https://orcid.org/0000-0002-1461-9977
Abstract
Flow around two identical wall-mounted trapezoidal bluff bodies, arranged in tandem, is numerically investigated at a Reynolds number of 750,000. The investigation employs Reynolds-averaged Navier–Stokes (RANS) equations and the k–ω SST turbulence model. The effect due to the change of the angular orientation of the inclined faces (α) of this bluff body and the pitch distance (L/D) on hydrodynamic quantities and turbulence quantities is investigated. Furthermore, the drag coefficient and Strouhal number have also been evaluated to understand the vortex shedding and flow pattern-related phenomena. For d and intermediate types of bluff bodies, the streamwise mean velocity, cross-stream mean velocity, turbulence kinetic energy, and recirculation length decrease with the increase of α or L/D. Significant changes are also observed in the case of Strouhal number. Reduction in drag coefficient and recirculation length is observed with increased L/D at a constant α for d-type bluff bodies. The change of α and L/D also creates the formation of a periodic von Kármán vortex street at downstream of the second bluff body in the case of L/D = 7, making the flows more complex and unstable. The maximum size of the recirculation bubble occurs in the case of L/D = 10 at α = 30 deg. The investigation provides valuable insight into the complex dynamics of tandem configurations of wall-mounted bluff bodies.
References
1.
Abdullah
, M. M.
, Walsh
, K. K.
, Grady
, S.
, and Wesson
, G. D.
, 2005
, “Modeling Flow Around Bluff Bodies
,” J. Comput. Civ. Eng.
, 19
(1
), pp. 104
–107
.10.1061/(ASCE)0887-3801(2005)19:1(104)2.
Kulkarni
, P. R.
, Singh
, S. N.
, and Seshadri
, V.
, 2005
, “Behaviour of Ship Funnel Exhaust in the Wake of a Bluff Body
,” Royal Institution of Naval Architects International Conference—Marnie CFD 2005 Fourth International Conference on Marine Hydrodynamics
, Southampton, UK, Mar. 30–31, pp. 115
–124
.https://www.researchgate.net/publication/272654240_Behaviour_of_ship_funnel_exhaust_in_the_wake_of_a_bluff_body3.
Goh
, S. C.
, Boopathy
, S. R.
, Krishnaswami
, C.
, and Schlüter
, J. U.
, 2016
, “Tow Testing of Savonius Wind Turbine Above a Bluff Body Complemented by CFD Simulation
,” Renewable Energy
, 87
(1
), pp. 332
–345
.10.1016/j.renene.2015.10.0154.
Wang
, J.
, Zhao
, G.
, Zhang
, M.
, and Zhang
, Z.
, 2018
, “Efficient Study of a Coarse Structure Number on the Bluff Body During the Harvesting of Wind Energy
,” Energy Sources, Part A: Recover., Util., Environ. Eff.
, 40
(15
), pp. 1788
–1797
.10.1080/15567036.2018.14869165.
Bashir
, M. B.
, Benson
, S. D.
, Evans
, M.
, and Murphy
, A. J.
, 2017
, “Simulations of Dynamic Interaction Between a Bluff Body and Installation Vessel During Launch and Recovery in Rough Seas
,” ASME
Paper No. OMAE2017-61319.10.1115/OMAE2017-613196.
Panda
, J. P.
, 2023
, “Machine Learning for Naval Architecture, Ocean and Marine Engineering
,” J. Mar. Sci. Technol.
, 28
(1
), pp. 1
–26
.10.1007/s00773-022-00914-57.
Kong
, H.
, Roussinova
, V.
, and Stoilov
, V.
, 2019
, “Renewable Energy Harvesting From Water Flow
,” Int. J. Environ. Stud.
, 76
(1
), pp. 84
–101
.10.1080/00207233.2018.14949288.
Latif
, U.
, Uddin
, E.
, Abdullah
, C.
, Ali
, Z.
, Sajid
, M.
, Akhtar
, K.
, and Shah
, S. R.
, 2020
, “Experimental Investigation of Energy Harvesting Behind a Bluff Body
,” J. Renewable Sustainable Energy
, 12
(3
), p. 033301.10.1063/1.51443479.
Ohya
, Y.
, 2014
, “Bluff Body Flow and Vortex—Its Application to Wind Turbines
,” Fluid Dyn. Res.
, 46
(6
), p. 061423
.10.1088/0169-5983/46/6/06142310.
Andersen
, M.
, Yin
, G.
, and Ong
, M. C.
, 2021
, “Numerical Simulations of Flow Around Wall-Mounted Square and Trapezoidal Structures at High Reynolds Numbers
,” ASME J. Offshore Mech. Arct. Eng.
, 143
(1
), p. 011902
.10.1115/1.404754111.
Tachie
, M. F.
, and Adane
, K. K.
, 2007
, “PIV Study of Shallow Open Channel Flow Over d- and k-Type Transverse Ribs
,” ASME J. Fluids Eng.
, 129
(8
), pp. 1058
–1072
.10.1115/1.274691012.
Spedding
, G. R.
, 1997
, “The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number
,” J. Fluid Mech.
, 337
, pp. 283
–301
.10.1017/S002211209600455713.
Krajnović
, S.
, and Davidson
, L.
, 2002
, “Large-Eddy Simulation of the Flow Around a Bluff Body
,” AIAA J.
, 40
(5
), pp. 927
–936
.10.2514/2.172914.
Asadollahi
, N.
, Nistor
, I.
, and Mohammadian
, A.
, 2019
, “Numerical Investigation of Tsunami Bore Effects on Structures, Part I: Drag Coefficients
,” Nat. Hazards
, 96
(1
), pp. 285
–309
.10.1007/s11069-018-3542-215.
Ramesh
, J. P.
, Sivakumar
, K.
, and Mugendiran
, V.
, 2020
, “Investigation of Wake Aerodynamics in Bluff Body for UAV Application
,” J. Mech. Eng.
, 10
(2
), pp. 27
–34
.10.26634/jme.10.2.1676916.
Li
, X.
, Xiao
, Q.
, Wang
, E.
, Peyrard
, C.
, and Gonçalves
, R. T.
, 2023
, “The Dynamic Response of Floating Offshore Wind Turbine Platform in Wave-Current Condition
,” Phys. Fluids
, 35
(8
), p. 087113.10.1063/5.015891717.
Mu
, A.
, Huang
, Z.
, Liu
, A.
, Yang
, B.
, Wang
, J.
, Qian
, Y.
, and Wang
, H.
, 2022
, “Bluff Body Vortex-Induced Vibration Control of Floating Wind Turbines Based on a Novel Intelligent Robust Control Algorithm
,” Phys. Fluids
, 34
(11
), p. 114103.10.1063/5.012182918.
Arie
, M.
, Kiya
, M.
, Tamura
, H.
, and Kanayama
, Y.
, 1975
, “Flow Over Rectangular Cylinders Immersed in a Turbulent Boundary Layer (Part-1: Correlation Between Pressure Drag and Boundary-Layer Characteristics)
,” Bull. JSME
, 18
(125
), pp. 1260
–1268
.10.1299/jsme1958.18.126019.
Arie
, M.
, 1977
, “Flow Over Rectangular Cylinders Immersed in a Turbulent Boundary Layer. Part 2
,” Chem. Pharm. Bull.
, 12
, p. 2091
.10.1299/jsme1958.18.126920.
Antoniou
, J.
, and Bergeles
, G.
, 1988
, “Development of the Reattached Flow Behind Surface-Mounted Two-Dimensional Prisms
,” ASME J. Fluids Eng.
, 110
(2
), pp. 127
–133
.10.1115/1.324352421.
Martinuzzi
, R.
, and Tropea, C., 1993
, “The Flow Around Surface-Mounted, Prismatic Obstacles Placed in a Fully Developed Channel Flow
,” ASME J. Fluids Eng.
, 115
(1
), pp. 85
–92
.22.
Acharya
, S.
, Dutta
, S.
, Myrum
, T. A.
, and Baker
, R. S.
, 1994
, “Turbulent Flow Past a Surface-Mounted Two-Dimensional Rib
,” ASME J. Fluids Eng.
, 116
(2
), pp. 238
–246
.10.1115/1.291026123.
Liu
, Y. Z.
, Ke
, F.
, and Sung
, H. J.
, 2008
, “Unsteady Separated and Reattaching Turbulent Flow Over a Two-Dimensional Square Rib
,” J. Fluids Struct.
, 24
(3
), pp. 366
–381
.10.1016/j.jfluidstructs.2007.08.00924.
Gamel
, H.
, Salizzoni
, P.
, Soulhac
, L.
, Méjean
, P.
, Marro
, M.
, Grosjean
, N.
, and Carissimo
, B.
, 2014
, “Turbulent Kinetic Energy Budget and Dissipation in the Wake of 2D Obstacle: Analysis of the k-ε Closure Model
,” ASME
Paper No. FEDSM2014-21489.10.1115/FEDSM2014-2148925.
Afgan
, I.
, Kahil
, Y.
, Benhamadouche
, S.
, and Sagaut
, P.
, 2011
, “Large Eddy Simulation of the Flow Around Single and Two Side-by-Side Cylinders at Subcritical Reynolds Numbers
,” Phys. Fluids
, 23
(7
), p. 075101.10.1063/1.359626726.
Burattini
, P.
, and Agrawal
, A.
, 2013
, “Wake Interaction Between Two Side-by-Side Square Cylinders in Channel Flow
,” Comput. Fluids
, 77
, pp. 134
–142
.10.1016/j.compfluid.2013.02.01427.
Han
, L.
, Riviere
, N.
, Chatelain
, M.
, and Mignot
, E.
, 2020
, “Recirculation Zone Downstream Lateral Expansions of Open Channel Flow
,” Phys. Fluids
, 32
(11
), p. 115119.10.1063/5.001834328.
Barman
, K.
, Debnath
, K.
, and Mazumder
, B. S.
, 2019
, “Turbulence Over Chains of Hemispherical Ribs Under Waves in a Current
,” Water Resour. Res.
, 55
(1
), pp. 55
–75
.10.1029/2017WR02037929.
Jasim
, R. A.
, Hussen
, W. Q.
, Abdullah
, M. F.
, and Zulkifli
, R.
, 2023
, “Numerical Simulation of Characterization of Hydraulic Jump Over an Obstacle in an Open Channel Flow
,” J. Adv. Res. Fluid Mech. Therm. Sci.
, 106
(1
), pp. 1
–15
.10.37934/arfmts.106.1.11530.
Menter
, F. R.
, 1993
, “Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows
,” AIAA
Paper No. 93-2906.10.2514/6.93-290631.
Jones
, W. P.
, and Launder
, B. E.
, 1973
, “The Calculation of Low-Reynolds-Number Phenomena With a Two-Equation Model of Turbulence
,” Int. J. Heat Mass Transfer
, 16
(6
), pp. 1119
–1130
.10.1016/0017-9310(73)90125-732.
Wilcox
, D. C.
, 1998
, Turbulence Modeling for CFD
, 3
rd ed., DCW Industries
, La Canada, CA
.33.
Xinyu
, L.
, Changzhi
, C.
, and Zengnan
, D.
, 1995
, “Écoulements Turbulents À Surface Libre En Canaux Lisses Avec Différentes Pentes
,” J. Hydraul. Res.
, 33
(3
), pp. 333
–347
.10.1080/0022168950949857534.
Fatahi
, M.
, Akdogan
, G.
, Dorfling
, C.
, and Van Wyk
, P.
, 2021
, “Numerical Study of Microplastic Dispersal in Simulated Coastal Waters Using CFD Approach
,” Water (Switzerland)
, 13
(23
), p. 3432
.10.3390/w1323343235.
Barton
, I. E.
, 1998
, “Comparison of SIMPLE- and PISO-Type Algorithms for Transient Flows
,” Int. J. Numer. Methods Fluids
, 26
(4
), pp. 459
–483
.10.1002/(SICI)1097-0363(19980228)26:4<459::AID-FLD645>3.0.CO;2-U36.
Jang
, D. S.
, Jetli
, R.
, and Acharya
, S.
, 1986
, “Comparison of the PISO, SIMPLER, and SIMPLEC Algorithms for the Treatment of the Pressure-Velocity Coupling in Steady Flow Problems
,” Numer. Heat Transfer
, 10
(3
), pp. 209
–228
.10.1080/1040778860891351737.
Balduzzi
, F.
, Bianchini
, A.
, Ferrara
, G.
, and Ferrari
, L.
, 2016
, “Dimensionless Numbers for the Assessment of Mesh and Timestep Requirements in CFD Simulations of Darrieus Wind Turbines
,” Energy
, 97
, pp. 246
–261
.10.1016/j.energy.2015.12.11138.
Adanta
, D.
, Ibrahim
, M. M.
, Sari
, D. P.
, Syofii
, I.
, and Saputra
, M. A. A.
, 2022
, “Application of the Grid Convergency Index Method and Courant Number Analysis for Propeller Turbine Simulation
,” J. Adv. Res. Fluid Mech. Therm. Sci.
, 96
(2
), pp. 33
–41
.10.37934/arfmts.96.2.334139.
Chamoli
, S.
, Joshi
, A.
, Rana
, S.
, Bhattacharaya
, S.
, Gupta
, A.
, Ghansela
, S.
, Thianpong
, C.
, and Eiamsa-Ard
, S.
, 2023
, “Numerical Methodology to Reduce the Drag and Control Flow Around a Cam-Shaped Cylinder Integrated With Backward Splitter Plate
,” Computation
, 11
(10
), p. 196
.10.3390/computation1110019640.
Borah
, R.
, Jain
, S.
, Joshi
, D. V.
, and Saha
, U. K.
, 2021
, “Flow Characterization of Bluff Bodies: A Two-Dimensional Transformation From Square to Triangular Cylinder
,” ASME J. Fluids Eng.
, 143
(11
), p. 111302
.10.1115/1.405131041.
Umeyama Motohiko
, G. F.
, 1992
, “Velocity Distribution in Uniform Sediment-Laden Flow
,” ASCE
, 118
, pp. 989
–1001
.10.1061/(ASCE)0733-9429(1992)118:2(229)42.
Baracu
, T.
, and Grigoras-Benescu
, S.
, 2011
, “Computational Analysis of the Flow Around a Cylinder and of the Drag Force
,” 2nd Conference of the Young Researchers from TUCEB
, Bucharest, Romania, Nov., pp. 16–26.https://d1wqtxts1xzle7.cloudfront.net/37486395/Baracu_T__Grigoras-Benescu_S_Computational_analysis_of_the_flow_around_a_cylinder_and_of_the_drag_force_post_final_sssss-libre.pdf?1430630637=&response-content-disposition=inline%3B+filename%3DComputational_analysis_of_the_flow_aroun.pdf&Expires=1728553780&Signature=SqoS49ng3ZXvVL7w0kpnmiBt97VE5mzKSMcMmdDl4V9A~hYZ94RzVetFIxi4GoDhhi1qFmcMhj2rvY58cxI67h3h6bUVFVj2NGaLpSkG352mqD2bAyyMPtpalis592Y~6GTOBZxMNxlLZodZQRb5nYAk~js-CzyPdR9k4ir~AmI0pvQ0aNl2Kcyzl0JPqmQzJuVE8IJH~PjR1ZmQASXloGSN6~fq2fpAAM737dljomXH71a2iTVRMeAek92ZxFuy9Vt-FUHm2dKMFyfkoweapmhJc6gwyYCxV4h~NUinbJs4FKphGu7MiVDVta~buVlSn1yjZh~CFM~y2PeApvyw__&Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA43.
Garcia-Ribeiro
, D.
, Malatesta
, V.
, Moura
, R. C.
, and Cerón-Muñoz
, H. D.
, 2023
, “Assessment of RANS-Type Turbulence Models for CFD Simulations of Horizontal Axis Wind Turbines at Moderate Reynolds Numbers
,” J. Braz. Soc. Mech. Sci. Eng.
, 45
(11
), pp. 1
–21
.10.1007/s40430-023-04488-044.
Bai
, C. J.
, and Wang
, W. C.
, 2016
, “Review of Computational and Experimental Approaches to Analysis of Aerodynamic Performance in Horizontal-Axis Wind Turbines (HAWTs)
,” Renewable Sustainable Energy Rev.
, 63
(2016
), pp. 506
–519
.10.1016/j.rser.2016.05.07845.
Zhu
, B.
, Sun
, X.
, Wang
, Y.
, and Huang
, D.
, 2017
, “Performance Characteristics of a Horizontal Axis Turbine With Fusion Winglet
,” Energy
, 120
, pp. 431
–440
.10.1016/j.energy.2016.11.09446.
Farhan
, A.
, Hassanpour
, A.
, Burns
, A.
, and Motlagh
, Y. G.
, 2019
, “Numerical Study of Effect of Winglet Planform and Airfoil on a Horizontal Axis Wind Turbine Performance
,” Renewable Energy
, 131
, pp. 1255
–1273
.10.1016/j.renene.2018.08.01747.
Constantinescu
, G. S.
, Krajewski
, W. F.
, Ozdemir
, C. E.
, and Tokyay
, T.
, 2007
, “Simulation of Airflow Around Rain Gauges: Comparison of LES With RANS Models
,” Adv. Water Resour.
, 30
(1
), pp. 43
–58
.10.1016/j.advwatres.2006.02.01148.
Iqbal Qureshi
, M. Z.
, and Chan
, A. L. S.
, 2020
, “Influence of Eddy Viscosity Parameterisation on the Characteristics of Turbulence and Wind Flow: Assessment of Steady RANS Turbulence Model
,” J. Build. Eng.
, 27
, p. 100934
.10.1016/j.jobe.2019.10093449.
Glegg
, S.
, Morin
, B.
, Atassi
, O.
, and Reba
, R.
, 2008
, “Using RANS Calculations of Turbulent Kinetic Energy to Provide Predictions of Trailing Edge Noise
,” AIAA
Paper No. 2008-2993.10.2514/6.2008-299350.
Umlauf
, L.
, and Burchard
, H.
, 2003
, “A Generic Length-Scale Equation for Geophysical Turbulence Models
,” J. Mar. Res.
, 61
(2
), pp. 235
–265
.10.1357/00222400332200508751.
Gu
, H.
, Liu
, M.
, Li
, X.
, Huang
, H.
, Wu
, Y.
, and Sun
, F.
, 2018
, “The Effect of a Low-Frequency Structure on Passive Scalar Transport in the Flow Over a Surface-Mounted Rib
,” Flow, Turbul. Combust.
, 101
(3
), pp. 719
–740
.10.1007/s10494-018-9929-z52.
Hwang
, R. R.
, Chow
, Y. C.
, and Peng
, Y. F.
, 1999
, “Numerical Study of Turbulent Flow Over Two-Dimensional Surface-Mounted Ribs in a Channel
,” Int. J. Numer. Methods Fluids
, 31
(4
), pp. 767
–785
.10.1002/(SICI)1097-0363(19991030)31:4<767::AID-FLD902>3.0.CO;2-A53.
Garciá
, C.
, 2020
, “Kármán Vortex Street in Incompressible Fluid Models
,” Nonlinearity
, 33
, pp. 1625
–1676
.10.1088/1361-6544/ab630954.
Wu
, C. J.
, Wang
, L.
, and Wu
, J. Z.
, 2007
, “Suppression of the Von Kármán Vortex Street Behind a Circular Cylinder by a Travelling Wave Generated by a Flexible Surface
,” J. Fluid Mech.
, 574
, pp. 365
–391
.10.1017/S002211200600415055.
Schatzman
, J. C.
, 1981
, “A Model for Von Karman Vortex Street
,” Ph.D. thesis
, California Institute of Technology, Pasadena, CA.https://thesis.library.caltech.edu/1751/4/schatzman_jc_1981.pdf56.
Buresti
, G.
, 1998
, “Vortex Shedding From Bluff Bodies
,” Wind Effects on Buildings and Structures, CRC Press, Boca Raton, FL, pp. 61
–95
.57.
Knisely
, C. W.
, 1990
, “Strouhal Numbers of Rectangular Cylinders at Incidence: A Review and New Data
,” J. Fluids Struct.
, 4(4) pp. 371
–393
.10.1016/0889-9746(90)90137-T
