@techreport{oai:jaxa.repo.nii.ac.jp:00041250,
 author = {貝津, 吉城 and 後藤, 雅享 and 上野, 一郎 and 河村, 洋 and Kaizu, Yoshiki and Goto, Masayuki and Ueno, Ichiro and Kawamura, Hiroshi},
 month = {Sep},
 note = {One of the purposes of the space environment utilization such as a space station is the process of a new material. Uniform or high quality material can be formed on the ground owing to the natural convection by the buoyancy effect and sedimentation by the density difference. On the other hand, the buoyancy effect can be reduced in the space environment. Thus a high-quality material processing is expected to be enabled. Floating zone method is one of the likely candidates of the material processing methods under the microgravity. In this method the both ends of the material rod are cooled down, and the center is heated to melt. Molten liquid sustained between the rods is called liquid bridge. This melt zone is slowly moved vertically and thus a uniform single crystal is produced. The material in the liquid phase is sustained by the surface tension. Generally the surface tension of a liquid decreases with increasing temperature. Because a temperature variation exists along the free surface, the difference of the surface tension is originated from the temperature difference. Thus a flow occurs in a liquid bridge even under the microgravity. This flow is called as thermocapillary or Marangoni convection. Though this convection can occur also on the ground, it is usually hidden in the action of the buoyancy. And this phenomenon is hardly recognized in the usual observation. On the other hand, thermocapillary convection becomes dominant under the microgravity because the influence of the buoyancy is strongly reduced. Therefore, the analysis of the thermocapillary convection is primary important for the material formation under the microgravity. The configuration of the floating zone method is called as full zone model. For the sake of simplicity, half zone model is preferred in the fundamental research on the ground. Half zone model is the part of the liquid bridge in the full zone model. In this study, the upper disk is heated up and the other one is cooled down. From existing researches, thermocapillary convection exhibits the oscillatory flow under a certain condition. And the free surface vibration is observed with the oscillatory flow in the terrestrial experiments. An influence of surface vibration upon the flow field instability must be evaluated to understand the mechanism of the oscillatory flow. However existing numerical simulation are performed without considering the free surface movement. Consequently the purpose of this research is to analyze the three dimensional thermocapillary convection numerically with consideration of the free surface movement. The numerical analysis of thermocapillary convection was performed by the finite difference method using boundary fitted coordinate. The free surface deformation was considered in this calculation. As the results, the free surface deformation is obtained from the beginning of the thermocapillary convection to the steady one. The cases of different Marangoni number are calculated and its influence on the thermocapillary convection are analyzed., 資料番号: AA0010763006, レポート番号: NASDA-TMR-000006E},
 title = {Numerical calculations and stability analysis: Numerical simulation of Marangoni convection in consideration of free surface displacement},
 year = {2000}
}