Abstract
Processes of the onset oscillation in the thermocapillary convection under the Earth's gravity are investigated by the numerical simulation and experiments in a floating half zone of large Prandtl number with different volume ratio. Both computational and experimental results show that the steady and axisymmetric convection turns to the oscillatory convection ofm=1 for the slender liquid bridge, and to the oscillatory convection before a steady and 3D asymmetric state for the case of a fat liquid bridge. It implies that, there are two critical Marangoni numbers related, respectively, to these two bifurcation transitions for the fat liquid bridge. The computational results agree with the results of ground-based experiments.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chun CH, West W. Experiments on the transition from the steady to the oscillatory Marangoni-convection of a floating zone under reduced gravity effect.Acta Astronautica, 1979, 6(9): 1073–1082
Preisser F, Schwabe D, Scharmm A. Steady and thermocapillary convection in liquid columns with free cylindrical surface.J Fluid Mechanics, 1983, 126: 545–567
Cao ZH, You HT, Tang ZM, et al. Experimental investigation of thermocapillary convection in half floating zone.Adv Space Res, 1991, 11(7): 229–232
Smith MK, Davis SH. Instabilities of dynamic thermocapillary liquid layers, Part I: Convective instabilities.J Fluid Mech, 1983, 132: 119–144
Xu JJ, Davis SH. Convective thermocapillary instability in liquid bridges.Phys Fluid, 1984, 27(5): 1102–1107
Wanschura M, Shevtsova VM, KuhlmannHC, et al. Convective instability mechanisms in thermocapillary liquid bridges.J Phys Fluids, 1995, 7(5): 912–925
Chen QS, Hu WR. Effect of liquid bridge volume on instability of floating half zone convection.International J Heat and Mass Transfer, 1998, 41(5): 825–837
Rupp R, Muller G, Neumann G. Three-dimensional time dependent modeling of the Marangoni convection in zone melting configurations for gas.J Crystal Growth, 1989, 97(1): 34–41
Levenstam M, Amberg G. Hydrodynamical instabilities of thermocapillary flow in a half-zone.J Fluid Mech, 1995, 297: 357–372
Savino R, Monti R. Oscillatory Marangoni convection in cylindrical liquid bridge.Phys Fluids, 1996, 8(1): 2906–2921
Tang ZM, Hu RW. Influence of liquid bridge volume on the onset of oscillation in floating half-zone convection III: Three-dimensional model.J Crystal Growth, 1999, 207(3): 239–246
Wu JH. A hybrid method of fractional steps withL ∞—stability for numerical modelling of aquatic environments.Research and Development on Hydrodynamics, 1985(1): 27–36
Bejan A, Tien CL. Fully developed natural counterflow in a long horizontal pipe with different end temperatures.Int J Heat Mass Transfer, 1978, 21(6): 701–708
Tang ZM, Hu WR, Imaishi N. Two bifurcation transitions of the floating half zone convection in a fat liquid bridge of largePr number.Int Journal of Heat and Mass Transfer, 2001, 44(7): 1299–1307
Ar Y, Tang ZM, Han JH, et al. The measurement of azimuthal velocity field for oscillatory thermocapillary convection.Microgr Sci and Tech, 1998, 10(3): 129–135
Lee J, Lee DJ, Lee JH. On the mechanism of oscillation in a simulated floating zone.J Crystal Growth, 1955, 152(4): 341–346
Schwabe D, Hintz P, Frank S. New features of thermocapillary convection infloating zones revealed by tracer particle accumulation structures (PAS).Microgravity Sci Technol, 1996, 9(3): 163–168
Frank S, Schwabe D. Temporal and spatial elements of thermocapillary convection in floating zones.Experiment in Fluids, 1997, 23(3): 234–251
Chen QS, Hu WR. Instability from steady and axial-symmetric to steady and asymmetric floating half zone convection in a fat liquid bridge of largePr number.Chinese Physics Letter, 1999, 16(11): 822–823
Author information
Authors and Affiliations
Additional information
The project supported by the National Natural Science Foundation of China (19789201) and the Ministry of Science and Technology of China (95-yu-34)
Rights and permissions
About this article
Cite this article
Zemei, T., Yan, A., Zhonghua, C. et al. Two bifurcation transition processes in floating half zone convection of larger Prandtl number fluid. Acta Mech Sinica 18, 328–341 (2002). https://doi.org/10.1007/BF02487785
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02487785