A semi-analytical model of the velocity profile for a conduit-multilayer matrix system  

作　　者：Shuai Zhang Xiaoli Liu Enzhi Wang 

机构地区：[1]State Key Laboratory of Hydroscience and Engineering,Key Laboratory of Hydrosphere Sciences of the Ministry of Water Resources,and Department of Hydraulic Engineering,Tsinghua University,Beijing,100084,China

出　　处：《Journal of Rock Mechanics and Geotechnical Engineering》2025年第2期915-930,共16页岩石力学与岩土工程学报(英文)

基　　金：financially supported by the National Natural Science Foundation of China(Grant Nos.52079068,52090081);the State Key Laboratory of Hydroscience and Engineering(Grant No.2021-KY-04).

摘　　要：The flow field characteristics of the conduit-matrix system(CMS)have consistently been a primary area of interest to researchers.However,under the long-term influence of water flow,the hydraulic conductivity of the matrix surrounding the conduit often deforms differentially along the conduit axis,resulting in the development of a conduit-multilayer matrix system(CMMS).This renders conventional models inadequate in accurately describing the flow field characteristics of CMMS.In this study,a semi-analytical model with second-order accuracy is developed to investigate the velocity profile characteristics of CMMS by coupling the Navier-Stokes(N–S)equations in the conduit and the Darcy-Brinkman(D-B)equation in the multilayer matrices.In this model,the interface between the conduit and the matrix satisfies the velocity continuity and stress jumping condition.In contrast,different matrix interfaces require both velocity and stress to be equal.The model's validity is verified through Lattice Boltzmann Method(LBM)simulation,COMSOL simulation,and experimental data under different conduit apertures,matrix region numbers,and matrix permeability characteristics.Moreover,the current model predicts discharges with higher accuracy than the Hagen-Poiseuille law and Darcy's law(the maximum error between the present model and the test is 7.24%).Furthermore,the existing Poiseuille's law,conduit-matrix model,and conduit-matrix1-matrix2 model are all special cases of the current semi-analytical model,thereby indicating its broader applicability.Sensitivity results reveal that the flow velocities in the surrounding matrix and the conduit regions also increase when the permeability of the matrix in proximity to the conduit increases.Additionally,as the stress jumping coefficient at the interface approaches zero,the transition from free flow to seepage becomes smoother.

关 键 词：Flow field characteristics Velocity profile Conduit aperture Stress jumping Conduit-matrix system(CMS) 

分 类 号：O35[理学—流体力学]