0
Research Papers: Porous Media

Lattice Boltzmann Simulation of Mass Transfer Coefficients for Chemically Reactive Flows in Porous Media

[+] Author and Article Information
A. Xu, L. Shi, J. B. Xu

Department of Mechanical and
Aerospace Engineering,
HKUST Energy Institute,
The Hong Kong University of Science
and Technology,
Hong Kong 999077, China

T. S. Zhao

Fellow ASME
Department of Mechanical and
Aerospace Engineering,
HKUST Energy Institute,
The Hong Kong University of Science
and Technology,
Hong Kong 999077, China
e-mail: metzhao@ust.hk

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 23, 2016; final manuscript received October 17, 2017; published online January 23, 2018. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 140(5), 052601 (Jan 23, 2018) (8 pages) Paper No: HT-16-1823; doi: 10.1115/1.4038555 History: Received December 23, 2016; Revised October 17, 2017

We present lattice Boltzmann (LB) simulations for the mass transfer coefficient from bulk flows to pore surfaces in chemically reactive flows for both ordered and disordered porous structures. The ordered porous structure under consideration consists of cylinders in a staggered arrangement and in a line arrangement, while the disordered one is composed of randomly placed cylinders. Results show that the ordered porous structure of staggered cylinders exhibits a larger mass transfer coefficient than ordered porous structure of inline cylinders does. It is also found that in the disordered porous structures, the Sherwood number (Sh) increases linearly with Reynolds number (Re) at the creeping flow regime; the Sh and Re exhibit a one-half power law dependence at the inertial flow regime. Meanwhile, for Schmidt number (Sc) between 1 and 10, the Sh is proportional to Sc0.8; for Sc between 10 and 100, the Sh is proportional to Sc0.3.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Zhao, T. S. , Xu, C. , Chen, R. , and Yang, W. W. , 2009, “ Mass Transport Phenomena in Direct Methanol Fuel Cells,” Prog. Energy Combust. Sci., 35(3), pp. 275–292. [CrossRef]
Xu, Q. , and Zhao, T. , 2015, “ Fundamental Models for Flow Batteries,” Prog. Energy Combust. Sci., 49, pp. 40–58. [CrossRef]
Whitaker, S. , 1999, The Method of Volume Averaging, Vol. 13, Springer Science & Business Media, Dordrecht, The Netherlands. [CrossRef]
Davit, Y. , Bell, C. G. , Byrne, H. M. , Chapman, L. A. , Kimpton, L. S. , Lang, G. E. , Leonard, K. H. , Oliver, J. M. , Pearson, N. C. , Shipley, R. J. , Waters, S. L. , Whiteley, J. P. , Wood, B. D. , and Quintard, M. , 2013, “ Homogenization Via Formal Multiscale Asymptotics and Volume Averaging: How Do the Two Techniques Compare?,” Adv. Water Resour., 62(Pt. B), pp. 178–206. [CrossRef]
Xu, Q. , and Zhao, T. , 2013, “ Determination of the Mass-Transport Properties of Vanadium Ions Through the Porous Electrodes of Vanadium Redox Flow Batteries,” Phys. Chem. Chem. Phys., 15(26), pp. 10841–10848. [CrossRef] [PubMed]
Rashapov, R. R. , and Gostick, J. T. , 2016, “ In-Plane Effective Diffusivity in PEMFC Gas Diffusion Layers,” Transp. Porous Media, 115(3), pp. 411–433. [CrossRef]
Mattila, K. , Puurtinen, T. , Hyväluoma, J. , Surmas, R. , Myllys, M. , Turpeinen, T. , Robertsen, F. , Westerholm, J. , and Timonen, J. , 2016, “ A Prospect for Computing in Porous Materials Research: Very Large Fluid Flow Simulations,” J. Comput. Sci., 12, pp. 62–76. [CrossRef]
Xu, A. , Shyy, W. , and Zhao, T. , 2017, “ Lattice Boltzmann Modeling of Transport Phenomena in Fuel Cells and Flow Batteries,” Acta Mech. Sin., 33(3), pp. 555–574. [CrossRef]
Pan, C. , Luo, L.-S. , and Miller, C. T. , 2006, “ An Evaluation of Lattice Boltzmann Schemes for Porous Medium Flow Simulation,” Comput. Fluids, 35(8), pp. 898–909. [CrossRef]
Chai, Z. , Shi, B. , Lu, J. , and Guo, Z. , 2010, “ Non-Darcy Flow in Disordered Porous Media: A Lattice Boltzmann Study,” Comput. Fluids, 39(10), pp. 2069–2077. [CrossRef]
Wang, M. , Wang, J. , Pan, N. , and Chen, S. , 2007, “ Mesoscopic Predictions of the Effective Thermal Conductivity for Microscale Random Porous Media,” Phys. Rev. E, 75(3), p. 036702. [CrossRef]
Yao, Y. , Wu, H. , and Liu, Z. , 2017, “ Pore Scale Investigation of Heat Conduction of High Porosity Open-Cell Metal Foam/Paraffin Composite,” ASME J. Heat Transfer, 139(9), p. 091302. [CrossRef]
Kuwahara, F. , Shirota, M. , and Nakayama, A. , 2001, “ A Numerical Study of Interfacial Convective Heat Transfer Coefficient in Two-Energy Equation Model for Convection in Porous Media,” Int. J. Heat Mass Transfer, 44(6), pp. 1153–1159. [CrossRef]
Saito, M. B. , and De Lemos, M. J. , 2006, “ A Correlation for Interfacial Heat Transfer Coefficient for Turbulent Flow Over an Array of Square Rods,” ASME J. Heat Transfer, 128(5), pp. 444–452. [CrossRef]
Pallares, J. , and Grau, F. , 2010, “ A Modification of a Nusselt Number Correlation for Forced Convection in Porous Media,” Int. Commun. Heat Mass Transfer, 37(9), pp. 1187–1190. [CrossRef]
Torabi, M. , Torabi, M. , and Peterson, G. , 2016, “ Heat Transfer and Entropy Generation Analyses of Forced Convection Through Porous Media Using Pore Scale Modeling,” ASME J. Heat Transfer, 139(1), p. 012601. [CrossRef]
Jeong, N. , Choi, D. H. , and Lin, C.-L. , 2008, “ Estimation of Thermal and Mass Diffusivity in a Porous Medium of Complex Structure Using a Lattice Boltzmann Method,” Int. J. Heat Mass Transfer, 51(15), pp. 3913–3923. [CrossRef]
Chai, Z. , Huang, C. , Shi, B. , and Guo, Z. , 2016, “ A Comparative Study on the Lattice Boltzmann Models for Predicting Effective Diffusivity of Porous Media,” Int. J. Heat Mass Transfer, 98, pp. 687–696. [CrossRef]
Grucelski, A. , and Pozorski, J. , 2015, “ Lattice Boltzmann Simulations of Heat Transfer in Flow Past a Cylinder and in Simple Porous Media,” Int. J. Heat Mass Transfer, 86, pp. 139–148. [CrossRef]
Gamrat, G. , Favre-Marinet, M. , and Le Person, S. , 2008, “ Numerical Study of Heat Transfer Over Banks of Rods in Small Reynolds Number Cross-Flow,” Int. J. Heat Mass Transfer, 51(3), pp. 853–864. [CrossRef]
Sheikholeslami, M. , and Shehzad, S. , 2017, “ Magnetohydrodynamic Nanofluid Convection in a Porous Enclosure Considering Heat Flux Boundary Condition,” Int. J. Heat Mass Transfer, 106, pp. 1261–1269. [CrossRef]
Xu, A. , Shi, L. , and Zhao, T. , 2018, “ Lattice Boltzmann Simulation of Shear Viscosity of Suspensions Containing Porous Particles,” Int. J. Heat Mass Transfer, 116, pp. 969–976. [CrossRef]
Qian, Y. , d'Humières, D. , and Lallemand, P. , 1992, “ Lattice BGK Models for Navier-Stokes Equation,” EPL (Europhys. Lett.), 17(6), pp. 479–572. [CrossRef]
Lallemand, P. , and Luo, L.-S. , 2000, “ Theory of the Lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability,” Phys. Rev. E, 61(6), p. 6546. [CrossRef]
Wang, J. , Wang, D. , Lallemand, P. , and Luo, L.-S. , 2013, “ Lattice Boltzmann Simulations of Thermal Convective Flows in Two Dimensions,” Comput. Math. Appl., 65(2), pp. 262–286. [CrossRef]
Xu, A. , Shi, L. , and Zhao, T. , 2017, “ Accelerated Lattice Boltzmann Simulation Using GPU and OpenACC With Data Management,” Int. J. Heat Mass Transfer, 109, pp. 577–588. [CrossRef]
Zhang, T. , Shi, B. , Guo, Z. , Chai, Z. , and Lu, J. , 2012, “ General Bounce-Back Scheme for Concentration Boundary Condition in the Lattice-Boltzmann Method,” Phys. Rev. E, 85(1), p. 016701. [CrossRef]
Patankar, S. , Liu, C. , and Sparrow, E. , 1977, “ Fully Developed Flow and Heat Transfer in Ducts Having Streamwise-Periodic Variations of Cross-Sectional Area,” ASME J. Heat Transfer, 99(2), pp. 180–186. [CrossRef]
Zhang, J. , and Kwok, D. Y. , 2006, “ Pressure Boundary Condition of the Lattice Boltzmann Method for Fully Developed Periodic Flows,” Phys. Rev. E, 73(4), p. 047702. [CrossRef]
Yoshino, M. , and Inamuro, T. , 2003, “ Lattice Boltzmann Simulations for Flow and Heat/Mass Transfer Problems in a Three-Dimensional Porous Structure,” Int. J. Numer. Methods Fluids, 43(2), pp. 183–198. [CrossRef]
Guo, Z.-L. , Zheng, C.-G. , and Shi, B.-C. , 2002, “ Non-Equilibrium Extrapolation Method for Velocity and Pressure Boundary Conditions in the Lattice Boltzmann Method,” Chin. Phys., 11(4). pp. 366–374. [CrossRef]
Nakayama, A. , 2014, “ A Note on the Confusion Associated With the Interfacial Heat Transfer Coefficient for Forced Convection in Porous Media,” Int. J. Heat Mass Transfer, 79, pp. 1–2. [CrossRef]
Lange, K. J. , Sui, P.-C. , and Djilali, N. , 2010, “ Pore Scale Simulation of Transport and Electrochemical Reactions in Reconstructed PEMFC Catalyst Layers,” J. Electrochem. Soc., 157(10), pp. B1434–B1442. [CrossRef]
Chen, L. , Wu, G. , Holby, E. F. , Zelenay, P. , Tao, W.-Q. , and Kang, Q. , 2015, “ Lattice Boltzmann Pore-Scale Investigation of Coupled Physical-Electrochemical Processes in C/Pt and Non-Precious Metal Cathode Catalyst Layers in Proton Exchange Membrane Fuel Cells,” Electrochimica Acta, 158, pp. 175–186. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Demonstration of the boundary location for heterogeneous reaction

Grahic Jump Location
Fig. 2

Schematic drawing of a bank of square rods: (a) periodic structure; (b) a single unit cell

Grahic Jump Location
Fig. 3

Isotherms of forced convection in a bank of square rods (ε=0.51): (a) Re = 20, Pr = 1, (b) Re = 112, Pr = 1, (c) Re = 20, Pr = 7, and (d) Re = 112, Pr = 7

Grahic Jump Location
Fig. 4

Comparison of interfacial heat transfer correlations

Grahic Jump Location
Fig. 5

Unit cells of ordered porous medium: (a) square inline and (b) square staggered

Grahic Jump Location
Fig. 6

Comparison of the dimensionless effective permeability (Ke/L2) for two types of unit cells: (a) ε = 0.97, (b) ε = 0.94, (c), ε = 0.88, and (d) ε = 0.83

Grahic Jump Location
Fig. 7

Comparison of the dimensionless mass transfer coefficient (Sh) for two types of unit cells: (a) ε = 0.97, (b) ε = 0.94, (c), ε = 0.88, and (d) ε = 0.83

Grahic Jump Location
Fig. 8

Geometries of the disordered porous structure: (a) porous structure A, (b) porous structure B, (c) porous structure C, (d) porous structure D, (e) porous structure E, and (f) porous structure F

Grahic Jump Location
Fig. 9

Pore size distribution of the disordered porous structure

Grahic Jump Location
Fig. 10

Streamlines (left-hand side) and concentration field (right-hand side) in porous structure A from creeping flow regime to inertial flow regime: (a) Re = 0.025, (b) Re = 6.75, and (c) Re = 45.53

Grahic Jump Location
Fig. 11

Correlations between Sherwood number and Reynolds number: (a) Sh = a + b RecScd and (b) Sh′ = Sh−a

Grahic Jump Location
Fig. 12

Correlations between Sherwood number and Schmidt number: (a) Sh = a + b RecScd and (b) Sh′ = Sh−a

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In