Feedback control of oscillatory thermocapillary convection in a half-zone liquid bridge

Journal of Fluid Mechanics

Volumn 496, Issue , 2003, Pages 193-211

  Shiomi, J ^a   Kudo, M ^b   Ueno, I ^b   Kawamura, H ^b   Amberg, G ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^b TOKYO UNIVERSITY OF SCIENCE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ASPECT RATIO; BIFURCATION (MATHEMATICS); FEEDBACK CONTROL; FLOW VISUALIZATION; SENSORS;

FLOW STRUCTURES; THERMOCAPILLARY CONVECTION;

FLUID MECHANICS;

CAPILLARY ACTION; CONVECTION; FEEDBACK MECHANISM; FLOW VISUALIZATION; FLUID MECHANICS; LIQUID BRIDGE; PROCESS CONTROL;

EID: 1142293972     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112003006323     Document Type: Article

References (32)

1. BAU, H. H. 1999 Control of Marangoni-Bénard convection. Intl J. Heat Mass Transfer 42, 1327-1341.
2. BENZ, S., HINZ, P., RILEY, R. J. & NEITZEL, G. P. 1998 Instability of thermocapillary-buoyancy convection in shallow layers. Part 2. Suppression of hydrothermal waves. J. Fluid Mech. 359, 165-180.
3. CHANG, C. E. & WILCOX, W. R. 1976 Analysis of surface tension driven flow in floating zone melting. Intl J. Heat Mass Transfer 19, 355-356.
4. CHUN, C. H. & WUEST, W. 1979 Experiments on the transition from the steady to the oscillatory Marangoni-convection of a floating zone under reduced gravity effect. Acta Astron. 6, 1073-1082.
5. GOUPILLAUD, P., GROSSMANN, A. & MORLET, J. 1984 Cycle-octave and related transforms in seismic signal analysis. Geoexploration 23, 85-102.
6. HOWLE, L. E. 1997 Control of Rayliegh-Bénard convection in a small aspect ratio container. Intl J. Heat Mass Transfer 40, 817-822.
7. HU, W. R., SHU, J. Z., ZHOU, R. & TANG, Z. M. 1994 Influence of liquid bridge volume on the onset of oscillation in floating zone convection. J. Cryst. Growth 142, 379-384.
8. IOOSS, G. & JOSEPH, D. D. 1989 Elementary Stability and Bifurcation Theory, 2nd edn. Springer.
9. KAWAMURA, H., UENO, I. & ISHIKAWA, T. 2002 Study of thermocapillary flow in a liquid bridge towards an on-orbit experiment aboard the International Space Station. Adv. Space Res. 29, 611-618.
10. KUHLMANN, H. C. & RATH, H. J. 1993 Hydrodynamic instabilities in cylindrical thermocapillary liquid bridges. J. Fluid Mech. 247, 247-274.
11. LEVENSTAM, M. & AMBERG, G. 1995 Hydrodynamical instabilities of thermocapillary flow in a half-zone. J. Fluid Mech. 297, 357-372.
12. LEVENSTAM, M., AMBERG, G. & WINKLER, C. 2001 Instabilities of thermocapillary convection in a half-zone at intermediate Prandtl numbers. Phys. Fluids 13, 807-816.
13. LEYPOLDT, J., KUHLMANN, H. C. & RATH, H. J. 2000 Three-dimensional numerical simulation of thermocapillary flows of cylindrical liquid bridges. J. Fluid Mech. 414, 285-314.
14. MAY, R. M. 1976 Simple mathematical models with very complicated dynamics. Nature 261, 459-467.
15. NEITZEL, G. P., CHANG, K. T., JANKOWSKI, D. F. & MITTELMANN, H. D. 1993 Linear stability theory of thermocapillary convection in a model of the float-zone crystal-growth process. Phys. Fluids A 5, 108-114.
16. OR, A. C. & KELLY, R. E. 2001 Feedback control of weakly nonlinear Rayleigh-Bénard-Marangoni convection. J. Fluid Mech. 440, 27-47.
17. OR, A. C., KELLY, R. E., CORTELEZZI, L. & SPEYER, J. L. 1999 Control of long-wavelength Marangoni-Bénard convection. J. Fluid Mech. 387, 321-341.
18. OTT, E., GREBOGI, C. & YORKE, J. A. 1990 Controlling chaos. Phys. Rev. Lett. 64, 1196-1199.
19. PETROV, V., MUEHLNER, K. A., VANHOOK, S. J. & SWINNEY, H. L. 1998 Model-independent nonlinear control algorithm with application to a liquid bridge experiment. Phys. Rev. E 58, 427-433.
20. PETROV, V., SCHATZ, M. F., MUEHLNER, K. A., VANHOOK, S. J., MCCORMICK, W. D., SWIFT, J. B. & SWINNEY, H. L. 1996 Nonlinear control of remote unstable states in a liquid bridge convection experiment. Phys. Rev. Lett. 77, 3779-3782.
21. PREISSER, F., SCHWABE, D. & SCHARMANN, A. 1983 Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface. J. Fluid Mech. 126, 545-567.
22. SCHWABE, D., HINTZ, P. & FRANK, S. 1996 New features of thermocapillary convection in floating zones revealed by tracer particles accumulation structures (PAS). Microgravity Sci. Technol. 9, 163-168.
23. SCHWABE, D. & SCHARMANN, A. 1979 Some evidence for the existence and magnitude of a critical Marangoni number for the onset of oscillatory flow in crystal growth melts. J. Cryst. Growth 6, 125-131.
24. SHIOMI, J. & AMBERG, G. 2002 Active control of a global thermocapillary instability. Phys. Fluids 14, 3039-3045.
25. SHIOMI, J., AMBERG, G. & ALFREDSSON, P. H. 2001 Active control of oscillatory thermocapillary convection. Phys. Rev. E 64, 031205.
26. TANG, J. & BAU, H. H. 1993 Feedback control stabilization of the no-motion state of a fluid confined in a horizontal, porous layer heated from below. J. Fluid Mech. 257, 485-505.
27. TANG, J. & BAU, H. H. 1998 Experiments on the stabilization of the no-motion state of a fluid layer heated from below and cooled from above. J. Fluid Mech. 363, 153-171.
28. UENO, I., TANAKA, S. & KAWAMURA, H. 2003 Oscillatory and chaotic thermocapillary convection in a half-zone liquid bridge. Phys. Fluids 15, 408-416.
29. VELTEN, R., SCHWABE, D. & SCHARMANN, A. 1991 The periodic instability of thermocapillary convection in cylindrical liquid bridges. Phys. Fluids A 3, 267-279.
30. WANG, Y., SINGER, J. & BAU, H. H. 1992 Controlling chaos in a thermal convection loop. J. Fluid Mech. 237, 479-498.
31. WANSCHURA, M., SHEVTSOVA, V. M., KUHLMANN, H. C. & RATH, H. J. 1995 Convective instability mechanisms in thermocapillary liquid bridges. Phys. Fluids 7, 912-925.
32. YUEN, P. K. & BAU, H. H. 1996 Rendering a subcritical Hopf bifurcation supercritical. J. Fluid Mech. 317, 91-109.