Direct numerical simulation of particulate flows for three different length scales: Macro, micro and meso

The work done in this research is concerned with Direct Numerical Simulation (DNS) of fluid-solid flow problems. The Navier-Stokes equations, governing the motion of the fluid are solved coupled with the equations of rigid body motion of the particles. Particulate flow problem corresponding to three length scales named here as macro, micro and meso are considered. We follow distributed Lagrange multiplier (DLM) approach for doing the DNS of solid-liquid flows. In the DLM approach the entire fluid-particle domain is considered to be a fluid. It is ensured that the 'fluid' occupying the particle domain moves rigidly by adding a rigidity constraint.; At 'macro' scale the unsteady Navier-Stokes equations are solved coupled with the particle equation of motion. Results are presented to demonstrate the effectiveness of the numerical algorithm in handling three dimensional regular and irregular geometries without significant additional computational overhead.; At 'micro' scales low Reynolds numbers are encountered. Hence, the non-linear convective term can be neglected. We develop a steady Stokes flow algorithm for particulate flow problems in this regime. Numerical results along with comparison with analytical results are presented for translational and rotational drag on a periodic array of spheres. A freely rotating sphere in a shear flow field is also considered.; Meso scale typically lies between tens of nanometers to a few microns. Thermal fluctuations influence the motion of particles lying in this length regime. This gives rise to random motion (Brownian motion) of the particles. We develop a DNS of the Brownian motion of particles by using fluctuating hydrodynamic equations. Numerical results are presented for the diffusion of a periodic array of spheres.