Research Papers: Flows in Complex Systems

Control of Wake Structure Behind a Square Cylinder by Magnetohydrodynamics

[+] Author and Article Information
S. Rashidi, M. Bovand

Department of Mechanical Engineering,
Ferdowsi University of Mashhad,
Mashhad 91775-1111, Iran

J. A. Esfahani

Department of Mechanical Engineering,
Ferdowsi University of Mashhad,
Mashhad 91775-1111, Iran
e-mail: abolfazl@um.ac.ir

H. F. Öztop

Department of Mechanical
Engineering Technology,
Firat University Elazig,
Elazig 23119, Turkey

R. Masoodi

School of Design and Engineering,
Philadelphia University,
4201 Henry Avenue,
Philadelphia, PA 19144

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 12, 2014; final manuscript received January 20, 2015; published online March 9, 2015. Assoc. Editor: Shizhi Qian.

J. Fluids Eng 137(6), 061102 (Jun 01, 2015) (8 pages) Paper No: FE-14-1580; doi: 10.1115/1.4029633 History: Received October 12, 2014; Revised January 20, 2015; Online March 09, 2015

In this paper, a two-dimensional (2D) numerical simulation has been performed for an unsteady magnetohydrodynamics (MHD) flow around a solid square cylinder placed in a channel. Computational simulations were done for the ranges of Reynolds and Stuart numbers of 1–250 and 0–10, respectively. Finite volume method (FVM) has been used to solve the unsteady Navier–Stokes equations. The effects of streamwise magnetic field on the flow separation and suppress of the vortex shedding are studied in detail for the above ranges. Additionally, four new empirical equations for wake length and Stuart number are suggested. Finally, a comparison is performed between the cases of with and without a channel to study the effect of channel walls. The obtained results revealed that Strouhal number decreases linearly with increasing Stuart number. Also, the flow distribution pattern changes from time-dependent pattern to steady-state by increasing Stuart number.

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Burattini, P., and Agrawal, A., 2013, “Wake Interaction Between Two Side-by-Side Square Cylinders in Channel Flow,” Comput. Fluids, 77(1), pp. 134–142. [CrossRef]
Armellini, A., Casarsa, L., and Giannattasio, P., 2009, “Separated Flow Structures Around a Cylindrical Obstacle in a Narrow Channel,” Exp. Therm. Fluid Sci., 33(4), pp. 604–619. [CrossRef]
Dehghan, M., Daneshipour, M., Valipour, M. S., Rafee, R., and Saedodin, S., 2015, “Enhancing Heat Transfer in Microchannel Heat Sinks Using Converging Flow Passages,” Energy Convers. Manage., 92, pp. 244–250. [CrossRef]
Dehghan, M., Rahmani, Y., Ganji, D. D., Saedodin, S., Valipour, M. S., and Rashidi, S., 2015, “Convection–Radiation Heat Transfer in Solar Heat Exchangers Filled With a Porous Medium: Homotopy Perturbation Method Versus Numerical Analysis,” Renewable Energy, 74, pp. 448–455. [CrossRef]
Dehghan, M., Jamal-Abad, M. T., and Rashidi, S., 2014, “Analytical Interpretation of the Local Thermal Non-Equilibrium Condition of Porous Media Imbedded in Tube Heat Exchangers,” Energy Convers. Manage., 85, pp. 264–271. [CrossRef]
Mirzaei, M., and Dehghan, M., 2013, “Investigation of Flow and Heat Transfer of Nanofluid in Microchannel With Variable Property Approach,” Heat Mass Transfer, 49(12), pp. 1803–1811. [CrossRef]
Suzuki, K., and Suzuki, H., 1994, “Instantaneous Structure and Statistical Feature of Unsteady Flow in a Channel Obstructed by a Square Rod,” Int. J. Heat Fluid Flow, 15(6), pp. 426–437. [CrossRef]
Kim, D. H., Yang, K. S., and Senda, M., 2004, “Large Eddy Simulation of Turbulent Flow Past a Square Cylinder Confined in a Channel,” Comput. Fluids, 33(1), pp. 81–96. [CrossRef]
Layek, G. C., Midya, C., and Gupta, A. S., 2008, “Influences of Suction and Blowing on Vortex Shedding Behind a Square Cylinder in a Channel,” Int. J. Non-Linear Mech., 43(9), pp. 979–984. [CrossRef]
Jafari, S., Salmanzadeh, M., Rahnama, M., and Ahmadi, G., 2010, “Investigation of Particle Dispersion and Deposition in a Channel With a Square Cylinder Obstruction Using the Lattice Boltzmann Method,” J. Aerosol Sci., 41(2), pp. 198–206. [CrossRef]
Abolfazli Esfahani, J., and Vaselbehagh, A. R., 2012, “LB Simulation of Heat Transfer in Flow Past a Square Unit of Four Isothermal Cylinders,” C. R. Mec., 340(7), pp. 526–535. [CrossRef]
Abolfazli Esfahani, J., and Vaselbehagh, A. R., 2013, “A Numerical Study on Shear Layer Behaviour in Flow Over a Square Unit of Four Cylinders at Reynolds Number of 200 Using the LB Method,” Prog. Comput. Fluid Dyn., 13(2), pp. 103–119. [CrossRef]
Nazari, M., Mohebbi, R., and Kayhani, M. H., 2014, “Power-Law Fluid Flow and Heat Transfer in a Channel With a Built-In Porous Square Cylinder: Lattice Boltzmann Simulation,” J. Non-Newtonian Fluid Mech., 204, pp. 38–49. [CrossRef]
Verhelst, J. M., and Nieuwstadt, F. T. M., 2004, “Visco-Elastic Flow Past Circular Cylinders Mounted in a Channel: Experimental Measurements of Velocity and Drag,” J. Non-Newtonian Fluid Mech., 116(2–3), pp. 301–328. [CrossRef]
Srikanth, S., Dhiman, A. K., and Bijjam, S., 2010, “Confined Flow and Heat Transfer Across a Triangular Cylinder in a Channel,” Int. J. Therm. Sci., 49(11), pp. 2191–2200. [CrossRef]
Takahashi, M., Aritomi, M., Inoue, A., and Matsuzaki, M., 1998, “MHD Pressure Drop and Heat Transfer of Lithium Single-Phase Flow in a Rectangular Channel Under Transverse Magnetic Field,” Fusion Eng. Des., 42(1–4), pp. 365–372. [CrossRef]
Xu, S. J., Zhang, N. M., and Ni, M. J., 2013, “Influence of Flow Channel Insert With Pressure Equalization Opening on MHD Flows in a Rectangular Duct,” Fusion Eng. Des., 88(5), pp. 271–275. [CrossRef]
Midya, C., Layek, G. C., Gupta, A. S., and Ray Mahapatra, T., 2004, “Magnetohydrodynamic Viscous Flow Separation in a Channel With Constrictions,” ASME J. Fluids Eng., 125(6), pp. 952–962. [CrossRef]
Hayat, T., Awais, M., Asghar, S., and Hendi, A. A., 2011, “Analytic Solution for the Magnetohydrodynamic Rotating Flow of Jeffrey Fluid in a Channel,” ASME J. Fluids Eng., 133(6), p. 061201. [CrossRef]
Hayat, T., Nawaz, M., Hendi, A. A., and Asghar, S., 2011, “MHD Squeezing Flow of a Micropolar Fluid Between Parallel Disks,” ASME J. Fluids Eng., 133(11), p. 111206. [CrossRef]
Shebalin, J. V., 2014, “Temperature and Entropy in Ideal Magnetohydrodynamic Turbulence,” ASME J. Fluids Eng., 136(6), p. 060901. [CrossRef]
Rashidi, S., Tamayol, A., Valipour, M. S., and Shokri, N., 2013, “Fluid Flow and Forced Convection Heat Transfer Around a Solid Cylinder Wrapped With a Porous Ring,” Int. J. Heat Mass Transfer, 63, pp. 91–100. [CrossRef]
Rashidi, S., Masoodi, R., Bovand, M., and Valipour, M. S., 2014, “Numerical Study of Flow Around and Through a Porous Diamond Cylinder With Different Apex Angels,” Int. J. Numer. Methods Heat Fluid Flow, 24(7), pp. 1504–1518. [CrossRef]
Rashidi, S., Bovand, M., Pop, I., and Valipour, M. S., 2014, “Numerical Simulation of Forced Convective Heat Transfer Past a Square Diamond-Shaped Porous Cylinder,” Transp. Porous Media, 102(2), pp. 207–225. [CrossRef]
Rashidi, S., Nouri-Borujerdi, A., Valipour, M. S., Ellahi, R., and Pop, I., 2015, “Stress-Jump and Continuity Interface Conditions for a Cylinder Embedded in a Porous Medium,” Transp. Porous Media (in press). [CrossRef]
Valipour, M. S., Rashidi, S., Bovand, M., and Masoodi, R., 2014, “Numerical Modeling of Flow Around and Through a Porous Cylinder With Diamond Cross Section,” Eur. J. Mech. B/Fluids, 46, pp. 74–81. [CrossRef]
Chatterjee, D., and Kumar Gupta, S., 2014, “Numerical Study of the Laminar Flow Past a Rotating Square Cylinder at Low Spinning Rates,” ASME J. Fluids Eng., 137(2), p. 021204. [CrossRef]
Dhiman, A. K., Chhabra, R. P., and Eswaran, V., 2005, “Flow and Heat Transfer Across a Confined Square Cylinder in the Steady Flow Regime: Effect of Peclet Number,” Int. J. Heat Mass Transfer, 48(21–22), pp. 4598–4614. [CrossRef]
Valipour, M. S., Masoodi, R., Rashidi, S., Bovand, M., and Mirhosseini, M., 2014, “A Numerical Study of Convection Around a Square Porous Cylinder Using Al2O3–H2O Nanofluid,” Therm. Sci., 18(4), pp. 1305–1314. [CrossRef]
Yen, S. C., and Yang, C. W., 2011, “Flow Patterns and Vortex Shedding Behavior Behind a Square Cylinder,” J. Wind Eng. Ind. Aerodyn., 99(8), pp. 868–878. [CrossRef]
Rahman, M. M., Öztop, H. F., Saidur, R., Mekhilef, S., and Al-Salem, K., 2013, “Finite Element Solution of MHD Mixed Convection in a Channel With a Fully or Partially Heated Cavity,” Comput. Fluids, 79, pp. 53–64. [CrossRef]
Barletta, A., Lazzari, S., Magyari, E., and Pop, I., 2008, “Mixed Convection With Heating Effects in a Vertical Porous Annulus With a Radially Varying Magnetic Field,” Int. J. Heat Mass Transfer, 51(25), pp. 5777–5784. [CrossRef]
Zare Ghadi, A., Goodarzian, H., Gorji-Bandpy, M., and Valipour, M. S., 2012, “Numerical Investigation of Magnetic Effect on Forced Convection Around Two-Dimensional Circular Cylinder Embedded in Porous Media,” Eng. Appl. Comput. Fluid Mech., 6(3), pp. 395–402. [CrossRef]
Valipour, M. S., Rashidi, S., and Masoodi, R., 2014, “Magnetohydrodynamics Flow and Heat Transfer Around a Solid Cylinder Wrapped With a Porous Ring,” ASME J. Heat Transfer, 136(6), p. 062601 [CrossRef]
Rashidi, A., Jazebi, F., and Brilakis, I., 2011, “Neuro-Fuzzy Genetic System for Selection of Construction Project Managers,” ASCE J. Constr. Eng. Manage., 137(1), pp. 17–29. [CrossRef]
Rashidi, A., Rashidi-Nejad, H., and Maghiar, M., 2014, “Productivity Estimation of Bulldozers Using Generalized Linear Mixed Models,” KSCE J. Civ. Eng., 18(6), pp. 1580–1589. [CrossRef]
Jazebi, F., and Rashidi, A., 2013, “An Automated Procedure for Selecting Project Managers in Construction Firms,” J. Civ. Eng. Manage., 19(1), pp. 97–106. [CrossRef]
Yoon, H. S., Chun, H. H., Ha, M. Y., and Lee, H. G., 2004, “A Numerical Study on the Fluid Flow and Heat Transfer Around a Circular Cylinder in an Aligned Magnetic Field,” Int. J. Heat Mass Transfer, 47(19–20), pp. 4075–4087. [CrossRef]
Sekhar, T. V. S., Sivakumar, R., Kumar, H., and Ravi kumar, T. V. R., 2007, “Effect of Aligned Magnetic Field on the Steady Viscous Flow Past a Circular Cylinder,” Appl. Math. Modell., 31(1), pp. 130–139. [CrossRef]
Rashidi, S., Dehghan, M., Ellahi, R., Riaz, M., and Jamal-Abad, M. T., 2015, “Study of Stream Wise Transverse Magnetic Fluid Flow With Heat Transfer Around an Obstacle Embedded in a Porous Medium,” J. Magn. Magn. Mater., 378, pp. 128–137. [CrossRef]
Grigoriadis, D. G. E., Sarris, I. E., and Kassinos, S. C., 2010, “MHD Flow Past a Circular Cylinder Using the Immersed Boundary Method,” Comput. Fluids, 39(2), pp. 345–358. [CrossRef]
Breuer, M., Bernsdorf, J., Zeiser, T., and Durst, F., 2000, “Accurate Computations of the Laminar Flow Past a Square Cylinder Based on Two Different Methods: Lattice-Boltzmann and Finite-Volume,” Int. J. Heat Fluid Flow, 21(2), pp. 186–196. [CrossRef]
Esfahani, J. A., and Shahabi, P. B., 2010, “Effect of Non-Uniform Heating on Entropy Generation for the Laminar Developing Pipe Flow of a High Prandtl Number Fluid,” Energy Convers. Manage., 51(11), pp. 2087–2097. [CrossRef]
Dulhani, J. P., Sarkar, S., and Dalal, A., 2014, “Effect of Angle of Incidence on Mixed Convective Wake Dynamics and Heat Transfer Past a Square Cylinder in Cross Flow at Re = 100,” Int. J. Heat Mass Transfer, 74, pp. 319–332. [CrossRef]
Selimefendigil, F., and Öztop, H. F., 2013, “Numerical Analysis of Laminar Pulsating Flow at a Backward Facing Step With an Upper Wall Mounted Adiabatic Thin Fin,” Comput. Fluids, 88, pp. 93–107. [CrossRef]
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York.


Grahic Jump Location
Fig. 1

Definition of the geometry and computational domain

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Fig. 2

Mesh distribution and subcomputational domains

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Fig. 3

Variation of wake length against Reynolds number

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Fig. 4

Comparison of computed Strouhal number with published literatures

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Fig. 5

Variation of Strouhal number as a function of Stuart number at Re = 100

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Fig. 6

Contours of streamline and vorticity for different Reynolds number (N = 0)

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Fig. 7

Contours of streamline and vorticity at different Stuart number (Re = 100)

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Fig. 8

Variation of critical Stuart number against Reynolds number

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Fig. 9

Variation of disappearance Stuart number against Reynolds number: (a) steady flow and (b) unsteady flow

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Fig. 10

Contour of Lorentz force just after the activation of the magnetic field




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