Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session G29: Porous Media Flows IV |
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Chair: Emmanuel Villermaux, Aix Marseille University Room: 32B |
Monday, November 19, 2012 8:00AM - 8:13AM |
G29.00001: Self-similarity in coupled Brinkman$\backslash$Navier-Stokes flows Ilenia Battiato Coupled flows through and over porous layers occur in a variety of natural phenomena, biological systems and industrial processes. In this work we derive self-similar solutions of flows through both a porous medium and a pure fluid. Self-similar filtration velocity and hydrodynamic shear profiles are obtained by means of asymptotic analysis in the limit of infinitely small permeability, and for both laminar and turbulent regimes over the porous medium. We show that a spatial length scale, related to the porous layer thickness, naturally emerges from the limiting process and suggests a more formal definition of thin and thick porous media. The results of the analysis are applied to porous media constituted of patterned cylindrical obstacles, which can freely deflect under the shear exerted by the fluid flowing through and over the forest. A self-similar solution for the bending profile of the elastic cylindrical obstacles is obtained as intermediate asymptotic, and applied to carbon nanotube (CNT) forests' response to aerodynamic stresses. This self-similar solution is successfully used to estimate flexural rigidity of CNTs by linear fit of appropriately rescaled maximum deflection and average velocity measurements. [Preview Abstract] |
Monday, November 19, 2012 8:13AM - 8:26AM |
G29.00002: Application of method of volume averaging coupled with time resolved PIV to determine transport characteristics of turbulent flows in porous bed Vishal Patil, James Liburdy Turbulent porous media flows are encountered in catalytic bed reactors and heat exchangers. Dispersion and mixing properties of these flows play an essential role in efficiency and performance. In an effort to understand these flows, pore scale time resolved PIV measurements in a refractive index matched porous bed were made. Pore Reynolds numbers, based on hydraulic diameter and pore average velocity, were varied from 400-4000. Jet-like flows and recirculation regions associated with large scale structures were found to exist. Coherent vortical structures which convect at approximately 0.8 times the pore average velocity were identified. These different flow regions exhibited different turbulent characteristics and hence contributed unequally to global transport properties of the bed. The heterogeneity present within a pore and also from pore to pore can be accounted for in estimating transport properties using the method of volume averaging. Eddy viscosity maps and mean velocity field maps, both obtained from PIV measurements, along with the method of volume averaging were used to predict the dispersion tensor versus Reynolds number. Asymptotic values of dispersion compare well to existing correlations. The role of molecular diffusion was explored by varying the Schmidt number and molecular diffusion was found to play an important role in tracer transport, especially in recirculation regions. [Preview Abstract] |
Monday, November 19, 2012 8:26AM - 8:39AM |
G29.00003: Dispersive and mixing characteristics for turbulent porous media flows based on local length and time scale measurements James Liburdy, Vishal Patil Porous media flows have a very wide range of applications, both in engineering applications and natural flows. Local mixing and dispersion is strongly influenced by the complex pore geometry. Understanding mixing properties requires knowledge of the range of scales present within the flow and how they vary with Reynolds number. Experiments have been conducted using time resolved two component PIV based on refractive index matching of the solid and liquid phases. The flow characteristics vary over a large range of Reynolds numbers, typically based on an average pore velocity and hydraulic diameter or bead size as the characteristic length. In this study we examine the effect of increased pore Reynolds number on the turbulence characteristics for Reynolds numbers from approximately 400 to 4000. In particular the integral and Kolmogorov length scales are estimated, along with the determination of the integral velocity and Eulerian time scales. These are then used to estimate the Lagrangian time scale. The asymptotic behavior associated with increasing pore Reynolds number is shown, and used to evaluate the scaling relationships. Results are also used to demonstrate the evaluation of the mechanical dispersion coefficient and that it compares well with results obtained using global methods such as solute breakthrough curves. [Preview Abstract] |
Monday, November 19, 2012 8:39AM - 8:52AM |
G29.00004: DNS of turbulent flow in a porous unit cell Sourabh Apte, Justin Finn, Brian Wood, James Liburdy Turbulent flows through packed beds and porous media are encountered in a number of natural and engineered systems, however our general understanding of moderate and high Reynolds number flows is limited to mostly empirical and macroscale relationships. In this work the porescale flow physics, which are important to properties such as bulk mixing performance and permeability, are investigated using Direct Numeric Simulation of flow through a periodic face centered cubic (FCC) unit cell. This low porosity arrangement of spheres is characterized by rapid flow expansions and contractions, and thus features an early onset to turbulence [Hill \& Koch, JFM 2002]. The simulations are performed using a fictitious domain approach [Apte et al, J. Comp. Physics 2009], which uses non-body conformal Cartesian grids, with resolution up to $D/\Delta=250$ ($354^3$ cells total). Simulations are performed at three pore Reynolds numbers, $Re_p = 300,~550$ and $950$, spanning a broad physical regime. The results are used to investigate the structure of turbulence in the Eulerian and Lagrangian frames, the distribution and budget of turbulent kinetic energy, and the characteristics of the energy spectrum in complex packed beds and porous media. [Preview Abstract] |
Monday, November 19, 2012 8:52AM - 9:05AM |
G29.00005: Transport in Porous Fins From Laminar to Turbulent Regime Filippo Coletti, Kenshiro Muramatsu, Brian Furciniti, Chris Elkins, John Eaton Lotus type porous metal has elongated pores of random size and spatial distribution but a common orientation. Sets of so-called lotus fins are obtained by slicing the metal into thin layers and stacking them in the flow path, forcing the fluid to pass through the pores. Lotus fins represent a promising alternative to metal foam heat exchangers, because they offer higher thermal conductivity and lower pressure drop. We have experimentally analyzed the fluid flow and heat transfer in lotus fins to determine their transport properties in a range of flow regimes. The investigated Reynolds numbers based on the pore diameter and inner velocity ranged from 100 to 4000. Three-dimensional mean velocity fields were obtained by magnetic resonance velocimetry performed on magnified replicas of the fins, allowing determination of the mechanical dispersion imposed by the random structure of the fins. Thermal measurements on non-conductive fins provided the global diffusivity coefficient, which accounts for molecular, mechanical and (at high Reynolds number) turbulent diffusion. The latter contribution was isolated and its relevance assessed as a function of the flow regime. [Preview Abstract] |
Monday, November 19, 2012 9:05AM - 9:18AM |
G29.00006: Instability onset and mixing by diffusive Rayleigh-Benard Convection in a Hele-Shaw Cell Dana Ehyaei, Ken Kiger The injection and eventual dissolution of carbon dioxide in deep saline aquifers has suggested as an effective means of carbon sequestration. Typical injection conditions produce a buoyantly stable source of CO2 layered on top of the brine, whose dissolution is greatly accelerated by the onset of dissolution-driven, negatively buoyant, convective plumes that develop at the interface. The current work is a study conducted within a Hele-shaw cell, as an analogue for porous media, using working fluids that are mixtures of methanol and ethylene glycol diffusing in water, imitating the convective behavior of CO2 in the brine. The underlying physics of the flow are examined by measuring the velocity field directly via PIV, using appropriate methods to allow quantitative measurement in this thin-gap flow. This technique allows for detailed measurement of the entire evolution of the velocity and vorticity field during onset, growth and saturation of the instabilities. Features of the flow, the mechanisms that govern it and accurate time scales form onset time to later time mixings would be discussed for different Rayleigh numbers ranging from 2000 to 15000. [Preview Abstract] |
Monday, November 19, 2012 9:18AM - 9:31AM |
G29.00007: Mixing properties of stationary flows in porous media Mihkel Kree, Emmanuel Villermaux The interplay between stretching of fluid particles and molecular diffusion leads to enhanced mixing of scalar concentration fields, like in random, turbulent flows. Similarly, the flow in a porous medium develops high strain rates due to the no-slip boundary condition at solid surfaces, altering substantially molecular mixing. We report here on experiments of mixing by a stationary flows in a three-dimensional random stack of solid spheres. Two distinctive fluorescent dyes (with concentrations $C_1$ and $C_2$) are injected from separate sources and their evolution through the medium is directly observed, this being made possible by matching the refractive indices of the spheres and of the flowing liquid. We quantify the dispersion, concentration distributions, and correlation between the two fields as a function of downstream distance. The value of initially negative correlation coefficient asymptotically reaches zero, meaning that the overall field $C_1+C_2$ is a random superposition of the individual fields. The relevant time (distances) scales for mixing are identified. [Preview Abstract] |
Monday, November 19, 2012 9:31AM - 9:44AM |
G29.00008: Macroscopic model of unstable two-phase flow in a Hele-Shaw cell Luis Cueto-Felgueroso, Ruben Juanes When a less viscous fluid displaces a more viscous one in the gap between two parallel plates (a Hele-Shaw cell) or in a porous medium, the displacement front is unstable, and the hydrodynamic instability that ensues is referred to as viscous fingering. The emerging pattern is characterized by branching structures, with an intrinsic length scale that depends on the fluid properties, essentially viscosity and surface tension between the fluids, the injection rate and gap size, and the wetting properties of the system. Here we present a continuum model of two-phase flow in Hele-Shaw cells that reproduces the observed displacement patterns. The key feature of our model is that it captures the dynamic distribution of fluids in the gap, in the sense that the thickness of the film of more viscous fluid left attached to the wall depends on the capillary number. [Preview Abstract] |
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