NUMERICAL STUDY OF NON-AQUEOUS PHASE LIQUID TRANSPORT IN A SINGLE FILLED FRACTURE BY LATTICE BOLTZMANN METHOD

In this article,the Non-Aqueous Phase Liquid(NAPL)transport in the single filled fracture was studied with the Shan-Chen multi-component multiphase Lattice Boltzmann Method(LBM)with special consideration of wettability effects.With the help of the model,the contact angle of the non-wetting phase and wetting phase interface at a solid wall could be adjusted.By considering a set of appropriate boundary conditions,the fractured conductivity was investigated in condition that the NAPL blocks the channels in the single filled fracture.In order to study the wettability effects on the NAPL transport,a constant driving force was introduced in the Shan-Chen multi-component multiphase LBM.Flow regimes with different wettabilities were discussed.Simulated results show that the LBM is a very instrumental method for simulating and studying the immiscible multiphase flow problems in single filled fracture.     

SIMULATION OF SOLUTE TRANSPORT IN FRACTURED NETWORK WITH A PROBABILITY METHOD

The simulation of solute transport in fractured rock mass has been conducted with the Finite Difference Method(FDM), Finite Element Method(FEM) and Finite Analysis Method(FAM), etc.. However, groundwater flow and solute transport is very complex in fractured network compared to the rocks matrix because water flow and tracer particles have different selections of pathways when they travel to the fractured intersections. It is difficult for traditional method to simulate the law of solute transport in fractured network. Hence a new simulation method, the probability method, is developed. In the method, transfer probabilities for fractured network are calculated using the flux of input and output from fractured intersection points, and travel times of tracer particles are determined with random numbers, dispersion parameter and velocity. Furthermore, corresponding computing program is developed using the FORTRAN language. The comparison between simulated and experimental results shows that the probability method is of considerable reliability and is an effective method to simulate solute transport in fractured network, and the case study of the Jinping I-Hydropower Station displays its wide application prospect.     

LABORATORY EXPERIMENTS ON SOLUTE TRANSPORT IN A PARTIAL TRANSFIXION SINGLE FRACTURE

In the study of solute transport in rough single fracture,the contact area is an important factor.The single fracture is defined as two categories in this article:the full transfixion single fracture and the partial transfixion single fracture.The purpose of this article is to research how the contact area affects the solute transport in partial transfixion single fracture.The contact area is generalized as square blocks with three sizes,and contact rate is variable,a series of experiments for solute transp...     

PARALLEL LATTICE BGK SIMULATION OF NATURAL CONVECTION IN A CAVITY

1.INTRODUCTIONOver the last two decades,the LBM has at-tracted much attention as a novel alternative nu-merical method different from traditional CFDmethod for si mulating complex fluid flows[1-3].Ithas already found extensive applications in si mula-ting the physical phenomena of various complexi-ties ranging fromflows in porous media[4],magne-to hydrodynamics[5],multidi mensional transientflow[6]and i mmiscible fluids[7]to turbulence[8,9].Compared with conventional numerical methods,t…     

SIMULATION OF SOLUTE TRANSPORT USING A COUPLING MODEL BASED ON FINITE VOLUME METHOD IN FRACTURED ROCKS

The discrete version of solute transport equation for porous matrix depicted with the continuum model and the discrete fractured-network model are derived for fractured rocks with the Finite Volume Method(FVM).The two models are coupled according to the continuity condition of hydraulic head and concentration and the conservation of flow flux and mass flux in the contact plane between porous matrix and fractures.Numerical results show that the simulated concentration of the coupling model based on the FVM a...     

A LATTICE BOLTZMANN METHOD FOR SIMULATION OF A THREE- DIMENSIONAL DROP IMPACT ON A LIQUID FILM

A single-phase free surface tracking model based on the Lattice Boltzmann Method （LBM）, which has capability of simulating liquid-gas system with the assumption that the gas phase has only negligible influence on the liquid phase, is utilized to simulate the flow of a drop impacting on a liquid film. Three typical outcomes in the flows, i.e., deposition, crown and splash, which have been observed in the previous experiments, are obtained in the present three dimensional numerical simulations. The numerical results are consistent with the experimental and analytical results available.     

EXPERIMENTAL STUDY OF THE NON-DARCY FLOW AND SOLUTE TRANSPORT IN A CHANNELED SINGLE FRACTURE

The characterization of fracture rocks is always a key issue in understanding the flow and solute transport in fractured media. This article studies the solute transport in a Channeled Single Fracture (CSF), a single fracture with contact in certain areas. The flow in a CSF often has preferential pathways and the transport in a CSF often has Break Through Curves (BTCs) with long tails. The Surface Contact Ratio (SCR), the ratio of the contact area to the total fracture area, is an important indicator for th...     

QUALIFICATION OF UNCERTAINTY FOR SIMULATING SOLUTE TRANSPORT IN THE HETEROGENEOUS MEDIA WITH SPARSE GRID COLLOCATION METHOD

The sparse grid collocation method is discussed to qualify the uncertainty of solute transport. The Karhunen-Loeve (KL) expansion is employed to decompose the log transformed hydraulic conductivity. The head, velocity and concentration fields are represented by the Lagrange polynomial expansion. A sparse grid collocation method is then used to reduce the original stochastic partial differential equations to a set of deterministic equations which is collocated at selected interpolation (collocation) points. The collocation points are constructed by the Smolyak algorithm. The accuracy, efficiency and convergence property of sparse grid collocation method are investigated by numerical experiments. The analysis shows that stochastic collocation strategy helps to decouple stochastic computations, and all the numerical computation is possible to be implemented by existing deterministic finite element codes. The proposed method provides an efficient way to evaluate the uncertainty of the solute transport in the heterogeneous media.     

SIMULATION OF THE TWO PHASE FLOW OF DROPLET IMPINGEMENT ON LIQUID FILM BY THE LATTICE BOLTZMANN METHOD

A Lattice Boltzmann Method (LBM) with two-distribution functions is employed for simulating the two-phase flow induced by a liquid droplet impinging onto the film of the same liquid on solid surface.The model is suitable for solution of twophase flow problem at high density and viscosity ratios of liquid to vapor and phase transition between liquid and its vapor.The roles of the vapor flow,the density ratio of liquid to vapor and the surface tension of the droplet in the splashing formation are discussed.It is concluded that the vapour flow induced by the droplet fall and splash in the whole impinging process may affect remarkably the splash behaviour.For the case of large density ratio of liquid to vapor a crown may engender after the droplet collides with the film.However,for the case of small density ratio of liquid to vapor a "bell" like splash may be observed.     

EXPERIMENTAL STUDY OF FRICTION FACTOR FOR GROUNDWATER FLOW IN A SINGLE ROUGH FRACTURE

To study the relationships between the friction factor f and the flow type in a single rough fracture, the formulae of f for both unconfined and confined flows are deduced based on previous studies. The relationships between f and the Reynolds number (Re) for different relative roughnesses are investigated experimentally. The Moody-type diagram, based on the deduced formula of f, is also plotted and the hydraulic characteristics of the flow in a rough fracture are analyzed. Results show that the Moody-type diagram of the experiment has a similar distribution to that of the conventional Moody diagram. It is found that the value of f in the experiment is much smaller than that of the conventional Moody diagram and turbulent flow appears easier for rough fractures, which can be explained by the separation phenomenon in boundary layers. The critical Re ranging from 650 to 700 in rough fractures is concluded based on the experimental results. It also can be concluded that the friction factor f is related not only with the Re and the relative roughness but also with the absolute roughness.     

APPLICATION OF LBM-SGS MODEL TO FLOWS IN A PUMPING-STATION FOREBAY

A 2-D Lattice Boltzmann Method (LBM) coupled with a Sub-Grid Stress (SGS) model is proposed and validated by flows around a non-submerged spur dike in a channel. And then the LBM-SGS model is further applied to flows in a pumping-station forebay. Shallow water equations are numerically solved by the LBM and the turbulence can be taken into account and modeled efficiently by the Large Eddy Simulation (LES) model. The bounce-back scheme of the non-equilibrium part of the distribution function is used at the inlet boundary, the normal gradient of the distribution function is set as zero at the outlet boundary and the bounce-back scheme is applied to the solid wall to ensure non-slip boundary conditions. Firstly, the model successfully predicts the flow characteristics around a spur dike, such as circulating flow, velocity and water depth distributions. The results are verified by the experimental data and compared to the results obtained by conventional Smagoringsky Model (SM) of LES. Finally, the LBM-SGS model is used to further predict the flow characteristics in a forebay, such as secondary flow and water level. The comparisons show that the model scheme has the capacity to simulate complex flows in shallow water with reasonable accuracy and reliability.