基于FVM和VOF的平面裂隙注浆数值模型
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摘要
为研究浆液在岩体裂隙中的运移机制,建立了基于有限体积法(FVM)和流体体积(VOF)原理的平板裂隙注浆数值模型。模型采用同位网格有限体法离散流动控制方程,为避免对振荡压强场求解失真问题,借助动量插值方法构造控制体界面流速,并考虑浆液扩散过程的两相流特征,利用VOF方法追踪两相移动界面,实现了同位网格架构下浆液流场的数值求解。选择无限大平板裂隙注浆算例对该模型进行了测试,结果表明,不同时刻浆液压强分布、流速、扩散范围等模拟结果与解析解吻合良好,显示了较高的求解精度,为研发裂隙注浆仿真系统奠定了基础。
To investigate the mechanism of grout spreading in jointed rocks, a numerical model for simulating planar fracture grouting is developed based on the finite volume method(FVM), the volume of fluid(VOF) method, and collocated grids. This model adopts a momentum interpolation method in its calculation of the flow rate at the control volume faces to avoid the distorted solution of oscillating pressure fields, and considers the two-phase flow characteristic of grout spreading, tracking the moving interface of two phases by VOF calculations. It is tested through application to the grouting in an infinite planar fracture and the results show that its calculations of grouting pressure field distribution, flow velocity and diffusion radius agree well with the analytical solution, thereby verifying a high accuracy in the calculations and laying a basis for developing a dedicated system for fracture grouting simulation.
To investigate the mechanism of grout spreading in jointed rocks, a numerical model for simulating planar fracture grouting is developed based on the finite volume method(FVM), the volume of fluid(VOF) method, and collocated grids. This model adopts a momentum interpolation method in its calculation of the flow rate at the control volume faces to avoid the distorted solution of oscillating pressure fields, and considers the two-phase flow characteristic of grout spreading, tracking the moving interface of two phases by VOF calculations. It is tested through application to the grouting in an infinite planar fracture and the results show that its calculations of grouting pressure field distribution, flow velocity and diffusion radius agree well with the analytical solution, thereby verifying a high accuracy in the calculations and laying a basis for developing a dedicated system for fracture grouting simulation.
引文
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[13]王福军.计算流体动力学分析——CFD软件原理与应用[M].北京:清华大学出版社,2004.WANG Fujun.Computational fluid dynamics analysis–CFD software principle and application[M].Beijing:Tsinghua University Press,2004.(in Chinese)
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[17]湛铠瑜,隋旺华,高岳.单一裂隙动水注浆扩散模型[J].岩土力学,2011,32(6):1659-1663.ZHAN Kaiyu,SUI Wanghua,GAO Yue.A model for grouting into single fracture with flowing water[J].Rock and Soil Mechanics,2011,32(6):1659-1663.(in Chinese)
[18]冯志强.破碎煤岩体化学注浆加固材料研制及渗透扩散特性研究[D].北京:煤炭科学研究总院,2007.FENG Zhiqiang.Material development and research of osmosis and diffusion on chemical grouting for extraordinary cracked coal and rockmass[D].Beijing:Coal Science Research Institute,2007.(in Chinese)
[2]张正安,杨具瑞,李续楠,等.水泥和速凝剂掺量对红黏土浆液性能影响研究[J].水力发电学报,2017,36(5):112-120.ZHANG Zheng’an,YANG Jurui,LI Xunan,et al.Influence of different contents of cement and quick-setting agent on performance of red clay slurry[J].Journal of Hydroelectric Engineering,2017,36(5):112-120.(in Chinese)
[3]Hassler L,Hakansson U,Stille H.Computer-simulated flow of grouts injointed rock[J].Tunnelling and Underground Space Technology,1992,7(4):441-446.
[4]Gustafson G,Stille H.Prediction of groutability from grout properties and hydrogeological data[J].Tunnelling and Underground Space Technology,1996,11(3):325-332.
[5]Eriksson M,Stille H,Andersson J.Numerical calculations for prediction of grout spread with account for filtration and varying aperture[J].Tunnelling and Underground Space Technology,2000,15(4):353-364.
[6]Saeidi O,Stille H,Torabi S R.Numerical and analytical analyses of the effects of different joint and grout properties on the rock mass groutability[J].Tunnelling and Underground Space Technology,2013,38(5):11-25.
[7]Yang M J,Yue Z Q,Lee P K K,et al.Prediction of grout penetration in fractured rocks by numerical simulation[J].Canadian Geotechnical Journal,2002,39(6):1384-1394.
[8]罗平平,陈蕾,邹正盛.空间岩体裂隙网络灌浆数值模拟研究[J].岩土工程学报,2007,29(12):1144-1148.LUO Pingping,CHEN Lei,ZOU Zhengsheng.Numerical simulation of grouting in space fracture network of rock mass[J].Chinese Journal of Geotechnical Engineering,2007,29(12):1144-1148.(in Chinese)
[9]刘健,刘人太,张霄,等.水泥浆液裂隙注浆扩散规律模型试验与数值模拟[J].岩石力学与工程学报,2012,31(12):2445-2452.LIU Jian,LIU Rentai,ZHANG Xiao,et al.Diffusion law model test and numerical simulation of cement fracture grouting[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(12):2445-2452.(in Chinese)
[10]朱明听.单一裂隙注浆扩散封堵机理的数值模拟研究[D].济南:山东大学,2013.ZHU Mingting.The numerical simulation of grouting diffusion and plugging mechanism based on single fracture[D].Jinan:Shandong University,2013.(in Chinese)
[11]赵鹏.基于浆液黏度时变特性的交叉裂隙注浆扩散规律[D].济南:山东大学,2016.ZHAO Peng.The diffusion law of cross fracture grouting based on time-dependent behavior of viscosity of grout[D].Jinan:Shandong University,2016.(in Chinese)
[12]Versteeg H,Malalasekera W.An Introduction to computational fluid dynamics:The finite volume method[M].England:Pearson Education Limited,2007.
[13]王福军.计算流体动力学分析——CFD软件原理与应用[M].北京:清华大学出版社,2004.WANG Fujun.Computational fluid dynamics analysis–CFD software principle and application[M].Beijing:Tsinghua University Press,2004.(in Chinese)
[14]Rhie C M,Chow W L.Numerical study of the turbulent flow past an airfoil with trailing edge separation[J].AIAA Journal,1983,21(11):1525-1532.
[15]刘儒勋,舒其望.计算流体力学的若干新方法[M].北京:科学出版社,2003.LIU Ruxun,SHU Qiwang.Some new methods in computational fluid dynamics[M].Beijing:Science Press,2003.(in Chinese)
[16]Rudman M.Volume-tracking method for interfacial flow calculation[J].International Journal for Numerical Methods in Fluids,1997,24(7):671-691.
[17]湛铠瑜,隋旺华,高岳.单一裂隙动水注浆扩散模型[J].岩土力学,2011,32(6):1659-1663.ZHAN Kaiyu,SUI Wanghua,GAO Yue.A model for grouting into single fracture with flowing water[J].Rock and Soil Mechanics,2011,32(6):1659-1663.(in Chinese)
[18]冯志强.破碎煤岩体化学注浆加固材料研制及渗透扩散特性研究[D].北京:煤炭科学研究总院,2007.FENG Zhiqiang.Material development and research of osmosis and diffusion on chemical grouting for extraordinary cracked coal and rockmass[D].Beijing:Coal Science Research Institute,2007.(in Chinese)