Arzhang Khalili

Tortuosity-porosity relation in porous media flow

We study numerically the tortuosity-porosity relation in a microscopic model of a porous medium arranged as a collection of freely overlapping squares. It is demonstrated that the finite-size, slow relaxation and discretization errors, which were ignored in previous studies, may cause significant underestimation of tortuosity. The simple tortuosity calculation method proposed here eliminates the need for using complicated, weighted averages. The numerical results presented here are in good agreement with an empirical relation between tortuosity (T) and porosity (varphi) given by T-1 proportional, variantlnvarphi , that was found by others experimentally in granule packings and sediments. This relation can be also written as T-1 proportional, variantRSvarphi with R and S denoting the hydraulic radius of granules and the specific surface area, respectively. Applicability of these relations appears to be restricted to porous systems of randomly distributed obstacles of equal shape and size.

Transition layer thickness at a fluid-porous interface

The length scale of the transition region between a porous layer and its overlying fluid layer is experimentally studied. The experimental setup consists of a rectangular channel, in which a fluid layer flows over a porous bed. Using particle image velocimetry and refractive index matching, two-dimensional velocity measurements in the interfacial region were performed. The thickness of this transition layer, defined by the height below the permeable interface up to which the velocity decreases to the Darcy scale, is measured and compared with the permeability and the matrix grain size. It was observed that the thickness of the transition zone, δ, is of the order of the grain diameter, and hence, much larger than the square root of the permeability as predicted by previous theoretical studies. The Reynolds number and the fluid height over the porous substrate were found to affect the gradient of the horizontal velocity component at the interfacial region while the length scale of the transition layer remai...

Flow visualization in porous media via Positron Emission Tomography

We demonstrate here the use of a non-invasive technique based on Positron Emission Tomography (PET) in visualizing and in making quantitative measurements of scalar transport through natural opaque permeable sediments. Along with various other possibilities, this technique has the potential to help improve the understanding of processes that take place at the seabeds between the porewater and the overlying water, which result in exchange of nutrients, toxins and solute. Unlike many other methods, PET is able to produce full three-dimensional pictures of the percolation of fluid through not only “constructed” but also natural porous media.

Double-diffusive natural convection in an anisotropic porous cavity with opposing buoyancy forces: multi-solutions and oscillations

Abstract Natural convection by combined heat and mass transfer with opposing horizontal heat and solute gradients has been investigated in an anisotropic porous cavity using the Darcy model. The porous medium is assumed to be both hydrodynamically and thermally anisotropic. The principal directions of the permeability tensor are taken oblique to the gravity vector, while those of thermal and solutal diffusivity coincide with horizontal and vertical coordinate axes. Special attention is given to understand the effect of anisotropic parameters on the existence of unsteady permanent oscillations and multiple steady-state solutions. From the study of analytical solutions, which can be regarded as a verification of the numerical results, simultaneously, it is found that there exists an interval of buoyancy ratio, I NM , depending on the parametric values, in which multiple solutions exist. For the unsteady case a similar interval, I NO , for the buoyancy ratio has been observed numerically, in which permanent oscillations exist. Periodicity of the oscillation changes drastically by changing the permeability of the medium. The results indicate that the maximum I NM and I NO interval are attained at an orientation angle of θ =45°. The local direction of the flow changes because of the variation in the extent of the thermal and concentration layers, the opposite buoyant mechanism, and anisotropic parameters.

Computation of flow through a fluid-sediment interface in a benthic chamber

In this paper we present a single-domain approach for the solution of flow in a composite region made up of a pure fluid layer and an underlying saturated porous layer. As an example, we compute the unsteady, axisymmetric flow and scalar transport in a stationary cylindrical container with a rotating lid, filled to the midheight with a porous material and to the top with water. A generalized equation known as the Brinkman-extended Darcy equation is solved inside the porous medium, along with the incompressible Navier–Stokes equations in the upper fluid layer. Comparisons with experimental data previously obtained by the authors for flow in the same geometry show good agreement, thus verifying the accuracy of the present computations. The results indicate that a single-domain approach can provide good predictions of interfacial flow, thereby obviating the need for ad hoc interface conditions. The existence of a thin Brinkman layer below the interface is observed. Radial profiles of computed velocity components adjacent to the interface show remarkable similarity, despite vast differences in magnitudes, showing that good matching between the two different flows has been achieved by the present single-domain approach.

Influence of Prandtl number on stability of mixed convective flow in a vertical channel filled with a porous medium

Buoyancy opposed mixed convection is considered in a vertical channel filled with an isotropic, porous medium, in which the motion of an incompressible fluid is induced by external pressure gradients and buoyancy forces. The Brinkman-Wooding-extended Darcy model has been used to study the instability mechanisms of the basic flow and its dependence on the Prandtl number (Pr) of the fluid. The stability analysis indicated that for the same Reynolds number (Re), the fully developed base flow was highly unstable for a fluid with high Pr. For a porous medium with a Darcy number (Da) of 10−6 and Pr⩾0.7, two different types of instability, Rayleigh-Taylor (R-T) and buoyant instability, are observed. The R-T instability mode is observed for relatively small values of Re. Further, the results show that for Da=10−5 and Pr<1, the spectrum of the energy profile is abrupt and sudden, whereas the same is smooth when Da=10−6. In the case of R-T instability, the critical value of Ra at low Re is given by −2.47∕Da. Though...

Onset of convection in a porous layer with net through-flow and internal heat generation

Onset of convection in a horizontal porous layer is investigated including the effects of through-flow and a uniformly distributed internal heat generation for different types of hydrodynamic boundary conditions. The instability parameter is either a Darcy-external or Darcy-internal Rayleigh number which has been determined numerically using Galerkin technique. When the boundary conditions at the top and bottom are not identical, it is found that a small amount of through-flow in one particular direction destabilizes the system in the absence of heat generation. However, in the presence of an internal heat generation, through-flow in one direction destabilizes the system even if the boundary conditions at the two boundaries are of the same type and the destabilization is found to be more with the increase in internal Rayleigh number.

Stability of mixed convection in an anisotropic vertical porous channel

This paper addresses the stability of mixed convective buoyancy assisted flow due to external pressure gradient and buoyancy force in a vertical fluid saturated porous channel with linearly varying wall temperature. The porous medium is assumed to be both hydrodynamically and thermally anisotropic. Two different types of temperature perturbations, (i) zero temperature and (ii) zero heat flux, have been considered to study the effect of anisotropic permeability and thermal diffusivity on the flow stability. The stability analysis indicated that the least stable mode is two-dimensional. Furthermore, the results show that for the same Reynolds number, the fully developed base flow is highly unstable (stable) for high (low) permeable porous media as well as for a porous medium with small (large) thermal diffusivity ratio. Depending on the magnitude of all parameters studied, three types of instabilities (shear, thermal, and mixed instability) occurred. The transition of instability from one type to another took place smoothly, except when the permeability ratio exceeded 6. Based on the value of the permeability ratio, the flow in an anisotropic medium for a specific Reynolds number may be either more or less stable than the flow in an isotropic medium. In addition, the fully developed flow is more stable for relatively small values of the modified Darcy number than for larger values. The effect of Brinkman as well as Forchheimer terms are negligible for the set of other parameters studied here. In contrast to a pure viscous fluid or an isotropic porous medium, which are characterized by unicellular convective cells, in anisotropic porous media convective cells may be unicellular or bicellular. The stability analysis of mixed convection in channels filled either with a viscous fluid or with an isotropic saturated porous medium may be obtained as special cases of the general study presented here.

On the stability of double diffusive convection in a porous layer with throughflow

SummaryThe effect of throughflow on the stability of double diffusive convection in a porous layer is investigated for different types of hydrodynamic boundary conditions. The lower and upper boundaries are assumed to be insulating to temperature and concentration perturbations. The resulting eigenvalue problem is solved by the Galerkin technique. The curvature of the basic temperature as well as solute concentration gradients significantly affects the stability of the system. It is observed that, for a suitable choice of parametric values, Hopf bifurcation occurs always prior to direct bifurcation, and the throughflow alters the nature of bifurcation. In contrast to the single component system, it is found that throughflow is (a) destabilizing even if the lower and upper boundaries are of the same type, and (b) stabilizing as well as destabilizing, irrespective of its direction, when the boundaries are of different types.

Diffusion-limited retention of porous particles at density interfaces

Downward carbon flux in the ocean is largely governed by particle settling. Most marine particles settle at low Reynolds numbers and are highly porous, yet the fluid dynamics of this regime have remained unexplored. We present results of an experimental investigation of porous particles settling through a density interface at Reynolds numbers between 0.1 and 1. We tracked 100 to 500 μm hydrogel spheres with 95.5% porosity and negligible permeability. We found that a small negative initial excess density relative to the lower (denser) fluid layer, a common scenario in the ocean, results in long retention times of particles at the interface. We hypothesized that the retention time was determined by the diffusive exchange of the stratifying agent between interstitial and ambient fluid, which increases excess density of particles that have stalled at the interface, enabling their settling to resume. This hypothesis was confirmed by observations, which revealed a quadratic dependence of retention time on particle size, consistent with diffusive exchange. These results demonstrate that porosity can control retention times and therefore accumulation of particles at density interfaces, a mechanism that could underpin the formation of particle layers frequently observed at pycnoclines in the ocean. We estimate retention times of 3 min to 3.3 d for the characteristic size range of marine particles. This enhancement in retention time can affect carbon transformation through increased microbial colonization and utilization of particles and release of dissolved organics. The observed size dependence of the retention time could further contribute to improve quantifications of vertical carbon flux.