Convection In Porous Medium Research Articles

On predicting the onset of transient convection in porous media saturated with Non-Newtonian liquid

The onset of transient convection in non-Newtonian liquid immersing porous media was simulated using a Computational Fluid Dynamics (CFD) package for the thermal boundary condition of Fixed Surface Temperature (FST). Most of the simulated values of stability criteria were found to be in good agreement with the predicted and theoretical values of transient critical Rayleigh number for non-Newtonian liquid defined by Tan and Thorpe (1992) for power-law fluids. The critical transient Rayleigh numbers for convection in porous media were found to be in good agreement with theoretical values by using apparent viscosity µapp at zero shear. The critical time and critical depth for transient heat conduction were then determined accurately that

Dual Solutions for Opposing Mixed Convection in Porous Media

The problem of steady mixed convection boundary layer flow on a cooled vertical permeable circular cylinder embedded in a fluid-saturated porous medium is studied. Here, we evaluate the flow and heat transfer characteristics numerically for various values of the governing parameters and demonstrate the existence of dual solutions beyond a critical point.

Effect of Carreau-Yasuda rheological parameters on subcritical Lapwood convection in horizontal porous cavity saturated by shear-thinning fluid

The present study is focused on Lapwood convection in isotropic porous media saturated with non-Newtonian shear thinning fluid. The non-Newtonian rheological behavior of the fluid is modeled using the general viscosity model of Carreau–Yasuda. The convection configuration consists of a shallow porous cavity with a finite aspect ratio and subject to a vertical constant heat flux, whereas the vertical walls are maintained impermeable and adiabatic. An approximate analytical solution is developed on the basis of the parallel flow assumption, and numerical solutions are obtained by solving the full governing equations. The Darcy model with the Boussinesq approximation and energy transport equations are solved numerically using a finite difference method. The results are obtained in terms of the Nusselt number and the flow fields as functions of the governing parameters. A good agreement is obtained between the analytical approximation and the numerical solution of the full governing equations. The effects of the rheological parameters of the Carreau-Yasuda fluid and Rayleigh number on the onset of subcritical convection thresholds are demonstrated. Regardless of the aspect ratio of the enclosure and thermal boundary condition type, the subcritical convective flows are seen to occur below the onset of stationary convection. Correlations are proposed to estimate the subcritical Rayleigh number for the onset of finite amplitude convection as a function of the fluid rheological parameters. Linear stability of the convective motion, predicted by the parallel flow approximation, is studied, and the onset of Hopf bifurcation, from steady convective flow to oscillatory behavior, is found to depend strongly on the rheological parameters. In general, Hopf bifurcation is triggered earlier as the fluid becomes more and more shear-thinning.

Instability and Route to Chaos in Porous Media Convection

A review of the research on the instability of steady porous media convection leading to chaos, and the possibility of controlling the transition from steady convection to chaos is presented. The governing equations consisting of the continuity, the extended Darcy, and the energy equations subject to the assumption of local thermal equilibrium and the Boussinesq approximation are converted into a set of three nonlinear ordinary differential equations by assuming two-dimensional convection and expansion of the dependent variables into a truncated spectrum of modes. Analytical (weak nonlinear), computational (Adomian decomposition) as well as numerical (Runge-Kutta-Verner) solutions to the resulting set of equations are presented and compared to each other. The analytical solution for the transition point to chaos is identical to the computational and numerical solutions in the neighborhood of a convective fixed point and deviates from the accurate computational and numerical solutions as the initial conditions deviate from the neighborhood of a convective fixed point. The control of this transition is also discussed.

Experimental Study of Density-driven Convection in Porous Media by Using MRI

Density-driven convection is known as one of the physical phenomena for CO2 injection in saline aquifers, which accelerates the transfer of CO2 into the groundwater, increases the dissolution rate and shorten the dissolution time, thus it is favourable for long-term CO2 injection and the practical interest of storage security. Understanding how the occurrence and form of convective fingers is crucial to understanding the role of that Density-driven-convection behaviour. The purpose of this paper is to design a visual experimental set-up based on the MRI technique and present new analogue fluid pairs that reconstructed the convective process. The density-driven convection was formed by two miscible liquids at the interface demonstrated by fingers. We observed the development and growth of density-driven fingers of two-phase fluid i.e., water/ deuterium oxide, and brine/ deuterium oxide at different permeability porous media. Experiments indicated that the relationship of convection onset time to Rayleigh number changed with the density difference and permeability. We present an experimental study for the Rayleigh number in the range 583.279 to 2054.111. The results show that the higher permeability and density difference is conducive to shorten the convection onset time. The motivation behind this results is related to the implications for predicts the CO2 dissolution trapping time and accumulations in geological storage of carbon dioxide.

Transitional behaviour of convective patterns in free convection in porous media

The present study focuses on the transition between steady convective patterns in fluid-saturated porous media. We conduct experiments to identify the transition point from the single- to double-cell pattern in a two-dimensional porous medium. We then perform a basin stability analysis to assess the relative stability of different convective modes. The resulting basin stability diagram not only provides the domains of coexistence of different modes, but it also shows that the likelihood of finding convective patterns depends strongly on the Rayleigh number. The experimentally observed transition point from single- to double-cell mode agrees well with the stochastically preferred mode inferred from the basin stability diagram.

Role of thermal disequilibrium on natural convection in porous media: Insights from pore-scale study.

The present study investigates the role of thermal nonequilibrium on natural convection in a fluid-saturated porous medium heated from below. We conduct high-resolution direct numerical simulation at the pore scale in a two-dimensional regular porous structure by means of the thermal lattice-Boltzmann method (LBM). We perform a combination of linear stability analysis of continuum-scale heat transfer models, and pore-scale and continuum-scale simulations to study the role of thermal conductivity contrasts among phases on natural convection. The comparison of pore-scale lattice-Boltzmann simulations with linear stability analysis reveals that traditional continuum-scale models fail to capture the correct onset of convection, convection mode, and heat transfer when the thermal conductivity of the solid obstacles does not match that of the fluid.

An improved lattice Boltzmann method for solid-liquid phase change in porous media under local thermal non-equilibrium conditions

This paper presents an improved lattice Boltzmann (LB) method to simulate solid-liquid phase change with natural convection in porous media under local thermal non-equilibrium (LTNE) conditions. In this method, three distribution functions are respectively adopted for flow field, and temperature field of the PCM and solid matrix. Different from previous models, the present model for temperature field incorporates the total enthalpy and a free parameter in the equilibrium distribution function, and thus could have high computational efficiency by avoiding iteration procedure to deal with phase change. The present model is validated by the melting with natural convection in a square cavity filled with a metal foam. It is found that the numerical results are in good agreement with other numerical results, and the present method could preserve higher accuracy due to numerical diffusion reduction through keeping the relaxation time at around unity as well as tuning the free parameters properly.

A new general model for phase-change heat transfer of waxy crude oil during the ambient-induced cooling process

ABSTRACTThe thermal process during shutdown (a stoppage state of the pipeline), of which the essence is an irregular phase-change process accompanied by natural convection, non-Newtonian behavior, and sometimes turbulence, is a critical problem in crude oil transportation engineering. An accurate calculation of the thermal process during shutdown is more than necessary for the safety of crude oil pipeline; however, it faces some challenges due to the complexity of the phase change. In this study, the phase change of waxy crude oil during the cooling process is divided into four stages, which includes a pure liquid natural convection, solid/liquid dispersion natural convection, coexistence of dispersion system natural convection and porous media natural convection, and pure porous media convection, according to different heat transfer mechanisms on different stages. Based on this division, a general phase-change heat transfer model is proposed for the thermal calculation of waxy crude oil during shutdown. Compared with the previous research, this model appropriately includes the influences of non-Newtonian behavior, phase evolution as well as turbulence. With the proposed model, the temperature drop characteristic of a sample pipeline is analyzed and the influencing factors are investigated.

Throughflow and G-jitter effects on chaotic convection in an anisotropic porous medium

Abstract The present article is to investigate the effect of various parameters on chaotic convection in an anisotropic porous medium under gravity modulation. For this, the problem is reduced into Lorenz system (non-autonomous) by employing truncated Galerkin expansion method. It is found that the system shows either chaotic or periodic nature for suitable values of scaled Rayleigh number. The influence of amplitude of modulation is to advance the chaotic nature in the system while that of frequency of modulation has tendency to delay the chaotic behaviour. The effects of Peclet number and anisotropic parameters on the chaotic system are also studied and found these are delay the chaotic nature. The phase portrait and time domain diagrams of the Lorenz system for suitable parametric values has been used to analysed the system. Finally, we conclude that the system has either chaotic or periodic solution depending upon the values of the parameters.

Onset of Darcy–Benard Penetrative Convection in Porous Media

Onset of Darcy–Benard Penetrative Convection in Porous Media

Dissolution in anisotropic porous media: Modelling convection regimes from onset to shutdown

In the present study, we use direct numerical simulations to examine the role of non-isotropic permeability on solutal convection in a fluid-saturated porous medium. The dense solute injected from the top boundary is driven downwards by gravity and follows a complex time-dependent dynamics. The process of solute dissolution, which is initially controlled by diffusion, becomes dominated by convection as soon as fingers appear, grow, and interact. The dense solute finally reaches the bottom boundary where, due to the prescribed impermeable boundary, it starts filling the domain so to enter the shutdown stage. We present the entire transient dynamics for large Rayleigh-Darcy numbers, Ra, and non-isotropic permeability. We also try to provide suitable and reliable models to parametrize it. With the conceptual setup presented here, we aim at mimicking the process of liquid CO2 sequestration into geological reservoirs.

Simulation of double diffusive convection in fluid-saturated porous media by lattice Boltzmann method

The research on double diffusive convection in porous media is important to deepen our insights into sustainable development and environment protection. A lattice Boltzmann (LB) model for REV (representative elementary volume) scale simulation of double diffusive convection in fluid-saturated porous media is proposed in the present work. It can work well not only for porous media with uniform porosity but also for non-uniform porous media. Several benchmark tests are adopted to validate its capability. The good agreement with previous publications demonstrates its applicability. It can provide an alternative numerical tool for modelling complex heat and mass transfer in fluid-saturated porous media beyond double diffusive convection, such as heat and moisture transfer in multi-layer building materials.

Stability of gravitationally unstable double diffusive transient boundary layers with variable viscosity in porous media

We study the double diffusive convection (DDC) in porous media through linear stability analysis (LSA) and direct numerical simulations (DNS). Unlike the previous studies that assume static solutal or thermal fields, the developed model is able to capture the transient behavior of both fields. We show that under the assumption of static field, the role of Lewis number cannot be distinguished. Under transient fields, we conclude that higher Lewis numbers result in earlier instability of the boundary layers. Moreover, the effect of viscosity contrast is explained in terms of the mobility of the boundary layer. The DNS results confirm the validity of LSA predictions. We also obtain the critical Rayleigh number and show that in the presence of viscosity contrast, it can be much smaller than the conventional limit of 4π2. This study provides a better understanding of the transient nature of DDC in the presence of viscosity variations. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2471–2482, 2017

Numerical simulation of three-dimensional double-diffusive natural convection in porous media by boundary element method

The paper presents numerical results for three-dimensional double-diffusive natural convection in a cubic enclosure fully filled with fluid saturated porous media. Two opposite vertical walls of the enclosure are subjected to different values of temperature and concentration, which causes buoyant and diffusive flow in the porous media domain. Mathematical model is based on the Brinkman-extended Darcy formulation as a governing momentum equation, which is coupled with the energy and species equations. The three-dimensional boundary element method based solver was used to solve the obtained set of partial differential equations. The existing numerical algorithm primarily derived for the pure fluid flow simulations was adopted to simulate transport phenomena in porous media. It is based on the combination of single and subdomain boundary element method, which solves the velocity-vorticity formulation of the governing equations. In the paper the influence of some governing parameters, specially the Rayleigh number, Darcy number and buoyancy coefficient are investigated in order to analyze the heat and mass transfer through porous enclosure. The numerical code is verified by comparison of the results with available previous numerical data found in the literature.

Mesoscopic pore-scale simulations of natural convection of porous media in closed square cavity by using LBM

A lattice Boltzmann model is applied to simulate natural convection of porous media in closed square cavity. The numerical simulation is conducted to investigate the influences of porosity on fluid flows and the effect of thermal conductivity ratio of solid matrix to fluid on heat transfer. Micro X-CT has been used to obtain 2D optical image of various slice with different location. A construction porous model has been established accurately by 2D optical micro X-CT image of porous media. A fluid –solid conjugate heat transfer model has been applied to the established construction porous model by using Lattice Boltzmann method.This paper confirms the reliability and the computational efficiency of the lattice Boltzmann method in simulating natural convection in porous media at mesoscopic pore-scale.The temperature field is simulated by a simplified thermal energy distribution function which neglects the compression work done by the pressure and the viscous heat dissipation. A comprehensive parametric study of natural convective flows is carried out for various values of Rayleigh number.

Stability analysis of dissolution-driven convection in porous media

We study the stability of dissolution-driven convection in the presence of a capillary transition zone and hydrodynamic dispersion in a saturated anisotropic porous medium, where the solute concentration is assumed to decay via a first-order chemical reaction. While the reaction enhances stability by consuming the solute, porous media anisotropy, hydrodynamic dispersion, and capillary transition zone destabilize the diffusive boundary layer that is unstably formed in a gravitational field. We perform linear stability analysis, based on the quasi-steady-state approximation, to assess critical times, critical wavenumbers, and neutral stability curves as a function of anisotropy ratio, dispersivity ratio, dispersion strength, material parameter, Bond number, Damköhler number, and Rayleigh number. The results show that the diffusive boundary layer becomes unstable in anisotropic porous media where both the capillary transition zone and dispersion are considered, even if the geochemical reaction is significantly large. Using direct numerical simulations, based on the finite difference method, we study the nonlinear dynamics of the system by examining dissolution flux, interaction of convective fingers, and flow topology. The results of nonlinear simulations confirm the predictions from the linear stability analysis and reveal that the fingering pattern is significantly influenced by combined effects of reaction, anisotropy, dispersion, and capillarity. Finally, we draw conclusions on implications of our results on carbon dioxide sequestration in deep saline aquifers.

On the Occurrence of Stationary Convection in Triply Diffusive Convection in Porous Medium: Darcy Model

On the Occurrence of Stationary Convection in Triply Diffusive Convection in Porous Medium: Darcy Model

Effect of the Thickness of Porous Medium on Natural Convection Heat Transfer with Thermal Radiation in Building Envelope

With the development of living standards and energy conservation awareness, people pay more and more attention to the building energy saving and evaluation of building thermal performance. This paper deals with the effect of the thickness of wall on natural convection heat transfer with thermal radiation in a building room with porous medium envelope. The governing equations for the momentum and heat transfer in both free fluid and porous medium were solved by the finite element method. Comparisons with experimental and numerical results in the literature have been carried out. Effects of the thickness of wall on natural convection and heat transfer in both free fluid and porous medium were analyzed. It was found that The Nuc at the interface decrease with increase of thickness of porous media until d≤0.25, and there is no change in Nuc as d is further increased. When d reaches a certain value, the flow field and the temperature field won’t change as d increases.

Experimental and Numerical Study of the Onset of Transient Natural Convection in a Fractured Porous Medium

In this study, analysis of transient natural convection in a porous medium with a vertical fracture across it in a rectangular enclosure was performed experimentally and numerically. A number of thermocouples in distinctive distances in the model were used to measure temperature distribution and confirm the numerical simulations. A detailed CFD simulation was carried out, which was based on the finite volume method to extend our experimental observations. The onset of transient natural convection in the fractured porous media was observed by experimental setup and successfully simulated by numerical analysis. A modified Rayleigh number for the constant surface temperature at the bottom boundary condition of the model was calculated in this study (i.e., use of $$K_\mathrm{avg}$$ instead of K), which was near to the theoretical value of linear stability analysis. Moreover, the critical time of the onset convection in the fractured model was predicted. The average Nusselt number was estimated to be about 3.5 for this fractured porous model.