Hostname: page-component-6b989bf9dc-wj8jn Total loading time: 0 Render date: 2024-04-13T19:08:05.123Z Has data issue: false hasContentIssue false

Thermal effects on the wake of a heated circular cylinder operating in mixed convection regime

Published online by Cambridge University Press:  06 October 2011

H. Hu*
Department of Aerospace Engineering, Iowa State University, Ames, IA 50011, USA
M. M. Koochesfahani
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA
Email address for correspondence:


The thermal effects on the wake flow behind a heated circular cylinder operating in the mixed convection regime were investigated experimentally in the present study. The experiments were conducted in a vertical water channel with the heated cylinder placed horizontally and the flow approaching the cylinder downwards. With such a flow arrangement, the direction of the thermally induced buoyancy force acting on the fluid surrounding the heated cylinder would be opposite to the approach flow. During the experiments, the temperature and Reynolds number of the approach flow were held constant. By adjusting the surface temperature of the heated cylinder, the corresponding Richardson number () was varied between 0.0 (unheated) and 1.04, resulting in a change in the heat transfer process from forced convection to mixed convection. A novel flow diagnostic technique, molecular tagging velocimetry and thermometry (MTV&T), was used for qualitative flow visualization of thermally induced flow structures and quantitative, simultaneous measurements of flow velocity and temperature distributions in the wake of the heated cylinder. With increasing temperature of the heated cylinder (i.e. Richardson number), significant modifications of the wake flow pattern and wake vortex shedding process were clearly revealed. When the Richardson number was relatively small (), the vortex shedding process in the wake of the heated cylinder was found to be quite similar to that of an unheated cylinder. As the Richardson number increased to , the wake vortex shedding process was found to be ‘delayed’, with the wake vortex structures beginning to shed much further downstream. As the Richardson number approached unity (), instead of having ‘Kármán’ vortices shedding alternately at the two sides of the heated cylinder, concurrent shedding of smaller vortex structures was observed in the near wake of the heated cylinder. The smaller vortex structures were found to behave more like ‘Kelvin–Helmholtz’ vortices than ‘Kármán’ vortices, and adjacent small vortices would merge to form larger vortex structures further downstream. It was also found that the shedding frequency of the wake vortex structures decreased with increasing Richardson number. The wake closure length and the drag coefficient of the heated cylinder were found initially to decrease slightly when the Richardson number was relatively small (), and then to increase monotonically with increasing Richardson number as the Richardson number became relatively large (). The average Nusselt number () of the heated cylinder was found to decrease almost linearly with increasing Richardson number.

Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


1. Badr, H. M. 1983 A theoretical study of laminar mixed convection from a horizontal cylinder in a cross stream. Intl J. Heat Mass Transfer 26, 639653.CrossRefGoogle Scholar
2. Badr, H. M. 1984 Laminar combined convection a horizontal cylinder – parallel and contra flow regimes. Intl J. Heat Mass Transfer 27, 1527.CrossRefGoogle Scholar
3. Berger, E. & Wille, R. 1972 Periodic flow phenomena. Annu. Rev. Fluid Mech. 4, 313.CrossRefGoogle Scholar
4. Bohl, D. & Koochesfahani, M. M. 2009 MTV measurements of the vortical field in the wake of an aerofoil oscillating at high reduced frequency. J. Fluid Mech. 620, 6388.CrossRefGoogle Scholar
5. Chang, K. S. & Sa, J. Y. 1990 The effect of buoyancy on vortex shedding in the near wake of a circular cylinder. J. Fluid Mech. 220, 253266.CrossRefGoogle Scholar
6. Dumouchel, F., Lecordier, J. C. & Paranthoen, P. 1998 The effective Reynolds number of a heated cylinder. Intl J. Heat Mass Transfer 40 (12), 17871794.CrossRefGoogle Scholar
7. Ferraudi, G. J. 1988 Elements of Inorganic Photochemistry. Wiley-Interscience.Google Scholar
8. Gendrich, C. P. & Koochesfahani, M. M. 1996 A spatial correlation technique for estimating velocity fields using molecular tagging velocimetry (MTV). Exp. Fluids 22 (1), 6777.CrossRefGoogle Scholar
9. Gendrich, C. P., Koochesfahani, M. M. & Nocera, D. G. 1997 Molecular tagging velocimetry and other novel application of a new phosphorescent supramolecule. Exp. Fluids 23, 361372.CrossRefGoogle Scholar
10. Hartmann, W. K., Gray, M. H. B., Ponce, A. & Nocera, D. G. 1996 Substrate induced phosphorescence from cyclodextrin–lumophore host–guest complex. Inorg. Chim. Acta 243, 239248.CrossRefGoogle Scholar
11. Hatton, A. P., James, D. D. & Swire, H. W. 1970 Combined forced and nature convection with low speed air flow over horizontal cylinders. J. Fluid Mech. 42, 1731.CrossRefGoogle Scholar
12. Hu, H., Jin, Z., Nocera, D., Lum, C. & Koochesfahani, M. 2010 Experimental investigations of micro-scale flow and heat transfer phenomena by using molecular tagging techniques. Meas. Sci. Technol. 21 (8) 085401(15pp).CrossRefGoogle Scholar
13. Hu, H. & Koochesfahani, M. M. 2003 A novel technique for quantitative temperature mapping in liquid by measuring the lifetime of laser induced phosphorescence. J. Vis. 6 (2), 143153.CrossRefGoogle Scholar
14. Hu, H. & Koochesfahani, M. M. 2005 The wake behavior behind a heated cylinder in forced and mixed convection regimes. In ASME Summer Heat Transfer Conference, San Francisco, CA, USA, 17–22 July 2005, ASME-HT2005-72766.Google Scholar
15. Hu, H. & Koochesfahani, M. M. 2006 Molecular tagging velocimetry and thermometry (MTV&T) technique and its application to the wake of a heated circular cylinder. Meas. Sci. Technol. 17 (6), 12691281.CrossRefGoogle Scholar
16. Hu, H., Lum, C. & Koochesfahani, M. M. 2006 Molecular tagging thermometry with adjustable temperature sensitivity. Exp. Fluids 40 (5), 753763.CrossRefGoogle Scholar
17. Incropera, F. P. & Dewitt, D. 2001 Introduction to Heat Transfer, 4th edn. John Wiley & Sons.Google Scholar
18. Kieft, R. N., Rindt, C. C. M. & van Steenhoven, A. A. 1999 The wake behaviour behind a heated horizontal cylinder. Exp. Therm. Fluid Sci. 19, 193193.CrossRefGoogle Scholar
19. Koochesfahani, M. M. 1999 Molecular tagging velocimetry (MTV): progress and applications. AIAA Paper No. AIAA-99-3786.CrossRefGoogle Scholar
20. Koochesfahani, M. M., Cohn, R. K., Gendrich, C. P. & Nocera, D. G. 1996 Molecular tagging diagnostics for the study of kinematics and mixing in liquid phase flows. In Proceedings of the 8th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 8–11 July 1996, vol. I, pp. 1.2.1–1.2.12; Also in Developments in Laser Techniques and Fluid Mechanics, 1997 (ed. R. J. Adrian, D. F. G. Durao, F. Durst, M. V. Heitor, M. Maeda, J. Whitelaw), chapter 2, section 1, p. 125. Springer.Google Scholar
21. Koochesfahani, M. M. & Nocera, D. 2007 Molecular tagging velocimetry. In Handbook of Experimental Fluid Dynamics (ed. Foss, J., Tropea, C. & Yarin, A. ), chapter 5.4. Springer.Google Scholar
22. Krauce, J. R. & Tariuk, J. D. 1985 An interferometer study of mixed convection from a horizontal cylinder. In Proceedings of 23rd National Heat Transfer Conference, Denver, Colorado, 1985.Google Scholar
23. Maas, W. J. P. M., Rindt, C. C. & van Steenhoven, A. A. 2003 The influence of heat on the 3D-transition of von Kármán vortex street. Intl J. Heat Mass Transfer 46, 30693081.CrossRefGoogle Scholar
24. Michaux-Leblond, N. & Belorgey, M. 1997 Near wake behaviour of a heated circular cylinder: viscosity–buoyancy duality. Exp. Therm. Fluid Sci. 15, 91100.CrossRefGoogle Scholar
25. Morgan, V. T. 1975 The overall heat transfer from smooth circular cylinders. Adv. Heat Transfer 11, 199264.CrossRefGoogle Scholar
26. Noto, K., Ishida, H. & Matsumoto, R. 1985 A breakdown of the Kármán vortex street due to the nature convection. In Flow Visualization III (ed. Yang, W. J. ), pp. 348352. Springer.Google Scholar
27. Oertel, H. Jr 1990 Wakes behind blunt bodies. Annu. Rev. Fluid Mech. 22, 539564.CrossRefGoogle Scholar
28. Oosthuizen, P. H. & Madan, S. 1970 Combined convective heat transfer from horizontal cylinders in air. J. Heat Transfer 92, 11941196.CrossRefGoogle Scholar
29. Oosthuizen, P. H. & Madan, S. 1971 The effect of flow direction on combined convective heat transfer from cylinders to air. J. Heat Transfer 93, 240242.CrossRefGoogle Scholar
30. Park, H. G., Dabiri, D. & Gharib, M. 2001 Digital particle image velocimetry/thermometry and application to the wake of a heated circular cylinder. Exp. Fluids 30, 327338.CrossRefGoogle Scholar
31. Ponce, A., Wong, P. A., Way, J. J. & Nocera, D. G. 1993 Intense phosphorescence trigged by alcohol upon formation of a cyclodextrin ternary complex. J. Phys. Chem. 97, 1113711142.CrossRefGoogle Scholar
32. Pringsheim, P. 1949 Fluorescence and Phosphorescence. Interscience.Google Scholar
33. Roshko, A. 1954 On the development of turbulent wakes from vortex streets. NACA Report 1191.Google Scholar
34. Schlichting, H. 1979 Boundary-Layer Theory, 7th edn. McGraw-Hill.Google Scholar
35. Shafii, M. B., Lum, C. L. & Koochesfahani, M. M. 2010 In-situ LIF temperature measurements in aqueous ammonium chloride solution during uni-directional solidification. Exp. Fluids 48, 651662.CrossRefGoogle Scholar
36. van Steenhoven, A. A. & Rindt, C. C. M. 2003 Flow transition behind a heated cylinder. Intl J. Heat Fluid Flow 24, 322333.CrossRefGoogle Scholar
37. Thomson, S. L. & Maynes, D. 2001 Spatially resolved temperature measurement in a liquid using laser induced phosphorescence. J. Fluid Engng 123, 293302.CrossRefGoogle Scholar
38. Vít, T., Ren, M., Travnicek, Z., Marsik, F. & Rindt, C. C. M. 2007 The influence of temperature gradient on the Strouhal–Reynolds number relationship for water and air. Exp. Therm. Fluid Sci. 31, 751760.CrossRefGoogle Scholar
39. Wang, A., Travnicek, Z. & Chia, K. 2000 On the relationship of effective Reynolds number and Strouhal number for the laminar vortex shedding of a heated circular cylinder. Phys. Fluids 12 (6), 14011410.CrossRefGoogle Scholar
40. Williamson, C. H. K. 1988 Defining a universal and continuous Strouhal–Reynolds number relationship for the laminar vortex shedding of a circular cylinder. Phys. Fluids 31 (10), 27422744.CrossRefGoogle Scholar
41. Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477526.CrossRefGoogle Scholar
42. Xie, Y., Hu, H. & Ganapathysubramanian, B. 2010 Phase transitions in vortex shedding in the wake of a heated circular cylinder at low Reynolds number. In Proceedings of 47th Annual Technical Meeting of Society of Engineering Science, 3–6 October, 2010, Ames, Iowa.Google Scholar
43. Zdravkovich, M. 1997 Flow Around Circular Cylinders, vol. 1. Oxford University Press.CrossRefGoogle Scholar
44. Zhukauskas, A. 1972 Heat transfer from tubes in cross flow. In Advances in Heat Transfer (ed. Hartnett, J. P. & Irvine, T. F. Jr ), vol. 8. Academic.Google Scholar