Liquid-saturated Porous Medium Research Articles

NANOFLUID FILM FALLING ON A NON-DARCY POROUS VERTICAL PLATE EVAPORATOR

A numerical analysis of the falling nanofilm evaporation on a vertical porous wetted wall by mixed convection was performed. The right-wall was dry and isothermal, while the left wall was embedded in a non-Darcy porous medium filled with nanofilm (water + low fraction volume of copper nanoparticles) and exposed to a uniform heat flux from the outside. The nanofluid film made up the liquid, while dry air and water vapor comprised the gas mixture. The results obtained from this study pertain to the impact of porosity, thickness of the porous layer, concentration of nanoparticles on heat and mass exchange, and liquid film evaporation. The results indicate that mass and heat exchange, as well as liquid film evaporation, are improved in the case of nanofilm by introducing a liquid-saturated porous medium. It is shown that in the case of a porous layer, the dispersion of the nanoparticles into water film ameliorates the liquid film evaporation of the plate evaporator and weakly improves the mass and heat exchange.

Theoretical Prediction of the Number of Bénard Cells in Low-Porosity Cylindrical/Rectangular Enclosures Saturated by a Fast Chemically Reacting Fluid

Many applications including chemical engineering and meteorology require the study of a chemically driven convection in cylindrical, as well as rectangular enclosures. The present paper reports a unified analysis of a chemically driven convection in densely packed porous cylindrical/rectangular enclosures saturated by a chemically reactive binary fluid mixture. Employing the degeneracy technique and the single-term Galerkin method involving Bessel functions in a linear stability analysis, an analytical expression for the critical Rayleigh number, Rac, was obtained. An analytical expression for the number of cells that manifest in a given enclosure, at the onset of convection, was derived from Rac. The connection between the stabilizing and destabilizing effects of various parameters and the size or the number of Bénard cells that manifest are described in detail. The results depicted that the chemical parameters related to the heat of reaction destabilize and the parameter depending inversely on the rate of the chemical reaction stabilizes the system. In the latter case, a greater number of smaller cells were formed in the system compared to the former case. Hence, we concluded that the chemically reactive fluid advances the onset of convection compared to the chemically non-reactive fluid. The results of a similar problem in rectangular enclosures of infinite horizontal extent and chemically non-reactive liquid-saturated porous medium were recovered as limiting cases. Thus, the present model presents a unified analysis of six individual problems.

Effect of liquid saturated porous medium on heat transfer from thermoelectric generator

Effect of liquid saturated porous medium on heat transfer from thermoelectric generator

On one inverse dynamic problem of poroelasticity for a layered medium

An inverse dynamic problem of poroelasticity of a piecewise-smooth shear coefficient is considered using additional information on oscillations of free surface points. It is believed that Goupill's hypothesis about the equal propagation time of perturbations through the layers of a liquid-saturated porous medium has been fulfilled. Recursive formulas for recovering the unknown shift coefficient are obtained.

Thermal energy transport of radioactive nanofluid flow submerged with microorganisms with zero mass flux condition

The importance of nanoparticles has evolved over the twenty-first century due to crucial applications in numerous thermophysical systems and increased sustainability. Based on improvements, the current work plans to explore Darcy free convection around an isothermal vertical cone with a fixed apex half-angle pointing downward in a nano liquid saturated porous medium. It is considered that the medium consists of oxytactic microorganisms with nanoparticles. The cone is subjected to nanoparticles concentration and oxytactic microorganisms’ density. The impacts of Brownian movement and thermophoresis are involved in the model for nanoliquids. Solar radiation and convective heating phenomena are added to the energy equation to increase the thermal distribution phenomena. Zero mass flux phenomena are applied at the boundary. Employing appropriate non-dimensional parameters transforms a system of nonlinear ordinary differential equations. These equations are solved mathematically by the 4th order Runge-Kutta method along with a shooting algorithm. The leading dimensionless parameters, such as velocity, nanoparticles concentration, temperature, oxytactic microorganism's density, and local numbers (Nusselt, Sherwood, density) for microorganisms are examined in detail. Mathematical computation is carried out for different values that define the flow properties. It is observed that nanoparticle concentration diminishes by increasing the Brownian movement. Furthermore, the motile organism profile declines with an increment in bioconvection Lewis number.

Natural convection of a binary liquid in cylindrical porous annuli/rectangular porous enclosures with cross-diffusion effects under local thermal non-equilibrium state

The present article reports an analytical study of the double diffusive natural convection (DDNC) in cylindrical porous annuli (CPA) and rectangular porous enclosures (RPE), which are handled in a unified way using the curvature parameter, saturated by a binary liquid under the assumption of local thermal non-equilibrium (LTNE) state. The buoyancy forces (thermal and solutal) driving the flow are assumed to be induced by the maintenance of constant and uniform heat and mass fluxes applied along the vertical (radial) walls and insulation of both horizontal walls of the annuli/rectangular enclosures. The Darcy-Boussinesq equations with LTNE assumption between the fluid and solid phases are employed to model the problem of DDNC in a binary liquid-saturated porous medium with cross-diffusion effects. The analytical results are obtained by employing the Oseen-linearization transformation technique in the study. The influence of various dimensionless parameters on heat and mass transports of the system are depicted using the Nusselt and Sherwood numbers and isotherms plots, and the obtained results are analysed with the physical explanation. Special attention is given to understand the effect of LTNE parameter and cross-diffusion parameters on heat and mass transports of the system. Different aspect ratio values are chosen to obtain the results of three types of CPA/RPE (shallow, square and tall). Among these CPA/RPE, maximum and minimum heat and mass transports are achieved in the cases of shallow and tall CPA/RPE, respectively. The results of the pure thermal convection problem is obtained at the zero value of buoyancy ratio and solute Rayleigh number. The increasing value of N magnifies the heat and mass transports in the system due to the augmented buoyancy effect resulted from the thermal and solutal gradients. The increase of solid inner cylinder radius, by fixing its volume, makes the annulus slender which yields to decrease the heat and mass transports in the system. The effects of LTNE parameter and cross-diffusion parameters on heat and mass transports of the system are clearly brought out. The results of LTE model are obtained at the infinite value of ratio of porosity modified thermal conductivities, γ, as a particular case of the present model. From the study, we conclude that the shallow porous annulus and tall rectangular enclosure are best suited in the design of heat removal and heat storage systems, respectively.

Enhanced saturation of liquid-saturated porous medium with atmosphere gases due to surface temperature oscillations

We study the non-isothermal diffusion transport of a poorly soluble substance in a porous liquid-saturated medium being in contact with the reservoir of this substance. The surface temperature of a half-space porous medium oscillates in time, which creates a decaying temperature wave propagating deep into sediments. Since the solubility exponentially strongly depends on temperature, a decaying running solubility wave forms in the porous medium. In such a system, the zones of saturated solution and non-dissolved phase coexist with the zones of undersaturated solution. The effect is considered for the case of annual oscillation of the surface temperature of water-saturated ground being in contact with atmosphere. We reveal the phenomenon of formation of a near-surface bubbly horizon due to the temperature oscillation for one- and two-component solutes. In the case of a two-component solute, the solubility depends on the composition of the nondissolved phase, which necessitates the construction of a corresponding mathematical model of dissolution of multicomponent mixtures. We develop an analytical theory of the phenomenon of formation of the bubbly horizon. In both analytical theory and numerical simulations, the temperature dependence of the molecular diffusion coefficient is taken into account. In the presence of a propagating temperature wave, the nonlinear interaction between this dependence and the temperature dependence of the solubility creates an additional nonzero contribution to the mean-over-period mass flux. For multicomponent solutions, we report the formation of a diffusive boundary layer, which is not possible for single-component solutions. We construct an analytical theory for this boundary layer and derive effective boundary conditions for the problem of the diffusive transport beyond this layer. Theoretical results are in fair agreement with the results of numerical simulation.

Effect of thermal non-equilibrium and internal heat source on Brinkman–Bénard convection

In the paper, we make a linear stability analysis in a Newtonian, liquid-saturated high porous medium in the presence of a heat source under the assumption of local thermal non-equilibrium(LTNE). The heat source is represented by an internal Rayleigh number RI and is considered in two ways (i) internal heat source in a liquid phase (RIl) and (ii) internal heat source in a solid phase (RIs). The internal heat generation parameter’s effect is to destabilize the onset of stationary convection due to an increase in the system’s energy. The results of local thermal equilibrium are obtained as a limiting case of the problem. The effect of various parameters on the onset of convection is analyzed and depicted graphically.

EVOLUTION OF LINEAR WAVES IN A POROUS MEDIUM SATURATED WITH A BUBBLE LIQUID

Background The study of the processes of propagation of pressure waves in liquid-saturated porous media is associated not only with solving practical problems of underwater acoustics, seismics, object protection, non-destructive testing, etc., but it is also necessary to understand the fundamental foundations of wave processes. in such environments. Aims and Objectives Investigation of the evolution of a pulse of finite duration in a porous medium saturated with a gas-liquid mixture. Analysis of two situations of the location of bubbles in a porous medium. The first, when the bubble envelopes several pores, and the second situation - gas bubbles are much smaller than the pore sizes and are located on the pore walls. Results The dynamics of linear waves in a porous medium filled with a gas-liquid mixture has been studied. The influence of the determining factors of a bubbly liquid (volumetric content, dispersion of bubbles) and a porous medium on the shape and decay of impulse disturbances is analyzed.

Unsteady natural convection in a liquid-saturated porous enclosure with local thermal non-equilibrium effect

Stability analysis of free convection in a liquid-saturated sparsely-packed porous medium with local-thermal-non-equilibrium (LTNE) effect is presented. For the vertical boundaries free–free, adiabatic and rigid–rigid, adiabatic are considered while for horizontal boundaries it is the stress-free, isothermal and rigid–rigid, isothermal boundary combinations we consider. From the linear theory, it is apparent that there is advanced onset of convection in a shallow enclosure followed by that in square and tall enclosures. Asymptotic analysis of the thermal Rayleigh number for small and large values of the inter-phase heat transfer coefficient is reported. Results of Darcy–Benard convection (DBC) and Rayleigh–Benard convection can be obtained as limiting cases of the study. LTNE effect is prominent in the case of Brinkman–Benard convection compared to that in DBC. Using a multi-scale method and by performing a non-linear stability analysis the Ginzburg–Landau equation is derived from the five-mode Lorenz modal. Heat transport is estimated at the lower plate of the channel. The effect of the Brinkman number, the porous parameter and the inter-phase heat transfer coefficient is to favour delayed onset of convection and thereby enhanced heat transport while the porosity-modified ratio of thermal conductivities shows the opposite effect.

Natural Convection Heat and Mass Transfer in the Vertical Cylindrical Porous Channel Under the Effects of Time-Periodic Boundary Condition

Abstract Heat and mass transfer are investigated numerically with steady-state laminar natural convection through a vertical cylindrical enclosure filled with a liquid-saturated porous medium. The vertical wall is under a constant magnetic field and various durations of periodic heating boundary condition; the top and bottom surfaces are kept at a constant cold temperature. Continuity, momentum, and energy equations are transformed to dimensionless equations. The finite difference approach with the line successive over-relaxation (LSOR) method is used to obtain the computational results. This study covers the heat transfer, the temperature distribution, and the velocity field in the domain under the variation of different parameters. The code used is validated by modifying it to analyze the Nusselt number in the existing experimental literature of Izadpanah et al. (1998, “Experimental and Theoretical Studies of Convective Heat Transfer in a Cylindrical Porous Medium,” Int. J. Heat Fluid Flow, 19(6), pp. 629–635). This work shows that Nusselt number decreases (with varying gradient) as the aspect ratio increases, and that it increases as the Rayleigh number increases. The centerline temperature has a proportional relationship with the heating amplitude and the heating period (as the system receives more heat) and is inversely proportional with Rayleigh number. Increasing the Rayleigh number causes increased convective velocity, which affects the position of the hot region, and causes a decrease in the temperature field. Increasing the aspect ratio results in a warm stream at the center of the cylinder, and when the time period of the heating increases, the circulation becomes faster and the intensity of the temperature contour layers decreases. In this work, a correlation for Nu as a function of the mentioned parameters is developed.

Experimental study of different factors on dynamic characteristics of dispersed bubbles rising motion behavior in a liquid-saturated porous media

It is of great significance to understand the dynamic mechanism of dispersed non-aqueous gas bubbles in a porous media to develop hydrocarbon reservoirs for enhanced oil recovery (EOR). In this work, series of experiments about bubbles rising motion behavior in different influence factors were conducted through video photography enhanced with image analysis. The results showed that with the increase of the bubble length and the glass beads size, the average velocity of bubbles ascended first and then tended to be stable, which was mainly controlled by the buoyancy and the drag resistance force. On the contrary, the average velocity decreased with the pore-throat ratio increasing for bubbles with 20 mm length, which resulted from the decrease of buoyancy and the increment of drag force and interface tension due to the more liquid-gas contact area in the pores and throats occupied by the bubble. The bubbles average velocity showed the same trend with the increase of inclination angles and liquid viscosities, and the maximum average velocities were 50°–60° of inclination angle and 40%–50% of mass fraction, respectively.

Magnetization exchange in a single pore due to diffusion in internal fields: Simulation and experiment

Nuclear magnetic resonance measurements of spin relaxation are used in studies of liquid-saturated porous media where multidimensional relaxation correlations probe interpore diffusion and other transport processes. However, the magnetic susceptibility contrast between the solid and liquid results in pore-scale field inhomogeneities that influence all measurements of transverse ${T}_{2}$ relaxation time. In a previous publication we conjectured that experimentally observed exchange phenomena can correspond to intrapore diffusion between localized volumes of coherent magnetization generated by these internal gradients, rather than interpore diffusion. Here, we use a finite-element method to explore the decay of magnetization in a single pore (interstice between spheres) for the Carr-Purcell-Meiboom-Gill and two-dimensional ${T}_{2}\text{\ensuremath{-}}{T}_{2}$ exchange experiments. These simulations permit direct visualization of the time-dependent distribution of magnetization in the pore. The chosen grain size and susceptibility contrast are matched to values for Bentheimer sandstone, allowing for a comparison of simulated and experimental results. Despite the simplicity of the model pore geometry, the salient features of the magnetization decay observed experimentally are reproduced in simulation. We demonstrate that intrapore magnetization transfer can explain observations of diffusive exchange in porous materials characterized by a monomodal pore size distribution and large internal gradients.

MHD natural convective flow through a porous medium in a square cavity filled with liquid gallium

This article contains a computational study of free convective flow through a square enclosure filled with liquid gallium saturated porous medium in the presence of a uniform inclined magnetic field. Lower boundary of enclosure is considered to be heated uniformly, upper horizontal boundary is taken insulated, left wall of the cavity is heated linearly, and right wall is heated linearly or taken cold. Navier–Stokes equations governing the flow problem are first exposed to penalty method to eliminate the pressure terms and then Galerkin FEM is employed to solve reduced equations. Grid independent results are achieved and shown in tabular form for numerous ranges of physical flow parameters. To ensure the accuracy of developed code, computed results are compared with those available in earlier studies through figures. It is found that the strength of streamlines circulation is increased due to increase in Darcy number while imposition of vertical magnetic field instead of horizontal magnetic field causes slow rate of increase in strength of streamlines circulation. Whereas, in the case of linearly heated right wall, the average Nusselt number is an increasing function of the Darcy number, and vertical magnetic field causes higher values for average Nusselt number as compared to horizontal magnetic field along bottom and side walls of cavity. Contrarily, in the case of cold right wall, the horizontal magnetic field results in higher values of average Nusselt number as compared to the vertical magnetic field case, and the average Nusselt number reduces as we move along lower and right boundary while increases along left wall with increase in distance.

Propagation of elastic waves in saturated porous medium containing a small amount of bubbly fluid

It is very important to understand the acoustical properties of porous medium. To study the relationship between acoustical and other physical properties of porous medium will help us to use acoustical tools for determining the physical properties of porous medium. Many researchers have paid much attention to the properties of acoustic wave propagation in the gassy marine sediments based on the Biot model which is popularly used to predict the dispersion and attenuation of sound in saturated porous medium. The patchy model which contains gas inside the spherical water predicts that the existence of gas just has little effect on the propagation of acoustic wave in porous medium when the gas content is very small. However, the presence of a small number of bubbles in a fluid saturated sediment will lead to different acoustic responses. As is well known, the bubble vibration theory proposed by Keller and Miksis shows that a small number of bubbles existing in the liquid will have a great influence on sound velocity and attenuation. Therefore, in order to study the effect of a small amount of gas existing in fluid saturated porous medium on the property of acoustic wave propagation, we investigate a bubbly liquid saturated porous medium and consider the case of the bubbles vibrating linearly under the action of sound waves. First, we derive the continuity equation of the seepage according to the mass conservation of the pore fluid and the relationship between porosity differentiation and pore fluid pressure differentiation. Then, the bubble linear vibration theory given by Commander is used to deal with the time derivative of gas volume fraction in the continuity equation of the seepage, The bubble linear vibration theory gives the relationship between instantaneous bubble radius and background pressure of the medium. Through this relationship, we obtain the equation of time derivative of gas volume fraction and time derivative of pore fluid pressure. Then, we combine the obtained equation with the continuity equation of seepage, and obtain the modified continuity equation of seepage whose form is similar to that of Biot model. Finally, the modified Biot's equations for fluid saturated porous medium containing a small amount of bubbly fluid is obtained. As is well known, an effective density fluid model for acoustic propagation in sediments, derived from Biot theory, just can predict the acoustic properties of the fast compressional waves. However, the present model can predict the acoustic properties of fast, slow compressional waves and shear waves propagating in sediments. Through numerically calculating the dispersion, attenuation, amplitude ratios of pore fluid displacement to solid displacement for fast and slow compressional waves, it is found that the existence of a small number of bubbles has an influence on the acoustic properties of both the fast compressional waves and the slow compressional waves, especially the velocity of the fast compressional wave. In addition, the low-frequency speed approximation formula for the fast compressional wave is also presented. The approximate formula directly indicates the relationship between the velocity of fast compressional wave and the parameters of porous medium such as the gas volume fraction and the bubble radius. This study shows that the influence of a small number of bubbles in fluid saturated on acoustic wave propagation is noticeable. The modified Biot model presented in this paper provides one model to study the properties of acoustic waves in fluid saturated porous medium with a small number of bubbles.

Waves in porous media saturated with bubbly liquid

Wave processes in a porous medium saturated with bubbly liquid, taking into account the nonlinearity of the oscillations of the bubbles, are numerically investigated. The nonlinearity is accounted in the equation of gas state and the equation of Rayleigh - Lamb. Numerical study in the framework of nonlinear model is performed for the first time. The dispersion relations for linear waves in a porous medium containing bubbly liquid, as well as for the main acoustic mode in a cylindrical cavity in such a medium, are obtained. Frequency dependences of velocity and attenuation of harmonic waves in a cylindrical waveguide are calculated. The influence properties of the bubbly liquid saturated porous medium on the wave velocity and attenuation and the penetration depth of perturbation into the surrounding porous medium are analyzed. The passage of the step wave from fluid into a porous medium saturated with bubbly liquid is investigated. The influence of porous medium parameters and intensity of the incident wave on the wave evolution in bubbly liquid saturated porous medium is studied. The calculation results show good qualitative agreement with the experimental data of other authors.

Numerical simulation of two-phase flow in porous media using a wavelet based phase-field method

An understanding of the transport and dynamics of two fluids in porous media, as well as the bubbly flow regime, is important for many engineering applications, such as enhanced oil recovery (EOR) method, drilling technology, multiphase production system, etc. In this respect, the dependence of capillary stresses on the excess free-energy of a thin interfacial layer formed by two immiscible fluids is not fully clear, particularly in porous media. Of particular interests are the closure models for interphase forces which often hinder the reliable prediction of the homogeneous flow regime. This article presents a multiphase Computational Fluid Dynamics (CFD) study of bubbles in homogeneous porous media to model the flow of oil and gas, and investigates a closure model that is based on the Allen-Cahn phase-field method, where the capillary stress is derived from the excess free-energy. The governing dynamics is simulated with the volume averaged Navier-Stokes equations extended for multiphase flow in porous media. The equations have been discretized by a wavelet transform method to accurately capture the topological change of the fluid-fluid interface. To validate the closure model for interphase forces, the results of the present phase-field method have been compared with that from experiments, as well as from reference numerical models. An excellent agreement among the results from present phase-field simulations, experiments, and some reference numerical simulations has been observed. The terminal velocity of the rising gas bubble in a liquid saturated porous medium, as well as in a pure liquid has been investigated. The bubble rising velocity in both cases have been compared with respect to the theoretical and experimental results. The study illustrates how the bubble dynamics in porous media depend on the excess free energy of a thin interfacial layer formed by two immiscible fluids.

Numerical study on a bubble dynamic generated by ultrasound waves in liquid-saturated porous media

In this paper, the effect of increasing or decrea-sing energy transferred by ultrasound waves on the dy-namics of a cavitation vapor bubble in a confined space such as pores of a porous medium saturated liquid is in-vestigated. The main motivation of this investigation is identifying and understanding the mechanisms of the en-hanced oil recovery using ultrasound waves method in order to be able to recognize the limitations and important parameters in this method. Boundary element method for the numerical solution is used. The problem is solved for the cases with and without surface tension. Numerical re-sults show that by increasing the amount of energy trans-ferred to the liquid filled cavity, bubble growth and col-lapse rates shows a significant increase which results the acceleration of liquid particles around the vapor bubble at both ends of the cavity. As a result, the exerted force on the possible obstacles, like sand particles or trapped oil droplets, increases and moves them. Consequently the permeability of the porous medium increases. Increasing the permeability of oil well, leads to Enhanced Oil Recov-ery. The numerical results show that with increasing energy transferred to saturated liquid cavity, no significant changes occurs during the life time of the vapor bubble. The results also show that the effect of surface tension on the results, given the scale of the problem, is not signifi-cant.DOI: http://dx.doi.org/10.5755/j01.mech.22.6.17275

Transient Heat and Solute Transfers in Liquid-Saturated Porous Media

We investigate transient heat and solute transfers in liquid-saturated porous media. The macroscopic equivalent models are obtained by a homogenization process from the pore-scale description. The large value of the Lewis number in liquid mixtures introduces a possible separation of scales between the heat and solute diffusion wavelengths \(L^{\mathrm{heat}}\) and \(L^{\mathrm{solute}}\) at a given excitation time. Thus, two separations of scales could be present between the pore scale of characteristic length l and \(L^{\mathrm{heat}}\) and \(L^{\mathrm{solute}}\). Depending on the ratio of these two separations of scales results in different equivalent macroscopic models or in non-homogenizable situations. Among numerous possibilities, we present two different homogenizable problems and a non-homogenizable situation. As the characteristic excitation time is decreased, the solute pseudo-wavelength and the heat pseudo-wavelength increase; a unique separation of scales between both solute and heat transfers and the pore scale appears, and we recover the classical macroscopic thermodiffusion model.

Formation of bubbly horizon in liquid-saturated porous medium by surface temperature oscillation.

We study nonisothermal diffusion transport of a weakly soluble substance in a liquid-saturated porous medium in contact with a reservoir of this substance. The surface temperature of the porous medium half-space oscillates in time, which results in a decaying solubility wave propagating deep into the porous medium. In this system, zones of saturated solution and nondissolved phase coexist with ones of undersaturated solution. The effect is first considered for the case of annual oscillation of the surface temperature of water-saturated ground in contact with the atmosphere. We reveal the phenomenon of formation of a near-surface bubbly horizon due to temperature oscillation. An analytical theory of the phenomenon is developed. Further, the treatment is extended to the case of higher frequency oscillations and the case of weakly soluble solids and liquids.