Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session R16: Porous Media III |
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Chair: Thomas Ward, North Caroina State University Room: 319 |
Tuesday, November 22, 2011 12:50PM - 1:03PM |
R16.00001: Mathematical modelling of membrane separation Frank Vinther Membrane separation is commonly used in chemistry and chemical engineering, where the separation of one or several species of molecules is of interest. This presentation will presents mathematical modelling of the dynamic interplay between the transport equations through the membrane and the transport equations within the bulk solution. Thus, resulting in a system of PDE's with time varying boundary conditions. The model is used for predicting optimal parameters for separation processes. [Preview Abstract] |
Tuesday, November 22, 2011 1:03PM - 1:16PM |
R16.00002: Reynolds number dependent flow regime characteristics for flow in porous media James Liburdy, Vishal Patil The flow characteristics of distinct flow regimes in porous media and the evolution with Reynolds number is poorly understood at high Reynolds numbers. Typical means of measurement are MRI imaging, PTV and PIV, the latter two require refractive index matching. This study presents PIV measurements in a porous bed of spherical beads, for pore Reynolds numbers from 100 to 1500 resulting in flow in the inertial, unsteady inertial and turbulent flow regimes. The bed is a cube with five bead diameters on a side, with 15 mm beads. Measurements are based on two dimensional slices (five along the optical axis) using two fields of view; the first is four beads by four beads, and the second is of individual pores to provide highly spatial resolution. Fluorescent dye studies are presented. Velocity data are analyzed based on statistical results of two dimensional time series vector fields with emphasis on (i) identification of Reynolds number dependent flow structures (spatial and temporal), (ii) delineation of flow regime transitions, (iii) establishing pore-based fluctuation energy budgets and (iv) illustration of local dispersion characteristics. The goal is to provide statistical flow structure characteristics at the pore level for high Reynolds number flows to better understand dispersion characteristics. [Preview Abstract] |
Tuesday, November 22, 2011 1:16PM - 1:29PM |
R16.00003: Pressure driven flow in porous tubular membranes Nils Tilton, Denis Martinand, Eric Serre, Richard Lueptow We consider the steady laminar flow of a Newtonian incompressible fluid in a porous tubular membrane with pressure-driven transmembrane flow. Due to its fundamental importance to membrane filtration systems, this flow has been studied extensively both analytically and numerically, yet a robust analytic solution has not been found. The problem is challenging due to the coupling between the transmembrane pressure and velocity with the simultaneous coupling between the axial pressure gradient and the axial velocity. We present a robust analytical solution which incorporates Darcy's law on the membrane surface. The solution is in the form of an asymptotic expansion about a small parameter related to the membrane permeability. We verify the analytical solution with comparison to 2-D spectral direct numerical simulations of ultrafiltration and microfiltration systems with typical operating conditions, as well as extreme cases of cross-flow reversal and axial flow exhaustion. In all cases, the agreement between the analytical and numerical results is excellent. Finally, we use the analytical and numerical results to provide guidelines about when common simplifying assumptions about the permeate flow may be made. Specifically, the assumptions of a parabolic axial velocity profile and uniform transmembrane velocity are valid only for small permeabilities. [Preview Abstract] |
Tuesday, November 22, 2011 1:29PM - 1:42PM |
R16.00004: The Effect of Inlet Swirler Design on Passive Control of Combustion Noise and Instability Alex Borsuk, Ajay Agrawal, Justin Williams The use of porous inert media (PIM) in the reaction zone of a swirl-stabilized lean-premixed combustor provides a passive method of controlling combustion noise and instability. Swirl-stabilized combustors use an inlet swirler that imparts a swirling motion to the reactant flow and stabilizes the flame. In this study, the effect of swirler design and swirl number on combustion without and with PIM has been investigated experimentally, using a methane-fueled quartz combustor at atmospheric pressure. Swirler vane angle was varied to obtain swirl numbers of 0.45, 0.78, and 1.10. Swiler location was varied to obtain recess depth in the premixer tube of 0, 2.5, and 5 cm. Experiments were conducted at a constant air flow rate of 300 SLPM and equivalence ratios of 0.7, 0.75, and 0.8. PIM geometries with increasing and decreasing flow cross-sectional area were tested. The performance of each test case is compared by measuring sound pressure levels (SPL) with a microphone probe and observing the flame behavior. Results indicate that PIM can be effective in reducing noise and instability over a wide range of operating conditions. Total SPL reductions of up to 7.6 dBA were observed with PIM. [Preview Abstract] |
Tuesday, November 22, 2011 1:42PM - 1:55PM |
R16.00005: How to Model the Lift Generation in a Highly Compressible Porous Media Q. Wu, R. Nathan, S. Santhanam, T. Gacka Lift generation in highly compressible porous media under rapid compression continues to be an important topic in porous media flow for its superior potential in soft lubrication and squeeze damping. Although significant progress has been made in the study of the lift generation experimentally and theoretically (Wu et al., Journal of Fluid Mechanics 542, 281, 2005; Barabadi, et al., Journal of Heat Transfer, 131(10), 101006, 2009), how to theoretically characterize lifting forces remains unclear. In this paper the permeability of the porous media was measured using a permeater, and then dynamically compacted in a porous-walled cylinder piston apparatus. The obtained pore pressure generation was compared to two different theoretical models, a plug flow model and a consolidation model used in Wu et al. (2005) and Barabadi, et al. (2009). It shows that the consolidation model is appropriate. Furthermore, a viscoelastic model, containing a nonlinear spring in conjunction with a linear viscoelastic Generalized Maxwell mechanical module, is developed to characterize the solid phase lifting force, showing excellent agreement with experimental data. The paper presented herein, conclusively demonstrates the validity of the theoretical approach developed by Wu et al. (2005) and provides a meaningful approach in characterizing forces that contribute to lift generation in soft porous media under rapid compression. [Preview Abstract] |
Tuesday, November 22, 2011 1:55PM - 2:08PM |
R16.00006: From Red Cells to Soft Porous Lubrication T. Gacka, R. Nathan, L. Wu, Q. Wu Feng and Weinbaum (\textit{J. Fluid. Mech}., \textbf{422}, 282, 2000), inspired by the enhanced lift phenomena in downhill skiing, developed a new lubrication theory for highly compressible porous media where significantly increased lifting force was predicted as a planing surface glided over a soft porous layer; suggesting superior potential use of porous media for soft lubrication. In this study, we experimentally examine the lift generation phenomena by developing a novel soft porous bearing that consists of a running conveyer belt covered with a soft, 100{\%} polyester, porous sheet, and a stationary, fully instrumented, inclined, planar, upper board. Pore pressure was generated as the upper boundary glides over the soft porous bearing and was measured by pressure sensors. One observed that the pore pressure distribution is consistent with predictions by Feng and Weinbaum (2000), and is a function of the relative velocity between the planing surface and the running belt, the mechanical properties (e.g. porosity, permeability and stiffness) and thickness of the porous layer, as well as the compression ratios at the leading and trailing edges. A load cell is used to characterize the performance of the porous bearing, by comparing pore pressure to total lifting forces. The study presented herein significantly improves our understanding of the behavior of highly compressible porous media under fast compression. [Preview Abstract] |
Tuesday, November 22, 2011 2:08PM - 2:21PM |
R16.00007: Probing the permeability of porous media by NMR measurement of stochastic dispersion dynamics Tyler Brosten, Robert Maier, Sarah Codd, Sarah Vogt, Joseph Seymour A generalized short-time expansion of hydrodynamic dispersion is derived using non-linear response theory. The result is in accordance with the well-known reduced cases of shear flow in ducts and pipes. In terms of viscous dominated (low Reynolds number) flow in porous media the generalized expansion facilitates the measurement of permeability by PGSE-NMR measurement of time dependent molecular displacement dynamics. To be more precise, for porous media characterized by a homogeneous permeability coefficient along the direction of flow $K$, and fluid volume fraction $\varepsilon $, the effective dispersion coefficient $D(t)=\langle \vert $\textbf{R}-$\langle $\textbf{R}$\rangle \vert ^{2}\rangle $/6$t$ of molecular displacements \textbf{R} due to flow and diffusion for a saturating fluid of molecular diffusivity $\kappa $ in viscous dominated flow is shown to be partially governed by the coefficient of permeability at short times. The short-time expansion is shown to be in agreement with pulsed field gradient spin echo NMR measurement of $D(t)$ in a random sphere pack media and analogous pore-scale random-walk particle tracking transport simulation. [Preview Abstract] |
Tuesday, November 22, 2011 2:21PM - 2:34PM |
R16.00008: Instability of methane hydrate stability zone in permafrost deposits Dmitriy Lyubimov, Ekaterina Kolchanova, Tatyana Lyubimova, Oleg Zikanov As a part of a broad study of the dynamics of natural deposits of methane hydrates, we analyze the instability of the interface between the hydrate-bearing zone and the underlying gas-saturated layer. Conditions of Arctic permafrost with temperature below the ice melting point are considered. The physical model includes the Darcy filtration of gas, conduction and convection heat transfer, and the dynamic boundary conditions including the hydrate dissociation at the interface. The method of linear stability analysis is used. It is found that the system is stable and, thus, can exist only at relatively small thicknesses of both layers and at low-to-moderate permeability of the sediments. At larger thicknesses and higher permeability, the interface between the two layers is unstable to monotonic perturbations. The results do not support the hypothesis that the interface instability may lead to accelerating self-sustained dissociation of natural methane hydrates in the conditions of increasing global temperature. [Preview Abstract] |
Tuesday, November 22, 2011 2:34PM - 2:47PM |
R16.00009: Direct simulation of the flow over a porous layer of large porosity Panagiotis-Dimitrios Antoniadis, Miltiadis V. Papalexandris In this talk we report on direct numerical simulations of constant-density flow over and through a layer of a porous medium with large porosity. Initially the fluid is at rest and the flow is driven by a constant pressure gradient. Periodic boundary conditions are used along the streamwise direction, whereas no-slip conditions are specified on the bottom boundary which also coincides with the lower end of the porous strip. Further, outflow conditions are imposed on the top boundary of the computational domain, which is located sufficiently far from the porous medium. As the flow evolves, a boundary layer is formed on the lower end of the porous strip and an additional transition zone is formed right above its upper end. Due to the steep velocity gradients across this zone, a Kelvin-Helmholtz instability is onset which leads to the formation of a mixing layer. We present and analyze the characteristics of vortex pairing and growth rate of this mixing layer. Finally, we discuss the results of a parametric study with respect to the porosity of the medium. [Preview Abstract] |
Tuesday, November 22, 2011 2:47PM - 3:00PM |
R16.00010: Micro-scale flow simulation and colloid transport modeling in saturated porous media Queming Qiu, Hui Gao, Jie Han, Yan Jin, Lian-Ping Wang Adequate understanding of the mechanisms governing colloid retention by soil porous media is essential to the prediction and monitoring of the transport of contaminants through groundwater in the subsurface environment. In this talk, we focus on the representation of micro-scale flow and colloid-grain surface interactions in a computational approach. First, micro-scale viscous flows in a model porous media with different domain sizes and geometric configurations are simulated by the mesoscopic lattice Boltzmann method. A Lagrangian colloid tracking model is then used to study the dynamics of colloidal particles under the action of Brownian force, hydrodynamic forces, and physicochemical forces. The modeling and analysis of colloid transport will incorporate the effects of flow speed, solution ionic strength, collector surface roughness, and blocking effect, etc. Simulation results are used to study the unique nature of retention by the secondary energy minimum. Comparisons are made with parallel experimental results obtained from confocal microscopy. To speed up our colloid tracking modeling, parallel implementation using Message Passing Interface (MPI) is performed and the related scalability results will also be presented. [Preview Abstract] |
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