Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session A3: Porous Media Flows I: Convection |
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Chair: J.M. McDonough, University of Kentucky Room: 3004 |
Sunday, November 23, 2014 8:00AM - 8:13AM |
A3.00001: A theoretical relationship between porosity and permeability J.M. McDonough, Tingting Tang The equations of fluid motion for flow in porous media typically contain the physical parameters porosity and permeability. The first of these is simply a ratio of fluid volume to overall flow-region volume and is easily estimated. Permeability, on the other hand, is more difficult to predict and must usually be calculated using correlations from laboratory experiments for specific porous materials. A well-known example is the Kozeny--Carmen relationship (see, e.g., Carmen, {\it Flow of Gases Through Porous Media}, 1956) expressing permeability in terms of porosity for flow in packed beds of solids. In general, there is not a one-to-one permeability-porosity relationship, and this causes difficulties when simulating flows in domains of widely differing porosity. Here we present the derivation of a formula relating these two quantities. We assume validity of using entropy generation rate maximization to set the stable state in non-equilibrium phenomena (Glansdorff and Prigogine, {\it Physica}, 1970). This leads to a first-order ordinary differential equation for porosity in terms of permeability which can be solved exactly, resulting in the desired formula for permeability in terms of porosity (as well as strain rates and temperature from the entropy generation formula). [Preview Abstract] |
Sunday, November 23, 2014 8:13AM - 8:26AM |
A3.00002: Structure and Stability of High Rayleigh-Number Periodic-Orbit Solutions in Porous Medium Convection Baole Wen, Gregory Chini, John Gibson Direct numerical simulations (DNS) indicate that the instantaneous flow in buoyancy-driven porous medium convection self-organizes into recurring quasi-coherent structures, suggesting that the basic physics can be understood in terms of these ``building blocks" and the patterns they form. In this investigation, we use a Newton-hookstep searching algorithm to compute numerically-exact time-periodic (i.e. periodic orbit) solutions to the porous medium convection problem in small laterally-periodic domains at extreme values of the Rayleigh number. Four types of periodic-orbit solutions with different symmetries are presented, and their periods, stability, and heat-transport properties are quantified. Our results confirm that the periodic orbits capture many features of typical quasi-coherent structures observed in DNS of ``turbulent" porous medium convection. [Preview Abstract] |
Sunday, November 23, 2014 8:26AM - 8:39AM |
A3.00003: Buoyant convection from a discrete source in a leaky porous medium Morris Flynn, Mark Roes, Diogo Bolster The application of turbulent plume theory in describing emptying filling boxes has yielded novel strategies for the natural ventilation of buildings. Making the plume laminar and having it fall through a porous medium yields a new problem of fundamental significance, insights from which may be applied in minimizing the contamination of groundwater by chemicals leached from waste piles. We review the theory for porous media plumes then adapt to the case of an emptying filling box. The long-time solution consists of two ambient layers, each of which has a uniform density. The lower and upper layers are comprised of fluid that is respectively discharged by the plume and advected into the box through the upper opening. Our theory provides an estimate for both the height and thickness of the associated interface in terms of e.g.~the source volume and buoyancy fluxes, the outlet area and permeability and the depth-averaged solute dispersion coefficient, which varies with the far-field horizontal flow speed. Complementary laboratory experiments are provided for the case of a line source plume and show very good agreement with model predictions. Our measurements also show that the permeability, $k_f$, of the lower opening decreases with the density of the fluid being discharged. [Preview Abstract] |
Sunday, November 23, 2014 8:39AM - 8:52AM |
A3.00004: Effect of viscous coupling in multiphase flow in porous media Juan C. Padrino, Xia Ma, Duan Z. Zhang Multiphase flow in porous media has traditionally been modeled by the extension of Darcy's law. This is accomplished by the introduction of the concept of relative permeability, which depends on fluid saturations only. In cases of fluids with significant viscosity difference, additional representation of fluid interactions of viscous nature, not accounted for by Darcy's law, are needed. In this work we report on new approaches to modeling viscous coupling between phases. Our analysis starts with the ensemble phase averaged momentum equation for multiphase flow. The averaged momentum equation leads to an equation system similar to Darcy's law, but with additional force terms representing interaction between fluids. These forces arise from the fact that the less viscous fluid pushes the more viscous one to flow through the porous matrix, as shown in our calculation based on the bundle-of-tubes model [Yang et al., 2009, Int. J. Multiphase Flow, 35, 628]. These forces are therefore proportional to the viscosity of the more viscous fluid and the relative velocity between fluids. Based on the formulation developed from the bundle-of-tubes model, we performed numerical simulations of a laboratory experiment of multiphase flows in a porous matrix. Comparisons with the experimental data and other numerical results are presented and discussed. [Preview Abstract] |
Sunday, November 23, 2014 8:52AM - 9:05AM |
A3.00005: ABSTRACT WITHDRAWN |
Sunday, November 23, 2014 9:05AM - 9:18AM |
A3.00006: Boundary layer convection in a radiatively cooled porous medium Joseph Hitchen, Andrew Wells In the polar winter, porous sea ice grows by losing heat to the atmosphere through radiative cooling. Sea ice is a reactive, porous medium so cooling causes solidification and creates density gradients in the ice pore space. Previous studies of mushy-layer convection have used highly-conducting boundary conditions with fixed temperatures but we consider the impact of surface radiative cooling using a mixed boundary condition where the heat flux is linked to the evolving boundary temperature. To build initial insight, we consider convective instability in a deep porous layer cooled from above. Using the Biot number to characterise the relative strengths of thermal conduction in the ice and atmospheric heat exchange, we use an energy stability method to determine the critical Rayleigh number, wavenumber and time for convection to occur, driven by density gradients in a transiently growing boundary layer. In the highly conducting limit, we find similar behaviour to previous studies, but a new regime is identified for lower conductivities with a transition region between the two. Calculations suggest that the Biot number for Arctic sea ice may fall in the transitional regime, and therefore the effects of radiative cooling may be important for ice growth. [Preview Abstract] |
Sunday, November 23, 2014 9:18AM - 9:31AM |
A3.00007: Isotherms Around a Heated Horizontal Cylinder Embedded in a Porous Medium \'Ayax Hernando Torres Victoria, Mario Sanchez Rosas, Fernando Arag\'on Rivera, Fausto Alejandro S\'anchez Cruz, Abraham Medina Ovando This work presents an experimental study of free and forced convection phenomena that occur in the vicinity of a heated cylinder embedded in a fluid saturated porous medium. The characteristic distribution of the conformed temperature gradients in the porous medium due to pure free convection, and under the action of a continuous and uniform stream were investigated through the use of four different configurations: first by inducing an air stream from below the heated cylinder, second, by placing an air stream on the left hand side of the heat source, third by an air stream acting from the top of the heat source, and fourth by varying the injection angles. The resulting conformation of the buoyant plumes surrounding the heated cylinder when all phenomena reach the steady state were analyzed with an infrared camera. Correspondence is found with the theoretical and numerical solutions proposed by Kurdyumov and Li\~{n}\'{a}n (2000). [Preview Abstract] |
Sunday, November 23, 2014 9:31AM - 9:44AM |
A3.00008: Numerical study of thermally stratified flows of a fluid overlying a highly porous material Panagiotis D. Antoniadis, Miltiadis V. Papalexandris In this talk we are concerned with thermally stratified flows in domains that contain a macroscopic interface between a highly porous material and a pure-fluid domain. Our study is based on the single-domain approach according to which the same set of governing equations is employed both inside the porous medium and in the pure-fluid domain. Also, the mathematical model that we employ treats the porous skeleton as a rigid solid that is in thermal non-equilibrium with the fluid. First, we present briefly the basic steps of the derivation of the mathematical model. Then, we present and discuss numerical results for both thermally stratified shear flows and natural convection. Our discussion focuses on the role of thermal stratification on the flows of interest and on the effect of thermal non-equilibrium between the solid matrix and the fluid inside the porous medium. [Preview Abstract] |
Sunday, November 23, 2014 9:44AM - 9:57AM |
A3.00009: Phase-Change Modelling in Severe Nuclear Accidents Christopher Pain, Dimitrios Pavlidis, Zhihua Xie, James Percival, Jefferson Gomes, Omar Matar, Moji Moatamedi, Ali Tehrani, Alan Jones, Paul Smith This paper describes progress on a consistent approach for multi-phase flow modelling with phase-change. Although, the developed methods are general purpose the applications presented here cover core melt phenomena at the lower vessel head. These include corium pool formation, coolability and solidification. With respect to external cooling, comparison with the LIVE experiments (from Karlsruhe) is undertaken. Preliminary re-flooding simulation results are also presented. These include water injection into porous media (debris bed) and boiling. Numerical simulations follow IRSN's PEARL experimental programme on quenching/re-flooding. [Preview Abstract] |
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