The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision ter...The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow,the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations.Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale(SGS)model,in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor,is proposed to model the two-phase governing equations by applying dimension analyses.Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls,the velocity and pressure fields,and the volumetric concentration are calculated.The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.展开更多
Due to the high heterogeneity and complexity of water flow movement for multiple karst water-bearing mediums,the evaluation,effective development,and utilization of karst water resources are significantly limited.Matr...Due to the high heterogeneity and complexity of water flow movement for multiple karst water-bearing mediums,the evaluation,effective development,and utilization of karst water resources are significantly limited.Matrix flow is usually laminar,whereas conduit flow is usually turbulent.The driving mechanisms of water exchange that occur between the karst conduit and its adjacent matrix are not well understood.This paper investigates the hydrodynamic characteristics and the mechanism of flow exchange in dual water-bearing mediums(conduit and matrix)of karst aquifers through laboratory experimentation and numerical simulation.A karst aquifer consisting of a matrix network and a conduit was proposed,and the relationship between the water exchange flux and hydraulic head differences generated from the laboratory experiments was analyzed.Two modes of experimental tests were performed with different fixed water level boundaries in the laboratory karst aquifer.The results indicate that the water exchange capacity was proportional to the square root of hydraulic head differences.The linear exchange term in the conduit flow process(CFP)source program was modified according to experimental results.The modified CFP and the original CFP model experimental data results were compared,and it was found that the modified CFP model had better fitting effects.These results showed that the water exchange mechanism between conduit and matrix is very important for solid-liquid interface reaction,water resource evaluation,and understanding of karst hydrodynamic behavior.展开更多
基金The project supported by the National Natural Science Foundation of China (50176022)
文摘The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules.Assuming that the solid-phase velocity distributions obey the Maxwell equations,the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow,the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations.Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale(SGS)model,in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor,is proposed to model the two-phase governing equations by applying dimension analyses.Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls,the velocity and pressure fields,and the volumetric concentration are calculated.The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.
基金funded by the Guangxi Natural Science Foundation(2018JJA150153)China Geological Survey Research Fund(JYYWF20180402)the project of China Geological Survey(DD20190342)。
文摘Due to the high heterogeneity and complexity of water flow movement for multiple karst water-bearing mediums,the evaluation,effective development,and utilization of karst water resources are significantly limited.Matrix flow is usually laminar,whereas conduit flow is usually turbulent.The driving mechanisms of water exchange that occur between the karst conduit and its adjacent matrix are not well understood.This paper investigates the hydrodynamic characteristics and the mechanism of flow exchange in dual water-bearing mediums(conduit and matrix)of karst aquifers through laboratory experimentation and numerical simulation.A karst aquifer consisting of a matrix network and a conduit was proposed,and the relationship between the water exchange flux and hydraulic head differences generated from the laboratory experiments was analyzed.Two modes of experimental tests were performed with different fixed water level boundaries in the laboratory karst aquifer.The results indicate that the water exchange capacity was proportional to the square root of hydraulic head differences.The linear exchange term in the conduit flow process(CFP)source program was modified according to experimental results.The modified CFP and the original CFP model experimental data results were compared,and it was found that the modified CFP model had better fitting effects.These results showed that the water exchange mechanism between conduit and matrix is very important for solid-liquid interface reaction,water resource evaluation,and understanding of karst hydrodynamic behavior.
