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FINE SCALE STRUCTURE AND FRACTAL GEOMETRY OF TURBULENT SCALAR MIXING AT HIGH SCHMIDT NUMBERS

Sachinori Ishimoto
Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8850, Japan

Makoto Sato
Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8850, Japan

Takehiko Seo
Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8850, Japan

Mamoru Tanahashi
Department of Mechanical and Aerospace Engineering Tokyo Institute of Technology 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan

Toshio Miyauchi
Dept. Mechanical and Aerospace Eng., Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan; Organization for the Strategic Coordination of Research and Intellectual Properties Meiji University 1-1-1 Higashimita, Tama-ku, Kawasaki, Kanagawa, Japan

Аннотация

Direct numerical simulations (DNS) of temporally developing turbulent mixing layer with non-reactive and reactive scalar transport up to Sc = 30.0 have been conducted to investigate the fractal geometry of scalar surfaces in turbulence. Although contour lines of scalar include small scale wrinkling for high Sc, global pattern is similar to that of moderate Sc cases. Effects of Schmidt number and chemical reaction are discussed by applying fractal analyses based on a box-counting method for scalar surfaces obtained from DNS. For high Sc, two fractal dimensions can be delined. The first fractal can be observed in relatively large scales. The dimension of the first fractal coincides with that of moderate Sc number case in the inertial subrange (D ~ 2.5). The second fractal dimension of non-reactive scalar can be defined in small scales and shows larger values (about 2.8), which denotes self-similarity of scalar surfaces smaller than the Kolmogorov length. The second fractal dimension of reactive scalar decreases to 2.65 due to the chemical reaction. The inner cutoff of the second fractal reaches to about 10 times Batchelor length scale for high Sc.