Session K15: Porous Media Flows: Convection and Heat Transfer (8:45am - 9:30am CST)

Modelling and simulation of natural convection in cavities with immersed internally heated porous structures

In this talk we are concerned with three-dimensional natural convection in domains that contain immersed porous structures heated internally. The formulation of the problem is based on the single-domain approach which incorporates porosity as a field variable. Also, the solid matrix is not in thermal equilibrium with the fluid inside the porous structure. A homogeneous boiling model is also implemented to take account of the phase change that may occur when water reaches the saturation temperature. The numerical scheme is based on a fractional-step time-marching scheme coupled with a projection method for the computation of the pressure. First, we present briefly the formulation of the mathematical model and describe the basic aspects of the proposed numerical algorithm. Then, we present and discuss numerical results from a series of test cases for the problem in hand. Emphasis is placed on the effect of thermal non-equilibrium between the solid matrix and the fluid inside the porous medium.   

Lagrangian Approach for Hydrodynamic Dispersion in Porous Media

Realizing that the nature of dispersion in porous media is Lagrangian, we define a Peclet number by a Lagrangian length scale that takes molecular diffusion, advection and medium geometry into consideration. A lattice Boltzmann method is used to simulate the flow in packed beds containing mono-disperse, bi-disperse and tri-disperse spheres with different packing configurations. Then, Lagrangian Particle Tracking is applied to track the trajectories of particles with Schmidt numbers between 100 to 10,000, as they move in the simulated flow fields. The numerical approach has been validated previously [1-3]. These data allow the direct calculation of dispersion coefficients and Lagrangian time (or length) scales. The effective diffusivity is determined based on the dispersion coefficient of particles at a static flow field. It is found that while there is no unique form of equations to relate the dispersion coefficients to the effective diffusivity and the Eulerian Peclet number, a linear dependence on the Lagrangian Peclet number is observed. The slope of the line varies with the medium structural properties and can be predicted a-priori, making as strong case that the Lagrangian approach is not only natural, but also offers an accurate representation of hydrodynamic dispersion in porous media. References: [1] R. Voronov, et al., \textit{J. Biomech.}, 43(7), 1279--1286, 2010. [2] N. H. Pham, et al., \textit{Phys. Rev. E.}, 89(3), 1--13, 2014. [3] R. S. Voronov, et al. \textit{Int. J. Numer. Methods Fluids}, 67(4), 501--517, 2011.   

Thermal convection in an enclosure with a heat-generating porous cylinder

In this work, a numerical simulation will be performed for flow and heat transfer in a square enclosure with a porous cylinder with internal heat generation. Considering the two-domain approach, the Darcy-Brinkman-Forchheimer extended model will be applied for the flow in the porous region, and the Navier-Stokes equation will be used to model the flow in the homogenous fluid region. To obtain a better coupling flow and heat transfer at the porous-fluid interface, a stress jump condition together with continuities of velocity and normal stress and a continuity of heat flux as well as temperature will be exerted. The finite volume method based on the body-fitted and multi-block grids will be used to solve the governing equations. The effects of the Darcy number, Rayleigh number, porosity, and the Prandtl number on the flow pattern and heat transfer will be discussed. The flow and thermal characteristics will be presented in terms of streamlines and temperature distributions. The heat transfer rate, quantified by the Nusselt number, at different physical parameters will be also investigated.   

Longitudinal conduction effects on both the fluid and the wall of a porous microchannel.

In previous works, the conjugate heat transfer problem was studied in a porous microchannel between parallel plates, subjected to a uniform heat flux on the external wall of the microchannel; the parameter $\alpha $\textunderscore c/$\varepsilon $\textunderscore h\textasciicircum 2 was a dimensionless conjugate heat transfer parameter in the wall, played a crucial role in the temperature profiles of both the fluid and the wall. However, in this work another parameter $\alpha $\textunderscore c/$\varepsilon $\textasciicircum 2 is analyzed, which fulfills the role of being a dimensionless conjugate heat transfer parameter in the fluid. Therefore, it is necessary to analyze in a coupled way, the transversal and longitudinal heat conduction effects on the porous medium and on the microchannel wall.   

Interfacial thermal transport in partially porous channel flow at turbulent flow regimes

We investigate interfacial thermal transport in a partially porous channel via laboratory experiments to evaluate the effect of porous medium microstructure at varying Reynolds numbers. Previous direct numerical simulations for partially porous channel flow indicate that large vortex structures enhance turbulent heat transfer at the porous medium-unobstructed flow interface. Commercially-available Aluminum foams with nominal pore sizes 10 ppi and 40 ppi are attached to a heater block and placed in a forced convection arrangement adjacent to an unobstructed channel. Measurements of pressure drop and temperatures are made across the porous section for bulk Reynolds number varying from 500 to 1500 to characterize friction factors and Nusselt numbers. Heat transfer efficiency with respect to pumping power requirements is evaluated. Particle Image Velocimetry (PIV) measurements made at a subset of these Reynolds numbers are being analyzed to test for the emergence of interfacial vortex structures, and quantify their effect on interfacial thermal transport.   

Buoyant convection in porous media: Two-layered separated by an inclined permeability jump

We report upon both the early- and late-time dynamics of buoyancy driven flow leading to gravity current flow in a two-layered (upper- and lower-layer) porous media separated by an inclined permeability jump. The early-time dynamics is studied by deriving a Darcy equation-based analytical model that assumes a sharp-interface to exist between the gravity current and the ambient fluids, considering the layers are of semi-infinite thicknesses. We thereby predict the along-slope propagation of the gravity current noses all the way to runout, a state characterized by a balance between gravity current influx and outflux (due to draining). Experiments further reveal a complicated flow structure with the formation of two distinct interfaces. Herein, the nose of the flow fronts corresponding to up- and downdip gravity currents are used to quantify the transient and steady state behaviors and are further corroborated with theoretical predictions. The late-time dynamics is also study in a purely experimental context by introducing a finite lower-layer depth which allows the formation of `secondary-gravity currents' in the lower-layer which has significant influence on the dynamics of the `primary-gravity currents' in the upper-layer. Furthermore, the addition of vertical boundaries allows us to distinguish between two qualitatively different filling regimes, i.e. sequentially vs. simultaneously of upper- and lower-layers. Parameter combinations conducive to one or the other filling regime are identified.   

An axisymmetric solid-liquid phase change model based on Lattice Boltzmann method for phase change material (PCM) melting with porous media

Phase change material (PCM) is widely used in thermal energy storage systems as it can absorb and release a large amount of heat during the phase change process. Both experimental and numerical studies of PCM have increased substantially in the past two decades. Among them, the phase change in porous media is one of the important topics. In this paper, a solid-liquid phase change model is developed based on the Lattice Boltzmann method (LBM) to simulate transient phase change in porous media. Double distribution functions coupled with multi-relaxation-time (MRT) scheme are utilized in LBM. An enthalpy updating scheme is also applied to determine the liquid fraction of PCM. The basic model without phase change scheme is first verified with the simulation of axisymmetric thermal flow in a vertical annulus with and without porous media. The model integrated with the phase change scheme is tested by simulating the PCM phase change in a vertical cylinder with porous media. The results show a good agreement with the published numerical and experimental results, indicating that the present model can serve as an accurate tool for simulating the axisymmetric convective thermal flow and PCM phase change within porous media.