A Darcy-Law Based Model for Heat and Moisture Transfer in a Hill Cave

A hill can be regarded as an environmental carrier of heat.Water,rocks and the internal moisture naturally pre-sent in such environment constitute a natural heat accumulator.In the present study,the heat and moisture trans-fer characteristics in a representative hill cave have been simulated via a method relying on the Darcy’s law.The simulations have been conducted for both steady and unsteady conditions to discern the influence of permeability and geometric parameters on the thermal and moisture transfer processes.The reliability of the simulation has been verified through comparison of the numerical results with the annual observation data.As revealed by the numericalfindings,the internal temperature of the hill accumulator is proportional to the permeability,outside surface temperature,overground height,underground constant temperature layer depth,and underground tem-perature of the hill,and it is inversely proportional to the horizontal size of the hill.Moreover,in the considered case,the order of magnitude of the permeability of the hill is contained in the range 10-15–10-13,and displays a certain sensitivity to the rainwater seepage.

Non-Darcy Flow in Molding Sands

Darcy’s law is widely used to describe the flow in porous media in which there is a linear relationship between fluid velocity and pressure gradient. However, it has been found that for high numbers of Reynolds this law ceases to be valid. In this work, the Ergun equation is employed to consider the non-linearity of air velocity with the pressure gradient in casting sands. The contribution of non-linearity to the total flow in terms of a variable defined as a non-Darcy flow fraction is numerically quantified. In addition, the influence of the shape factor of the sand grains on the non-linear flow fraction is analyzed. It is found that for values of the Reynolds number less or equal than 1, the contribution of non-linearity for spherical particles is around 1.15%.

OPTIMAL ERROR ESTIMATES OF A DECOUPLED SCHEME BASED ON TWO-GRID FINITE ELEMENT FOR MIXED NAVIER-STOKES/DARCY MODEL

Although the two-grid finite element decoupled scheme for mixed Navier-Stokes/ Darcy model in literatures has given the numerical results of optimal convergence order, the theoretical analysis only obtain the optimal error order for the porous media flow and a non-optimal error order for the fluid flow. In this article, we give a more rigorous of the error analysis for the fluid flow and obtain the optimal error estimates of the velocity and the pressure.

Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration

A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h = H2. Both theoretical analysis and numerical experiments illustrate the efficiency of the algorithm for solving the coupled problem.

A Fractal Orifice-Throat Model for Seepage Characteristics of Multiscale Porous Media

The seepage characteristics of multiscale porous media is of considerable significance in many scientific and engineering fields.The Darcy permeability is one of the key macroscopic physical properties to characterize the seepage capacity of porous media.Therefore,based on the statistically fractal scaling law of porous media,fractal geometry is applied to model the multiscale pore structures.And a two-dimensional fractal orifice-throat model with multiscale and tortuous characteristics is proposed for the seepage flow through porous media.The analytical expression for Darcy permeability of porous media is derived,which is validated by comparing with available experimental data.The results show that the Darcy permeability is significantly influenced by porosity,orifice-throat fractal dimension,minimum to maximum diameter ratio,orifice-throat ratio and tortuosity fractal dimension.The present results are helpful for understanding the seepage mechanism of multiscale porous media,and may provide theoretical basis for unconventional oil and gas exploration and development,porous phase transition energy storage composites,CO2 geological sequestration,environmental protection and nuclear waste treatment,etc.

Motion of a permeable shell in a spherical container filled with non-Newtonian fluid

This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied. Stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components, the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis.

Stokes'first problem for the fourth order fluid in a porous half space

In this study, the flow of a fourth order fluid in a porous half space is modeled. By using the modified Darcy＇s law, the flow over a suddenly moving flat plate is studied numerically. The influence of various parameters of interest on the velocity profile is revealed.

Linear instability of the electrified free interface between two cylindrical shells of viscoelastic fluids through porous media

In this paper, we have discussed the linear stabil- ity analysis of the electrified surface separating two coaxial Oldroyd-B fluid layers confined between two impermeable rigid cylinders in the presence of both interfacial insoluble surfactant and surface charge through porous media. The case of long waves interfacial stability has been studied. The dispersion relation is solved numerically and hence the ef- fects of various parameters are illustrated graphically. Our results reveal that the influence of the physicochemical pa- rameterβ is to shrink the instability region of the surface and reduce the growth rate of the unstable normal modes. Such important effects of the surfactant on the shape of in- terfacial structures are more sensitive to the variation of the βcorresponding to non-Newtonian fluids-model compared with the Newtonian fluids model. In the case of long wave limit, it is demonstrated that increasing r, has a dual role in- fluence （de-stabilizing effects） depending on the viscosity of the core fluid. It has a destabilizing effect at the large values of the core fluid viscosity coefficient, while this role is ex- changed to a regularly stabilizing influence at small values of such coefficient.

Hydroelastic Response of VLFS with An Attached Submerged Horizontal Solid/Porous Plate Under Wave Action

The hydroelastic responses of a submerged horizontal solid/porous plate attached at the front of a very large rectangular floating structure(VLFS)under wave action has been investigated in the context of linear water wave theory.Darcy’s law is adopted to represent energy dissipation in pores.It is assumed that the porous plates are made of material with very fine pores so that the normal velocity across the perforated porous is linearly associated with the pressure drop.In the analytic method,the eigenfunction expansion-matching method(EEMM)for multiple domains is applied to solve the hydrodynamic problem and the elastic equation of motion is solved by the modal expansion method.The performance of the proposed submerged horizontal solid/porous plate can be significantly enhanced by selecting optimal design parameters,such as plate length,horizontal position,submerged depth and porosity.It is concluded that good damping effect can be achieved through installation of solid and porous plate.Porous plate has better damping effect at low frequencies,while solid plate has better damping effect at high frequencies.The optimal ratio of plate length to water depth is 0.25-0.375,and the optimal ratio of submerged depth to water depth is 0.09-0.181.

On the Application of the Lattice Boltzmann Method to Predict Soil Meso Seepage Characteristics

In this study,a two-dimensional approach is elaborated to study with the lattice Boltzmann method(LBM)the seepage of water in the pores of a soil.Firstly,the D2Q9 model is selected to account for the discrete velocity distribution of water flow.In particular,impermeability is considered as macroscopic boundary condition for the left and right domain sides,while the upper and lower boundaries are assumed to behave as pressure boundaries controlled by different densities.The micro-boundary conditions are implemented through the standard rebound strategy and a non-equilibrium extrapolation scheme.Matlab is used for the development of the related algorithm.Finally,the influence of porosity,permeability,osmotic pressure and other factors is assessed with regard to seepage characteristics and the ensuing results are compared with Darcy’s law.The computations show that,for fixed initial conditions,the pore structure has a certain influence on the local velocity of seepage,but the overall state is stable,and the average velocity of each layer is the same.The larger the pore passage is,the faster the flow velocity is,and vice versa.For low permeability,the numerical results are consistent with the Darcy's law.The greater the pressure difference between the inlet and outlet of seepage,the greater the seepage rate.The relationship between them is linear(yet in good agreement with Darcy’s law).

The Reflection of Normal Incident Waves by Absorbing-Type Breakwaters

This paper investigates the reflection of normal incident waves produced by absorbing-type breakwaters. The absorbing-type breakwaters in this study consist of a vertical porous plate, a submerged permeable caisson, and an impermeable back wall. The flow field is divided into four regions： a porous caisson region, and three pure water regions. Under the assumptions of linear wave theory, Darcy＇s law in the perforated wall, and the pore velocity potential theory of Sollitt and Cross （1972） in the porons caisson region, this study creates a 2-D BEM model to calculate the reflection coefficients of water waves using several breakwater properties. This numerical model is calibrated by previous numerical studies and limiting cases for a partially perforated-wall caisson breakwater and a vertical porous breakwater with an impermeable back wall. Generally speaking, the wave dissipation in absorbing-type breakwaters is bigger than that for a partially perforatedwall caisson breakwater. The reflection coefficient values imply the performance of wave absorbers in this study. Therefore, we examine the major factors that affect the reflection coefficient.

Analysis of Flow Models for Aerostatic Thrust Bearings with Porous Material

The numerical determination of static characteristics of bearings allows a cost-efficient and fast pre-design.In this study,two flow models for aerostatic thrust bearings with pressurized porous material are presented and analyzed.The models are based on the coupling of the Reynolds equation for lubricants(REL)and the determination of pressure drop through porous material by Darcy’s law.The simplified model is based on the assumption of a one-dimensional axial flow through porous media.The extended model considers the three-dimensional flow in the porous body.The analysis includes pressurized air from 4 to 9 bar(a)with nominal clearance of 5 to 60μm,Commercial CFD(computational fluid dynamics)software was used to verify the results.The extended model allows a more accurate prediction about the performance in the critical gap range.In total,the results show good agreement with CFD within a short computation time.

Motion through spherical droplet with non-homogenous porous layer in spherical container

The problem of the creeping flow through a spherical droplet with a non-homogenous porous layer in a spherical container has been studied analytically.Darcy’s model for the flow inside the porous annular region and the Stokes equation for the flow inside the spherical cavity and container are used to analyze the flow.The drag force is exerted on the porous spherical particles enclosing a cavity,and the hydrodynamic permeability of the spherical droplet with a non-homogeneous porous layer is calculated.Emphasis is placed on the spatially varying permeability of a porous medium,which is not covered in all the previous works related to spherical containers.The variation of hydrodynamic permeability and the wall effect with respect to various flow parameters are presented and discussed graphically.The streamlines are presented to discuss the kinematics of the flow.Some previous results for hydrodynamic permeability and drag forces have been verified as special limiting cases.

Experimental Study on Aero Conductivity of Porous Media

To study the variation pattern of aero conductivity of different porous media under low pressure conditions, three kinds of media are selected. These include sandy clay loam, fine sand, and medium sand, and air us fluid to conduct soil column ventilation tests. Pressure at both ends of the colruns is measured under different ventilation flow rates during testing. The test results show that the aero conductivity, solved by Darcy＇s law, is not a coustant. It is a variable, which increases first when air flow velocity is less than 0. 258 7 cm/s for sandy clay loam, 0. 637 3 cm/s for fine sand and then decreases when air flow velocity is bigger than that with the increase of the ventilation flow rate when the medium is determined. By analyzing various factors that influence the flow resistance, the reasons for variation in aero conductivity are found us follows： first, the change of pore structure results in better ventilation; second, the relatiouship hetwcen pressure head loss and air flow velocity is nonlinear, and it is beyond the condition of the Iminar flow domain to which Darcy＇ s law can he applied, when the air flow rate increases to a certain value and the flow velocity is in the transition range to turbulent flow.

The Exponential Law Between Dwell Time and the Strength of PBX Substitute Material

Polymer-bonded sugars(PBSs)can be used as a substitute material for polymerbonded explosives(PBXs)due to their ability to simulate the mechanical properties of PBXs.In the process of pressing a PBS,the length of the dwell time has a significant impact on the mechanical properties of the PBS.This reinforcing effect is based on the residual pressure causing the binder to flow and gradually fill each defect.Through the use of Darcy5s principle of binder infiltration and viscoelastic theory,an exponential relationship between the compressive strength of PBS and the dwell time has been derived.From the experiments,it was found that the extreme forces that correspond to the compaction stage of the PBS samples with different dwell times were almost the same;this indicates that there is tolerance to damage during the compaction stage.The existence of the compaction stage is related to the brittleness of the PBS.The experimental results showed that as the dwell time increased,the rate of damage evolution of the specimen decreased.

Numerical simulation of non-Darcian flow through a porous medium

This work reports on fluid flow in a fluid-saturated porous medium, accounting for the boundary and inertial effects in the momentum equation. The flow is simulated by Brinkman-Forchheimer-extended Darcy formulation （DFB）, using MAC （Marker And Cell） and Chorin pressure iteration method. The method is validated by comparison with analytic results. The effect of Reynolds number, Darcy number, porosity and viscosity ratio on velocity is investigated. As a result, it is found that Darcy number has a decisive influence on pressure as well as velocity, and the effect of viscosity ratio on velocity is very strong given the Darcy number. Additional key findings include unreasonable choice of effective viscosity can involve loss of important physical information.