Oscillatory Thermocapillary Flow in Cylindrical Columns of High Prand시 Number Fluids

  • Lee, Kyu-Jung (Department of Mechanical Engineering, Korea University) ;
  • Yasuhiro Kamotani (Department of Mechanical and Aerospace Engineering, Case Western Reserve University) ;
  • Simon Ostrach (Department of Mechanical and Aerospace Engineering, Case Western Reserve University)
  • 발행 : 2001.06.01

초록

Oscillartory thermocapillary flow of high Prandtl number fluids in the half-zone configuration is investigated. Based on experimental observations, one oscillation cycle consists of an active period where the surface flow is strong and the hot corner region is extended and a slow period where the opposite occurs. It is found that during oscillations the deformation of free surface plays an important role and a surface deformation parameter S correlates the experimental data well on the onset of oscillations. A scaling analysis is performed to analyze the basic steady flow in the parametric ranges of previous ground-based experiments and shows that the flow is viscous dominant and is mainly driven in the hot corner. The predicted scaling laws agree well with the numerical results. It is postulated that the oscillations are caused by a time lag between the surface and return flows. A deformation parameter S represents the response time of the return flow to the surface flow.

키워드

참고문헌

  1. Carpenter, B.M. and Homsy, G.M., 1990, 'High Marangoni Number Convection in a Square Cavity,' Part II, Physic. Fluids A, 2, pp. 137-149 https://doi.org/10.1063/1.857763
  2. Chen, J.C., Chen, W.C., and Hwu, F.S., 1991, 'Numerical Computations of Unsteady Thermocapillary Convection in a Rectangular Cavity with Surface Deformation,' In Heat Transfer in Metals and Containerless Processing and Manufacturing, ASME Publication HTD-Vol. 162, pp. 89-95
  3. Chen, J.C. and Chin, G.H., 1995, 'Linear Stability Analysis of Thermocapillary Convection in the Floating Zone, ' J. Crystal Growth, Vol. 154, No. 1-2, pp. 98-107 https://doi.org/10.1016/0022-0248(95)00095-X
  4. Chen, Q.S., and Hu, W.R., 1998, 'Influence of Liquid Bridge Volume on Instability of Floating Half Zone Convection,' Int. J. Heat Mass Transfer, Vol. 41, Nos. 6-7, pp, 825-837 https://doi.org/10.1016/S0017-9310(97)00183-X
  5. Chun, C.H. and Wuest, W., 1979, 'Experiments on the Transition from Steady to the Oscillatory Marangoni Convection of a Floating Zone Under Reduced Gravity Effect,' Acta Astronautica 6, pp. 1073-1082 https://doi.org/10.1016/0094-5765(79)90056-0
  6. Chun, C.H., 1980, 'Experiments on Steady and Oscillatory Temperature Distribution in a Floating Zone Due to the Marangoni Convection,' Acta Astronautica 7, pp. 479-488 https://doi.org/10.1016/0094-5765(80)90037-5
  7. Kamotani, Y.Ostrach, S. and Vargas, M., 1984, 'Oscillatory Thermocapillary Convection in a Simulated Floating Zone Configuration,' J. Crystal Growth 66, pp. 83-90 https://doi.org/10.1016/0022-0248(84)90079-4
  8. Kamotani, Y. and Lee, K. J., 1989, 'Oscillatory Therrnocapillary Flow in a Liquid Column Heated by a Ring Heater,' PCH Physico-Chemical Hydrodynamics 11, pp. 729-736
  9. Lai, C.L., 1990, 'Unsteady Thermocapillary Flows and Free Surface Oscillations in Reduced Gravity Environments,' Acta Astronautica 21, pp. 171-181 https://doi.org/10.1016/0094-5765(90)90109-X
  10. Lee, J., Lee, D.J., and Lee, J.H., 1995, 'On the Mechanism of Oscillation in a Simulated Floating Zone,' J. Crystal Growth, Vol. 152, pp. 341-346 https://doi.org/10.1016/0022-0248(95)00098-4
  11. Monti, R., 1987, 'On the Onset of the Oscillatory Regimes in Marangoni Flows,' Acta Astronautica 15, pp. 557-560 https://doi.org/10.1016/0094-5765(87)90156-1
  12. Monti, R. and Fortezza, F., 1991, 'The Scientific Results of the Experiment on Oscillatory Marangoni Flow Performed in Telescience on Texus 23,' Microgravity Quarterly 1, pp. 163-171
  13. Napolitano, L.G., Monti, R., and Russo, G., 1986, 'Marangoni Convection in One- and Two-Liquids Floating Zones,' Naturwissenchaften 73, pp.352-355 https://doi.org/10.1007/BF00367263
  14. Ostrach, S., 1977, 'Motion Induced by Capillary,' In Physicochemical Hydrodynamics, V.G. Levich Festschrift 2, pp. 571-589, Advanced Publication
  15. Ostrach, S., Kamotani, Y., and Lai, C.L., 1985, 'Oscillatory Thermocapillary Flows,' PCH Physico-Chemical Hydrodynamics 6, pp. 585-599
  16. Patankar, S.V., 1980, Numerical Heat transfer and Fluid Flow, McGraw-Hill
  17. Preisser, F., Schwabe, D., and Scharmann, A., 1983, 'Steady and Oscillatory Thermocapillary Convection in Liquid Columns with Free Cylindrical Surface,' J. Fluid Mech. 126, pp. 545-567 https://doi.org/10.1017/S0022112083000324
  18. Rupp, R., Muller, G., and Neumann, G., 1989, 'Three-Dimensional Time Dependent Modeling of the Marangoni Convection in Zone Melting Configurations for GaAs,' J. Crystal Growth 97, pp. 34-41 https://doi.org/10.1016/0022-0248(89)90244-3
  19. Schwabe, D., Scharmann, A., Preisser, F., and Oeder, R., 1978, 'Experiments on Surface Tension Driven Flow in Floating Zone Melting,' J. Crystal Growth 43, pp. 305-312 https://doi.org/10.1016/0022-0248(78)90387-1
  20. Schwabe, D., Preisser, F., and Scharmann, A., 1982, 'Verification of the Oscillatory State of Thermocapillary Convection in a Floating Zone Under Low-Gravity,' Acta Astronautica 9, pp. 265-273 https://doi.org/10.1016/0094-5765(82)90030-3
  21. Schwabe, D., Velten, R., and Scharmann, A., 1990, 'The Instability of Surface Tension Driven Flow in Models for Floating Zones Under Normal and Reduced Gravity,' J. Crystal Growth 99, pp. 1258-1264
  22. Shen, Y., Neitzel, G.P., Jankowski, D.F., and Mittlemann, H.D., 1990, 'Energy Stability of Thermocapillary Convection in a Model of the Float-Zone Crystal-Growth Process,' J. Fluid Mech, 217, pp. 639-660 https://doi.org/10.1017/S002211209000088X
  23. Velten, R., Schwabe, D., and Scharmann, A., 1991, 'The Periodic Instability of Thermocapillary Convection in Cylindrical Liquid Bridges,' Phys. Fluids A3, pp. 267-279 https://doi.org/10.1063/1.858135
  24. Xu, J-J. and Davis, S.H., 1984, 'Convective Thermocapillary Instabilities in Liquid Bridges,' Phys. Fluids 27, pp. 1102-1107 https://doi.org/10.1063/1.864756
  25. Wanschura, M., Shevtsove, V.M., Kuhlmann, H.C., and Rath, H.J., 1995, 'Convective Instability Mechanisms in Thermocapillary Liquid Bridges', Physics Fluids, Vol. 7, No. 5, pp. 912-925 https://doi.org/10.1063/1.868567
  26. Zebib, A., Homsy, G.M., and Meiburg, E., 1985, 'High Marangoni Number Convection in a Square Cavity,' Phys. Fluids 28, pp. 3467-3476 https://doi.org/10.1063/1.865300