The vortex particle method (VPM) is a mesh-free approach to computational fluid dynamics (CFD) solving the Navier-Stokes equations in their velocity-vorticity form. The VPM uses a Lagrangian scheme, which not only avoids the hurdles of mesh generation, but it also conserves vortical structures over long distances with minimal numerical dissipation while being orders of magnitude faster than conventional mesh-based CFD. However, VPM is known to be numerically unstable when vortical structures break down close to the turbulent regime. In this study, we reformulate the VPM as a large eddy simulation (LES) in a scheme that is numerically stable, without increasing its computational cost. A new set of VPM governing equations are derived from the LES-filtered Navier-Stokes equations. The new equations reinforce conservation of mass and angular momentum by reshaping the vortex elements subject to vortex stretching. In addition to the VPM reformulation, a new anisotropic dynamic model of subfilter-scale (SFS) vortex stretching is developed. This SFS model is well suited for turbulent flows with coherent vortical structures where the predominant cascade mechanism is vortex stretching. Extensive validation is presented, asserting the scheme comprised of the reformulated VPM and SFS model as a meshless LES that accurately resolves large-scale features of turbulent flow. Advection, viscous diffusion, and vortex stretching are validated through simulation of isolated and leapfrogging vortex rings. Mean and fluctuating components of turbulent flow are validated through simulation of a turbulent round jet, in which Reynolds stresses are resolved directly and compared to experimental measurements. Finally, the computational efficiency of the scheme is showcased in the simulation of an aircraft rotor in hover, showing our meshless LES to be 100x faster than a mesh-based LES with similar fidelity. The ability to accurately and rapidly assess unsteady interactional aerodynamics is a shortcoming and bottleneck in the design of various next-generation aerospace systems: from electric vertical takeoff and landing (eVTOL) aircraft to airborne wind energy and wind farms. For instance, current models used in preliminary design fail to predict and assess configurations that may lead to the wake of a rotor impinging on another rotor or a wing during an eVTOL transition maneuver. In the second part of this dissertation, we address this shortcoming as we present a variable-fidelity CFD framework based on the reformulated VPM for simulating complex interactional aerodynamics. We further develop our meshless LES scheme to include rotors and wings in the computational domain through actuator models. A novel, vorticity-based, actuator surface model (ASM) is developed for wings, which is suitable for rotor-wing interactions when a wake impinges on the surface of a wing. This ASM imposes the no-flow-through condition at the airfoil centerline by calculating the circulation that meets this condition and by immersing the associated vorticity following a pressure-like distribution. Extensive validation of rotor-rotor and rotor-wing interactions predicted with our LES is presented, simulating two side-by-side rotors in hover, a tailplane with tip-mounted propellers, and a wing with propellers mounted mid-span. To conclude, the capabilities of the framework are showcased through the simulation of a multirotor tiltwing vehicle. The vehicle is simulated mid maneuver as it transitions from powered lift to wing-borne flight, featuring rotors with variable RPM and variable pitch, tilting of wings and rotors, and significant rotor-rotor and rotor-wing interactions from hover to cruise. Thus, the reformulated VPM provides aircraft designers with a high-fidelity LES tool that is orders of magnitude faster than mesh-based CFD, while also featuring variable-fidelity capabilities.

<P> The work presented m this thesis focused on using the hybrid Unsteady Reynolds-Averaged Navier-Stokes (URANS)/Large Eddy Simulation (LES) methodology to investigate the flow pulsation phenomenon in compound rectangular channels for isothermal flows. The specific form of the hybrid URANS/LES approach that was used is the Strelets (2001) version of the Detached Eddy Simulation (DES). It is of fundamental interest to study the problem of flow pulsations, as it is one of the most important mechanisms that directly affect the heat transfer occurring in sub-channel geometries such as those in nuclear fuel bundles. The predictions associated with the heat transfer and fluid flow in sub-channel geometry can be used to develop simplified physical models for sub-channel mixing for use in broader safety analysis codes. The primary goal of the current research work was to determine the applicability of the DES approach to predict the flow pulsations in sub-channel geometries. It was of interest to see how accurately the dynamics associated with the flow pulsations can be resolved from a spatial-temporal perspective using the specific DES model. The research work carried out for this thesis was divided into two stages. </p> <p> In the first stage of the research work, effort was concentrated to primarily understand the field of sub-channel flow pulsations and its implications from both an experimental and numerical point of view. It was noted that unsteady turbulence modeling approaches have great potential in providing insights into the fundamentals of sub-channel flow pulsations. It was proposed that for this thesis work, the Shear Stress Transport (SST) based DES model be used to understand the dynamics associated with sub-channel flow pulsations. To the author's knowledge the DES-SST based turbulence model has never been used for resolving the effects of sub-channel flow pulsations. Next, the hybrid URANS/LES turbulence modeling technique was reviewed in great detail to understand the philosophy of the hybrid URANS/LES technique and its ability to resolve fundamental flows of interest. Effort was directed to understand the switching mechanism (which blends the URANS region with the LES region) in the DES-SST model for fully wall bounded turbulent flows without boundary layer separation. To the author's knowledge, the DES-SST model has never been used on a fully wall bounded turbulent flow problem without boundary layer separation. Thus, the DES-SST model was first completely validated for a fully developed turbulent channel flow problem without boundary layer separation. </p> <p> In the second stage of the research work, the DES-SST model was used to study the flow pulsation phenomena on two rectangular sub-channels connected by a gap, on which extensive experiments were conducted by Meyer and Rehme (1994). It was found that the DES-SST model was successful in resolving significant portion of the flow field in the vicinity of the gap region. The span-wise velocity contours, velocity vector plots, and time traces of the velocity components showed the expected cross flow mixing between the sub-channels through the gap. The predicted turbulent kinetic energy showed two clear peaks at the edges of the gap. The dynamics of the flow pulsations were quantitatively described through temporal auto-correlations, spatial cross-correlations and power spectral functions. The numerical predictions were in general agreement with the experiments in terms of the quantitative aspects. From an instantaneous time scale point of view, the DES-SST model was able to identify different flow mixing patterns. The pulsating flow is basically an effect of the variation of the pressure field which is a response to the instability causing the fluid flow pulsations. Coherent structures were identified in the flow field to be comprised of eddies, shear zones and streams. Eddy structures with high vorticity and low pressure cores were found to exist near the vicinity of the gap edge region. A three dimensional vorticity field was identified and found to exist near the gap edge region. The instability mechanism and the probable cause behind the quasi-periodic fluid flow pulsations was identified and related to the inflectional stream-wise velocity profile. Simulations were also performed with two different channel lengths in comparison to the reference channel length. Different channel length studies showed similar statistical description of the flow field. However, frequency independent results were not obtained. In general, simulations performed using the DES-SST model were successful in capturing the effects of the fluid flow pulsations. This modeling technique has great potential to be used for actual rod bundle configurations. </p> / Thesis / Doctor of Philosophy (PhD)

Knowledge of the detailed flow dynamics at the interior of branching corals is critical for a full understanding of nutrient uptake, mass transport, wave dissipation, and other essential processes. These physiological processes depend on the local velocity field, local concentration gradients of nutrients and waste, and the turbulent stresses developed on and above the coral surface. Though the large-scale hydrodynamics over coral reefs are well studied, the interior hydrodynamics, between the branches, remains uncharacterized due to limited optical and acoustic access to the interior. In the current thesis, a three-dimensional immersed boundary method in the large eddy simulation framework was used to compute the flow inside several branching coral colony geometries in order to study the effects of branch density and surface structure on the flow fields in the coral interiors. Two different Pocillopora colony species were studied at different Reynolds numbers. A ray-tracing algorithm was used for capturing the arbitrary branches of these complex geometries to obtain the three-dimensional flow fields within these colonies for the first time. The analysis showed the formation of vortices at the colony interior that stir the water column and thus passively enhance mass transport, compensating for the reduced mean velocity magnitude compared to the free stream value, within the densely branched Pocillopora meandrina colony. Further analysis showed that the mean streamwise velocity profile changes shape along the streamwise direction inside P. meandrina, whereas the mean velocity profile did not change shape from the front to the back for the loosely branched Pocillopora colony, Pocillopora eydouxi. Moreover, turbulent flow field quantities were computed for both these structures, and for two almost identical Montipora capitata colony geometries, one with, and one without roughness elements called verrucae. The analyses demonstrated significant differences in the mean velocity profiles, Reynolds stress, and other flow quantities with changes in colony branch density and surface structure. / Doctor of Philosophy / Coral reefs are the largest marine ecosystem, and play a critical role in protecting coastal areas against flooding and erosion. The majority of the world's corals are currently under threat from rising ocean temperatures, which disrupt the symbiotic relationship between the coral polyp and its symbiont algae causing coral bleaching. Bleaching involves processes mediated by the flow at the coral surface, but relatively little is known regarding the local flow dynamics between the branches of coral reefs. The current research seeks to characterize internal coral hydrodynamics, leading to insights about many critical physiological and other processes in corals, like drag formation, mixing, and mass or nutrient transport to and from the coral. In the current study, the influence of the coral branch density and surface structure on the resulting interbranch flow field were investigated by simulating the flow resulting from uniform oncoming ocean flow conditions using three-dimensional immersed boundary large eddy simulations. The detailed velocity and pressure fields were found throughout the interior of the colonies studied. A distinct mass transport mechanism was found inside one densely branched colony studied. For this coral, Pocillopora meandrina, the flow speed reduces substantially inside the coral because of the high branch density. But corals depend on the ocean flow to bring nutrients to the polyps on their surface. We found that P. meandrina sheds hundreds of small vortices from its branches, which stir the overlying water column, increasing the mass transport rate, and compensating almost exactly for the reduced flow in the interior. The study also included computing the flow through three other coral colony geometries, and comparisons of their mean velocity profiles and turbulent flow statistics in order to examine the impact of the colony branch density and surface structures on the resulting hydrodynamic flow field. The current investigation of coral hydrodynamics may lead to an increased understanding of coral health and physiological activity, and may help in designing effective interventions for the challenges facing corals, which could have impacts in the fields of coral restoration, coastal protection, and public policy in the United States and abroad.

Water quality in river systems is an important issue, and relies on various factors including our ability to predict how effluents from outfalls mix with river water. However, predicting mixing in rivers, and especially in river bends, remains a difficult problem to solve. The goal of this project is to develop a comprehensive picture of the mixing mechanisms of an effluent jet in a river bend. This is done with experiments in both bend flumes in the University of Ottawa Water Resources Engineering Laboratory. The large bend flume is 1 m in width, and contains a single 135° bend of radius 1.5 m, and the small flume has a channel width of 0.2 m with a 135° bend of radius 0.3 m. The experiments in the large flume used acoustic Doppler velocimeters to measure velocity, and the experiments in the small flume used particle image velocimetry to track flow fields. Large eddy simulation (LES) were also completed using the same channel geometry as the small flume. To complete the parametric analysis on mixing of a neutrally buoyant effluent jet in a channel bend, 35 flow conditions, from seven channel aspect ratios and five momentum ratios, are modelled using LES. Each flow condition is also modelled without the jet present. Particle image velocimetry data from the small bend flume validates the LES models. Additionally, acoustic Doppler velocimeter tests were completed in the large bend flume under two different flume flow rates, two jet flow rates, and two aspect ratios. These models and measurements provide a broad range of the parameters under investigation. The experiments in the large bend flume establish the shape of the jet's trajectory within the channel bend, and how it differs from a trajectory in a straight crossflow. From these experiments, it is established that the centre position of the secondary circulation cell is an important parameter for determining the position of the jet. Through the LES models, more details of the 3D velocity and effluent distributions are available, allowing for a detailed analysis of how the secondary circulation develops and how the jet vortices change the development patterns. A method for clustering instantaneous vortices to separate sub-cells of secondary circulation is established, and is used to set a baseline for the development of secondary flow in a channel bend without a jet. The effect of an added jet was investigated in detail for a single flow condition, and then with machine learning techniques to develop a parametrical model incorporating both channel and jet flow conditions. The best performing machine learning model for the parametrisation of secondary flow cells with the jet is the ANFIS model coupled with a decision tree classifying the presence of each sub-cell; without the jet, the best-performing model is the ANFIS model without any additional classification. The effluent distribution is well-characterised using multiple linear regression. The addition of a jet changes the relative strengths of secondary circulation sub-cells and their circulation development and retention characteristics, though the total circulation in the bend is not strongly affected by the jet.

Cold flow inside a Solid Fueled Ramjet (SFRJ) is simulated using large eddy simulations (LES). A finite element method using a Discontinuous Galerkin bases has been implemented in the open-sourced multi-physics software SU2. Novel LES formulations of the fuel-gas boundary conditions and the heat release due to mixing are obtained using integration by parts over the discontinuous Galerkin bases. The Smagorisnki and wall-adapted subgrid stress model for the scalar variance have been implemented and investigated in twodimensions. Spectral Proper Orthogonal Decomposition is used to analyze CFD results to determine acoustic modes in the ramjet. Peak acoustic frequencies are compared between between numerical and experimental results. Comparisons are made between simulations performed with a 2D axisymmetric domain and full 3D domain. Cold-flow LES simulations show that there are two dominant acoustic modes (St ≡ f/f0 = {3, 18}) in the ramjet and their frequency appears to be invariant to the cavity configuration. The first peak corresponds to a longitudinal mode associated to the chamber fundamental oscillations (with length scale Lc). The second is characterized with radial fluctuations in the mixing chamber and features the maximum chamber radius of the ramjet as its scaling length. Mixed (radial and axial) modes in the intermediate frequency range reveal the effect of a slanted aft wall on the acoustics. Three-dimensional cold flow simulations predicted weak non-symmetric (azimuthal) modes. Hot-flow simulations show a substantial increase in the mean chamber pressure with the addition of the cavity, indicating that it enhances flame-holding in solid-fuel ramjets, in agreement with the experiments. The analysis of the ramjet acoustic modes shows the emergence of low frequency modes in the cavity cases, in agreement with the experiments. Using SPOD, these modes were associated with low frequency breathing of the recirculation region at the nozzle throat. Perturbations are localized in the throat region because of the Mach number pressure scaling. These modes do not seem to affect the pressure fluctuation and thus combustion in the chamber. Together with the emergence of low frequency vortical modes, the cavity supports a decrease in the high-wave number harmonics of the ramjet chamber acoustic mode. These fluctuations are supported by non-linear amplification of the fundamental mode, which is enhanced by the thermo-acoustic coupling. / Master of Science / Novel propulsion designs, such as solid fuel ramjets, present the opportunity of optimizing cavity shapes using additive manufacturing and three-dimensional printing to improve fuelair mixing and lowering the thermo-acoustic feedback. In this work a computational model for solid fuel ramjets is developed and applied to laboratory firing tests performed by Prof Young's group at the advanced propulsion laboratory at Virginia Tech. In order to capture the fine mixing scales a novel discretization of the reactive Navier-Stokes using discontinuous Galerkin bases is implemented in an open source CFD code popular with aerospace graduate students and researchers. Subgrid modelling is implemented to determine the effect of small scales on the PMMA combustion mechanism developed at Virginia Tech. Numerical methods are used to simulate the turbulent flow of air through an axisymmetric cavity.

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