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 H3: Porous Media Flows V: Theory |
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Chair: Markus Schmuck, Heriot-Watt University Room: 3004 |
Monday, November 24, 2014 10:30AM - 10:43AM |
H3.00001: Feedback-induced phase transitions in active porous media Samuel Ocko, L. Mahadevan We consider a reduced-complexity model for an active porous medium where flow and resistance are coupled to each other i.e. the porous medium is modified by the flow and in turn modifies the flow. Using numerical simulations, we show that this results in both channelization and wall-building transitions depending on the form of the feedback. A continuum model allows us to understand the qualitative features of the resulting phase diagram, and suggests ways to realize complex architectures using simple rules in engineered systems. [Preview Abstract] |
Monday, November 24, 2014 10:43AM - 10:56AM |
H3.00002: Dynamics of clogging in drying porous media C. Nadir Kaplan, L. Mahadevan Drying in porous media pervades a range of phenomena from brine evaporation arrested in porous bricks, causing efflorescence, i.e. salt aggregation on the surface where vapor leaves the medium, to clogging of reservoir rocks via salt precipitation when carbon dioxide is injected for geological storage. During the process of drying, the permeability and porosity of the medium may change due to the solute accumulation as a function of the particle concentration, in turn affecting the evaporation rate and the dynamics of the fluid flow imposed by it. To examine the dynamics of these coupled quantities, we develop a multiphase model of the particulate flow of a saline suspension in a porous medium, induced by evaporation. We further provide dimensional arguments as to how the salt concentration and the resulting change in permeability determine the transition between efflorescence and salt precipitation in the bulk. [Preview Abstract] |
Monday, November 24, 2014 10:56AM - 11:09AM |
H3.00003: Simplified model for fouling of a pleated membrane filter Pejman Sanaei, Linda Cummings Pleated filter cartridge are widely used to remove undesired impurities from a fluid. A filter membrane is sandwiched between porous support layers, then pleated and packed in to an annular cylindrical cartridge. Although this arrangement offers a high ratio of surface filtration area to volume, the filter performance (measured, e.g., by graph of total flux versus throughput for a given pressure drop), is not as good as a flat filter membrane. The reasons for this difference in performance are currently unclear, but likely factors include the additional resistance of the porous support layers upstream and downstream of the membrane, the pleat packing density (PPD) and possible damage to the membrane during the pleating process. To investigate this, we propose a simplified mathematical model of the filtration within a single pleat. We consider the fluid dynamics through the membrane and support layers, and propose a model by which the pores of the membrane become fouled (i) by particles smaller than the membrane pore size ; and (ii) by particles larger than the pores.We present some simulations of our model, investigating how flow and fouling differ between not only flat and pleated membranes, but also for support layers of different permeability profiles. [Preview Abstract] |
Monday, November 24, 2014 11:09AM - 11:22AM |
H3.00004: Interception efficiency in flow of power-law fluids past confined porous bodies Setareh Shahsavari, Gareth McKinley Understanding the flow of power-law fluids through porous media is important for a wide range of filtration and sedimentation processes. In this study, the mobility of power-law fluids through porous media is investigated numerically and we use parametric studies to systematically understand the individual roles of geometrical characteristics, rheological properties as well as flow conditions. In addition, an analytical solution is presented that can be used as a modified Darcy law for generalized Newtonian fluids. Building on this modified Darcy law, the incompressible laminar flow of power-law and Carreau fluids past a confined porous body is modeled numerically. From the simulations we calculate the flow interception efficiency, which provides a measure of the fraction of streamlines that intercept a porous collector. Finally, the interception efficiency of power-law fluids are compared with the case of a Newtonian fluid. The focus of this work is principally for flow of inelastic fluids in fibrous media; however, the methodology can also be extended to other porous media. [Preview Abstract] |
Monday, November 24, 2014 11:22AM - 11:35AM |
H3.00005: On the determination of a generalized Darcy equation for yield stress fluid in porous media using a LB TRT scheme Laurent Talon, Thibaud Chevalier Non-Newtonian fluids have practical applications in very different domains. Indeed, polymer mixture, paints, slurries, colloidal suspensions, emulsions, foams or heavy oil present complex rheologies. Among the large number of different non-Newtonian fluids an important class of behavior is represented by the yield-stress fluids, viz. fluids that require a minimum of stress to flow. Yield stress fluids are usually modelled as a Bingham fluid or by the Herschel-Bulkley equation. However, simulating flow of a Bingham fluid in porous media still remains a challenging task as the yield stress may significantly alter the numerical stability and precision. In the present work, we use a Lattice-Boltzmann TRT scheme to determine this type of flow in a synthetic porous medium or fracture. Different pressure drops $\Delta P$ have been applied in order to derive a generalization of the Darcy's equation. Three different scaling regimes can be distinguished when plotting the dimensionless flow rate $q$ as function of the distance to the critical pressure $\Delta P - \Delta P_c$. In this presentation, we will investigate the importance of the heterogeneities on those flowing regimes. [Preview Abstract] |
Monday, November 24, 2014 11:35AM - 11:48AM |
H3.00006: New upscaled equations for multiphase flows in porous media based on a phase field formulation for general free energies Markus Schmuck, Marc Pradas, Grigorios A. Pavliotis, Serafim Kalliadasis Based on thermodynamic and variational principles we formulate novel equations for mixtures of incompressible fluids in strongly heterogeneous domains, such as composites and porous media, using elements from the regular solution theory. Starting with equations that fully resolve the pores of a porous medium, represented as a periodic covering of a single reference pore, we rigorously derive effective macroscopic phase field equations under the assumption of periodic and strongly convective flow. Our derivation is based on the multiple scale method with drift and our recently introduced splitting strategy for Ginzburg-Landau/Cahn-Hilliard-type equations [1]. We discover systematically diffusion-dispersion relations (including Taylor-Aris-dispersion) as in classical convection-diffusion problems. Our results represent a systematic and efficient computational strategy to macroscopically track interfaces in heterogeneous media which together with the well-known versatility of phase field models forms a promising basis for the analysis of a wide spectrum of engineering and scientific applications such as oil recovery, for instance.\\[4pt] [1] M. Schmuck, M. Pradas, G.A. Pavliotis and S. Kalliadasis, Nonlinearity {\bf 26}:3259-3277 2013. [Preview Abstract] |
Monday, November 24, 2014 11:48AM - 12:01PM |
H3.00007: Oscillation-Free Methods for Modeling Fluid-Porous Interfaces Using Segregated Solvers on Unstructured Grids Milos Stanic, Markus Nordlund, Arkadiusz Kuczaj, Edoardo Frederix, Bernard Geurts Porous media flows can be found in a large number of fields ranging from engineering to medical applications. A volume-averaged approach to simulating porous media is often used because of its practicality and computational efficiency. Derivation of the volume-averaged porous flow equations introduces additional porous resistance terms to the momentum equation. When discretized these porous resistance terms create a body force discontinuity at the porous-fluid interface, which may lead to spurious oscillations if not accounted for properly. A variety of numerical techniques has been proposed to solve this problem, but few of them have concentrated on collocated grids and segregated solvers, which have wide applications in academia and industry. In this work we discuss the source of the spurious oscillations, quantify their amplitude and apply interface treatments methods that successfully remove the oscillations. The interface treatment methods are tested in a variety of realistic scenarios, including the porous plug and Beaver-Joseph test cases and show excellent results, minimizing or entirely removing the spurious oscillations at the porous-fluid interface. This research was financially supported by Philip Morris Products S.A. [Preview Abstract] |
Monday, November 24, 2014 12:01PM - 12:14PM |
H3.00008: Description of multiphase flows in porous media using an effective convective Cahn-Hilliard equation Rajagopal Vellingiri, Marc Pradas, Markus Schmuck, Serafim Kalliadasis Immiscible two-phase flows in porous media find a variety of applications such as microfluidics, oil extraction from reservoirs and chromatography, to name but a few. In this study, we investigate the dynamics of interfaces in porous media using an effective convective Cahn-Hilliard equation which was derived in [1] from a Stokes-Cahn-Hilliard equation for microscopic heterogeneous domains by means of a homogenization methodology. We consider different types of microstructures, including periodic and non-periodic, observing that the macroscopic model is able to retain the microscopic features, hence indicating that our formulation provides an efficient and systematic computational framework to track interfaces in porous media. \\[4pt] [1] M. Schmuck, M. Pradas, G.A. Pavliotis and S. Kalliadasis, 2013 ``Derivation of effective macroscopic Stokes--Cahn--Hilliard equations for periodic immiscible flows in porous media,'' Nonlinearity {\bf 26} 3259-3277. [Preview Abstract] |
Monday, November 24, 2014 12:14PM - 12:27PM |
H3.00009: Continuum approach for aerothermal flow through ablative porous material using discontinuous Galerkin discretization. Pierre Schrooyen, Philippe Chatelain, Koen Hillewaert, Thierry E. Magin The atmospheric entry of spacecraft presents several challenges in simulating the aerothermal flow around the heat shield. Predicting an accurate heat-flux is a complex task, especially regarding the interaction between the flow in the free stream and the erosion of the thermal protection material. To capture this interaction, a continuum approach is developed to go progressively from the region fully occupied by fluid to a receding porous medium. The volume averaged Navier-Stokes equations are used to model both phases in the same computational domain considering a single set of conservation laws. The porosity is itself a variable of the computation, allowing to take volumetric ablation into account through adequate source terms. This approach is implemented within a computational tool based on a high-order discontinuous Galerkin discretization. The multi-dimensional tool has already been validated and has proven its efficient parallel implementation. Within this platform, a fully implicit method was developed to simulate multi-phase reacting flows. Numerical results to verify and validate the methodology are considered within this work. Interactions between the flow and the ablated geometry are also presented. [Preview Abstract] |
Monday, November 24, 2014 12:27PM - 12:40PM |
H3.00010: Propagation of viscous currents on porous substrate with finite entry pressure Roiy Sayag, Jerome A. Neufeld We study the propagation of viscous gravity currents over a thin porous substrate with finite capillary entry pressure. Near the origin, where the current is deep, propagation of the current coincides with leakage through the substrate. At the nose of the current, where the depth reduces below a critical threshold, drainage is absent. Consequently the flow can be characterised by the evolution of the drainage front and the fluid front at the nose. We analyze this flow using numerical and analytical techniques combined with laboratory-scale experiments. We find that at early times the position of both fronts is proportional to $t^{1/2}$, similar to an axisymmetric gravity current without drainage. At later time the growing effect of drainage inhibits spreading. However, as the drainage front approaches a steady position at which the horizontal flux in the current is nonzero the asymptotic propagation of the fluid front approaches a similarity solution $\propto t^{1/2}$, implying a diminishing impact of the draining domain on the propagating nose. [Preview Abstract] |
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