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Experiment of a thermal plume on an open cylinder

Published online by Cambridge University Press:  25 October 2023

Wei Zhang Open the ORCID record for Wei Zhang [Opens in a new window] ,
Bingchuan Nie Open the ORCID record for Bingchuan Nie [Opens in a new window]  and
Feng Xu Open the ORCID record for Feng Xu [Opens in a new window]
Wei Zhang
Affiliation:
School of Physical Science and Engineering, Beijing Jiaotong University, Beijing 100044, China
Bingchuan Nie
Affiliation:
School of Physical Science and Engineering, Beijing Jiaotong University, Beijing 100044, China
Feng Xu*
Affiliation:
School of Physical Science and Engineering, Beijing Jiaotong University, Beijing 100044, China
*
†Email addresses for correspondence: fxu@bjtu.edu.cn
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Abstract

In this study, we performed a set of experiments of the thermal plume on an open cylinder heated from below and a simple scaling analysis. The flow structure of the plume was visualized using the shadowgraph technique, and the temperature at specific points was measured using a thermistor. Transient plumes in a developing stage, an equilibrating stage and a fully developed stage were described. The new scaling laws of the stem radius and the velocity of the rising plume were presented, which are different from those on a two-dimensional heated plate due to the cylindrical effect and agree with experimental results. In the fully developed stage, there is a transition route of the plume from a steady to chaotic state with an increase in the Rayleigh number, which involves a series of bifurcations. A reverse bifurcation from a periodic (Ra = 1.17 × 106) back to a steady (Ra = 1.30 × 106) state has been observed in the experiment, which is referred to as the period bubbling bifurcation. Thus, the present experimental results validate the previous numerical results presented by Zhang et al. (Phys. Fluids, vol. 33 (6), 2021, 064110). The bifurcation diagram, spectral analysis and attractor are used to characterize the transitional plume. In addition, the heat and mass transfer have also been quantified.

JFM classification

Convection: Plumes/thermals
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 974 , 10 November 2023 , A6
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Atkinson, J.W. & Davidson, P.A. 2019 The evolution of laminar thermals. J. Fluid Mech. 878, 907–931.CrossRefGoogle Scholar
Batchelor, G.K. 1954 Heat convection and buoyancy effects in fluids. Q. J. R. Meteorol. Soc. 80, 339–358.CrossRefGoogle Scholar
Bhamidipati, N. & Woods, A.W. 2017 On the dynamics of starting plumes. J. Fluid Mech. 833, 1–12.CrossRefGoogle Scholar
Bier, M. & Bountis, T.C. 1984 Remerging Feigenbaum trees in dynamical systems. Phys. Lett. A 104, 239–244.CrossRefGoogle Scholar
Broomhead, D.S. & King, G.P. 1986 Extracting qualitative dynamics from experimental data. Physica D 20, 217–236.CrossRefGoogle Scholar
Chen, T.S. & Tzuoo, K.L. 1982 Vortex instability of free convection flow over horizontal and inclined surfaces. J. Heat Transfer 104, 637–643.CrossRefGoogle Scholar
Davaille, A., Limare, A., Touitou, F., Kumagai, I. & Vatteville, J. 2011 Anatomy of a laminar starting thermal plume at high Prandtl number. Exp. Fluids 50, 285–300.CrossRefGoogle Scholar
Fay, J.A. 1973 Buoyant plumes and wakes. Annu. Rev. Fluid Mech. 5, 151–160.CrossRefGoogle Scholar
Grassberger, P. & Procaccia, I. 1983 Characterization of strange attractors. Phys. Rev. Lett. 50, 346–349.CrossRefGoogle Scholar
Guha, A. & Sengupta, S. 2016 Effects of finiteness on the thermo-fluid-dynamics of natural convection above horizontal plates. Phys. Fluids 28 (6), 063603.CrossRefGoogle Scholar
Hasnaoui, M., Bilgen, E. & Vasseur, P. 1990 Natural convection above an array of open cavities heated from below. Numer. Heat Transfer A-Appl. 18, 463–482.CrossRefGoogle Scholar
Hattori, T., Armfield, S.W. & Kirkpatrick, M.P. 2012 Transitional ventilated filling box flow with a line heat source. Intl J. Heat Mass Transfer 55, 3650–3665.CrossRefGoogle Scholar
Hattori, T., Bartos, N., Norris, S.E., Kirkpatrick, M.P. & Armfield, S.W. 2013 Experimental and numerical investigation of unsteady behavior in the near-field of pure thermal planar plumes. Exp. Therm. Fluid Sci. 46, 139–150.CrossRefGoogle Scholar
Hilborn, R.C. 2001 Chaos and Nonlinear Dynamics, 2nd edn. Oxford University Press.Google Scholar
Hunt, R. & Bremer, T. 2011 Classical plume theory: 1937–2010 and beyond. J. Appl. Math. 76, 424–448.Google Scholar
Jiang, Y., Nie, B.C. & Xu, F. 2019 Scaling laws of buoyant flows on a suddenly heated horizontal plate. Intl Commun. Heat Mass Transfer 105, 58–64.CrossRefGoogle Scholar
Kaminski, E. & Jaupart, C. 2003 Laminar starting plumes in high-Prandtl number fluids. J. Fluid Mech. 478, 287–298.CrossRefGoogle Scholar
Khrapunov, E. & Chumakov, Y. 2020 Structure of the natural convective flow above to the horizontal surface with localized heating. Intl J. Heat Mass Transfer 152 (3), 119492.CrossRefGoogle Scholar
Kondrashov, A. & Burkova, E. 2018 Stationary convective regimes in a thin vertical layer under the local heating from below. Intl J. Heat Mass Transfer 118, 58–65.CrossRefGoogle Scholar
Kondrashov, A., Sboev, I. & Dunaev, P. 2016 Evolution of convective plumes adjacent to localized heat sources of various shapes. Intl J. Heat Mass Transfer 103, 298–304.CrossRefGoogle Scholar
Kondrashov, A., Sboev, I. & Dunaev, P. 2017 Heater shape effects on thermal plume formation. Intl J. Therm. Sci. 122, 85–91.CrossRefGoogle Scholar
Kozanoglu, B. & Lopez, J. 2007 Thermal boundary layer and the characteristic length on natural convection over a horizontal plate. Heat Mass Transfer 43, 333–339.CrossRefGoogle Scholar
Lewandowski, W.M., Bieszk, H. & Cieslinski, J. 1992 Free convection from horizontal screened plates. Heat Mass Transfer 27, 481–488.Google Scholar
List, E.J. 1982 Turbulent jets and plumes. Annu. Rev. Fluid Mech. 14, 189–212.CrossRefGoogle Scholar
Lopez, J.M. & Marques, F. 2013 Instabilities of plumes driven by localized heating. J. Fluid Mech. 736, 616–640.CrossRefGoogle Scholar
Mellado, J.P. 2012 Direct numerical simulation of free convection over a heated plate. J. Fluid Mech. 712, 418–450.CrossRefGoogle Scholar
Métivier, C., Li, C. & Magnin, A. 2017 Origin of the onset of Rayleigh-Bénard convection in a concentrated suspension of microgels with a yield stress behaviour. Phys. Fluids 29 (10), 104102.CrossRefGoogle Scholar
Moses, E., Zocchi, G. & Libchaber, A. 1993 An experimental study of laminar plumes. J. Fluid Mech. 251, 581–601.CrossRefGoogle Scholar
Olson, P., Schubert, G. & Anderson, C. 1993 Structure of axisymmetric mantle plumes. J. Geophys. Res. 98, 6829–6844.CrossRefGoogle Scholar
Patterson, J.C., Graham, T., Schöpf, W. & Armfield, S.W. 2002 Boundary layer development on a semi-infinite suddenly heated vertical plate. J. Fluid Mech. 453, 39–55.CrossRefGoogle Scholar
Patterson, J.C. & Imberger, J. 1980 Unsteady natural convection in a rectangular cavity. J. Fluid Mech. 100, 65–86.CrossRefGoogle Scholar
Pera, L. & Gebhart, B. 2006 Laminar plume interactions. J. Fluid Mech. 68, 259–271.CrossRefGoogle Scholar
Plourde, F., Pham, M.V., Kim, S.D. & Balachandar, S. 2008 Direct numerical simulations of a rapidly expanding thermal plume: structure and entrainment interaction. J. Fluid Mech. 604, 99–123.CrossRefGoogle Scholar
Qiao, M., Gao, Z. & Xu, F. 2021 Experimental study of transient convective flows from a suddenly heated groove. Intl J. Heat Mass Transfer 179, 121701.CrossRefGoogle Scholar
Qiao, M., Tian, Z.F., Nie, B.C. & Xu, F. 2018 a The route to chaos for plumes from a top-open cylinder heated from underneath. Phys. Fluids 30 (12), 124102.CrossRefGoogle Scholar
Qiao, M., Tian, Z.F., Yang, Q.S. & Xu, F. 2020 Transition to chaos for buoyant flows in a groove heated from below. Phys. Fluids 32 (5), 054104.CrossRefGoogle Scholar
Qiao, M., Xu, F. & Saha, S.C. 2018 b Numerical study of the transition to chaos of a buoyant plume from a two-dimensional open cavity heated from below. Appl. Math. Model. 61, 577–592.CrossRefGoogle Scholar
Rogers, M.C. & Morris, S.W. 2009 Natural versus forced convection in laminar starting plumes. Phys. Fluids 21, 356.CrossRefGoogle Scholar
Rotem, Z. & Claassen, L. 1969 Natural convection above unconfined horizontal surfaces. J. Fluid Mech. 38, 173–192.CrossRefGoogle Scholar
Rossby, H.T. 1965 On thermal convection driven by non-uniform heating from below: an experimental study. Deep-Sea Res. 12, 9–16.Google Scholar
Ruelle, D. & Takens, F. 1971 On the nature of turbulence. Commun. Math. Phys. 20, 167–192.CrossRefGoogle Scholar
Saxena, A., Kishor, V., Singh, S. & Srivastava, A. 2018 Experimental and numerical study on the onset of natural convection in a cavity open at the top. Phys. Fluids 30 (5), 057102.CrossRefGoogle Scholar
Shlien, D.J. 1976 Some laminar thermal and plume experiments. Phys. Fluids 19, 1089–1098.CrossRefGoogle Scholar
Shlien, D.J. 1978 Transition of the axisymmetric starting plume cap. Phys. Fluids 21 (12), 2154–2158.CrossRefGoogle Scholar
Sparrow, E.M., Husar, R.B. & Goldstein, R.J. 1970 Observations and other characteristics of thermals. J. Fluid Mech. 41, 793–800.CrossRefGoogle Scholar
Theerthan, S.A. & Arakeri, J.H. 2000 Planform structure and heat transfer in turbulent free convection over horizontal surfaces. Phys. Fluids 12, 884–894.CrossRefGoogle Scholar
Torrance, K.E., Orloff, L. & Rockett, J.A. 1969 Experiments on natural convection in enclosures with localized heating from below. J. Fluid Mech. 36, 21–31.CrossRefGoogle Scholar
Townsend, A.A. 1959 Temperature fluctuations over a heated horizontal surface. J. Fluid Mech. 5, 209–241.CrossRefGoogle Scholar
Turner, J.S. 1962 The starting plume in neutral surroundings. J. Fluid Mech. 13, 356–368.CrossRefGoogle Scholar
Vincent, A.P., Yuen, D.A. & Munqer, D. 2012 On the dynamics of 3-D single thermal plumes at various Prandtl numbers and Rayleigh numbers. Geophys. Astrophys. Fluid Dyn. 106, 138–156.CrossRefGoogle Scholar
Vouros, A. & Panidis, T. 2012 Statistical analysis of turbulent thermal free convection over a horizontal heated plate in an open top cavity. Exp. Therm. Fluid Sci. 36, 44–55.CrossRefGoogle Scholar
Xu, A., Shi, L. & Xi, H.D. 2019 Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection. Phys. Fluids 31 (12), 125101.CrossRefGoogle Scholar
Xu, F., Patterson, J.C. & Lei, C. 2008 An experimental study of the unsteady thermal flow around a thin fin on a sidewall of a differentially heated cavity. Intl J. Heat Fluid Flow 29, 1139–1153.CrossRefGoogle Scholar
Xu, F., Patterson, J.C. & Lei, C. 2009 Transient natural convection flows around a thin fin on the sidewall of a differentially heated cavity. J. Fluid Mech. 639, 261–290.CrossRefGoogle Scholar
Zhang, W., Qiao, M., Nie, B.C. & Xu, F. 2021 Period bubbling bifurcation and transition to chaotic state of convective flow on a top-open cylinder. Phys. Fluids 33 (6), 064110.CrossRefGoogle Scholar