https://orcid.org/0000-0002-9349-2256
Abstract
The wall-modeled-large eddy simulation (WMLES) technique was used to analyze turbulent flow in a porous medium composed of a staggered arrangement of square cylinders. The study focused on a porosity range of 0.3–0.8 at a pore Reynolds number of 104. The research provides novel information on pressure and shear force distributions around the cylinders and time-averaged values of particle drag and fluctuating lift coefficients. Results indicate that flow physics are mainly driven by an expansion region in front of the central particle and another one in the rear, where the flow is contracted and strongly accelerated. In the first region, velocities, turbulence kinetic energy (k), and its dissipation rate (ε) are attenuated by a sudden pressure increase, while in the contraction region, the effect is the opposite. As porosity decreases, flow gradients and the overall levels of k, ε, and normalized Reynolds stresses become more significant. Turbulent anisotropy increases as porosity decreases below 0.6. Hydrodynamic stresses in the last interval present relatively uniform levels, which is a unique feature that may be considered in designing dedicated engineering devices with controlled stresses.
References
1.
Dybss
, A.
, and Edwards
, R. W.
, 1984
, “A New Look at Porous Media Fluid Mechanics -Darcy to Turbulent
,” Fundamentals of Transport Phenomena in Porous Media, Proceedings of the NATO Advanced Study Institute on Mechanics of Fluids in Porous Media
, J.
Bear
, and Y.
Corapcioglu
, eds., Martinus Nijhoff Publishers
, Delaware
, pp. 199
–256
.2.
Chen
, J.
, Liu
, C.
, Li
, Y.
, Huang
, Y.
, Yuan
, X.
, and Yu
, G.
, 2007
, “Experimental Investigation of Single-Phase Flow in Structured Packing by LDV
,” Chin. J. Chem. Eng.
, 15
(6
), pp. 821
–827
.10.1016/S1004-9541(08)60009-93.
Daviero
, G. J.
, Roberts
, P. J. W.
, and Maile
, K.
, 2001
, “Refractive Index Matching in Large-Scale Stratified Experiments
,” Exp. Fluids
, 31
(2
), pp. 119
–126
.10.1007/s0034800002604.
Hassan
, Y. A.
, and Dominguez-Ontiveros
, E. E.
, 2008
, “Flow Visualization in a Pebble Bed Reactor Experiment Using PIV and Refractive Index Matching Techniques
,” Nucl. Eng. Des.
, 238
(11
), pp. 3080
–3085
.10.1016/j.nucengdes.2008.01.0275.
Khayamyan
, S.
, Lundström
, T. S.
, Gren
, P.
, Lycksam
, H.
, and Hellström
, J. G. I.
, 2017
, “Transitional and Turbulent Flow in a Bed of Spheres as Measured With Stereoscopic Particle Image Velocimetry
,” Transp. Porous Media
, 117
(1
), pp. 45
–67
.10.1007/s11242-017-0819-y6.
Jin
, Y.
, and Kuznetsov
, A. V.
, 2017
, “Turbulence Modeling for Flows in Wall Bounded Porous Media: An Analysis Based on Direct Numerical Simulations
,” Phys. Fluids
, 29
(4
), p. 045102
.10.1063/1.49790627.
Jin
, Y.
, Uth
, M. F.
, Kuznetsov
, A. V.
, and Herwig
, H.
, 2015
, “Numerical Investigation of the Possibility of Macroscopic Turbulence in Porous Media: A Direct Numerical Simulation Study
,” J. Fluid Mech.
, 766
(2
), pp. 76
–103
.10.1017/jfm.2015.98.
Uth
, M. F.
, Jin
, Y.
, Kuznetsov
, A. V.
, and Herwig
, H.
, 2016
, “A Direct Numerical Simulation Study on the Possibility of Macroscopic Turbulence in Porous Media: Effects of Different Solid Matrix Geometries, Solid Boundaries, and Two Porosity Scales
,” Phys. Fluids
, 28
(6
), p. 065101
.10.1063/1.49495499.
Rasam
, A.
, Brethouwer
, G.
, Schlatter
, P.
, Li
, Q.
, and Johansson
, A. V.
, 2011
, “Effects of Modelling, Resolution and Anisotropy of Subgrid-Scales on Large Eddy Simulations of Channel Flow
,” J. Turbul.
, 12
(1
), pp. N10
–N19
.10.1080/14685248.2010.54192010.
Kuwahara
, F.
, Yamane
, T.
, and Nakayama
, A.
, 2006
, “Large Eddy Simulation of Turbulent Flow in Porous Media
,” Int. Commun. Heat Mass Transfer
, 33
(4
), pp. 411
–418
.10.1016/j.icheatmasstransfer.2005.12.01111.
Kundu
, P.
, Kumar
, V.
, Hoarau
, Y.
, and Mishra
, I. M.
, 2016
, “Numerical Simulation and Analysis of Fluid Flow Hydrodynamics Through a Structured Array of Circular Cylinders Forming Porous Medium
,” Appl. Math. Modell.
, 40
(23–24
), pp. 9848
–9871
.10.1016/j.apm.2016.06.04312.
Shams
, A.
, Roelofs
, F.
, Komen
, E. M. J.
, and Baglietto
, E.
, 2014
, “Large Eddy Simulation of a Randomly Stacked Nuclear Pebble Bed
,” Comput. Fluids
, 96
(3
), pp. 302
–321
.10.1016/j.compfluid.2014.03.02513.
Alonzo-Garcia
, A.
, Mendoza-Rosas
, A. T.
, Díaz-Viera
, M. A.
, Martínez-Delgadillo
, S. A.
, and Martínez-Mendoza
, E. G.
, 2021
, “Assessment of Low-Re Turbulence Models and Analysis of Turbulent Flow in Porous Media Consisting of Square Cylinders With Different Diameter Ratios
,” ASME J. Fluids Eng. Trans. ASME
, 143
(1
), p. 011402
.10.1115/1.404828414.
Pedras
, M. H. J.
, and de Lemos
, M. J. S.
, 2001
, “Simulation of Turbulent Flow in Porous Media Using a Spatially Periodic Array and a Low Re Two-Equation Closure
,” Numer. Heat Transfer, Part A
, 39
(1
), pp. 35
–59
.10.1080/10407780145845615.
Kundu
, P.
, Kumar
, V.
, and Mishra
, I. M.
, 2014
, “Numerical Modeling of Turbulent Flow Through Isotropic Porous Media
,” Int. J. Heat Mass Transfer
, 75
(4
), pp. 40
–57
.10.1016/j.ijheatmasstransfer.2014.03.02016.
Nakayama
, A.
, and Kuwahara
, F.
, 1999
, “A Macroscopic Turbulence Model for Flow in a Porous Medium
,” ASME J. Fluids Eng.
, 121
(2
), pp. 427
–433
.10.1115/1.282222717.
González-Neria
, I.
, Yáñez-Varela
, J. A.
, Martínez-Delgadillo
, S. A.
, Rivadeneyra-Romero
, G.
, and Alonzo-Garcia
, A.
, 2021
, “Analysis of the Turbulent Flow Patterns Generated in Isotropic Porous Media Composed of Aligned or Centered Cylinders
,” Int. J. Mech. Sci.
, 199
(3
), p. 106396
.10.1016/j.ijmecsci.2021.10639618.
Pedras
, M. H. J.
, and de Lemos
, M. J. S.
, 2001
, “On the Mathematical Description and Simulation of Turbulent Flow in a Porous Medium Formed by an Array of Elliptic Rods
,” ASME J. Fluids Eng. Trans. ASME
, 123
(4
), pp. 941
–947
.10.1115/1.141324419.
Yang
, J.
, Zhou
, M.
, Li
, S. Y.
, Bu
, S. S.
, and Wang
, Q. W.
, 2014
, “Three-Dimensional Numerical Analysis of Turbulent Flow in Porous Media Formed by Periodic Arrays of Cubic, Spherical, or Ellipsoidal Particles
,” ASME J. Fluids Eng. Trans. ASME
, 136
(1
), p. 011102
.10.1115/1.402536520.
Celik
, I. B.
, Cehreli
, Z. N.
, and Yavuz
, I.
, 2005
, “Index of Resolution Quality for Large Eddy Simulations
,” ASME J. Fluids Eng.
, 127
(5
), pp. 949
–958
.10.1115/1.199020121.
Ahmed
, H. E.
, Salman
, B. H.
, Kherbeet
, A. S.
, and Ahmed
, M. I.
, 2018
, “Optimization of Thermal Design of Heat Sinks: A Review
,” Int. J. Heat Mass Transfer
, 118
, pp. 129
–153
.10.1016/j.ijheatmasstransfer.2017.10.09922.
Kashevskii
, B. E.
, 2005
, “Magnetophoretic Properties of a Volume-Ordered System of Rectangular Ferrocylinders
,” J. Eng. Phys. Thermophys.
, 78
(3
), pp. 455
–462
.10.1007/s10891-005-0081-y23.
Allard
, J. F.
, and Atalla
, N.
, 2009
, Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials
, Wiley, Inc
., New Jersey
.24.
Seol
, C.
, Hong
, J.
, and Kim
, T.
, 2023
, “Flow Around Porous Square Cylinders With a Periodic and Scalable Structure
,” Exp. Therm. Fluid Sci.
, 144
(9
), p. 110864
.10.1016/j.expthermflusci.2023.11086425.
Wood
, B. D.
, He
, X.
, and Apte
, S. V.
, 2020
, “Modeling Turbulent Flows in Porous Media
,” Annu. Rev. Fluid Mech.
, 52
(1
), pp. 171
–203
.10.1146/annurev-fluid-010719-06031726.
Ansys
, 2013
, Fluent Theory Guide
, ANSYS Inc
., Canonsburg, PA, Vol. 15317
, pp. 724
–746
.27.
Shur
, M. L.
, Spalart
, P. R.
, Strelets
, M. K.
, and Travin
, A. K.
, 2008
, “A Hybrid RANS-LES Approach With Delayed-DES and Wall-Modelled LES Capabilities
,” Int. J. Heat Fluid Flow
, 29
(6
), pp. 1638
–1649
.10.1016/j.ijheatfluidflow.2008.07.00128.
Kuwata
, Y.
, and Suga
, K.
, 2015
, “Large Eddy Simulations of Pore-Scale Turbulent Flows in Porous Media by the Lattice Boltzmann Method
,” Int. J. Heat Fluid Flow
, 55
(6
), pp. 143
–157
.10.1016/j.ijheatfluidflow.2015.05.01529.
Çengel
, Y. A.
, and Cimbala
, J. M.
, 2020
, Fluid Mechanics Fundamentals and Applications
, McGraw-Hill
, New York
.30.
Yoshizawa
, A.
, and Horiuti
, K.
, 1985
, “A Statistically-Derived Subgrid-Scale Kinetic Energy Model for the Large-Eddy Simulation of Turbulent Flows
,” J. Phys. Soc. Jpn.
, 54
(8
), pp. 2834
–2839
.10.1143/JPSJ.54.283431.
Lam
, C. K. G.
, and Bremhorst
, K.
, 1981
, “A Modified Form of the K-ɛ Model for Predicting Wall Turbulence
,” ASME J. Fluids Eng.
, 103
(3
), pp. 456
–460
.10.1115/1.324081532.
Yen
, S. C.
, Wu
, S. F.
, and San
, K. C.
, 2016
, “Modulation of Wake Flow and Aerodynamic Behaviors Around a Square Cylinder Using an Upstream Control Bar
,” Exp. Therm. Fluid Sci.
, 70
(9
), pp. 139
–147
.10.1016/j.expthermflusci.2015.09.00933.
Bäbler
, M. U.
, Morbidelli
, M.
, and Bałdyga
, J.
, 2008
, “Modelling the Breakup of Solid Aggregates in Turbulent Flows
,” J. Fluid Mech.
, 612
(6
), pp. 261
–289
.10.1017/S002211200800298X34.
Wyrobnik
, T. A.
, Ducci
, A.
, and Micheletti
, M.
, 2020
, “Advances in Human Mesenchymal Stromal Cell-Based Therapies – Towards an Integrated Biological and Engineering Approach
,” Stem Cell Res.
, 47
(7
), p. 101888
.10.1016/j.scr.2020.10188835.
Sun
, R.
, Yu
, P.
, Zuo
, P.
, and Alvarez
, P. J. J.
, 2022
, “Bacterial Concentrations and Water Turbulence Influence the Importance of Conjugation Versus Phage-Mediated Antibiotic Resistance Gene Transfer in Suspended Growth Systems
,” ACS Environ. Au
, 2
(2
), pp. 156
–165
.10.1021/acsenvironau.1c0002736.
Jeong
, J.
, and Hussain
, F.
, 1995
, “On the Identification of a Vortex
,” J. Fluid Mech.
, 285
(7
), pp. 69
–94
.10.1017/S0022112095000462
