Application of Multifractal Analysis to Evaluation of Multicomponent Fluid Mixing Pattern

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  • Shiba Takako
    Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University
  • Hirata Yushi
    Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University
  • Inoue Yoshiro
    Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University

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Other Title
  • マルチフラクタル解析の多種流体系の混合パターン評価への応用
  • マルチフラクタル カイセキ ノ タシュ リュウタイケイ ノ コンゴウ パターン ヒョウカ エノ オウヨウ

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Abstract

A new method of multifractal analysis to evaluate the fluid mixing pattern of three kinds of fluid components is proposed. The geometrical characteristics of mixing pattern are expressed on a spectral surface of quasi-local fractal dimension vector q, whose dimension agrees with the number of fluid components, and quasi-global fractal dimension f(q). In ordinary multifractal analysis, local and grabal fractal dimensions are related with an escort probability measure P (β), which is a function of single scan parameter β. In the present analysis, the scan parameter vector β whose dimension is the same as q is newly introduced. The multifractal variables are calculated by scanning independently each component of β. In the analysis of mixing pattern of many fluids, it is important to select the fluid components and subregion (or support) that contains the fluid in question. Depending on the combination of fluid and support, many different multifractal spectra are obtained. Complex intermixing between two or more fluid components can be analyzed quantitatively with these spectra.

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