Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session D30: Porous Media Flows II: Mixing and Turbulence |
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Chair: James Liburdy, Oregon State University Room: 408 |
Sunday, November 24, 2013 2:15PM - 2:28PM |
D30.00001: Stretching, Coalescence and Mixing in Porous Media Tanguy Le Borgne, Marco Dentz, Emmanuel Villermaux We study scalar mixing in heterogeneous conductivity fields, whose structural disorder varies from weak to strong. A range of stretching regimes is observed depending on the level of structural heterogeneity, measured by the log-conductivity field variance. We propose a unified framework to quantify the overall concentration distribution predicting its shape and rate of deformation as it progresses towards uniformity in the medium. The scalar mixture is represented by a set of stretched lamellae whose rate of diffusive smoothing is locally enhanced by kinematic stretching. Overlap between the lamellae is enforced by confinement of the scalar line support within the dispersion area. Based on these elementary processes, we derive analytical expressions for the concentration distribution, resulting from the interplay between stretching, diffusion and random overlaps, holding for all field heterogeneities, residence times, and Peclet numbers. [Preview Abstract] |
Sunday, November 24, 2013 2:28PM - 2:41PM |
D30.00002: Solute Blob Evolution and Mixing Dynamics in a Darcy Scale Heterogeneous Porous Medium Marco Dentz, Tanguy Le Borgne, Felipe de Barros We study the mixing behavior of a dissolved substance that evolves from a solute blob in a two-dimensional heterogeneous porous medium. The study scale is mesoscopic so that flow is governed by Darcy's law. Heterogeneity is induced by spatially variable permeability. The fundamental mechanism governing the evolution and mixing dynamics of a solute blob are the competition of the stretching action of a material line and diffusion. We formulate the transport problem in a Lagrangian framework and consider the motion of solute particles that form the blob, in the coordinate system attached to the material element on which it originates. The blob evolution is fully characterized by the stochastic time series of stretching and shear rates of the material segment in its own coordinate system. Theses stochastic series are investigated numerically using random wak particle tracking simulation. In this stochastic framework, we study the ensemble concentration PDF, concentration entropy and scalar dissipation rate. The aim is to relate the mixing properties to the appearance of coherent structures as quantified by the Okubo-Weiss measure and its Lagrangian counterpart. [Preview Abstract] |
Sunday, November 24, 2013 2:41PM - 2:54PM |
D30.00003: Scale Estimation for Turbulent Flows in Porous Media Vishal Patil, James Liburdy Flow in porous media, once extended into the turbulent flow regime can become very complex due to the nature of the flow geometry and related scales of motion. The ability to model porous media turbulence flow has been hampered by the inability to develop an appropriate understanding of the complexities associated with the impact of pore scale dynamics on the overall turbulence contributions to dispersion and mixing. In this paper we use direct PIV measurements of the turbulence within a randomly packed porous bed of uniform size spheres to better understand scaling distributions. Refractive index matching was used to obtain time resolved velocity vector data within specific pores to compare turbulence quantities versus pore Reynolds numbers. Results are used to determined the characteristics of scales associated with velocity, length and time. The large scale events, within the domain of the pore size are evaluated based on correlation functions within the pore. In addition, estimates of the Komolgorov scales are presented versus pore Re based on integral scale results. The relationships between characteristics pore sizes, pore Re, the integral scales and turbulent statistics are presented and shown to reach an asymptotic limit for large pore Re. [Preview Abstract] |
Sunday, November 24, 2013 2:54PM - 3:07PM |
D30.00004: Direct Numerical Simulation of a turbulent channel flow over Slippery Liquid-Infused Porous Surfaces Isnardo Arenas, Paolo Orlandi, Stefano Leonardi Direct Numerical Simulations of two superposed fluids in a turbulent channel have been performed at Re ranging from 180 to 400. With respect to previous studies in the present numerical simulation both the flow inside the porous media and the overlying flow has been resolved. Three different substrates have been considered: longitudinal and transverse square cavities and array of circular cylinders. A tracking interface algorithm has been developed using the level set technique. The velocity profiles at the interface present a kink, which is due to the different viscosity. In fact, at the interface the stress is the same in the two fluids and then to a larger viscosity it corresponds a smaller gradient of velocity. Surface tension decreases the turbulence levels consequently, a drag reduction of about 15\% can be observed. The stability of the interface is crucial to achieve drag reduction. Even for higher viscosity near the wall, drag reduction is observed. This should be due to the suppression of wall normal velocity fluctuations and to a decrease of turbulent production at the interface. The value of the viscosity inside the patterned surface appears to be less critical than the stability of the interface to achieve drag reduction. [Preview Abstract] |
Sunday, November 24, 2013 3:07PM - 3:20PM |
D30.00005: Dynamics of temporally-evolving shear layers on the interface between a porous medium and a pure fluid Panagiotis D. Antoniadis, Miltiadis V. Papalexandris In this talk we present results from our study on the dynamics of flows at the macroscopic interface between a porous medium and a pure fluid. To this end, we employ a variation of the unsteady Darcy-Brinkman equation, which is valid both inside and outside the porous medium. The major advantage of this approach is that it does not require additional interface conditions. In the first part of the talk, we present a linear stability analysis for unbounded shear layers on the interfaces of interest. According to our analysis, these layers are unconditionally unstable, regardless of the porosity of the medium. Subsequently, we present results of three-dimensional simulations of such shear layers. According to these simulations, the velocity gradients across the interface result in the onset of a Kelvin-Helmholtz instability which grows over time, leading to spanwise roller formation and pairings. There is also concurrent formation of thin ``rib'' vortices, as in the case of single-phase plane mixing layers. Important characteristics of the flow, such as self-similarity and growth rate of the shear layer, are also discussed. [Preview Abstract] |
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