Non-porous Media Research Articles

Using impacts of deep-level mining to research karst hydrology—a Darcy-based approach to predict the future of dried-up dolomitic springs in the Far West Rand goldfield (South Africa). Part 2: predicting inter-compartmental flow and final groundwater tables

Some of the world’s deepest goldmines operate below dolomitic karst aquifers in the Far West Rand (FWR) goldfield, South Africa. Associated impacts include the continuous dewatering of karst aquifers for over six decades and irreversible changes of the hydrogeological setting. Affecting an area of approximately 400 km2 by drawing down the water table up to 700 m, these impacts, and the large amounts of data generated in the process, are used as unique research opportunities to better understand the complex karst hydrology. The focus of this study is on predicting final water table elevations in rewatered aquifers after mining ceases taking the fact that mines hydraulically linked previously disconnected aquifers into account. While part 1 of this series develops the conceptual model, this second part utilises large sets of pertinent data to calculate actual flow rates for predicting the fate of dried up springs after mine closure. Following a Darcy-based approach first applied by Swart et al. (Environ Geol 44:751–770, 2003a) it is not only predicted that the springs will flow again but also shown that linear relationships exist between flow rates through a combined system of karst-fractured aquifers overlying the mine void and the associated hydraulic head driving them. This suggests that—at this scale—porous media-based equations can be meaningfully used to predict flow in non-porous media.

A modified two-stage pulse tube cryocooler utilizing double-inlet and multi-mesh regenerator

In this paper a thermally coupled Stirling-type two-stage pulse tube cryocoolers (TSPTC) is studied using a one-dimensional (1-D) CFD code. After validating the results of the simulations, effects of synchronous utilization of multi-mesh regenerator and double-inlet on the performance of the TSPTC are investigated. Results of simulations show that non-oscillating friction factors do not possess sufficient accuracy for calculation of oscillating friction losses in non-porous media. Whereas, using oscillating friction factor of non-porous media leads to sufficient accurate results. According to the results, using multi-mesh regenerator and double-inlet increases the COP and decreases the minimum attainable temperature of the system. It is observed that a minimum temperature of 18.2K is attainable using optimum multi-mesh regenerator and double-inlet; whereas, for a simple TSPTC with a uniform mesh regenerator, a minimum temperature of 26.4K is concluded.

Thermal performance analysis of porous-microchannel heat sinks with different configuration designs

Three-dimensional models of porous-microchannel heat sinks (porous-MCHSs) with different configuration designs, such as rectangular, outlet enlargement, trapezoidal, thin rectangular, block, and sandwich distributions, are verified in this work. Hydraulic and thermal performances of the porous-MCHSs with various configuration designs are investigated from the pumping power, heat transfer coefficient, and temperature control effectiveness, results with Reynolds number ranging from 45 to 1350. The results reveal that the thermal performances can be improved using the porous configuration designs and can increase with a large Reynolds number. Both the sandwich and the trapezoidal distribution designs have the best heat transfer efficiency, cooling performance, and convective performance. In particular, the thermal performance of the rectangular, outlet enlargement, thin rectangular, or block distribution designs are not necessarily better than the nonporous medium for lower pumping power. In addition, adding a porous medium to the channel leads to a significant increase in the pressure drop. Among the six porous configuration designs, the lowest pressure drop was observed for a sandwich distribution design. Hence, the sandwich distribution design is the best porous-MCHS design when considering the thermal performance along with the pressure drop.

Numerical simulation of a two-stage pulse tube cryocooler considering influence of abrupt expansion/contraction joints

The accuracy of local energy loss correlations in simulation of abrupt expansion/contraction joints under oscillating flow conditions of pulse tube cryocoolers (PTCs) is investigated in this paper. Different friction losses of non-porous media are investigated as well. In this respect, detailed analyses of the flow and heat transfer in various components of a two-stage PTC under oscillating flow conditions are carried out by a developed 1-D code and also FLUENT software. Comparison of 2-D and 1-D simulations results shows that steady friction factors do not possess sufficiently accurate predictions of losses under oscillating flow conditions. Whereas, oscillating friction factors and steady local energy loss coefficients are successful in calculating of losses under oscillating flow conditions of the PTCs. Furthermore, considering flow streamlines in all components of the PTC, 2-D flow effects occurring in the abrupt expansion/contraction joints of the pulse tube sections with small aspect ratios (length to diameter ratio) reduces the accuracy of the supplied coefficients results in 1-D CFD code.

Time of flight transport equation in Eulerian reference frame

A general advection equation of time of flight (TOF) is developed in the Eulerian frame for unsteady state, which can be fully coupled with governing equations for primary variables like pressure, velocity, saturation and temperature. Both initial and boundary conditions are provided for TOF in a general form. The outlet boundary condition is more robust compared with published methods. The influence of dispersion on TOF is included for mixing or diffusion phenomena in both non-porous media flow and porous media flow. Arrival times can be solved by the same set of equations by assigning inlet boundary conditions on producer wells and outlet boundary conditions on injector wells. Neutral fluid particle velocity for multiphase flow is discussed. Published saturation velocities can only track water saturation at water fronts. A more general form is developed, based on neutral fluid particle velocity that can track water saturation at both water fronts and swept regions.Several examples from non-porous media flow with and without dispersion to porous media flow are demonstrated. The advection equation of TOF with corresponding boundary conditions is very similar to traditional governing transport equations which can be solved by the same method. Time dependent properties like fluid rheology during hydraulic fracturing and catalyst particle activity can be coupled with other transport variables, such as temperature, for optimization.

Modeling and Analysis of Flow, Thermal, and Energy Fields Within Stacks of Thermoacoustic Engines Filled With Porous Media

For this article, an analytical study has been conducted on the flow and energy transfer of unsteady compressible oscillating flow through channels filled with porous medium representing stack in thermoacoustic engines/refrigerators. The flow in the porous material is described by the Darcy momentum equation. Analytical expressions for oscillating velocity, temperature in the porous layer, complex Nusselt number, and energy flux density are obtained after simplifying and solving the governing differential equations with reasonable approximations (such as long wave, short stack, small amplitude oscillation, etc.). The result for heat transfer between the porous medium and the channel wall is expressed as a dimensionless Nusselt number. For the limiting case of nonporous medium, the Nusselt number obtained in the present study matches quantitatively with the expression available in the existing literature. The results reveal that the Nusselt number in oscillating flow is significantly enhanced (almost an order of magnitude) by employing sufficiently large thermal conductivity of porous media in a channel. The system of equations developed in the present study is a helpful tool for thermal engineers to design porous stacks for thermoacoustic devices.

Numerical Investigation of Forced Convective Heat Transfer Around and Through a Porous Circular Cylinder With Internal Heat Generation

In this study, convective heat transfer around and through a porous circular cylinder together with internal heat generation has been investigated numerically. Governing equations containing continuity, momentum, and energy equations have been developed in polar coordinate system in both porous and nonporous media based on single-domain approach. However, governing equations in porous medium are derived using intrinsic volume averaging method. The equations are solved numerically based on finite volume method over staggered grid arrangement. Also, pressure correction-based iterative algorithm, SIMPLE, is applied for solving the pressure linked equations. Reynolds and Peclet numbers (based on cylinder diameter and velocity of free stream) are from 1 to 40. Also, Darcy number (Da) varies within the range of 10-6≤Da≤10-2 and porosity is considered 0.9 for all calculations. The influence of Da and Re numbers on local and average Nu numbers has been investigated. It is found that the local and average Nu numbers increase with any increase in Da number. Two correlations of average Nu number are presented for high and low Da numbers.

Magnetogravitational Vortex-Sheet Instability of Two Superposed Conducting Fluids in Porous Medium Under Strong Magnetic Field

The instability of two superposed homogeneous streaming ‡uids is discussed under gravitational force and uniform magnetic eld in porous medium. The two streams are moving in opposite directions with equal velocities parallel to the horizontal plane. The solution has been obtained through the normal mode technique, and the most gen- eral dispersion relation has been obtained as 20th-order equation for the growth rate with quite complicated coe¢ cients. Solving numeri- caly the dispersion relation for appropriate boundary conditions with high Alfven and sound velocities, it is found that ‡uid velocities and porosity of porous medium have stabilizing e¤ects, and Alfven and sound velocities have destabilizing e¤ects, while medium permeabil- ity has a slightly stabilizing e¤ect, and the dynamic viscosities have slightly destabilizing e¤ect. The limiting cases of non-porous medium have also been studied for both streaming and stationary ‡uids. Key words : Hydrodynamic stability; Conducting ‡uids; Flows through porous media; Gravitational force; Magnetohydrodynamics

Differential Equations in Stability Analysis of Ferrofluids

The application of differential equations towards stability analysis of ferrofluids is analysis both in porous medium and nonporous medium and a comparative analysis is made. Weakly non- linear analysis is carried out. A mathematics model of the differential equations employed is presented. The non-dimensional thermal Rayleigh number Ra and magnetic Rayleigh number Rm are analysed with allowable range of parameter.

HYDROMAGNETIC ROTATING FLOWS OF AN OLDROYD-B FLUID IN A POROUS MEDIUM

In this article we consider the unsteady rotating flow of a magnetohydrodynamic (MHD) Oldroyd-B fluid for both constant and variable accelerated flows in a porous half space. The modified Darcy's law for an Oldroyd-B fluid is employed to model the governing equations. The exact solutions for these governing equations are obtained by employing the Laplace transform technique. The graphs are plotted for different values of dimensionless parameters. It is observed that the velocity field is strongly influenced by the porosity of the medium, applied magnetic field, fluid parameters and angular frequency. As a special case the obtained solutions are reduced to those for a hydrodynamic fluid in a non-porous medium. The corresponding solutions for a hydromagnetic Newtonian fluid in a porous medium are also recovered.

New exact solutions of Stokes' second problem for an MHD second grade fluid in a porous space

We investigate a problem describing the oscillating flow of an incompressible magnetohydrodynamic (MHD) second grade fluid in a porous half space. Exact solutions for sine and cosine oscillations are developed by applying the Laplace transform method. The total obtained solution is a sum of steady and transient solutions. Particular attention is given to the effects of magnetic and porous medium parameters on the velocity. It is shown that previous results for a non-porous medium and hydrodynamic fluid are the limiting cases of the present problem. The results for velocity are plotted and discussed carefully.

Mechanism of the reversibility of asphaltene precipitation in crude oil

Asphaltene precipitation and deposition occur in petroleum reservoirs as a change in pressure, temperature and liquid phase composition and reduce the oil recovery considerably. In addition to these, asphaltene precipitates may deposit in the pore spaces of reservoir rock and form plugging, which is referred to as a type of formation damage, i.e. permeability reduction. In all cases above, it is of great importance to know under which conditions the asphaltenes precipitate and to what extent precipitated asphaltenes can be re-dissolved. In other words, to what extent the process of asphaltene precipitation is reversible with respect to change in thermodynamic conditions. In present work, a series of experiments was designed and carried out to quantitatively distinguish the reversibility of asphaltene precipitation upon the change in pressure, temperature and liquid composition. Experiments were conducted in non-porous media. Generally it was observed that the asphaltene precipitation is a partial reversible process for oil under study upon temperature change with hysteresis. However, the precipitation of asphaltene as a function of mixture composition and pressure is nearly reversible with a little hysteresis.

Reversibility of asphaltene precipitation in porous and non-porous media

Precipitation and deposition of asphaltene particles in the pore spaces of reservoir rocks cause diffusivity reduction and wettability alteration in hydrocarbon reservoir which consequently, reduce the oil recovery considerably. It is of great importance to know the condition at which the asphaltene particles precipitate and also the extension by which precipitated asphaltene particles can be re-dissolved. In this study, the precipitation and re-dissolution of asphaltene particles in a crude oil have been investigated. Series of experiments, in both porous and non-porous media, have been designed and carried out to quantitatively evaluate the reversibility of asphaltene precipitation upon the change in pressure, temperature, and liquid composition. Experiments were conducted in both porous and non-porous media. For non-porous medium, it was observed that the asphaltene precipitation is a partially reversible process upon temperature change with hysteresis, while the precipitation of asphaltene as a function of mixture composition and pressure is nearly reversible with little hysteresis. In the case of porous medium, a slim tube apparatus was used as a one-dimensional reservoir model. After injection of several pore volumes of fresh oil, the oil was allowed to soak enough; then, all deposited asphaltene particles were re-dissolved completely in the crude oil.

Diffusion of Hydrogen in Single Crystals of Monoclinic-ZrO<sub>2</sub> and Yttrium Stabilized Cubic Zirconia

Transport of hydrogen through oxide layers formed on zirconium alloys has been the focus of studies associated with hydrogen ingress into nuclear reactor core components. The studies have shown that microstructure and microchemistry of the underlying alloy can affect the characteristics of the oxide and in turn the transport of hydrogen through the oxide and into the underlying metal. In certain cases the oxide layer can be a homogeneous medium for hydrogen diffusion, while in most cases it is found to be heterogeneous and comprised of homogeneous, nonporous and fully oxidized, cells surrounded by a network of fast diffusion paths for hydrogen. Since in such heterogeneous systems the derived diffusion parameter and the cell size are interdependent, an absolute diffusion parameter could only be derived if the cell size were known. However, no such information is available from the microstructural studies on the oxides grown on these alloys. Another alternative is to carry out the measurements in a material, which is homogeneous at least within the dimensions of a few μm - the range of the measurements. With this in mind, hydrogen diffusion measurements were carried out in a set of single crystal zirconia specimens with the prospect that the single crystals would provide a non-porous and homogeneous medium to study the diffusivity of hydrogen. These measurements show that the single crystal specimens, contrary to the initial thinking, are not entirely homogeneous and the results do not yield an absolute diffusion coefficient for hydrogen in zirconium oxides. The details and analyses of the results from the single crystal zirconia specimens are discussed in this paper.

NONLINEAR KELVIN-HELMHOLTZ INSTABILITY OF TWO SUPERPOSED DIELECTRIC FINITE FLUIDS IN POROUS MEDIUM UNDER VERTICAL ELECTRIC FIELDS

A weakly nonlinear theory of wave propagation in two superposed dielectric fluids streaming through porous media in the presence of vertical electric field and in the absence of surface charges at their interface is investigated in three dimensions. The method of multiple scales is used to obtain a dispersion relation for the linear problem and a Ginzburg-Landau equation with complex coefficients for the nonlinear problem, describing the behavior of the system. The stability of the system is discussed both analytically and numerically in both cases, and the corresponding stability conditions are obtained. It is found, in the linear case, that the stability criterion is independent of the medium permeability and that the medium porosity, surface tension, and dimension all have stabilizing effects the fluid viscosities, velocities, and depths have destabilizing effects, and the electric field has a dual role in the stability of the system. In the nonlinear analysis, it is found that the electric field has a stabilizing effect in two-dimensional disturbances and destabilizing effect in three-dimensional disturbances cases. The surface tension, fluid depths, and medium porosity have stabilizing effects in both two- and three-dimensional disturbance cases and the fluid viscosities, velocities, and medium permeability have destabilizing effects in both cases, and this stability or instability occurs faster for three-dimensional disturbance cases. It is found also that the system is unstable in the absence of fluid velocities or for nonporous media. Finally, the dimension was found to have a dual role (stabilizing as well as destabilizing) in the considered system, while it has a destabilizing effect in the case of nonporous media.

A Galerkin-type finite element solution for simulation of mass diffusion in the application of tissue engineering: Heterogeneous and non-porous media

This study is an effort to produce a generic and comprehensive solution to the simulation of mass diffusion through a multiphasic and heterogeneous material model. A Galerkin-type finite element formulation is developed to solve Fick's equation for steady-state and time-dependent analysis. The effect of the interface in modelling of a liquid-solid medium is presented in this work. To show the robustness of the proposed approach, the gas exchange (oxygen and carbon dioxide) process through the capillary network between the alveolar membrane and red blood cells has been analysed and then validated with experimental data. The current work is a significant asset to modelling the diffusion of oxygen between cells and scaffolds in tissue engineering or tissue regeneration/repair studies. It is one step towards the development of high-order elements for application of the simulation of mass transfer through a multiphasic and porous model with varying degrees of interconnectivity and pore size for tissue engineering applications.

Modeling and Analysis of Flow, Thermal, and Energy Fields Within Stacks of Thermoacoustic Engines Filled With Porous Media: A Conjugate Problem

Abstract In this paper, an analytical study has been conducted on the flow and energy transfer of an unsteady compressible oscillating flow through channels filled with porous media representing stacks in thermoacoustic engines and refrigerators. The flow in the porous material is described by the Darcy momentum equation. The thickness of the channel wall is considered to be nonzero, and the entire problem is treated as a conjugate heat transfer problem, i.e., by considering conduction heat transfer inside the channel walls. Analytical expressions for the oscillating temperature, complex Nusselt number, and energy flux density are obtained after linearizing and solving the governing differential equations with long wave, short stack, and small amplitude oscillation approximations. To verify the present study, the energy flux density expression derived in this paper is compared with the expression available in the existing thermoacoustic literature. The two expressions match quantitatively for the limiting case of infinitely large pores. For infinitely large pore limits, the Nusselt number (nondimensional heat transfer between the porous media and the channel wall) obtained in the present study also agrees quantitatively with the nonporous medium expression reported in the literature. The present study indicates that refrigeration performance comparable to that of a traditional plastic parallel plate stack is achievable using reticulated vitreous carbon foam (ϕ=0.95, Lck=2.11) as a porous medium, which is also supported by other researchers. The system of equations developed in the present study is a helpful tool for thermal engineers and physicists to design porous stacks for thermoacoustic devices.

Kelvin’s eigensystems in anisotropic poroelasticity

Correct interpretation and processing of seismic data must integrate a correct description of the mechanical behavior of rocks, taking into account facts such as the presence of anisotropy and porosity with or without a saturating fluid. This work discusses elasticity of porous media of arbitrary anisotropy type, with emphasis on the study of deformation states and the associated elastic constants. The stress-strain law is represented in seven dimensions. Dynamic parameters (i.e., the six stress components and fluid pressure) are linked with kinematical parameters (i.e., the six strain components and the local increase of fluid content) by a 7D poroelastic tensor. The model is based on the following mechanical interpretation: each eigenvector (eigenstrain) of the poroelastic tensor defines a fundamental deformation state of the medium and the seven eigenvalues (eigenstiffnesses) representthe genuine poroelastic parameters. The set of seven eigenstrains and corresponding eigenstiffnesses constitute the eigensystem of the poroelastic medium. Complete characterization of the eigensystems corresponding to different types of anisotropies encountered in geologic media is achieved. The first six eigenstrains do not differ substantially from the six eigenstrains in elastic nonporous media, which are well documented in the literature. In contrast, the next result is the existence of a seventh eigenstrain characterized by reduction of the total volume of the porous medium associated with an increase in fluid content. Finally, the analysis is applied to experimental data on a rock sample of Pfalz sandstone, considered as an arbitrarily anisotropic porous medium. Thus, more complex mechanical behaviors of rocks can be introduced naturally, including viscoelastic rheology (already published), frequency dependence, nonlinearity, and even hysteresis, as has been done recently in nonporous media.

The instability of nonlinear surface waves in an electrified liquid jet

We investigate the weakly nonlinear stability of surface waves of a liquid jet. In this work, the liquids are uniformly streaming through two porous media and the gravitational effects are neglected. The system is acted upon by a uniform tangential electric field, that is parallel to the jet axis. The equations of motion are linearly treated and solved in the light of nonlinear boundary conditions. Therefore, the boundary-value problem leads to a nonlinear characteristic second-order differential equation. This characterized equation has a complex nature. The nonlinearity is kept up to the third degree. It is used to judge the behavior of the surface evolution. According to the linear stability theory, we derive the dispersion relation that accounts for the growth waves. The stability criterion is discussed analytically and a stability picture is identified for a chosen sample system. Several special cases are recovered upon appropriate data choices. In order to derive the Ginsburg–Landau equation for the general case, in the nonlinear approach, we used the method of multiple timescales with the aid of the Taylor expansion. This equation describes the competition between nonlinearity and the linear dispersion relation. As a special case for non-porous media where there is no streaming, we obtained the well-known nonlinear Schrödinger equation as it has been derived by others. The stability criteria are expressed theoretically in terms of various parameters of the problem. Stability diagrams are obtained for a set of physical parameters. We found new instability regions in the parameter space. These regions are due to the nonlinear effects.

Effect of thermal radiation on unsteady mixed convection flow and heat transfer over a porous stretching surface in porous medium

An analysis is performed to investigate the effects of thermal radiation on unsteady boundary layer mixed convection heat transfer problem from a vertical porous stretching surface embedded in porous medium. The fluid is assumed to be viscous and incompressible. Numerical computations are carried out for different values of the parameters involved in this study and the analysis of the results obtained shows that the flow field is influenced appreciably by the unsteadiness parameter, mixed convection parameter, parameter of the porous medium and thermal radiation and suction at wall surface. With increasing values of the unsteadiness parameter, fluid velocity and temperature are found to decrease in both cases of porous and non-porous media. Fluid velocity decreases due to increasing values of the parameter of the porous medium resulting an increase in the temperature field in steady as well as unsteady case.