Towards High Fidelity Particle-laden Simulations Based on Volume-filtering: From Point-particle to Interface-resolved Descriptions.

This dissertation presents a volume filtering framework to solve particle-laden flows. Particle-laden flows are studied, employing the well-established Euler-Lagrange method, using the point-particle approximation. This approach requires the filter width to be much larger than the particle diameter. The method assumes that the particle is smaller than the Kolmogorov length scale. This thesis investigates how inertial particles at semi-dilute volume fractions modulate the flow characteristics for particles smaller than 1 in wall units, when dispersed within wall-bounded channel flows at friction Reynolds number of 180. The simulations are performed with 4 way coupling in order to account for high local concentration of particles, to capture mechanisms such as turbophoresis and preferential concentration. We show that drag attenuation or augmentation is determined by the particle inertia. As particle size is increased greater than 1 in wall units, the regime becomes finite-sized, requiring an interface-resolved description. To do this a novel Immersed Boundaries (IB) framework based on the concept of volume-filtering called the Volume-Filtered Immersed Boundary (VF-IB) method is presented. Transport equations are obtained by volume-filtering the Navier-Stokes equation and accounting for the stresses at the solid-fluid interface. Boundary conditions are transformed into bodyforces that appear as surface integrals on the right hand side of the filtered equation. The approach requires the filter width to be much smaller than the particle diameter in order to accurately resolve the interfacial dynamics. Several canonical tests are conducted for both stationary and moving immersed solids and report comparable results to the experimental and/or body-fitted simulations. Keep in mind, the VF-IB method reverts back to the Euler-Lagrange formulation if the filter width is significantly greater than the particle diameter. An artifact of volume-filtering is the emergence of unclosed terms we define as the sub-filter scale term. In order to characterize the contribution of this term on the solution, a more simpler case of a 2-D varying coefficient hyperbolic equation that has an exact solution is looked into. It is observed that the sub-filter scale term scales inversely with the square of the filter width. For fine interface resolution (i.e. small filter width), this value can be ignored with negligible effect to the accuracy of the numerical solution. However for coarse interface resolution (i.e. large filter width), including the sub-filter scale term significantly increases the accuracy of the numerical solution