Research Description:

Fluid Dynamics of a Spherical Cluster of Particles Immersed in a Fluid (with a Low Reynolds Number) Falling Under Gravity

The purpose of the research project is to understand the fluid mechanics that govern the topology of an initially spherical cluster of particles falling under gravity in a fluid of small but non-zero Reynolds number. Observations from numerical simulations of this system (with Re = 0.3) shows that the sphere first develops into a torus and that somewhat surprisingly no stray particles drift from the central mass. As the flow continues, the torus develops into a thin ring that becomes distorted and eventually fragments, with additional rings appearing on the boundary of the former ring.

A combination of analytical solutions and numerical methods will be used to understand: 1) how the initially spherical cluster becomes toroidal in shape 2) Why the radius of the torus increases with time 3) What mechanism leads to the instability of the ring, causing fragmentation into smaller rings. A finite element code will be used to solve the Navier-Stokes equations for axisymmetric fluid flow past a stationary ring. The resulting velocity field and pressure gradient will give insight to what is driving the changes in particle configuration.

Once this is accomplished, perturbations will be introduced on the ring to simulate variations in particle density within the ring. We wish to discover if the inertial flow around the torus can amplify the density perturbations and so lead to ring break up. Solutions of this problem will aid in the understanding of the dynamics of the actual system where the ring is composed of particles. Analytical solutions will serve as a guide and a check when performing more complex numerical calculations.