The purpose of this investigation is to computationally investigate instabilities appearing in the wake of a simulated helicopter rotor. Existing data suggests further understanding of these instabilities may yield design changes to the rotor blades to reduce the acoustic signature and improve the aerodynamic efficiencies of the aircraft. Test cases of a double-bladed and single-bladed rotor have been run to investigate the causes and types of wake instabilities, as well as compare them to the short wave, long wave, and mutual inductance modes proposed by Widnall[2]. Evaluation of results revealed several perturbations appearing in both single and double-bladed wakes, the origin of which was unknown and difficult to trace. This made the computations not directly comparable to theoretical results, and drawing into question the physical flight conditions being modeled. Nonetheless, they displayed a wake structure highly sensitive to both computational and physical disturbances; thus extreme care must be taken in constructing grids and applying boundary conditions when doing wake computations to ensure results relevant to the complex and dynamic flight conditions of physical aircraft are generated.

Over the past several years, there has been growing concern regarding concussions and traumatic brain injuries (TBIs) in all levels of sports. A concussion is a traumatic brain injury that occurs from a blow to the head. When a concussion occurs, the brain knocks against the walls of the skull. A concussion causes temporary loss of brain function leading to cognitive, physical, and emotional symptoms, such as confusion, vomiting,headache, nausea,depression, disturbed sleep, moodiness, and amnesia. Although the short-term effects of concussions are limited, the long-term effects of concussions, if untreated, can be devastating and even life-threatening. Concussions are having detrimental ramifications on society and it is important to know what these ramifications are. Concussions are a common occurrence in traditional physical sports such as soccer, basketball, and football. However, due to the violent nature of football (American football), concussions are more prevalent and the effects are more severe. Changes to rules and equipment, specifically helmets, have been made to reduce head impacts in football but there is not currently enough evidence to conclude that they significantly lessen the frequency and severity of concussions.

This study consisted of two fundamental experiments that examined the effects of surface parameters on baseball aerodynamics. The first experiment measured drag and lift coefficients in response to varied surface treatments of a non-spinning baseball. This experiment found that rougher surfaces (rubbing mud, increased ball usage, and scuffing) decrease drag coefficient by up to 0.05 for Reynolds numbers of up to 1.5x105 (wind speeds of 30 m/s or 67 mph). The maximum observed increase in lift coefficient was 0.20, caused by heavily scuffing the top of the ball. These results can be explained by boundary layer transition phenomena and asymmetry in the surface roughness of the ball. A decrease in drag coefficient of 0.05 can translate to an increase in the flight distance of a batted ball by as much as 50 ft (14%), and an increase of 0.20 in lift coefficient can increase flight distance by 70 ft (19%) \u2014 numbers that can easily mean the difference between a routine fly out and a monster home run. The second experiment measured drag and lift coefficients in response to varied stitch geometries of a non-spinning, 3D-printed baseball. Increasing stitch height, width, and spacing was found to increase drag coefficient, while increasing stitch length had little effect on lift coefficient. Increasing any parameter of the stitch geometry was found to increase lift coefficient. These results can be explained by boundary layer transition phenomena, blockage effects, and asymmetry in the stitch geometry of the ball. Future work would do well to repeat these experiments with a larger wind tunnel and a more sensitive force balance. These results should also be validated at higher wind speeds, and for spinning, rather than stationary baseballs. In addition, future work should explore the degree to which surface roughness and stitch geometry affect drag and lift coefficients at different ball orientations.

We studied left ventricular flow patterns for a range of rotational orientations of a bileaflet mechanical heart valve (MHV) implanted in the mitral position of an elastic model of a beating left ventricle (LV). The valve was rotated through 3 angular positions (0, 45, and 90 degrees) about the LV long axis. Ultrasound scans of the elastic LV were obtained in four apical 2-dimensional (2D) imaging projections, each with 45 degrees of separation. Particle imaging velocimetry was performed during the diastolic period to quantify the in-plane velocity field obtained by computer tracking of diluted microbubbles in the acquired ultrasound projections. The resulting velocity field, vorticity, and shear stresses were statistically significantly altered by angular positioning of the mechanical valve, although the results did not show any specific trend with the valve angular position and were highly dependent on the orientation of the imaging plane with respect to the valve. We conclude that bileaflet MHV orientation influences hemodynamics of LV filling. However, determination of ‘optimal’ valve orientation cannot be made without measurement techniques that account for the highly 3-dimensional (3D) intraventricular flow.

The central purpose of this work is to investigate the large-scale, coherent structures that exist in turbulent Rayleigh-Bénard convection (RBC) when the domain is large enough for the classical ”wind of turbulence” to break down. The study exclusively focuses on the structures that from when the RBC geometry is a cylinder. A series of visualization studies, Fourier analysis and proper orthogonal decomposition are employed to qualitatively and quantitatively inspect the large-scale structures’ length and time scales, spatial organization, and dynamic properties. The data in this study is generated by direct numerical simulation to resolve all the scales of turbulence in a 6.3 aspect-ratio cylinder at a Rayleigh number of 9.6 × 107 and Prandtl number of 6.7. Single and double point statistics are compared against experiments and several resolution criteria are examined to verify that the simulation has enough spatial and temporal resolution to adequately represent the physical system.

Large-scale structures are found to organize as roll-cells aligned along the cell’s side walls, with rays of vorticity pointing toward the core of the cell. Two different large- scale organizations are observed and these patterns are well described spatially and energetically by azimuthal Fourier modes with frequencies of 2 and 3. These Fourier modes are shown to be dominant throughout the entire domain, and are found to be the primary source for radial inhomogeneity by inspection of the energy spectra. The precision with which the azimuthal Fourier modes describe these large-scale structures shows that these structures influence a large range of length scales. Conversely, the smaller scale structures are found to be more sensitive to radial position within the Fourier modes showing a strong dependence on physical length scales.

Dynamics in the large-scale structures are observed including a transition in the global pattern followed by a net rotation about the central axis. The transition takes place over 10 eddy-turnover times and the subsequent rotation occurs at a rate of approximately 1.1 degrees per eddy-turnover. These time-scales are of the same order of magnitude as those seen in lower aspect-ratio RBC for similar events and suggests a similarity in dynamic events across different aspect-ratios.

This dissertation describes a process for interface capturing via an arbitrary-order, nearly quadrature free, discontinuous Galerkin (DG) scheme for the conservative level set method (Olsson et al., 2005, 2008). The DG numerical method is utilized to solve both advection and reinitialization, and executed on a refined level set grid (Herrmann, 2008) for effective use of processing power. Computation is executed in parallel utilizing both CPU and GPU architectures to make the method feasible at high order. Finally, a sparse data structure is implemented to take full advantage of parallelism on the GPU, where performance relies on well-managed memory operations.

With solution variables projected into a kth order polynomial basis, a k+1 order convergence rate is found for both advection and reinitialization tests using the method of manufactured solutions. Other standard test cases, such as Zalesak's disk and deformation of columns and spheres in periodic vortices are also performed, showing several orders of magnitude improvement over traditional WENO level set methods. These tests also show the impact of reinitialization, which often increases shape and volume errors as a result of level set scalar trapping by normal vectors calculated from the local level set field.

Accelerating advection via GPU hardware is found to provide a 30x speedup factor comparing a 2.0GHz Intel Xeon E5-2620 CPU in serial vs. a Nvidia Tesla K20 GPU, with speedup factors increasing with polynomial degree until shared memory is filled. A similar algorithm is implemented for reinitialization, which relies on heavier use of shared and global memory and as a result fills them more quickly and produces smaller speedups of 18x.

The application of novel visualization and modeling methods to the study of cardiovascular disease is vital to the development of innovative diagnostic techniques, including those that may aid in the early detection and prevention of cardiovascular disorders. This dissertation focuses on the application of particle image velocimetry (PIV) to the study of intracardiac hemodynamics. This is accomplished primarily though the use of ultrasound based PIV, which allows for in vivo visualization of intracardiac flow without the requirement for optical access, as is required with traditional camera-based PIV methods.

The fundamentals of ultrasound PIV are introduced, including experimental methods for its implementation as well as a discussion on estimating and mitigating measurement error. Ultrasound PIV is then compared to optical PIV; this is a highly developed technique with proven accuracy; through rigorous examination it has become the “gold standard” of two-dimensional flow visualization. Results show good agreement between the two methods.

Using a mechanical left heart model, a multi-plane ultrasound PIV technique is introduced and applied to quantify a complex, three-dimensional flow that is analogous to the left intraventricular flow. Changes in ventricular flow dynamics due to the rotational orientation of mechanical heart valves are studied; the results demonstrate the importance of multi-plane imaging techniques when trying to assess the strongly three-dimensional intraventricular flow.

The potential use of ultrasound PIV as an early diagnosis technique is demonstrated through the development of a novel elasticity estimation technique. A finite element analysis routine is couple with an ensemble Kalman filter to allow for the estimation of material elasticity using forcing and displacement data derived from PIV. Results demonstrate that it is possible to estimate elasticity using forcing data derived from a PIV vector field, provided vector density is sufficient.

The atomization of a liquid jet by a high speed cross-flowing gas has many applications such as gas turbines and augmentors. The mechanisms by which the liquid jet initially breaks up, however, are not well understood. Experimental studies suggest the dependence of spray properties on operating conditions and nozzle geom- etry. Detailed numerical simulations can offer better understanding of the underlying physical mechanisms that lead to the breakup of the injected liquid jet. In this work, detailed numerical simulation results of turbulent liquid jets injected into turbulent gaseous cross flows for different density ratios is presented. A finite volume, balanced force fractional step flow solver to solve the Navier-Stokes equations is employed and coupled to a Refined Level Set Grid method to follow the phase interface. To enable the simulation of atomization of high density ratio fluids, we ensure discrete consistency between the solution of the conservative momentum equation and the level set based continuity equation by employing the Consistent Rescaled Momentum Transport (CRMT) method. The impact of different inflow jet boundary conditions on different jet properties including jet penetration is analyzed and results are compared to those obtained experimentally by Brown & McDonell(2006). In addition, instability analysis is performed to find the most dominant insta- bility mechanism that causes the liquid jet to breakup. Linear instability analysis is achieved using linear theories for Rayleigh-Taylor and Kelvin- Helmholtz instabilities and non-linear analysis is performed using our flow solver with different inflow jet boundary conditions.

A design methodology for a new breed of launch vehicle capable of lofting small satellites to orbit is discussed. The growing need for such a rocket is great: the United States has no capabilities in place to quickly launch and reconstitute satellite constellations. A loss of just one satellite, natural or induced, could significantly degrade or entirely eliminate critical space-based assets which would need to be quickly replaced. Furthermore a rocket capable of meeting the requirements for operationally responsive space missions would be an ideal launch platform for small commercial satellites. The proposed architecture to alleviate this lack of an affordable dedicated small-satellite launch vehicle relies upon a combination of expendable medium-range military surplus solid rocket motor assets. The dissertation discusses in detail the current operational capabilities of these military boosters and provides an outline for necessary refurbishments required to successfully place a small payload in orbit. A custom 3DOF trajectory script is used to evaluate the performance of these designs. Concurrently, a parametric cost-mass-performance response surface methodology is employed as an optimization tool to minimize life cycle costs of the proposed vehicles. This optimization scheme is centered on reducing life cycle costs per payload mass delivered rather than raw performance increases. Lastly, a novel upper-stage engine configuration using Hydroxlammonium Nitrate (HAN) is introduced and experimentally static test fired to illustrate the inherent simplicity and high performance of this high density, nontoxic propellant. The motor was operated in both pulse and small duration tests using a newly developed proprietary mixture that is hypergolic with HAN upon contact. This new propellant is demonstrated as a favorable replacement for current space vehicles relying on the heritage use of hydrazine. The end result is a preliminary design of a vehicle built from demilitarized booster assets that complements, rather than replaces, traditional space launch vehicles. This dissertation proves that such capabilities exist and more importantly that the resulting architecture can serve as a viable platform for immediate and affordable access to low Earth orbit.

Many methods of passive flow control rely on changes to surface morphology. Roughening surfaces to induce boundary layer transition to turbulence and in turn delay separation is a powerful approach to lowering drag on bluff bodies. While the influence in broad terms of how roughness and other means of passive flow control to delay separation on bluff bodies is known, basic mechanisms are not well understood. Of particular interest for the current work is understanding the role of surface dimpling on boundary layers. A computational approach is employed and the study has two main goals. The first is to understand and advance the numerical methodology utilized for the computations. The second is to shed some light on the details of how surface dimples distort boundary layers and cause transition to turbulence. Simulations are performed of the flow over a simplified configuration: the flow of a boundary layer over a dimpled flat plate. The flow is modeled using an immersed boundary as a representation of the dimpled surface along with direct numerical simulation of the Navier-Stokes equations. The dimple geometry used is fixed and is that of a spherical depression in the flat plate with a depth-to-diameter ratio of 0.1. The dimples are arranged in staggered rows separated by spacing of the center of the bottom of the dimples by one diameter in both the spanwise and streamwise dimensions. The simulations are conducted for both two and three staggered rows of dimples. Flow variables are normalized at the inlet by the dimple depth and the Reynolds number is specified as 4000 (based on freestream velocity and inlet boundary layer thickness). First and second order statistics show the turbulent boundary layers correlate well to channel flow and flow of a zero pressure gradient flat plate boundary layers in the viscous sublayer and the buffer layer, but deviates further away from the wall. The forcing of transition to turbulence by the dimples is unlike the transition caused by a naturally transitioning flow, a small perturbation such as trip tape in experimental flows, or noise in the inlet condition for computational flows.