Effect of Particle Gravity on the Fractal Dimension of Particle Line in three-dimensional Turbulent Flows using Kinematic Simulation

In this study, the dispersion of heavy particles line in an isotropic and incompressible three-dimensional turbulent flow has been studied using the Kinematic Simulation techniques to find out the evolution of the line fractal dimension. The fractal dimension of the line is found in the case of different particle gravity (in practice, different values of particle drift velocity) in the presence of small particle inertia with a comparison with that obtained in the diffusion case of material line at the same Reynolds number. It can be concluded for the dispersion of heavy particles line in turbulent flow that the particle gravity affect the fractal dimension of the line for different particle gravity velocities in the range 0.2 < W < 2. With the increase of the particle drift velocity, the fractal dimension of the line decreases which may be explained as the particles pass many scales in their journey in the direction of the gravity and the particles trajectories do not affect by these scales at high particle drift velocities.

Authors:

• A. Abou El-Azm Aly
• F. Nicolleau
• T. M. Michelitsch
• A. F. Nowakowski

Keywords:

• Heavy particles
• two-phase flow
• Kinematic Simulation
• Fractal dimension.

References:

[1] E. Villermaux and Y. Gagne, Physical Review Letters, Vol. 73, No. 2,
pp. 252, 1994.
[2] F. Nicolleau, Phys. Fluids, Vol. 8, No. 10, pp. 2661, 1996.
[3] F. Nicolleau and A. ElMaihy, J. Fluid Mech., Vol. 517, pp. 229, 2003.
[4] P. Flohr and J. C. Vassilicos, J. Fluid Mech., Vol. 407, pp. 315, 2000.
[5] A. ElMaihy and F. Nicolleau, Phys. Rev. E 71, pp. 046307, 2005.
[6] F. Nicolleau and A. ElMaihy, Phys Rev. E 74, pp. 046302, 2006.
[7] N. A. Malik and J. C. Vassilicos, Phys. Fluids 11, pp. 1572, 1999.
[8] J. C. H. Fung, Ph.D. thesis, University of Cambridge, 1990.
[9] F. Nicolleau and J.C.Vassilicos, Physical Review Letters, Vol. 90, pp.
024503, 2003.
[10] M. R. Maxey and J. J. Riley, Physics of Fluids 26, pp. 883, 1983.
[11] M. R. Maxey and L.-P. Wang, Experimental Thermal and Fluid Science
Vol. 12, pp. 417, 1996.
[12] M. R. Maxey and L.-P. Wang, Fluid Dynamics Research 20, pp. 143,
1997.