAMY U E.Coupled continuum-discrete model for saturated granular soils[J].Journal of Engineering Mechanics,2005,131(4):413-426.
[6]周健,周凯敏,姚志雄,等.砂土管涌-滤层防治的离散元数值模拟[J].水利学报,2010,39(1):17-24.ZHOU Jian,ZHOU Kai-min,YAO Zhi-xiong,et al.Numerical simulation of piping-filter prevention in sandy soil by discrete element method[J].Journal of Hydraulic Engineering,2010,41(1):17-24.
[7]ZHOU J,LI Y X,JIA M C,et al.Numerical simulation of failure behavior of granular debris flows based on flume model tests[J].The Scientific World Journal,2013,2013(ID 603130):1-10.
[8]罗勇,龚晓南,吴瑞潜.颗粒流模拟和流体与颗粒相互作用分析[J].浙江大学学报(工学版),2007,41(11):1932-1936.LUO Yong,GONG Xiao-nan,WU Rui-qian.Analysis and simulation of fluid-particles interaction with particle flow code[J].Journal of Zhejiang University(Engineering Science),2007,41(11):1932-1936.
[9]王胤,艾军,杨庆.考虑粒间滚动阻力的CFD-DEM流固耦合数值模拟方法[J].岩土力学,2017,38(6):1-9.WANG Yin,AI Jun,YANG Qing.A CFD-DEM coupled approach to soil incorporating inter-particle rolling resistance[J].Rock and Soil Mechanics,2017,38(6):1-9.
[10]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,2014,35(5):793-801.JIANG Ming-jing,ZHANG Wang-cheng.Coupled CFD-DEM method for soils incorporating equation of state for liquid[J].Chinses Journal of Geotechnical Engineering,2014,35(5):793-801.
[11]GONIVA C,KLOSS C,HAGER A,et al.An open source CFD-DEM perspective[J].Progress in Computational Fluid Dynamics,2012,12(2):140-152.
[12]WANG Y,ZHOU L,WU Y,et al.New simple correlation formula for the drag coefficient of calcareous sand particles of highly irregular shape[J].Powder Technology,2018,326:379-392.
[13]BROWN P P,LAWLER D F.Sphere drag and settling velocity revisited[J].Journal of Environmental Engineering,2003,129(3):222-231.
[14]吴野,王胤,杨庆.考虑钙质砂细观颗粒形状影响的液体拖曳力系数试验研究[J].岩土力学,2018,39(9):3203-3212.WU Ye,WANG Yin,YANG Qing.Experimental study on the drag force coefficient of calcareous sand in liquid considering the effect of particle shape[J].Rock and Soil Mechanics,2018,39(9):3203-3212.
[15]ANDERSON T B,JACKSON R.Fluid mechanical description of fluidized beds.Equations of motion[J].Industrial&Engineering Chemistry Fundamentals,1967,6(4):527-539.
[16]WEN C Y,YU Y H.A generalized method for predicting the minimum fluidization velocity[J].AICh E Journal,1966,12:610-612.