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

The Tesla valve, originating from Nikola Tesla's "valvular conduit" patent in 1920, offers a unique solution to fluid control challenges by enabling unidirectional flow while impeding reverse flow. With applications ranging from fluid pumps to high-power engines, Tesla's design functions as a fluidic diode, inducing pressure drops across the valve to define its efficiency through diodicity. Through computational fluid dynamics (CFD) simulations using ANSYS Fluent, the impact of removing the bifurcated section on Tesla valve efficiency is explored. The T45-R, D-Valve, and GMF Valve designs are analyzed across a range of Reynolds numbers (Re). Results show that while the absence of bifurcation can lead to higher diodicity values due to increased flow divergence and vortex formation, efficiency varies depending on flow conditions. The T45-R valve exhibits linear diodicity increase with Reynolds number, plateauing at higher values due to reduced fluid inertia influence. Conversely, the D-Valve with bifurcation excels at lower Re values, while the non-bifurcated version proves more efficient at higher Re values. The GMF Valve with bifurcation demonstrates efficiency at lower Re values but decreases in effectiveness as Re rises, with the non-bifurcated version showing lower efficiency overall. Overall, this research provides insights into the fundamental physics and design considerations of Tesla valves, offering guidance for optimizing fluid control applications across diverse industries. The study underscores the importance of considering geometric variations and flow conditions when designing Tesla valves for specific applications, highlighting the intricate relationship between valve geometry, flow dynamics, and efficiency.

Four-Dimensional Emission Tomography (4DET) and Four-Dimensional Absorption Tomography (4DAT) are measurement techniques that utilize multiple 2D images (or projections) acquired via an optical device, such as a camera, to reconstruct scalar and velocity fields of a flow field being studied, using either emission- or absorption-based measurements, respectively. Turbulence is inherently three-dimensional, and thus research in the field benefits from a comprehensive understanding of coherent structures to fully explain the flow physics involved, for example, in the phenomena resulting from a turbulent jet. This thesis looks at the development, application and validity/practicality of emission tomography as an experimental approach to a obtaining a comprehensive understanding of coherent structures in turbulent flows. A pseudo test domain is decided upon, with a varying number of camera objects created to image the region of interest. Rays are then modelled as cylindrical volumes to build the weight matrix. Projection images are generated with Gaussian concentration defined as a spatial function of the domain to build the projection matrix. Finally, concentration within the domain, evaluated via the Least Squares method, is compared against original concentration values. The reconstruction algorithm is validated and checked for accuracy with DNS data of a steady turbulent jet. Reconstruction accuracy and a statistical analysis of the reconstructions are also presented.

Formula 1 car front wings have evolved significantly over the last fifty years. Looking back at the past decade shows significant changes made due to rules and regulations by the Federation Internationale de l'Automobile and an increased understanding of aerodynamic concepts. There seems to be a trend where aerodynamic design concepts, previously seen in aviation, are being applied to Formula 1 front wings; this helps race teams increase downforce and reduce drag. This thesis analyzes these changes made over the past years and relates the material back to material that was learned by the aviation industry and attempts to synthesize conceptual Formula 1 front Wing designs using VORLAX, a vortex lattice panel method, used in the aviation industry. This insight would be beneficial for Formula 1 teams as there are budget and time restrictions applied to Computational Fluid Dynamic and wind tunnel testing, but panel methods are run in a matter of seconds as opposed to hours or days. So, if verified, preliminary designs can be rapidly tested to optimize the workflow and reduce the time required for Computational Fluid Dynamic and wind tunnel testing.

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.

Advancements to a dual scale Large Eddy Simulation (LES) modeling approach for immiscible turbulent phase interfaces are presented. In the dual scale LES approach, a high resolution auxiliary grid, used to capture a fully resolved interface geometry realization, is linked to an LES grid that solves the filtered Navier-Stokes equations. Exact closure of the sub-filter interface terms is provided by explicitly filtering the fully resolved quantities from the auxiliary grid. Reconstructing a fully resolved velocity field to advance the phase interface requires modeling several sub-filter effects, including shear and accelerational instabilities and phase change. Two sub-filter models were developed to generate these sub-filter hydrodynamic instabilities: an Orr-Sommerfeld model and a Volume-of-Fluid (VoF) vortex sheet method. The Orr-Sommerfeld sub-filter model was found to be incompatible with the dual scale approach, since it is unable to generate interface rollup and a process to separate filtered and sub-filter scales could not be established. A novel VoF vortex sheet method was therefore proposed, since prior vortex methods have demonstrated interface rollup and following the LES methodology, the vortex sheet strength could be decomposed into its filtered and sub-filter components. In the development of the VoF vortex sheet method, it was tested with a variety of classical hydrodynamic instability problems, compared against prior work and linear theory, and verified using Direct Numerical Simulations (DNS). An LES consistent approach to coupling the VoF vortex sheet with the LES filtered equations is presented and compared against DNS. Finally, a sub-filter phase change model is proposed and assessed in the dual scale LES framework with an evaporating interface subjected to decaying homogeneous isotropic turbulence. Results are compared against DNS and the interplay between surface tension forces and evaporation are discussed.

This thesis focuses on the turbulent bluff body wakes in incompressible and compressible flows. An incompressible wake flow past an axisymmetric body of revolution at a diameter-based Reynolds number Re=5000 is investigated via a direct numerical simulation. It is followed by the development of a compressible solver using a split-form discontinuous Galerkin spectral element method framework with shock capturing. In the study on incompressible wake flows, three dominant coherent vortical motions are identified in the wake: the vortex shedding motion with the frequency of St=0.27, the bubble pumping motion with St=0.02, and the very-low-frequency (VLF) motion originated in the very near wake of the body with the frequencies St=0.002 and 0.005. The very-low-frequency motion is associated with a slow precession of the wake barycenter. The vortex shedding pattern is demonstrated to follow a reflectional symmetry breaking mode, with the detachment location rotating continuously and making a full circle over one vortex shedding period. The VLF radial motion with St=0.005 originates as m = 1 mode, but later transitions into m = 2 mode in the intermediate wake. Proper orthogonaldecomposition (POD) and dynamic mode decomposition (DMD) are further performed to analyze the spatial structure associated with the dominant coherent motions. Results of the POD and DMD analysis are consistent with the results of the azimuthal Fourier analysis. To extend the current incompressible code to be able to solve compressible flows, a computational methodology is developed using a high-order approximation for the compressible Navier-Stokes equations with discontinuities. The methodology is based on a split discretization framework with a summation-by-part operator. An entropy viscosity method and a subcell finite volume method are implemented to capture discontinuities. The developed high-order split-form with shock-capturing methodology is subject to a series of evaluation on cases from subsonic to hypersonic, from one-dimensional to three dimensional. The Taylor-Green vortex case and the supersonic sphere wake case show the capability to handle three-dimensional turbulent flows without and with the presence of shocks. It is also shown that higher-order approximations yield smaller errors than lower-order approximations, for the same number of total degrees of freedom.

This work aims to address the design optimization of bio-inspired locomotive devices in collective swimming by developing a computational methodology which combines surrogate-based optimization with high fidelity fluid-structure interactions (FSI) simulations of thunniform swimmers. Three main phases highlight the contribution and novelty of the current work. The first phase includes the development and bench-marking of a constrained surrogate-based optimization algorithm which is appropriate to the current design problem. Additionally, new FSI techniques, such as a volume-conservation scheme, has been developed to enhance the accuracy and speed of the simulations. The second phase involves an investigation of the optimized hydrodynamics of a solitary accelerating self-propelled thunniform swimmer during start-up. The third phase extends the analysis to include the optimized hydrodynamics of accelerating swimmers in phalanx schools. Future work includes extending the analysis to the optimized hydrodynamics of steady-state and accelerating swimmers in a diamond-shaped school. The results of the first phase indicate that the proposed optimization algorithm maintains a competitive performance when compared to other gradient-based and gradient-free methods, in dealing with expensive simulations-based black-box optimization problems with constraints. In addition, the proposed optimization algorithm is capable of insuring strictly feasible candidates during the optimization procedure, which is a desirable property in applied engineering problems where design variables must remain feasible for simulations or experiments not to fail. The results of the second phase indicate that the optimized kinematic gait of a solitary accelerating swimmer generates the reverse Karman vortex street associated with high propulsive efficiency. Moreover, the efficiency of sub-optimum modes, in solitary swimming, is found to increase with both the tail amplitude and the effective flapping length of the swimmer, and a new scaling law is proposed to capture these trends. Results of the third phase indicate that the optimal midline kinematics in accelerating phalanx schools resemble those of accelerating solitary swimmers. The optimal separation distance in a phalanx school is shown to be around 2L (where L is the swimmer's total length). Furthermore, separation distance is shown to have a stronger effect, ceteris paribus, on the propulsion efficiency of a school when compared to phase synchronization.

Theoretical analyses of liquid atomization (bulk to droplet conversion) and turbulence have potential to advance the computability of these flows. Instead of relying on full computations or models, fundamental conservation equations can be manipulated to generate partial or full solutions. For example, integral form of the mass and energy for spray flows leads to an explicit relationship between the drop size and liquid velocities. This is an ideal form to integrate with existing computational fluid dynamic (CFD), which is well developed to solve for the liquid velocities, i.e., the momentum equation(s). Theoretical adaption to CFD has been performed for various injection geometries, with results that compare quite well with experimental data. Since the drop size is provided analytically, computational time/cost for simulating spray flows with liquid atomization is no more than single-phase flows. Some advances have also been made on turbulent flows, by using a new set of perspectives on transport, scaling and energy distributions. Conservation equations for turbulence momentum and kinetic energy have been derived in a coordinate frame moving with the local mean velocities, which produce the Reynolds stress components, without modeling. Scaling of the Reynolds stress is also found at the first- and second-gradient levels. Finally, maximum-entropy principle has been used to derive the energy spectra in turbulent flows.

The study tested the parameterized neural ordinary differential equation (PNODE) framework with a physical system exhibiting only advective phenomenon. Existing deep learning methods have difficulty learning multiple dynamic, continuous time processes. PNODE encodes the input data and initial parameter into a set of reduced states within the latent space. Then the reduced states are fitted to a system of ordinary differential equations. The outputs from the model are then decoded back to the data space for a desired input parameter and time. The application of the PNODE formalism to different types of physical systems is important to test the methods robustness. The linear advection data was generated through a high-fidelity numerical tool for multiple velocity parameters. The PNODE code was modified for the advection dataset, whose temporal domain and spatial discretization varied from the original study configuration. The L2 norm between the reconstruction and surrogate model and the reconstruction plots were used to analyze the PNODE model performance. The model reconstructions presented mixed results. For a temporal domain of 20-time units, where multiple advection cycles were completed for each advection speed, the reconstructions did not agree with the surrogate model. For a reduced temporal domain of 5-time units, the reconstructions and surrogate models were in close agreement. Near the end of the temporal domain, deviations occurred likely resulting from the accumulation of numerical errors. Note, over the 5-time units, smaller advection speed parameters were unable to complete a cycle. The behavior for the 20-time units highlighted potential issues with imbalanced datasets and repeated features. The 5-time unit model illustrates PNODEs adaptability to this class of problems when the dataset is better posed.