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

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. In this study, the fractal dimension of the line is found for different cases of heavy particles inertia (different Stokes numbers) in the absence of the particle gravity with a comparison with the fractal dimension 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 inertia affect the fractal dimension of a line released in a turbulent flow for Stokes numbers 0.02 < St < 2. At the beginning for small times, most of the different cases are not affected by the inertia until a certain time, the particle response time τa, with larger time as the particles inertia increases, the fractal dimension of the line increases owing to the particles becoming more sensitive to the small scales which cause the change in the line shape during its journey. Keywords—Heavy particles, two-phase flow, Kinematic Simulation, Fractal dimension.