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

This dissertation investigates the complex dynamics of semi-dilute inertial particles suspended in vortices using the Eulerian-Lagrangian method. The study explores the modulation of flow induced by inertial particles, focusing on the characteristics of a single vortex, instability analysis within particle-laden flows, and the merging process of co-rotating vortices. Simulations reveal a preferential concentration mechanism, where inertial particles cluster around a void fraction bubble, accelerating the decay of the vortex tube. Small-scale clusters, arising from particle-trajectory crossings, induce significant gradients in the fluid vorticity field, contributing to rapid vortex breakdown. Within a specific Stokes number range, increased particle inertia results in faster vortex decay and stronger inhomogeneity in the particle phase. The instability mechanism in particle-laden flows is explored using a Rankine vortex model. Two-way coupling triggers azimuthal perturbations, leading to the breakdown of the vortex structure. Linear Stability Analysis and Two-Fluid modeling demonstrate that the dusty vortex flow exhibits unstable modes, with growth rates increasing with wavenumber. Eulerian-Lagrangian simulations validate these results, showing excellent agreement between computed and predicted growth rates. The dissertation also delves into the co-rotating vortex merger in a semi-dilute dusty flow. For weak inertial effects, merger experiences a delay compared to particle-free vortices. Under moderate inertial conditions, the merger process exhibits repulsion, increased separation, and eventual convective merger stages. Highly inertial particles stretch the vortex core, initiating a merger with an outcome of a particle-free vortex core surrounded by a halo of concentrated particles. In conclusion, the feedback force from the dispersed phase induces instability and significantly influences the dynamics of vortices in particle-laden flows. The findings contribute to a deeper understanding of the intricate interactions between inertial particles and vortical structures.

The current work aims to understand the influence of particles on scalar transport in particle-laden turbulent jets using point-particle direct numerical simulations (DNS). Such turbulence phenomena are observed in many applications, such as aircraft and rocket engines (e.g., engines operating in dusty environments and when close to the surface) and geophysical flows (sediment-laden rivers discharging nutrients into the oceans), etc.This thesis looks at systematically understanding the fundamental interplay between (1) fluid turbulence, (2) inertial particles, and (3) scalar transport. This work considers a temporal jet of Reynolds number of 5000 filled with the point-particles and the influence of Stokes number (St). Three Stokes numbers, St = 1, 7.5, and 20, were considered for the current work. The simulations were solved using the NGA solver, which solves the Navier-Stokes, advection-diffusion, and particle transport equations. The statistical analysis of the mean and turbulence quantities, along with the Reynolds stresses, are estimated for the fluid and particle phases throughout the domain. The observations do not show a significant influence of St in the mean flow evolution of fluid, scalar, and particle phases. The scalar mixture fraction variance and the turbulent kinetic energy (TKE) increase slightly for the St = 1 case, compared to the particle-free and higher St cases, indicating that an optimal St exists for which the scalar variation increases. The current preliminary study establishes that the scalar variance is influenced by particles under the optimal particle St. Directions for future studies based on the current observations are presented.

A novel CFD algorithm called LEAP is currently being developed by the Kasbaoui Research Group (KRG) using the Immersed Boundary Method (IBM) to describe complex geometries. To validate the algorithm, this research project focused on testing the algorithm in three dimensions by simulating a sphere placed in a moving fluid. The simulation results were compared against the experimentally derived Schiller-Naumann Correlation. Over the course of 36 trials, various spatial and temporal resolutions were tested at specific Reynolds numbers between 10 and 300. It was observed that numerical errors decreased with increasing spatial and temporal resolution. This result was expected as increased resolution should give results closer to experimental values. Having shown the accuracy and robustness of this method, KRG will continue to develop this algorithm to explore more complex geometries such as aircraft engines or human lungs.