This thesis presents a computational fluid dynamics (CFD) model of fluid flow driven by the motion of cilia, a cellular appendage found in organisms used to either move the fluid around them or to move themselves by propelling the fluid. Originating from an initial investigation to the flow patterns inside the third ventricle of a rat’s brain, this project expanded to improve the inadequacies of existing models of ciliary motion in fluid. This model was developed using the actuator line model to include the cilia motion to get an accurate representation of the cilia motion and its effect on the flow. This model not only provides exciting potential in various fields including soft robotics, biomedical research, environmental engineering, but also holds promise for drug delivery systems, and enhancing microfluidic designs. This thesis investigates the effect of the phase difference, the spacing and the frequency of the cilia motion on the fluid flow and the formation of the metachronal waves.

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.

Computing the fluid phase interfaces in multiphase flow is a challenging area of research in fluids. The Volume of Fluid andLevel Set methods are a few algorithms that have been developed for reconstructing the multiphase fluid flow interfaces. The thesis work focuses on exploring the ability of neural networks to reconstruct the multiphase fluid flow interfaces using a data-driven approach. The neural network model has liquid volume fraction stencils as an input, and it predicts the radius of the circle as an output of the network which represents a phase interface separating two immiscible fluids inside a fluid domain. The liquid volume fraction stencils are generated for randomly varying circle radii within a 1x1 domain using an open-source VOFI library. These datasets are used to train the neural network. Once the model is trained, the predicted circular phase interface from the neural network output is used to generate back the predicted liquid volume fraction stencils. Error norms values are calculated to assess the error in the neural network model’s predicted liquid volume fraction stencils with the actual liquid volume fraction stencils from the VOFI library. The neural network parameters are optimized by testing them for different hyper-parameters to reduce the error norms. So as to minimize the difference between the predicted and the actual liquid volume fraction stencils and errors in reconstructing the fluid phase interface geometry.

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.

Spray flows are important in a myriad of practical applications including fuel injection, ink-jet printing, agricultural sprays, and industrial processes. Two-phase sprays find particular use for spot cooling applications with high heat fluxes as in casting processes and power electronics. Computability of sprays in a cost-effective manner provides a path to optimize the design of nozzles to tune the spray characteristics for the needs of a particular application. Significant research has so far been devoted to understand and characterize spray flows better, be it from a theoretical, experimental or computational standpoint. The current thesis discusses a methodology for modeling primary atomization using the Quadratic Formula which is derived from an integral formulation of the governing equations. The framework is then applied to different examples of flat-fan hydraulic sprays. For each case, the spray is first resolved as a continuous fluid using the volume of fluid method. Atomization criterion is then applied to the velocity flow-field to determine the sites for primary atomization. At each site, local diameters for particle injection is determined using the quadratic formula. The trajectory of injected particles are then monitored through a particle tracking algorithm. The results from the numerical analysis are compared with experimental data to validate the computational framework.

The propulsion matrix provides a compact description of the locomotion of a single flagella molecular motor in a low Reynolds number environment. The locomotion properties of individual flagellar motors are central to bacterial behavior, including chemotaxis, pathogenesis, and biofilm formation. However, because conventional hydrodynamic measurement approaches require applied forces, torques, or fluid flows, it is not possible to directly measure the propulsion matrix for an individual microscale helical filament. Here, the limitations inherent to conventional measurement approaches are overcome using a combination of theoretical, experimental, and computational advancements. First, the relationship between the elements of the propulsion matrix with translational and rotational Brownian motion is derived using the fluctuation-dissipation theorem. Next, a volumetric fluorescent imaging using high resolution oblique plane microscopy with sufficient spatio-temporal resolution is conducted to resolve both translation and rotation of individual helical filaments isolated from E.coli's flagellar motor. Finally, a computational framework is developed to track individual helical filaments across six degrees of freedom, extract diffusion coefficients, and quantify the temporal correlation between translation and rotation. This study computed the maximum propulsion efficiency to be around 1.7%. Direct measurement of propulsion efficiency generally agrees with the ensemble and large-scale measurements previously performed using conventional hydrodynamic measurements. The findings suggest that the approach described here can be extended to more complex in-vitro experiments that evaluate microscale molecular motors. For example, evaluating sperm motility without inducing chemotaxis or utilizing a microfluidic setup.

As the push to develop ever more efficient aircraft increases, the use of lightweight composite materials to meet this push has increased. Traditional aircraft structural component sizing has revolved around the tensile yield strength of materials. Since composite materials excel in tensile strength, these traditional sizing tools provide overly optimistic weight reduction predictions. Furthermore, composite materials, in general, are weak under compression and shear. Thus, proper structural sizing yields heavier-than-expected designs. Nevertheless, a wing using thin, lightweight composites in the primary load-bearing components significantly impacts its static aeroelastic properties. These thin structures have a decreased flexural rigidity, making them more susceptible to bending. The bending of swept wings decreases the design wing twist and dihedral angle, potentially impacting the aerodynamic performance and the lateral stability and control, respectively. This work aims to determine what, if any, are the effects of excessive static aeroelastic properties on the aerodynamic performance of an aircraft. Does the perceived gain in the theoretical reduction in structural weight outweigh the potential reduction in aerodynamic performance?

In this dissertation, two types of passive air freshener products from Henkel, the wick-based air freshener and gel-based air freshener, are studied for their wicking mechanisms and evaporation performances.The fibrous pad of the wick-based air freshener is a porous medium that absorbs fragrance by capillary force and releases the fragrance into the ambient air. To investigate the wicking process, a two-dimensional multiphase flow numerical model using COMSOL Multiphysics is built. Saturation and liquid pressure inside the pad are solved. Comparison between the simulation results and experiments shows that evaporation occurs simultaneously with the wicking process. The evaporation performance on the surface of the wicking pad is analyzed based on the kinetic theory, from which the mass flow rate of molecules passing the interface of each pore of the porous medium is obtained. A 3D model coupling the evaporation model and dynamic wicking on the evaporation pad is built to simulate the entire performance of the air freshener to the environment for a long period of time. Diffusion and natural convection effects are included in the simulation. The simulation results match well with the experiments for both the air fresheners placed in a chamber and in the absent of a chamber, the latter of which is subject to indoor airflow. The gel-based air freshener can be constructed as a porous medium in which the solid network of particles spans the volume of the fragrance liquid. To predict the evaporation performance of the gel, two approaches are tested for gel samples in hemispheric shape. The first approach is the sessile drop model commonly used for the drying process of a pure liquid droplet. It can be used to estimate the weight loss rate and time duration of the evaporation. Another approach is to simulate the concentration profile outside the gel and estimate the evaporation rate from the surface of the gel using the kinetic theory. The evaporation area is updated based on the change of pore size. A 3D simulation using the same analysis is further applied to the cylindrical gel sample. The simulation results match the experimental data well.