Numerical study of vortex shedding in viscoelastic flow past an unconfined square cylinder

Mahmood Norouzi; Seyed Rasoul Varedi; Mahdi Zamani

Korea-Australia Rheology Journal, Vol.27, No.3, 213-225, August, 2015

DOI10.1007/s13367-015-0022-z Export Citation

Numerical study of vortex shedding in viscoelastic flow past an unconfined square cylinder

Mahmood Norouzi^†, Seyed Rasoul Varedi, and Mahdi Zamani¹

Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
¹Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

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In this paper, the periodic viscoelastic shedding flow of Giesekus fluid past an unconfined square cylinder is investigated numerically for the first time. The global quantities such as lift coefficient, Strouhal number and the detailed kinetic and kinematic variables like normal stress differences and streamlines have been obtained in order to investigate the flow pattern of viscoelastic flow. The effects of Reynolds number and polymer concentrations have been clarified in the periodic viscoelastic flow regime. Our particular interest is the effect of mobility parameter on the stability of two dimensional viscoelastic flows past an unconfined square cylinder. To fulfill this aim, the mobility parameter has been increased from 0 to 0.5 for different polymer concentrations. Results reveal that mobility factor noticeably affects the amplitude of lift coefficient and shedding frequency more strongly at higher polymer concentrations.

Keywords:square cylinder;vortex shedding;viscoelastic flow;mobility factor;polymer concentration

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[1] Balachandar S, Parker S, Phys. Fluids, 14, 3714 (2002)

[2] Bird RB, Wiest JM, Ann. Rev. Fluid Mech., 27, 169 (1995)

[3] Coelho PM, Pinho FT, J. Non-Newton. Fluid Mech., 110(2-3), 143 (2003)

[4] Coelho PM, Pinho FT, J. Non-Newton. Fluid Mech., 110(2-3), 177 (2003)

[5] Courant R, Isaacson E, Rees M, Pure Appl. Math., 5, 243 (1952)

[6] Franke R, Rodi W, Schonung B, J. Wind Eng. Ind. Aerodynamics, 35, 237 (1990)

[7] Giesekus H, 1994, Phanomenologische rheologie: eine Einfuhrung, Springer, Berlin.

[8] Jackson CP, J. Fluid Mech., 182, 23 (1987)

[9] Kim JM, Ahn KH, Lee SJ, Korea-Aust. Rheol. J., 21(1), 27 (2009)

[10] Leweke T, Provansal M, J. Fluid Mech., 288, 265 (1995)

[11] Luo SC, Tong XH, Khoo BC, J. Fluid Structures, 23, 227 (2007)

[12] Malvandi A, Ganji D, Int. J. Therm. Sci., 84, 196 (2014)

[13] McKinley GH, Armstrong RC, Brown RA, Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci., 344, 265 (1993)

[14] Norouzi M, Varedi SR, Maghrebi MJ, Shahmardan MM, J. Non-Newton. Fluid Mech., 197, 31 (2013)

[15] Oldroyd JG, Proc. Royal Soc. London, Series A: Math. Phys. Sci., 200, 523 (1950)

[16] Oliveira PJ, J. Non-Newton. Fluid Mech., 101(1-3), 113 (2001)

[17] Patankar SV, Spalding DB, Int. J. Heat Mass Transf., 15, 1787 (1972)

[18] Phan-Thien N, 2002, Understanding viscoelasticity: basics of rheology, Springer, Berlin.

[19] Richter D, Iaccarino G, Shaqfeh ES, J. Fluid Mech., 651, 415 (2010)

[20] Robichaux J, Balachandar S, Vanka SP, Phys. Fluids, 11, 560 (1999)

[21] Saha A, Biswas G, Muralidhar K, J. Eng. Mech., 125, 359 (1999)

[22] Saha A, Biswas G, Muralidhar K, Int. J. Heat Fluid Flow, 24, 54 (2003)

[23] Sahin M, Owens RG, J. Non-Newton. Fluid Mech., 123(2-3), 121 (2004)

[24] Sahu AK, Chhabra RP, Eswaran V, J. Non-Newton. Fluid Mech., 160(2-3), 157 (2009)

[25] Sahu AK, Chhabra RP, Eswaran V, J. Non-Newton. Fluid Mech., 165(13-14), 752 (2010)

[26] Sharma A, Eswaran V, Numer. Heat Transf. A-Appl., 45, 247 (2004)

[27] Sheard GJ, Fitzgerald MJ, Ryan K, J. Fluid Mech., 630, 43 (2009)

[28] Sohankar A, Norberg C, Davidson L, Phys. Fluids, 11, 288 (1999)

[29] Tamura T, Kuwahara K, J. Wind Eng. Ind. Aerodynamics, 33, 161 (1990)

[30] Usui H, Shibata T, Sanu Y, J. Chem. Eng. Jpn., 13, 77 (1980)

[31] Versteeg HK, Malalasekera W, 2007, An introduction to computational fluid dynamics: the finite volume method, Pearson Education, Harlow.

[32] Williamson C, Phys. Fluids, 31, 2742 (1988)

[33] Williamson CH, J. Fluid Mech., 328, 345 (1996)

[34] XUE SC, PHANTHIEN N, TANNER RI, J. Non-Newton. Fluid Mech., 59(2-3), 191 (1995)

[35] Zhang L, Balachandar S, J. Fluids Eng., 128, 1101 (2006)