球面調和関数を用いたスペクトル法による球状液滴内三次元過渡表面張力対流の数値解析手法

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  • Three-Dimensional Numerical Analysis on Transient Marangoni Convection in a Liquid Droplet Using Spherical Harmonic Spectral Method.
  • キュウメン チョウワ カンスウ オ モチイタ スペクトルホウ ニ ヨル キュウジョウ エキテキ ナイ 3ジゲン カト ヒョウメン チョウリョク タイリュウ ノ スウチ カイセキ シュホウ

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A method is developed to analyze the three-dimensional transient Marangoni convection in a liquid droplet heated by a concentric warm rigid sphere set in the center and cooled uniformly from its surroundings. As the system is unstable and the convection is very sensitive to the temperature gradients along the surface, it is required for the scheme to be highly accurate and be free from the effects of the polar singularities. For the purpose, a spherical harmonic spectral method is developed to analyze the flow and temperature fields in the droplet on the three-dimensional spherical coordinate system. The newly developed method gives almost the same pattern of results for two systems with the same pattern of initial temperature disturbances on coordinate systems which are shifted by 90° in each other. This indicates that the present method is free from the effects of the direction of the coordinate system, and shows the validity of the method.

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