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Vortex-Shedding Suppression in Mixed Convective Flow past a Heated Square Cylinder

Authors: A. Rashid, N. Hasan

Abstract:

The present study investigates numerically the phenomenon of vortex-shedding and its suppression in twodimensional mixed convective flow past a square cylinder under the joint influence of buoyancy and free-stream orientation with respect to gravity. The numerical experiments have been conducted at a fixed Reynolds number (Re) of 100 and Prandtl number (Pr) of 0.71, while Richardson number (Ri) is varied from 0 to 1.6 and freestream orientation, α, is kept in the range 0o≤ α ≤ 90o, with 0o corresponding to an upward flow and 90o representing a cross-flow scenario, respectively. The continuity, momentum and energy equations, subject to Boussinesq approximation, are discretized using a finite difference method and are solved by a semi-explicit pressure correction scheme. The critical Richardson number, leading to the suppression of the vortex-shedding (Ric), is estimated by using Stuart-Landau theory at various free-stream orientations and the neutral curve is obtained in the Ri-α plane. The neutral curve exhibits an interesting non-monotonic behavior with Ric first increasing with increasing values of α upto 45o and then decreasing till 70o. Beyond 70o, the neutral curve again exhibits a sharp increasing asymptotic trend with Ric approaching very large values as α approaches 90o. The suppression of vortex shedding is not observed at α = 90o (cross-flow). In the unsteady flow regime, the Strouhal number (St) increases with the increase in Richardson number.

Keywords: bluff body, buoyancy, free-stream orientation, vortex-shedding.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334389

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References:


[1] J. H. Gerrard, "The mechanism of the formation region of vortices behind bluff bodies", Journal of fluid mechanics, vol. 25, part 2, 1966, pp 401-413.
[2] E. A. Anderson and A. A. Szewczyk, "Effects of a splitter plate on the near wake of a circular cylinder in 2 and 3-dimensional flow configurations". Experiments in Fluids 23, 1997, pp 161-174.
[3] S. Mittal, "Effect of a ÔÇÿÔÇÿslip-- splitter plate on vortex shedding from a cylinder", Physics of fluids vol. 15, No. 3, 2003, pp 817-820.
[4] S. E. Razavi, V. Farhangmehe and F. Barar, "Impact of a splitter plate on flow and heat transfer around circular cylinder at low Reynolds numbers", Journal of applied sciences 8(7), 2008, pp 1286-1292.
[5] R. A. Kumar, C-H Sohn and B. H. L. Gowda, "Passive Control of Vortex-Induced Vibrations: An Overview", Recent patents on mechanical engineering, vol. 1, No. 1, Bentham Science Publishers Ltd., 2008, pp 1-11.
[6] Z. Chen and N. Aubry, "Active control of cylinder wake", Communications in nonlinear science and numerical simulation 10, 2005, pp 205-216.
[7] L. Cheng, Y. Zhou and M. M. Zhang, "Controlled vortex-induced vibration on a fix-supported flexible cylinder in cross-flow", Journal of sound and vibration 292, 2005, pp 279-299.
[8] J. Seidel, S. Siegel, C. Fagley, K. Cohen and T. McLaughlin, "Feedback control of a circular cylinder wake", Proc. IMechE Vol. 223 Part G: J. Aerospace Engineering, 2008, pp 379-392.
[9] M. Coutanceau and C. Menard, "Influence of rotation on the near wake development behind an impulsive started circular cylinder", J. fluid mech., 158, 1985, pp 399-446.
[10] S. Mittal, "Control of flow past bluff bodies using rotating control cylinders", Journal of fluids and structures 15, 2001, pp 291-326.
[11] D. Stojkovic, M. Breuer and F. Durst, "Effect of high rotation rates on the laminar flow around a circular cylinder", Physics of fluids vol. 14 No. 9, 2002, pp 3160-3178.
[12] S. Mittal and B. Kumar, "Flow past a rotating cylinder", J. fluid mech. Vol. 476, 2003, pp 303-344.
[13] A. Sharma and V. Eswaran, "Effect of aiding and opposing buoyancy on the heat and fluid flow across a square cylinder at Re = 100", Numerical heat transfer, part A, 45, 2004, pp 601-624.
[14] A. Sharma and V. Eswaran, "Effect of channel-confinement and aiding/opposing buoyancy on the two-dimensional laminar flow and heat transfer across a square cylinder", International journal of heat and mass transfer 48, 2005, pp 5310-5322.
[15] S. Bhattacharyya and S. Mahapatra, "Vortex shedding around a heated square cylinder under the influence of buoyancy", Heat mass transfer 41, 2005, pp 824-833.
[16] S. K. Singh, P. K. Panigrahi and K. Muralidhar, "Effect of buoyancy on the wakes of circular and square cylinders: a schlieren-interferometric study", Exp. fluids 43, 2007, pp 101-123.
[17] A. A. Kakade, S. K. Singh, P. K. Panigrahi and K. Muralidhar, "Schlieren investigation of the square cylinder wake: joint influence of buoyancy and orientation", Physics of fluids 22, 054107, 2010, pp 1-18.
[18] D.J. Tritton, "Physical fluid dynamics", ELBS edition chapter 13, 1979, pp 127-130.
[19] Z. U. A. Warsi, J. F. Thompson and C. M. Mastin, "Numerical Grid Generation", 1984.
[20] N. Hasan and S. Sanghi, "The dynamics of two-dimensional buoyancy driven convection in a horizontal rotating cylinder", Journal of heat transfer, vol. 126, 2004, pp 963-984.
[21] N. Hasan, S. F. Anwer and S. Sanghi, "On the outflow boundary condition for external incompressible flows: A new approach", Journal of computational physics 206, 2005, pp 661-683.
[22] C. M. Rhie and W. L. Chow, "Numerical study of the turbulent flow past an airfoil with trailing edge separation", AIAA J. vol. 21, issue 11, 1983, pp 1525-1532.
[23] A. A. Amsden and F. H. Harlow, "The SMAC method: A numerical technique for calculating incompressible fluid flows", Los Alamos scientific report, LA 4370, 1970.
[24] S. W. Kim and T. J. Benson, "Comparison of the SMAC, PISO and iterative time advancing schemes for unsteady flows", Computers and fluids, vol. 21, issue 3, 1992, pp 435-454.
[25] L. Cheng and S. Armfield, "A simplified marker and cell method for unsteady flows on non-staggered grids", International journal for numerical methods in fluids, Vol. 21, issue 1, 1995, pp 15-34.
[26] I. Orlanski, "A simple boundary condition for unbounded hyperbolic flows", Journal of computational physics vol. 21, 1976, pp 251-269.
[27] P. M. Gresho, "Incompressible fluid dynamics: some fundamental formulation issues", Annual review of fluid mechanics, vol. 23, 1991, pp 413-453.
[28] A. Sohankar, C. Norberg and L. Davidson, "Low-Reynolds-number flow around a cylinder at incidence: study of blockage, onset of vortex shedding and outlet boundary condition", International journal for numerical methods in fluids, vol. 26, 1998, pp 39-56.
[29] R. Ranjan, A. Dalal and G. Biswas, "A numerical study of fluid flow and heat transfer around a square cylinder at incidence using unstructured grids", Numerical heat transfer, part A, 54, 2008, pp 890-913.
[30] P. G. Drazin and W. H. Reid, "Hydrodynamic stability", Cambridge university press, chapter 7, 1981, pp 370-375.
[31] S. Turki, H. Abbassi, S. B. Nasrallah, "Two-dimensional laminar fluid flow and heat transfer in a channel with a built-in heated square cylinder", International journal of thermal sciences 42, 2003, pp 1105- 1113.