High-Prandtl-number linear stability for the classical half-zone problem

• Material Type: 規格・テクニカルリポート類
• Title: High-Prandtl-number linear stability for the classical half-zone problem
• Author/Editor: Kuhlmann, H. C.; Wanschura, M.; Nienhuser, Ch.; Leypoldt, J.; Rath, H. J.; 依田, 真一; Yoda, Shinichi
• Author Heading: Kuhlmann, H. C.; Wanschura, M.; Nienhuser, Ch.; Leypoldt, J.; Rath, H. J.; 依田, 真一; Yoda, Shinichi
• Publication, Distribution, etc.: 宇宙開発事業団
• Publication Date: 1999-09-30
• Publication Date (W3CDTF): 1999-09-30
• Alternative Title: 古典的なハーフゾーン問題に対する高プラントル数流体の線形安定性
• Periodical title: NASDA Technical Memorandum
• Pages: 187-240
• ISSN (Periodical Title): ISSN : 1345-7888
• Text Language Code: eng
• Subject Heading: 線形安定性解析; 熱毛細管流動; 液橋; プラントル数流体; 差分法; レイノルズ数; 数学モデル; マランゴニ対流; 3次元流動; 2次元流動; 微小重力; 速度場; linear stability analysis; thermocapillary flow; liquid bridge; Prandtl number fluid; finite difference method; Reynolds number; mathematical model; Marangoni convection; three dimensional flow; two dimensional flow; microgravity; velocity field
• Target Audience: 一般
• Note (General): The aim of this part of the Marangoni Project has been the investigation of the linear stability of the two dimensional steady thermocapillary flow in cylindrical liquid bridges with an emphasis on high Prandtl numbers. First, the problem is formulated mathematically and the numerical methods implemented are described. Among these are equidistant and stretched finite difference methods, Chebyshev collocation methods and combinations of both. The results obtained by these methods are documented in graphical and tabular form. It is found that, with the present approaches and the numerical hardware available, grid convergence for the linear stability boundaries is obtained up to a Prandtl number of Pr = 7. The instability mechanism is the same as the one found by Wanschura et al. For higher Prandtl numbers, grid convergence was not obtained. A multitude of test calculations has been performed to check various potential sources of errors, e.g., the influence of conservative and nonconservative formulations, noise and machine accuracy. Theoretical considerations lead to the conclusion that for a correct prediction of the stability boundaries, one has to accurately calculate the thermal dissipation of the perturbation-temperature field. Since, at high Prandtl numbers, heat is primarily dissipated in the thermal boundary layers, it is required to accurately resolve them. The present unconverged data yield the correct, i.e., the expected order of magnitude for the critical Reynolds numbers. Also, the structure of the critical modes and the most dangerous wave numbers are in rough agreement with the currently available experimental results. Iterative methods to solve the linear systems that are involved in the problem would allow for a higher grid resolution and could thus improve the convergence. However, an effective preconditioner for the bad conditioned matrices was not found. Finally, a mathematical model problem is suggested which is expected to exhibit, at critical conditions, boundary layers not as thin as the present model. It is hoped that grid convergence can be obtained for this model and that it will show a qualitatively correct behavior.; 資料番号: AA0002209007; レポート番号: NASDA-TMR-990007E
• Access Restrictions: インターネット公開
• Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）; https://irdb.nii.ac.jp
• Original Data Provider (Database): 宇宙航空研究開発機構 : 宇宙航空研究開発機構リポジトリ

• Summary, etc.: マランゴニ計画のこの部分の目的は、高プラントル数に重点を置いて円柱液橋における2次元定常熱毛細管流動の線形安定性を調べることである。まず、問題を数学的に定式化し、実行した数値解析法について記述する。ここには、等距離および拡大した差分法、チェビシェフのコロケーション法および両者の組合わさった方法が含ま...