A comparison of measured and modeled velocity fields for a laminar flow in a porous medium

Abstract Obtaining highly-resolved velocity data from experimental measurements in porous media is a significant challenge. The goal of this work is to compare the velocity fields measured in a randomly-packed porous medium obtained from particle image velocimetry (PIV) with corresponding fields predicted from direct numerical simulation (DNS). Experimentally, the porous medium was comprised of 15 mm diameter spherical beads made of optical glass placed in a glass flow cell to create the packed bed. A solution of ammonium thiocyanate was refractive-index matched to the glass creating a medium that could be illuminated with a laser sheet without distortion. The bead center locations were quantified using the imaging system so that the geometry of the porous medium was known very accurately. Two-dimensional PIV data were collected and processed to provide high-resolution velocity fields at a single plane within the porous medium. A Cartesian-grid-based fictitious domain approach was adopted for the direct numerical simulation of flow through the same geometry as the experimental measurements and without any adjustable parameters. The uncertainties associated with characterization of the pore geometry, PIV measurements, and DNS predictions were all systematically quantified. Although uncertainties in bead position measurements led to minor discrepancies in the comparison of the velocity fields, the axial and normal velocity deviations exhibited normalized root mean squared deviations ( NRMSD ) of only 11.32% and 4.74%, respectively. The high fidelity of both the experimental and numerical methods have significant implications for understanding and even for engineering the micro–macro relationship in porous materials. The ability to measure and model sub-pore-scale flow features also has relevance to the development of upscaled models for flow in porous media, where physically reasonable closure models must be developed at the sub-pore scale. These results provide valuable data in support of that goal.

[1]  Eugeny Y. Kenig,et al.  CFD-based analysis of the wall effect on the pressure drop in packed beds with moderate tube/particle diameter ratios in the laminar flow regime , 2009 .

[2]  D. Koch,et al.  The transition from steady to weakly turbulent flow in a close-packed ordered array of spheres , 2002, Journal of Fluid Mechanics.

[3]  D. Vortmeyer,et al.  Measured and modeled superficial flow profiles in packed beds with liquid flow , 1998 .

[4]  K. Markov,et al.  Elementary Micromechanics of Heterogeneous Media , 2000 .

[5]  S. Whitaker.  Flow in porous media I: A theoretical derivation of Darcy's law , 1986 .

[6]  M. L. Porter,et al.  Lattice-Boltzmann simulations of the capillary pressure–saturation–interfacial area relationship for porous media , 2009 .

[7]  Christopher J. Elkins,et al.  Magnetic resonance velocimetry: applications of magnetic resonance imaging in the measurement of fluid motion , 2007 .

[8]  I. G. Currie,et al.  PIV measurements of slow flow of a viscoelastic fluid within a porous medium , 2011 .

[9]  Francisco J. Valdés-Parada,et al.  Volume averaging: Local and nonlocal closures using a Green’s function approach , 2013 .

[10]  S. Wereley,et al.  Experimental and Computational Investigation of Flow Development and Pressure Drop in a Rectangular Micro-channel , 2006 .

[11]  I. G. Currie,et al.  Creeping flow through a model fibrous porous medium , 2006 .

[12]  Flow characterization using PIV measurements in a low aspect ratio randomly packed porous bed , 2013 .

[13]  P. Roache.  Perspective: A Method for Uniform Reporting of Grid Refinement Studies , 1994 .

[14]  R. V. Edwards,et al.  A New Look at Porous Media Fluid Mechanics — Darcy to Turbulent , 1984 .

[15]  Partha P. Mukherjee,et al.  Stochastic Microstructure Reconstruction and Direct Numerical Simulation of the PEFC Catalyst Layer , 2006 .

[16]  Reghan J. Hill,et al.  Moderate-Reynolds-number flow in a wall-bounded porous medium , 2002, Journal of Fluid Mechanics.

[17]  L. E. Scriven,et al.  NMR imaging of velocity profiles and velocity distributions in bead packs , 1996 .

[18]  Volker Schmidt,et al.  Stochastic modeling and direct simulation of the diffusion media for polymer electrolyte fuel cells , 2010 .

[19]  S. Ergun.  Fluid flow through packed columns , 1952 .

[20]  Sourabh V. Apte,et al.  A variable-density fictitious domain method for particulate flows with broad range of particle-fluid density ratios , 2013, J. Comput. Phys..

[21]  Glenn O. Brown,et al.  Evaluation of laboratory dolomite core sample size using representative elementary volume concepts , 2000 .

[22]  Robert S. Bernard,et al.  Simulation of flow through bead packs using the lattice Boltzmann method , 1998 .

[23]  F. Recasens,et al.  CFD study on particle-to-fluid heat transfer in fixed bed reactors: Convective heat transfer at low and high pressure , 2006 .

[24]  V. Nakoryakov,et al.  Experimental investigation of a turbulent filtrational flow , 1991 .

[25]  Lynn F. Gladden,et al.  Structure of packed beds probed by Magnetic Resonance Imaging , 2001 .

[26]  Anthony G. Dixon,et al.  Catalyst design by CFD for heat transfer and reaction in steam reforming , 2004 .

[27]  M. L. Porter,et al.  Upscaling microbial chemotaxis in porous media , 2009 .

[28]  Karsten E. Thompson,et al.  Effects of image resolution and numerical resolution on computed permeability of consolidated packing using LB and FEM pore-scale simulations , 2013 .

[29]  Jon M. Hiller,et al.  Three-dimensional reconstruction of a solid-oxide fuel-cell anode , 2006, Nature materials.

[30]  J. Liburdy,et al.  Turbulent flow characteristics in a randomly packed porous bed based on particle image velocimetry measurements , 2013 .

[31]  A. Ladd,et al.  Moderate-Reynolds-number flows in ordered and random arrays of spheres , 2001, Journal of Fluid Mechanics.

[32]  S. J. Kline,et al.  Describing Uncertainties in Single-Sample Experiments , 1953 .

[33]  Emmanuel Villermaux,et al.  Mixing by porous media , 2012 .

[34]  Ajit P. Yoganathan,et al.  Experimental studies of model porous media fluid dynamics , 1989 .

[35]  Ng Niels Deen,et al.  Ensemble correlation PIV applied to bubble plumes rising in a bubble column , 1999 .

[36]  Lynn F. Gladden,et al.  Single- and two-phase flow in fixed-bed reactors: MRI flow visualisation and lattice-Boltzmann simulations , 2001 .

[37]  Wolfgang Losert,et al.  Invited Article: Refractive index matched scanning of dense granular materials. , 2012, The Review of scientific instruments.

[38]  Lynn F. Gladden,et al.  Magnetic resonance imaging of liquid flow and pore structure within packed beds , 1997 .

[39]  Timothy D. Scheibe,et al.  Simulations of reactive transport and precipitation with smoothed particle hydrodynamics , 2007, J. Comput. Phys..

[40]  Balasingam Muhunthan,et al.  Representative Elementary Volume Analysis of Sands Using X-Ray Computed Tomography , 2007 .

[41]  Anthony G. Dixon,et al.  CFD as a Design Tool for Fixed-Bed Reactors , 2001 .

[42]  Xiaofan Yang,et al.  Direct numerical simulation of pore-scale flow in a bead pack: Comparison with magnetic resonance imaging observations , 2013 .

[43]  Gaël Epely-Chauvin,et al.  Experimental investigation into segregating granular flows down chutes , 2011 .

[44]  N. Patankar,et al.  A fast computation technique for the direct numerical simulation of rigid particulate flows , 2005 .

[45]  Anthony G. Dixon,et al.  Systematic mesh development for 3D CFD simulation of fixed beds: Contact points study , 2013, Comput. Chem. Eng..

[46]  W. E. Soll,et al.  Pore scale study of flow in porous media: Scale dependency, REV, and statistical REV , 2000 .

[47]  T. Kulp,et al.  Fluorescent particle image velocimetry: application to flow measurement in refractive index-matched porous media. , 1991, Applied optics.

[48]  Gianni Schena,et al.  Analysis of Hydraulic Permeability in Porous Media: From High Resolution X-ray Tomography to Direct Numerical Simulation , 2009 .

[49]  P. Viotti,et al.  Lagrangian Analysis of Nonreactive Pollutant Dispersion in Porous Media by Means of the Particle Image Velocimetry Technique , 1996 .

[50]  N. Patankar,et al.  A formulation for fully resolved simulation (FRS) of particle-turbulence interactions in two-phase flows , 2008 .

[51]  Thomas J. Kulp,et al.  Measurement of porous medium velocity fields and their volumetric averaging characteristics using particle tracking velocimetry , 1995 .

[52]  S. Wereley,et al.  A PIV Algorithm for Estimating Time-Averaged Velocity Fields , 2000 .

[53]  James A. Liburdy,et al.  Optical measurement uncertainties due to refractive index mismatch for flow in porous media , 2012 .

[54]  John S. Shrimpton,et al.  On the application of immersed boundary, fictitious domain and body-conformal mesh methods to many particle multiphase flows , 2012 .

[55]  Monica Moroni,et al.  Statistical mechanics with three-dimensional particle tracking velocimetry experiments in the study of anomalous dispersion. II. Experiments , 2001 .

[56]  Shuichiro Hirai,et al.  Inertial flow structures in a simple‐packed bed of spheres , 2003 .

[57]  Richard C. Martineau,et al.  Particle-Based Direct Numerical Simulation of Contaminant Transport and Deposition in Porous Flow , 2004 .

[58]  Grant T Gullberg,et al.  Imaging and modeling of flow in porous media using clinical nuclear emission tomography systems and computational fluid dynamics. , 2012, Journal of applied geophysics.

[59]  Anthony J. C. Ladd,et al.  The first effects of fluid inertia on flows in ordered and random arrays of spheres , 2001, Journal of Fluid Mechanics.

[60]  R. Glowinski,et al.  A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow , 2001 .

[61]  Mathieu Martin,et al.  A numerical method for fully resolved simulation (FRS) of rigid particle-flow interactions in complex flows , 2009, J. Comput. Phys..

[62]  P. Roache.  Conservatism of the Grid Convergence Index in Finite Volume Computations on Steady-State Fluid Flow and Heat Transfer , 2003 .

[63]  U. Hampel,et al.  Positron emission tomography in pebble beds. Part 1: Liquid particle deposition , 2014 .

[64]  S. Apte,et al.  Relative performance of body fitted and fictitious domain simulations of flow through fixed packed beds of spheres , 2013 .

[65]  U. Pietrzyk,et al.  Flow visualization in porous media via Positron Emission Tomography , 1998 .

[66]  George F. Pinder,et al.  Direct measurement of interstitial velocity field variations in a porous medium using fluorescent-particle image velocimetry , 1993 .

[67]  Jagadeesh Anmala,et al.  Dynamics of mixing and bimolecular reaction kinetics in aquifers , 2013, Stochastic Environmental Research and Risk Assessment.

[68]  P. Roache.  QUANTIFICATION OF UNCERTAINTY IN COMPUTATIONAL FLUID DYNAMICS , 1997 .

[70]  K. Ogawa,et al.  Three-dimensional velocity measurement of complex interstitial flows through water-saturated porous media by the tagging method in the MRI technique , 2001 .

[71]  L. Gladden.  Magnetic resonance: Ongoing and future role in chemical engineering research , 2003 .

[72]  Anthony G. Dixon,et al.  Packed Tubular Reactor Modeling and Catalyst Design using Computational Fluid Dynamics , 2006 .

[73]  M. Berger,et al.  An Adaptive Version of the Immersed Boundary Method , 1999 .