基于格子—玻尔兹曼方法的裂缝导流能力流固耦合

为了定量研究不同类型支撑剂填充裂缝的导流能力及其影响因素,借助离散元方法构建了不同粒径范围内支撑剂在不同缝宽裂缝中的堆积模型,利用耦合的固体力学和格子—玻尔兹曼方法,分析了在闭合压力作用下支撑剂在水力裂缝中的嵌入程度及缝宽变化,并以此为基础研究了支撑剂粒径和裂缝缝宽对水力裂缝渗透率和导流能力的影响。通过与实验数据进行对比验证了模型的准确性。模拟结果表明,随着初始缝宽的减小和支撑剂粒径的增大裂缝缝宽的减小程度不断增大,最大减小了31.95%,且初始缝宽对其影响较支撑剂粒径更为显著;水力裂缝的渗透率随着缝宽的减小和支撑剂粒径的增大而增大,但是随之应力敏感性更强,闭合压力作用下裂缝渗透率最大减小了93.37%;具有较高渗透率的窄裂缝,其导流能力相对于宽裂缝反而更小,说明相对于裂缝渗透率,裂缝宽度是影响裂缝导流能力的主要因素。

Reconstruction of 3-D digital cores using a hybrid method

A 3-D digital core describes the pore space microstructure of rocks. An X-ray micro CT scan is the most accurate and direct but costly method to obtain a 3-D digital core. In this study, we propose a hybrid method which combines sedimentation simulation and simulated annealing （SA） method to generate 3-D digital cores based on 2-D images of rocks. The method starts with the sedimentation simulation to build a 3-D digital core, which is the initial configuration for the SA method. We update the initial digital core using the SA method to match the auto-correlation function of the 2-D rock image and eventually build the final 3-D digital core. Compared with the typical SA method, the hybrid method has significantly reduced the computation time. Local porosity theory is applied to quantitatively compare the reconstructed 3-D digital cores with the X-ray micro CT 3-D images. The results indicate that the 3-D digital cores reconstructed by the hybrid method have homogeneity and geometric connectivity similar to those of the X-ray micro CT image. The formation factors and permeabilities of the reconstructed 3-D digital cores are estimated using the finite element method （FEM） and lattice Boltzmann method （LBM）, respectively. The simulated results are in good agreement with the experimental measurements. Comparison of the simulation results suggests that the digital cores reconstructed by the hybrid method more closely reflect the true transport properties than the typical SA method alone.

Numerical simulation of dynamic process for liquid film spreading by lattice Boltzmann method and its experimental verification

Combined with the kinetic model of liquid film spreading, a new numerical method of solid-liquid-gas three-phase flow was developed for the moving of contact line, which was a hybrid method of computational fluid dynamics and lattice Boltzmalm method （LBM）. By taking the effect of molecule force in droplet and the wall surface on liquid film into account, the changing law of contact angle with different surface tensions was analyzed on glass and aluminum foil surfaces. Compared with experimental results, the standard deviation by using LBM is less than 0.5°, which validates the feasibility of LBM simulation on the dynamic process of liquid film spreading. In addition, oscillations are discovered both at the initial and end phases. The phenomenon of retraction is also found and the maximum retraction angle is 7.58°. The obtained result shows that the retraction is proved to be correlative with precursor film by tracking the volume change of liquid film contour. Furthermore, non-dimensional coefficient 2 is introduced to measure the liquid film retraction capacity.

Thermal performance analysis of building construction with insulated walls in summer days and nights

In the present study,the insulation mechanism of building walls during the summer days and nights is investigated with a realistic approach to enhance their performance.A fiber layer,as a porous medium with air gaps,is used along the wall layers to decrease the energy loss.Meanwhile,the radiation heat flux variation during five days in a row has been considered for each side of the building,and it is tried to reach the optimum values for geometrical factors and find suitable insulation for each side of the building.A lattice Boltzmann method(LBM) based code is developed to simulate the actual chain of the heat transfer which consists of radiation,conduction,forced and natural convection combination within wall layers including fiber porous insulation.The results indicate that for the current insulation model,the effect of natural convection on the heat transfer is not negligible and the existence of the porous layer has caused a positive impact on the heat loss reduction by decreasing the circulation speed.Also,by using the optimum location and thickness for the insulation layer,it is showed that each side of the building has different rates of energy loss during a day,and for the appropriate insulation,they need to be evaluated separately.

Multiple-Relaxation-Time Lattice Boltzmann Approach to Richtmyer-Meshkov Instability

The aims of the present paper are twofold. At first, we further study the Multiple-Relaxation-Time （MRT） Lattice Boltzmann （LB） model proposed in [Europhys. Lett. 90 （2010） 54003]. We discuss the reason why the Gram Schmidt orthogonalization procedure is not needed in the construction of transformation matrix M; point out a reason why the Kataoka-Tsutahara model [Phys. Rev. E 69 （2004） 035701（R）] is only valid in subsonic flows. The yon Neumann stability analysis is performed. Secondly, we carry out a preliminary quantitative study on the Richtmyer- Meshkov instability using the proposed MRT LB model. When a shock wave travels from a light medium to a heavy one, the simulated growth rate is in qualitative agreement with the perturbation model by Zhang-Sohn. It is about half of the predicted value by the impulsive model and is closer to the experimental result. When the shock wave travels from a heavy medium to a light one, our simulation results are also consistent with physical analysis.

Impact of a background velocity field on solidification growth of single-crystal nuclei using the PF-LBM

To promote/inhibit ice formation in the natural environment and industrial systems,the growth and evolution process of ice single-crystal nuclei were simulated using the phase field-lattice Boltzmann method(PF-LBM),and the influence of a background flow field on the growth of single-crystal nucleus dendrites was also analyzed.The results show that the flow field makes dendrite growth asymmetric.The growth of dendrites is more developed on the upstream side than on the downstream side.The dendrite tip growth rate and tip radius are greater on the upstream side than on the downstream side.The solid phase ratio is greater with a background flow field than without one.The higher the flow velocity is,the more developed the dendrites on the upstream side,the faster the dendrites grow,and the higher the dendrite tip growth rate.The dendrites on the backflow side have a lower flow rate and a lower degree of supercooling than those on the upstream side,which inhibits the solidification process,the growth rate is slow,and the dendrites are underdeveloped.

Rotational Flow in a Narrow Annular Gap Based on Lattice Boltzmann Method

For comprehensive characteristics of flow in a gas bearing,lattice Boltzmann method(LBM)is applied for study of the two-dimensional flow between two eccentric cylinders with the inner one rotating at a high speed.The flow pattern and circumferential pressure distribution are discussed based on critical issues such as eccentricity ranging from 0.2 to 0.9,clearance ratio varying from 0.005 to 0.01 and rotating speed in the range of 3×104—1.8×105 r/min.The analysis and discussion on the circumferential pressure distribution affirmed the quasilinear relation between the extremum pressure and rotating speed.Furthermore,a high eccentricity and small clearance ratio contributes most to the fluctuation of the circumferential pressure distribution.The flow pattern inside the channel exhibits separation vortex under a large eccentricity.The conclusions drawn in this work give rise to prediction of the flow pattern in the gas bearing which is beneficial for evaluating the performance of as well as instructing the design and development.

Numerical Simulation of Two-Dimensional Flow over Three Cylinders by Lattice Boltzmann Method

The numerical simulation using the multiple relaxation time lattice Boltzmann method （MRT-LBM） is carried out for the purpose of investigating the two-dimensional flow around three circular cylinders. Among these three circular cylinders, one of the three cylinders on which a forced in-line vibrating is used to do this research and attempt to find out the effects of the moving cylinder and the other two rigid cylinders on the wake characteristics and vortex formation. As a benchmark problem to discuss the problem of lift coefficient r.m.s for these cylinders with spacing ratios T/ D between other rigid side-by-side cylinders, and the calculation is carried out with two compared cases at Reynolds number of 100, two of the cylinders are rigid and the other one is an in-line vibrated cylinder lying downstream, in addition, forced vibrating amplitude and frequency are A/D = 0.5 and fv= 0.4 （where A is the forced amplitude, D is the cylinder diameter, and fv stands for the vibrating frequency, respectively）. The calculated results not only indicate that the spacing ratios T/D （T is the center-to-center spacing between the two upstream cylinders） have influence on the wake patterns and the formation of vortex shedding, but also analyze the lift coefficient r.m.s for the three cylinders with the spacing ratios S/D （where S is the center-to-center spacing between the center of upstream two side-by-side cylinders and downstream cylinder）.

Lattice Boltzmann Study of Mixed Convection in a Cubic Cavity

The problem of the mixed convection in a cubic cavity is studied with lattice Boltzmann method. A multiple-relaxation-time lattice Boltzmann model for incompressible flow in the cubic cavity and another thermal lattice Boltzmann model for solving energy/temperature equation are proposed. The present models are first validated through a comparison with some available results, and then, we present a detailed parameter study on the mixed convection in the cubic cavity. The numerical results show that the flow and the Reynolds and Richardson numbers. temperature patterns change greatly with variations of

Effect of Viscosities on Mixing in A Patterned Micro Mixer

The effect of viscosity and viscosity difference and boundary patterned slip on mixing in a micro mixer has been numerically studied using lattice Boltzmann method （LBM）. The slip and no-slip ratio is not constant and varies irregularly, and viscosity is altered by changing the relaxation time in LBE equation. The slip boundary condition is simulated by specular reflection boundary and the no-slip boundary condition is simulated by bounce back boundary. It has been found that it is feasible to optimize the micro mixer design by combining the viscosity effect and boundary patterned ratio altogether.

Nonlinear Dynamics of Rayleigh Taylor Instabilities Studied with a Lattice Boltzmann Method

Multi-relaxation time lattice Boltzmann method is employed to study the later stages of Rayleigh Taylor instabilities. A heavy fluid is placed over an immiscible lighter fluid in an unstable equilibrium. Various initial disturbances are used to initiate the flow. The D2Q9 lattice arrangement is employed on the computational domain. The density distribution function is determined for both fluids, and a coloring function is used to highlight the two fluids. Interactive forces and body forces are modelled by using the Shah and Chert model. Three different initial disturbances are studied, and their late stages are examined. The classic mushroom structure can be seen on all three cases. Distortions of the mushroom structures are seen due to the effects of the boundary and the influence of the initial disturbance.

Solving generalized lattice Boltzmann model for 3-D cavity flows using CUDA-GPU

The generalized lattice Boltzmann equation(GLBE),with the addition of the standard Smagorinsky subgrid-stress(SGS) model,has been proved that it is more suitable for simulating high Reynolds number turbulent flows when compared with the lattice BGK Boltzmann equation(LBGK).However,the computing efficiency of lattice Boltzmann method(LBM) is too low to make it for practical applications,unless using a massive parallel computing clusters facility.In this study,the massive parallel computing power from an inexpensive graphic processor unit(GPU) and a typical personal computer has been developed for improving the computing efficiency,more than 100 times.This developed three-dimensional(3-D) GLBE-SGS model,with the D3Q19 scheme for simplifying collision and streaming courses,has been successfully used to study 3-D rectangular cavity flows with Reynolds number up to 10000.

Numerical simulation of immiscible liquid-liquid flow in microchannels using lattice Boltzmann method

Immiscible kerosene-water two-phase flows in microchannels connected by a T-junction were numerically studied by a Lattice Boltzmann (LB) method based on field mediators.The two-phase flow lattice Boltzmann model was first validated and improved by several test cases of a still droplet.The five distinct flow regimes of the kerosene-water system,previously identified in the experiments from Zhao et al.,were reproduced.The quantitative and qualitative agreement between the simulations and the experimental data show the effectiveness of the numerical method.The roles of the interfacial tension and contact angle on the flow patterns and shapes of droplets were discussed and highlighted according to the numerical results based on the improved two-phase LB model.This work demonstrated that the developed LBM simulator is a viable tool to study immiscible two-phase flows in microchannels,and such a tool could provide tangible guidance for the design of various microfluidic devices that involve immiscible multi-phase flows.

Lattice Boltzmann simulation of flow around two,three and four circular cylinders in close proximity

Cross-flows around two,three and four circular cylinders in tandem,side-by-side,isosceles triangle and square arrangements are simulated using the incompressible lattice Boltzmann method with a second-order accurate curved boundary condition at Reynolds number 200 and the cylinder center-to-center transverse or/and longitudinal spacing 1.5D,where D is the identical circular cylinder diameter.The wake patterns,pressure and force distributions on the cylinders and mechanism of flow dynamics are investigated and compared among the four cases.The results also show that flows around the three or four cylinders significantly differ from those of the two cylinders in the tandem and side-by-side arrangements although there are some common features among the four cases due to their similarity of structures,which are interesting,complex and useful for practical applications.This study provides a useful database to validate the simplicity,accuracy and robustness of the Lattice Boltzmann method.

Lattice Boltzmann simulation of fluid flow through coal reservoir's fractal pore structure

The influences of fractal pore structure in coal reservoir on coalbed methane(CBM) migration were analyzed in detail by coupling theoretical models and numerical methods.Different types of fractals were generated based on the construction thought of the standard Menger Sponge to model the 3D nonlinear coal pore structures.Then a correlation model between the permeability of fractal porous medium and its pore-size-distribution characteristics was derived using the parallel and serial modes and verified by Lattice Boltzmann Method(LBM).Based on the coupled method,porosity(ф),fractal dimension of pore structure(Db),pore size range(rmin,rmax) and other parameters were systematically analyzed for their influences on the permeability(ф) of fractal porous medium.The results indicate that:① the channels connected by pores with the maximum size(rmax) dominate the permeability,approximating in the quadratic law;② the greater the ratio of r max and r min is,the higher is;③ the relationship between D b and follows a negative power law model,and breaks into two segments at the position where Db ≌2.5.Based on the results above,a predicting model of fractal porous medium permeability was proposed,formulated as k=cfrnmax,where C and n(approximately equal to 2) are constants and f is an expression only containing parameters of fractal pore structure.In addition,the equivalence of the new proposed model for porous medium and the Kozeny-Carman model k=Crn was verified at Db =2.0.

Simulation of Gas Exothermic Chemical Reaction in Porous Media Reactor with Lattice Boltzmann Method

Exothermic reactor is the main part in a chemical heat pump. It involves complex multi-component exothermal chemical reaction in catalyst-filled porous media. The lattice Boltzmann method (LBM) is developed to simulate the characteristics of fluid flow, heat and mass transfer coupling chemical reaction in the exothermic reactor of the isopropanol/acetone/hydrogen chemical heat pump system. Fractal theory is used to structure a porous medium model in the reactor. The simulation results show that LBM is suitable for the simulation and the conversion has an optimal value with different inlet velocities.

AN EFFICIENT RED BLOOD CELL MODEL IN THE FRAME OF IB-LBM AND ITS APPLICATION

A two-dinmnsional red blood cell （RBC） membrane model based on elastic and Euler- Bernoulli beam theories is introduced in the frame of immersed boundary-lattice Boltz- mann method （IB-LBM）. The effect of the flexible membrane is handled by the immersed boundary method in which the stress exerted by the RBC on the ambient fluid is spread onto the collocated grid points near the boundary. The fluid dynamics is obtained by solving the discrete lattice Boltzmann equation. A ＂ghost shape＂, to which the RBC returns when restoring, is introduced by prescribing a bending force along the bound- ary. Numerical examples involving tumbling, tank-treading and RBC aggregation in shear flow and deformation and restoration in poiseuille flow are presented to verify the method and illustrate its efficiency. As an application of the present method, a ten-RBC colony being compressed through a stenotic microvessel is studied focusing the cell-cell interaction strength. Quantitative comparisons of the pressure and velocity on speci- fled microvessel interfaces are made between each aggregation case. It reveals that the stronger aggregation may lead to more resistance against blood flow and result in higher pressure difference at the stenosis.

Drive Control of Spiral Wave and Turbulence by a Target Wave in CGLE

Suppression of spiral wave and turbulence in the complex Cinzburg-Landau equation （CCLE） plays a prominent role in nonlinear science and complex dynamical system. In this paper, the nonlinear behavior of the proposed drive-response system, which consists of two coupled OGLEs, is investigated and controlled by a state error feedback controller with the lattice Boltzmann method. First, spiral wave appropriate parameters of the response system under the no-flux and turbulence are, respectively, generated by selecting boundary and perpendicular gradient initial conditions. Then, based on the random initial condition, the target wave yielded by introducing spatially localized inhomogeneity into the drive system is applied on the above response system. The numerical simulation results show that the spiral wave and turbulence existing in the response system could be successfully eliminated by the target wave in the drive system during a short evolution time. Furthermore, it turns out that the transient time for the drive course is related to the control intensity imposed on the whole media.