Oscillatory thermocapillary convection in open cylindrical annuli. Part 1. Experiments under microgravity

• Published in: Journal of fluid mechanics 2003-09, Vol.491, p.239-258, Article S002211200300541X
• Main Authors: SCHWABE, DIETRICH, ZEBIB, ABDELFATTAH, SIM, BOK-CHEOL
• Format: Article
• Language: English
• Subjects: Boundary conditions; Convection; Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Fluid dynamics; Fluid mechanics; Free surfaces; Fundamental areas of phenomenology (including applications); Gravity; Growth from melts; zone melting and refining; Heat conductivity; Hydrodynamic stability; Materials science; Mechanical engineering; Methods of crystal growth; physics of crystal growth; Physics; Studies; Surface-tension-driven instability
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S002211200300541X

We report results from microgravity experiments on thermocapillary convection in open annuli with outer radius $R_{o}{\,=\,}40\,\hbox{mm}$ and inner radius $R_{i}{\,=\,}20\,\hbox{mm}$ of various aspect ratios $Ar$. The measurements are from more than 230 equilibrated states in the $Ar$–Marangoni-number space. We found time-independent and oscillatory states and report some selected oscillation and Fourier spectra from thermocouple measurements. We measured the critical temperature difference $\uDelta T^{\hspace*{1pt}c}$ for the onset of temperature oscillations in the range $1{\,\le\,}Ar{\,\le\,}8$. We report supercritical oscillation periods and attribute the oscillations in the larger $Ar$ range to hydrothermal waves. This conclusion is supported by the values of the oscillation periods and of the critical Marangoni numbers in that $Ar$ range. The hydrothermal waves exhibit an internal corotating multicellular pattern. For the smaller $Ar$ and near the threshold we report $m$-fold temperature patterns on the free surface with $m$ decreasing for decreasing $Ar$. At $4\uDelta T^{\hspace*{1pt}c}$ these patterns become very irregular. Most of the findings are in accordance with the numerical results reported in Part 2 (Sim et al. (2003)). The experimental $\uDelta T^{\hspace*{1pt}c}$ are higher and the experimental periods $\tau^{c}$ are smaller than the numerical values for Biot number $Bi{\,=\,}0$. However, analysis of the experimental free-surface thermal boundary conditions shows that there was heat input to the free surface. Good agreement with numerical results for $\uDelta T^{\hspace*{1pt}c}$ and $\tau^{\hspace*{1pt}c}$ is obtained with $Bi{\,\ne\,}0$ (heat input).