Abstract: A study of isothermal flow in fractal domain is presented. The domain is a cavity where the boundaries are pre-fractals of the square Koch curve. Simulations are carried out considering pre-fractals of order 0 (square-cavity), 1 and 2. The fluid flow equations are solved by the finite volume method, using a structured staggered grid [1]. Some oscillations are detected at the kinetic energy for Reynolds number between 400 and 1000, but they are not verified for standard cavity under the same conditions. Such oscillations were observed by Goodrich et al. (1990), but for a deep cavity (aspect ratio equal 2) and for Reynolds number interval between 5000 and 10000. As expected, the mean kinetic energy decreases with the enhancement of the fractalization level.

References:

1. E. Doescher, H.F. Campos Velho, F.M. Ramos (2001): Isothermal Fluid Flow in Fractal Domains, Computational and Applied Mathematics (submitted).

2. J.W. Goodrich, K. Gustafson, K. Halasi (1990): Hopf Bifurcation in the Driven Cavity, Journal of Computational Physics, 90, 219-261.