# Flow Past Heated Bluff Bodies

## Abstract

Wakes behind heated cylinders, circular and square, have been experimentally investigated at low Reynolds numbers. The electrically heated cylinder is mounted in a vertical airflow facility such that the buoyancy aids the inertia of the main flow. The dimensionless parameters, namely, Reynolds number and Richardson number, are varied to examine flow behavior over a range of experimental conditions from the forced to the mixed convection regime. Laser schlieren has been used for visualization and analysis of the flow structures. The complete vortex-shedding sequence has been recorded using a high-speed camera. The dynamical characteristics of the vortical structures—their size, shape and phase, Strouhal number, and power spectra—are reported. On heating, the changes in the organized structures with respect to shape, size, and their movement are readily perceived from the instantaneous schlieren images before they reduce to a steady plume. The effect of cylinder orientation and oscillation on the wake are also discussed.

### Key words

Bluff bodies Vortex shedding Buoyancy Strouhal number Richardson number Orientation Inline oscillations Power spectra.### References

- 1.H.M. Badr, Laminar combined convection from a horizontal cylinder-parallel and contra flow regimes, Int J Heat Mass Transfer, Vol. 27(1), pp. 15–27, 1984.Google Scholar
- 2.A. Ben-Yaker and R.K. Hanson, Ultra-fast-framing schlieren system for studies of the time evolution of jets in supersonic cross flows, Expt. in Fluids, Vol. 32, pp. 652–666, 2002.Google Scholar
- 3.J. M. Chen and C. H. Liu, Vortex shedding and surface pressure on a square cylinder at incidence to a uniform air stream, Int. J. Heat Fluid Flow, Vol. 20, p. 592, 1999.Google Scholar
- 4.O. Cetiner and D. Rockwell, Streamwise oscillations of a cylinder in a steady current, Part 1. locked-on states of vortex formation and loading, J. Fluid Mech., Vol.427, pp.1–28, 2001. Also, A. Ongoren and D. Rockwell, Flow structure from an oscillating cylinder, part 2. Mode competition in the near wake, J. Fluid Mech., Vol.191, pp.225–245, 1988.Google Scholar
- 5.K.S. Chang and J.Y. Sa, The effect of buoyancy on the vortex shedding in the near wake of a circular cylinder, J Fluid Mech., Vol. 220, pp. 253–266, 1990.Google Scholar
- 6.F. Dumouchel, J.C. Lecordier and P. Paranthoen, The effective Reynolds number of a heated cylinder, Int J Heat Mass Transfer, Vol. 41(12), pp. 1787–1794, 1998.Google Scholar
- 7.S. Dutta, K. Muralidhar, and P. K. Panigrahi, Influence of the orientation of a square cylinder on the wake properties, Expt. Fluids, Vol. 34, p. 16, 2003.Google Scholar
- 8.C. Gau, S.X. Wu, and H.S. Su, Synchronization of vortex shedding and heat transfer enhancement over a heated cylinder oscillating with small amplitude in streamwise direction, J. Heat Transfer Trans. ASME, Vol.123, pp.1139–1148, 2001.Google Scholar
- 9.R. Govardhan and C. H. K. Williamson, Mean and fluctuating velocity fields in the wake of a freely vibrating cylinder, J. Fluids Struct., Vol. 15, p. 489, 2001.Google Scholar
- 10.O. M. Griffin, A note on bluff body vortex formation, J. Fluid Mech., Vol. 284, p. 217, 1995.Google Scholar
- 11.K. Hatanka and M. Kawahara,, A numerical study of vortex shedding around a heated-cooled cylinder by three-step Taylor-Galerkin Method, Int. J. Numerical For Methods in Fluids, Vol. 21, pp. 857–867, 1995.Google Scholar
- 12.D. R. Jonassen, G. S. Settles, and M. D. Tronosky, Schlieren PIV for turbulent flows, Opt. Lasers Engg., Vol. 44, p. 190, 2006.Google Scholar
- 13.W. Kim and J. Y. Yoo, Dynamics of vortex lock-on in a perturbed cylinder wake, Phys.. Fluids, Vol. 18, 074103(1–22), 2006.Google Scholar
- 14.C. W. Knisely, Strouhal numbers of rectangular cylinders at incidence: A review and new data, J. Fluids Struct., Vol. 4, p. 371, 1990.Google Scholar
- 15.E. Konstantinidis, S. Balabani, M. Yianneskis, The effect of flow perturbations on the near wake characteristics of a circular cylinder. J. Fluids Struct., Vol. 18, pp. 367–386, 2003.Google Scholar
- 16.J.C. Lecordier, L.W.B. Browne, S.L. Masson, F. Dumouchel and P. Paranthoen, Control of vortex shedding by thermal effect at low Reynolds numbers, Expt. Th. Fluid Sc., Vol. 21, pp. 227–237, 2000.Google Scholar
- 17.C. Lin and S.C. Hsieh, Convection velocity of vortex structures in the near wake of a circular cylinder, ASCE J. Engg. Mech., Vol. 129(10), pp. 1108–1118, 2003.Google Scholar
- 18.S.C. Luo, Y.T. Chew and Y.T. Ng, Characteristics of square cylinder wake transition flow, Phys.. Fluids, Vol. 15(9), pp. 2549–2559, 2003.Google Scholar
- 19.W.J.P.M. Maas, C.C.M. Rindt CCM and A.A. van Steenhoven, The influence of heat on the 3D-transition of the von Karman vortex street, Int J Heat Mass Transfer, Vol. 46, pp. 3069–3081, 2003.Google Scholar
- 20.J.H. Merkin, Mixed convection from a horizontal circular cylinder, Int J Heat Mass Transfer, Vol. 20, pp. 73–77, 1977.Google Scholar
- 21.N. Michaux-Leblond and M. Belorgey, Near wake behavior of a heated circular cylinder: viscosity-buoyancy duality, Exp. Therm. Fluid Sci., Vol. 15, pp. 91–100, 1997.Google Scholar
- 22.K. Noto, H. Ishida H and R. Matsumoto, A breakdown of the Karman vortex street due to natural convection, pp. 348–352,
*Flow Visualization*, Springer, Berlin, 1985.Google Scholar - 23.B. W. van Oudheusden, F. Scarano, N. P. van Hinsberg, and D. W. Watt, Phase-resolved characterization of vortex shedding in the near wake of a square-section cylinder at incidence, Expt. Fluids, Vol. 39, p. 86, 2005.Google Scholar
- 24.B.S.V. Patnaik, P.A.A. Narayana and K.N. Seetharamu,Numerical simulation of vortex shedding past a circular cylinder under the influence of buoyancy, Int. J. of Heat and Mass Transfer, Vol. 42, pp. 3495–3507, 1999.Google Scholar
- 25.J. Robichaux, S. Balachandar and S.P. Vanka, Three dimensional Floquet instability of the wake of a square cylinder, Phys. Fluids, Vol. 11(3), pp. 560–578, 1999.Google Scholar
- 26.M. Schumm, E. Berger and P.A. Monkewitz, Self-excited oscillations in the wake of two-dimensional bluff bodies and their control. J Fluid Mech., Vol. 271, pp. 17–53, 1994.Google Scholar
- 27.S. K. Singh, P. K. Panigrahi, and K. Muralidhar, Effect of buoyancy on the wakes of circular and square cylinders: A schlieren-interferometric study, Expt. Fluids, Vol. 43, p. 101, 2007. Also, 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, Vol. 22(5), 054107, 01–18, (2010).Google Scholar
- 28.K.M. Smith and J.C. Dutton, A procedure for turbulent structure convection velocity measurements using time-correlated images, Expt. Fluids, Vol. 27, pp. 244–250, 1999.Google Scholar
- 29.A. Sohankar, C. Norberg, and L. Davidson, Low Reynolds number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding and outlet boundary condition, Int. J. Numer. Methods Fluids, Vol. 26, p. 39, 1998.Google Scholar
- 30.A. Sohankar, C. Norberg and L. Davidson, Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers, Phys. Fluids, Vol. 11(2), pp. 288–306, 1999.Google Scholar
- 31.A. Wang, Z. Travnicek and K.C. Chia, On the relationship of effective Reynolds number and Strouhal number for the laminar vortex shedding of a heated circular cylinder, Phys. Fluids Vol. 12(6), pp. 1401–1410, 2000.Google Scholar