Convection In Fluid-saturated Porous Medium Research Articles

Lattice Boltzmann Simulations of Non-Homogeneous Li–O2 Battery Cathode: The Effect of Spatial and Temporal Porosity Variations

Abstract The porosity of the cathode in a lithium–oxygen battery is a crucial parameter that influences oxygen transport and active surface area availability. This study explores various cathode models with different initial porosity distributions and analyzes the porosity evolution during discharge. The objective is to maximize the active surface area utilization of the cathode and increase the battery’s discharge capacity. The simulations employ a recently developed lattice Boltzmann method (LBM) model proposed by Chen et al. (2017, “Simulation of Double Diffusive Convection in Fluid-Saturated Porous Media by Lattice Boltzmann Method,” Int. J. Heat Mass Transfer, 108, pp. 1501–1510), which is capable of handling spatial and temporal variations in diffusion coefficient values. The results demonstrate that a hierarchical porous cathode provides a better specific capacity than a uniform porous cathode with the same average initial porosity. The specific capacity increases as the magnitude of initial porosity variation in the domain increases. Furthermore, incorporating oxygen channels improves oxygen transport in the cathode and offers a better specific capacity than the hierarchical porous cathode. A combination of hierarchical porous media and oxygen channels delivers the best specific capacity among all the other cathode models, as it efficiently balances oxygen transport and active surface area.

Effect of Temperature Gradients and DC Electric Field on Electrothermal Convection in a Rotating Layer of Walter's-B Fluid Saturated Porous Media

Thermal convection in fluid-saturated porous media has diverse applications across geothermal energy utilisation, thermal insulation engineering, grain storage and understanding geodynamic processes. The thermal convection's physics is crucial for optimising the thermofluid system, improving energy efficiency, and enhancing our understanding of natural phenomena. The study examines how the initiation of electrothermal convection in a rotating viscoelastic fluid layer (Walter's B) is influenced by basic temperature gradients and a uniform vertical DC electric field, considering three different types of velocity boundary conditions: free-free, rigid-rigid, and lower rigid and upper free. By applying an electric field to a fluid, studying electrothermal convection helps engineers design effective cooling systems for electronics. The eigenvalue problem is solved by using the Galerkin technique. The Galerkin method is a widely used numerical technique for solving eigenvalue problems. The DC electric field effect exhibits a more stabilising effect for free-free boundaries than rigid and rigid-rigid boundaries. Moreover, the linear temperature profile exhibits a more stabilising effect than the parabolic temperature profile. The control of electrothermal convection on the system with the impact of other physical parameters is also discussed.

Compressibility Effect on Darcy Porous Convection

Perfectly incompressible materials do not exist in nature but are a useful approximation of several media which can be deformed in non-isothermal processes but undergo very small volume variations. In this paper, the linear analysis of the Darcy-Bénard problem is performed in the class of extended-quasi-thermal-incompressible fluids, introducing a factor beta which describes the compressibility of the fluid and plays an essential role in the instability results. In particular, in the Oberbeck-Boussinesq approximation, a more realistic constitutive equation for the fluid density is employed in order to obtain more thermodynamically consistent instability results. The critical Rayleigh-Darcy number for the onset of convection is determined, via linear instability analysis of the conduction solution, as a function of a dimensionless parameter widehat{beta } proportional to the compressibility factor beta, proving that widehat{beta } enhances the onset of convective motions.Article HighlightsThe onset of convection in fluid-saturated porous media is analyzed, taking into account fluid compressibility effect.The critical Rayleigh-Darcy number is determined in a closed algebraic form via linear instability analysis.The critical Rayleigh-Darcy number is shown to be a decreasing function of the dimensionless compressibility factor.

A space-time generalized finite difference method for solving unsteady double-diffusive natural convection in fluid-saturated porous media

In this paper, the space-time generalized finite difference scheme is proposed to effectively solve the unsteady double-diffusive natural convection problem in the fluid-saturated porous media. In such a case, it is mathematically described by nonlinear time-dependent partial differential equations based on Darcy's law. In this work, the space-time approach is applied using a combination of the generalized finite difference, Newton-Raphson, and time-marching methods. In the space-time generalized finite difference scheme, the spatial and temporal derivatives can be performed using the technique for spatial discretization. Thus, the stability of the proposed numerical scheme is determined by the generalized finite difference method. Due to the property of this numerical method, which is based on the Taylor series expansion and the moving-least square method, the resultant matrix system is a sparse matrix. Then, the Newton-Raphson method is used to solve the nonlinear system efficiently. Furthermore, the time-marching method is utilized to proceed along the time axis after a numerical process in one space-time domain. By using this method, the proposed numerical scheme can efficiently simulate the problems which have an unpredictable end time. In this study, three benchmark examples are tested to verify the capability of the proposed meshless scheme.

Towards the ultimate regime in Rayleigh–Darcy convection

Abstract

Multiple-relaxation-time lattice Boltzmann model for simulating double-diffusive convection in fluid-saturated porous media

A multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is developed for simulating double-diffusive convection in porous media at the representative elementary volume scale. In the model, the equilibrium moments of the temperature and concentration distributions have been modified, which makes the effective thermal diffusivity and heat capacity ratio as well as the effective mass diffusivity and porosity decoupled. Numerical tests demonstrate that the present model can serve as an accurate numerical method for simulating double-diffusive convection in porous media.

Generalized finite difference method for solving the double-diffusive natural convection in fluid-saturated porous media

In this paper, the generalized finite difference method (GFDM) combined with the Newton–Raphson method is proposed to accurately and efficiently simulate the steady-state double-diffusive natural convection in parallelogrammic enclosures filled with fluid-saturated porous media. The natural convection in fluid-saturated porous media, which is interesting in regard to the heat-transferring range, involves different physical compositions to affect the fluid flow. For the mathematical formulations of the natural convention, the governing equations are a system of highly-nonlinear partial differential equations, so the approximate solutions for the natural convention mainly depend on a suitable numerical scheme. In this study, the GFDM, a newly-developed meshless method, is adopted for the spatial discretization of the non-linear governing equations, since it can avoid setting up the mesh in the computational domain and implementing the numerical quadrature. The localization of the GFDM will result in a sparse system, while the derivatives at each node can be expressed as linear combinations of nearby function values with different weighting coefficients. After a system of nonlinear algebraic equations is yielded by the spatial discretization of the GFDM, the two-steps Newton–Raphson method is adopted to efficiently solve this resultant sparse system owing to the localization of the GFDM. Three numerical examples are presented to demonstrate the applicability and stability of the proposed meshless numerical scheme. Besides, the numerical results are compared with other solutions to show the accuracy of the proposed method.

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.

Effect of eccentricity on natural convection in fluid-saturated porous media in an elliptical annulus

In this paper, we summarize a numerical study of two-dimensional natural convection in an annular elliptical space fluid-saturated porous, by solving numerically the mass balance equations, momentum and energy, using Darcy’s law, Boussinesq approximation, vorticity-stream function formulation and the finite volumes method for the discretization of partial derivative equations. Both walls delimiting the annular space are maintained at two uniform different temperatures. The external parameters considered are the eccentricity of the inner elliptic wall (0.55, 0.688, 0.86, 0.9 and 0.999) and Rayleigh-Darcy number (R a m = 500). The results indicate that there are two main modes of natural convection: natural convection with only two cells and with more cells, their description is given in detail. The average equivalent conductivity is presented in terms of external parameters and allows us to see that it increases when the internal wall eccentricity increases.

Double-Diffusive Natural Convection in Anisotropic Porous Medium Bounded by Finite Thickness Walls: Validity of Local Thermal Equilibrium Assumption

Double-diffusive natural convection in fluid-saturated porous medium inside a vertical enclosure bounded by finite thickness walls with opposing temperature, concentration gradients on vertical walls as well as adiabatic and impermeable horizontal ones has been performed numerically. The Darcy model was used to predict fluid flow inside the porous material, while thermal fields are simulated based on two-energy equations for fluid and solid phases on the basis of a local thermal non-equilibrium model. Computations have been performed for different controlling parameters such as the buoyancy ratio $$N$$ , the Lewis number Le, the anisotropic permeability ratio $$R_\mathrm{p}$$ , the fluid-to-solid thermal conductivity ratio $$R_\mathrm{c}$$ , the interphase heat transfer coefficient $$\mathcal{H}$$ , the ratio of the wall thickness to its height $$D$$ , the wall-to-porous medium thermal diffusivity ratio $$R_\mathrm{w}$$ , and the solid-to-fluid heat capacity ratio $$\gamma $$ . Thus, the effects of the controlling parameters on heat and mass transfer characteristics are discussed in detail. Moreover, the validity domain of the local thermal equilibrium (LTE) assumption has been delimited for different set of the governing parameters. It has been shown that Le has a noticeable significant effect on fluid temperature profiles and that higher $$N$$ values lead to a significant enhancement in heat and mass transfer rates. Moreover, for higher $$\mathcal{H}, R_\mathrm{c}$$ , $$R_\mathrm{p}, R_\mathrm{w}$$ , or $$D$$ values and/or lower $$\gamma $$ values, the solid and fluid phases tend toward LTE.

The local RBF collocation method for solving the double-diffusive natural convection in fluid-saturated porous media

The local RBF (radial basis function) collocation method (LRBFCM) combined with the exponentially convergent scalar homotopy algorithm (ECSHA) is proposed to analyze the double-diffusive natural convection in parallelogrammic enclosures filled with fluid-saturated porous media. The LRBFCM, free from mesh and numerical quadrature, is proposed to efficiently and accurately analyze the double-diffusive natural convection. In comparing with other meshless methods, the concept of localization in LRBFCM can avoid the ill-conditioned and full matrix. By enforcing the satisfactions of governing equation at every interior node and boundary condition at every boundary node, a system of nonlinear algebraic equations (NAEs) will be formed by LRBFCM. Thus, the ECSHA is adopted to efficiently resolve the system of NAEs. The efficiency of the evolutionary process in solving NAEs is greatly improved since the calculation of the inverse of Jacobian matrix can be avoided. Two numerical examples will be provided to demonstrate the ability and accuracy of the proposed meshless scheme.

Effects of feedback control on chaotic convection in fluid-saturated porous media

Thermal convective instability in a fluid-saturated porous layer heated from below and cooled from above is investigated theoretically using dynamical systems approach. A feedback control strategy with an array of sensors situated at the top plate of the fluid layer is adopted. The Galerkin truncated approximation is employed to derive a low dimensional Lorenz-like model. It is shown that suppression or enhancement of chaotic convection is possible via feedback control.

Entropy generation analysis of thermally developing forced convection in fluid-saturated porous medium

Entropy generation for thermally developing forced convection in a porous medium bounded by two isothermal parallel plates is investigated analytically on the basis of the Darcy flow model where the viscous dissipation effects had also been taken into account. A parametric study showed that decreasing the group parameter and the Peclet number increases the entropy generation while for the Brinkman number the converse is true. Heatline visualization technique is applied with an emphasis on the Br < 0 case where there is somewhere that heat transfer changes direction at some streamwise location to the wall instead of its original direction, i.e., from the wall.

Natural convection in a porous medium coupled across an impermeable vertical wall with film condensation

This paper presents a theoretical study of thermofluid interaction between natural convection in fluid-saturated porous medium and film condensation, coupled through an impermeable vertical wall. The two heat transfer modes are analyzed separately. The solutions are matched on the wall. The complexion of this two-fluid problem is governed by a dimensionless interaction parameter which relates the heat transfer effectiveness of the two heat transfer mechanisms. The effect of this parameter on the flow and heat transfer is documented. Results regarding the overall heat transfer coefficient are obtained for a wide range of the independent parameters.

Convection and flow in porous media. Part 2. Visualization by shadowgraph

We present results for pattern formation at the onset of convection in fluid-saturated porous media obtained by a novel variation on the shadowgraphic technique (modified shadowgraphic technique). Both ordered and disordered media are used, each exhibiting distinct behaviour. Ordered porous media are constructed from grids of overlapping bars. Convective onset in this type of medium is characterized by a sharp, well-defined bifurcation to straight parallel rolls. The orientation of the convection rolls is determined by the number of bar layers, Nb; odd Nb leads to rolls with axes perpendicular to the direction of the top and bottom bars, and even Nb to rolls at 45° to the bars. Disordered porous layers are produced by stacking randomly drilled disks separated by spacers. In this system, we observe a rounded bifurcation to convection with localized convection near convective onset. More specifically, the flow patterns take on one of several different three-dimensional cellular structures after each cycling through convective onset. These observations may be described by two different mechanisms: random spatial fluctuations in the Rayleigh number (Zimmermann et al. 1993), and/or spatial variation in the thermal conductivity on the length scale of the convection wavelength (Braester &amp; Vadasz 1993).

Weak continuity in convection problems

Basic aspects of steady natural convection in fluid-saturated porous media are studied, such as the existence of weak solutions, some regularity properties, a minimax principle and the determination of a sufficient condition for uniqueness, which is very unlikely to happen if the Rayleigh number is not less than a critical value.

Transitions in time-dependent thermal convection in fluid-saturated porous media

Numerical simulations of single-cell, two-dimensional, time-dependent thermal convection in a square cross-section of fluid-saturated porous material heated uniformly from below reveal a series of transitions between distinct oscillatory dynamical regimes. With increasing Rayleigh number R, the flow first evolves from steady-state behaviour into periodic motion with a single frequency f which depends on R approximately according to . The two frequencies in the narrow transition regime may be locked to a rational ratio, in which case the flow is periodic, or they may be commensurate, in which case the flow is quasi-periodic. The spectral characteristics of numerical realizations of unsteady convection and the occurrences of transitions therein are highly dependent on truncation level in Galerkin schemes or resolution in finite-difference approaches.

Finite-amplitude cellular convection in a fluidsaturated porous layer

The local nonlinear stability of thermal convection in fluid-saturated porous media, subjected to an adverse temperature gradient, is investigated. The critical Rayleigh number at the onset of convection and the corresponding heat transfer are determined. An approximate analytical method is presented to determine the form and amplitude of convection. To facilitate the determination of the physically preferred cell pattern, a detailed study of both two- and three-dimensional motions is made and a very good agreement with available experimental data is found. The finite-amplitude effects on the horizontal wavenumber, and the effect of the Prandtl number on the motion are discussed in detail. We find that, when the Rayleigh number is just greater than the critical value, two dimensional motion is more likely than three-dimensional motion, and the heat transport is shown to have two regions for n =1. In particular, it is shown that optimum heat transport occurs for a mixed horizontal plan form formed by the linear combination of general rectangular and square cells. Since an infinite number of steady-state finite-amplitude solutions exist for Rayleigh numbers greater than the critical number A c * , a relative stability criterion is discussed th at selects the realized solution as that having the maximum mean-square temperature gradient.

Three-dimensional and multicellular steady and unsteady convection in fluid-saturated porous media at high Rayleigh numbers

In an effort to determine the characteristics of the various types of convection that can occur in a fluid-saturated porous medium heated from below, a Galerkin approach is used to investigate three-dimensional convection in a cube and two-dimensional convection in a square cross-section. Strictly two-dimensional, single-cell flow in a square cross-section is steady for Rayleigh numbers R between 4π2 and a critical value which lies between 300 and 320; it is unsteady at higher values of R. Double-cell, two-dimensional flow in a square cross-section becomes unsteady when R exceeds a value between 650 and 700, and triple-cell motion is unsteady for R larger than a value between 800 and 1000. Considerable caution must be exercised in attributing physical reality to these flows. Strictly two-dimensional, steady, multicellular convection may not be realizable in a three-dimensional geometry because of instability to perturbations in the orthogonal dimension. For example, even though single-cell, two-dimensional convection in a square cross-section is steady at R = 200, it cannot exist in either an infinitely long square cylinder or in a cube. It could exist, however, in a cylinder whose length is smaller than 0.38 times the dimension of its square cross-section. Three-dimensional convection in a cube becomes unsteady when R exceeds a value between 300 and 320, similar to the unicellular two-dimensional flow in a square cross-section. Nusselt numbers Nu, generally accurate to 1%, are given for the strictly two-dimensional flows up to R = 1000 and for three-dimensional convection in cubes up to R = 500. Single-cell, two-dimensional, steady convection in a square cross-section transports the most heat for R &lt; 97; this mode of convection is also stable in square cylinders of arbitrary length including the cube for R &lt; 97. Steady three-dimensional convection in cubes transports more heat for 97 [lsim ] R [lsim ] 300 than do any of the realizable two-dimensional modes. At R [gsim ] 300 the unsteady modes of convection in both square cylinders and cubes involve wide variations in Nu.