A panel method derived from inviscid irrotational flow theory and utilizing hyperboloid panels is developed and applied to the simulation of steady fully wetted flows inside water-jet pumps and rocket engine inducers. The source and dipole influence coefficients of the hyperboloid panels are computed using Gauss quadrature. The present method solves the boundary value problem subject to a uniform inflow directly by discretizing the blade, casing/shroud and hub geometries with panels. The Green's integral equation and the influence coefficients for the water-jet/inducer problem are defined and solved by allocating constant strength sources and dipoles on the blade, hub and casing surfaces and constant strength dipoles on the shed wake sheets from the rotor/ stator blades. The rotor- stator interaction is accomplished using an iterative procedure which considers the effects between the rotor and the stator, via circumferentially averaged induced velocities. Finally, the hydrodynamic performance predictions for the water-jet pump and the inducer from the present method are validated against existing experimental data and numerical results from Reynolds Averaged Navier- Stokes (RANS) solvers. / text

Continuous and discrete-time Successive Backward Sweep (SBS) methods for solving nonlinear optimal control problems involving terminal and control constraints are proposed in this dissertation. They closely resemble the Neighboring Extremals and Differential Dynamic Programming algorithms, which are based on the successive solutions to a series of linear control problems with quadratic performance indices. The SBS methods are relatively insensitive to the initial guesses of the state and control histories, which are not required to satisfy the system dynamics. Hessian modifications are utilized, especially for non-convex problems, to avoid singularities during the backward integration of the gain equations. The SBS method requires the satisfaction of the Jacobi no-conjugate point condition and hence, produces optimal solutions. The standard implementation of the SBS method for continuous-time systems incurs terminal boundary condition errors due to an algorithmic singularity as well as numerical inaccuracies in the computation of the gain matrices. Alternatives for boundary error reduction are proposed, notably the aiming point and the switching between two forms of the sweep expansion formulae. Modification of the sweep formula expands the domain of convergence of the SBS method and allows for a rigorous testing for the existence of conjugate points. Numerical accuracy of the continuous-time formulation of the optimal control problem can be improved with the use of symplectic integrators, which generally are implicit schemes in time. A time-explicit group preserving method based on the Magnus series representation of the state transition is implemented in the SBS setting and is shown to outperform a non-symplectic integrator of the same order. Discrete-time formulations of the optimal control problem, directly accounting for a specific time-stepping method, lead to consistent systems of equations, whose solutions satisfy the boundary conditions of the discretized problem accurately. In this regard, the second-order, implicit mid-point averaging scheme, a symplectic integrator, is adapted for use with the SBS method. The performance of the mid-point averaging scheme is compared with other methods of equal and higher-order non-symplectic schemes to show its advantages. The SBS method is augmented with a homotopy- continuation procedure to isolate and regulate certain nonlinear effects for difficult problems, in order to extend its domain of convergence. The discrete-time SBS method is also extended to solve problems where the controls are approximated to be impulsive and to handle waypoint constraints as well. A variety of highly nonlinear optimal control problems involving orbit transfer, atmospheric reentry, and the restricted three-body problem are treated to demonstrate the performance of the methods developed in this dissertation.

Since its introduction in 1997, the use of Detached Eddy Simulation (DES) and similar hybrid turbulence techniques has become increasingly popular in the field of CFD. However, with increased use some of the limitations of the DES model have become apparent. One of these is the dependence of DES on grid construction, particularly regarding the point of transition between the Reynolds-Averaged Navier-Stokes and Large Eddy Simulation models. An additional issue that arises with unstructured grids is the definition of the grid spacing in the implementation of a DES length scale. To lay the ground work to study these effects the Spalart-Allmaras one-equation turbulence model, SA based DES hybrid turbulence model, and the Scale Adaptive Simulation hybrid turbulence model are implemented in an unstructured grid CFD code, UNCLE. The implemented SA based DES model is validated for flow over a three-dimensional circular cylinder for three different turbulent Reynolds numbers. Validation included studying the pressure, skin friction coefficient, centerline velocity distributions averaged in time and space. Tools to output the mean velocity profiles and Reynolds stresses were developed. A grid generation code was written to generate a two/three dimensional circular cylinder grid to simulate flow over the cylinder in UNCLE. The models implemented and validated, and the additional tools mentioned will be used in the future.

A numerical solution algorithm based on finite volume method is developed for unsteady, two-dimensional, depth-averaged shallow water flow equations. The model is verified using test cases from the literature and free surface data obtained from measurements in a laboratory flume. Experiments are carried out in a horizontal, rectangular channel with vertical solid boxes attached on the sidewalls to obtain freesurface data set in flows where three-dimensionality is significant. Experimental data contain both subcritical and supercritical states. The shallow water equations are solved on a structured, rectangular grid system. Godunov type solution procedure evaluates the interface fluxes using an upwind method with an exact Riemann solver. The numerical solution reproduces analytical solutions for the test cases successfully. Comparison of the numerical results with the experimental two-dimensional free surface data is used to illustrate the limitations of the shallow water equations and improvements necessary for better simulation of such cases.

abstract: Reynolds-averaged Navier-Stokes (RANS) simulation is the industry standard for computing practical turbulent flows -- since large eddy simulation (LES) and direct numerical simulation (DNS) require comparatively massive computational power to simulate even relatively simple flows. RANS, like LES, requires that a user specify a “closure model” for the underlying turbulence physics. However, despite more than 60 years of research into turbulence modeling, current models remain largely unable to accurately predict key aspects of the complex turbulent flows frequently encountered in practical engineering applications. Recently a new approach, termed “autonomic closure”, has been developed for LES that avoids the need to specify any prescribed turbulence model. Autonomic closure is a fully-adaptive, self-optimizing approach to the closure problem, in which the simulation itself determines the optimal local, instantaneous relation between any unclosed term and the simulation variables via solution of a nonlinear, nonparametric system identification problem. In principle, it should be possible to extend autonomic closure from LES to RANS simulations, and this thesis is the initial exploration of such an extension. A RANS implementation of autonomic closure would have far-reaching impacts on the ability to simulate practical engineering applications that involve turbulent flows. This thesis has developed the formal connection between autonomic closure for LES and its counterpart for RANS simulations, and provides a priori results from FLUENT simulations of the turbulent flow over a backward-facing step to evaluate the performance of an initial implementation of autonomic closure for RANS. Key aspects of these results lay the groundwork on which future efforts to extend autonomic closure to RANS simulations can be based. / Dissertation/Thesis / Masters Thesis Aerospace Engineering 2017

Dam spillways and downstream areas are used to guide large flows of water during for example heavy rainfall. The large flows give way to turbulent pattern sand velocities that may damage the river banks or the dam structure. Investigation of these water patterns at certain flows are therefore done to examine at risk areas. In this study CFD simulations were performed for different flows with different boundary conditions for varying surface roughness level. Results were then compared to a previous model study from 2009. The ANSYS ecosystem was used in production of the 3D model, construction of mesh and running of simulations.The flow for the maximum discharge capacity of the sluices was simulated as well as the design flow which is the highest flow the dam is supposed to be able to withstand. In this report the flow has been modeled using RANS with the SST kω-model in a VOF transient setup. Results showed that for both the design flow and the maximum discharge capacity flow the energy conversion is functioning poorly and that a considerable backward circulation exists on the right riverside. This behavior could possibly injure the right dam structure by moving debris upwards against the stream.

<p>A study has been undertaken to investigate the flow structure in the vicinity of discontinuities in the surface of a high-speed air vehicle. The effect of gaps and steps on aerodynamic heating is of particular interest. The present    thesis presents Reynolds-averaged Navier Stokes  (RANS) calculations of this class of flow. This thesis consists of two studies: a parametric study of cavity flow at Mach 2 and a study to compare with wind tunnel experiments at Mach 6. The calculations for the parametric study used the Menter two-equation SST turbulence model at fully turbulent conditions. These are two-dimensional cavity flows that were carried out to identify the influence of cavity geometry on flow structure and heating distribution inside the cavity, and to categorize cavity flow regimes. The second study employed RANS calculations for conditions  corresponding to Mach 10 wind tunnel experiments carried out by Nestler et al. (AIAA Paper 1968-673) for Mach 6 boundary layer edge conditions. The SST model used in the parametric study was paired with the Menter oneequation transition model and the two-equation realizable κ-ϵ model in CFD++ was used for the computations. The results showed that, even with adjustment of model parameters, the Menter transition model cannot match the location of laminar to turbulent transition, but it demonstrated good agreement with the experimental data in fully turbulent conditions. The two-equation realizable κ-ϵ model, available in CFD++, was able to accurately model transition and showed favorable agreement for fully turbulent conditions as well.</p>

The ability of Reynolds Averaged Navier Stokes (RANS) models to predict the characteristics of a non-Body of Revolution (non-BOR) Ellipsoidal model is studied to establish the feasibility of utilizing RANS as a non-BOR concept design tool. Data unable to be obtained experimentally, such as streamwise and spanwise pressure gradients and yaw turn boundary layer characteristics, are also established. A range of conditions are studied including ahead, pitched up, steady 10 and 15 degree yaw turns, and unsteady 10 and 15 degree yaw turns. Simulation results show good agreement for ahead and pitched forces and moments. Straight ahead skin friction values also showed good agreement, providing even improved agreement over an LES model which utilized wall functions. Yaw turn conditions also showed good agreement for roll angles up to 10 degrees. Steady maneuvering forces and moments showed good agreement up to 10 degrees roll and separation calculations also showed good agreement up to 10 degrees roll. Unsteady maneuvering characteristics showed mixed results, with the normal force and pitching moment trends generally agreeing with experimental data, whereas the unsteady rolling moment did not tend to follow experimental trends. Two primary conditions, the change in curvature between the mid-body and elliptical ends and the accuracy of modeling of 3D flows with RANS, are discussed as sources of discrepancies between the experimental data and steady simulations greater than 10 degrees roll and unsteady rolling simulations. / Master of Science

<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)

Diffusion-weighted magnetic resonance imaging (dMRI) is a powerful tool for thecharacterisation of neural tissue microstructural features. The role of neural projectioncurvature on the diffusion signal was recently studied for three temporal regimes of the diffusion pulse sequence in search for a description of the different decay trends in the orientationally-averaged diffusion signal reported in in vivo human studies.This work experimentally investigates the effects of neural projection curvedness in one of these regimes, namely the short diffusion time regime. Multi-shell diffusion MRI acquisitions on fixed rat spinal cord were performed using a custom number of diffusion gradient directions on a vertical bore pre-clinical MRI scanner capable of generating 3000 mT/m. Diffusion was probed in three different q-values ranges [450, 970], [600, 1400] and [1500, 1750] mm-1 using diffusion pulse durations of 1.4,2 and 2.5ms, respectively. Noise correction was performed on the diffusion data and the orientationally-averaged signal was computed for each shell using a weighted mean. The signal from selected regions in the sample was then fitted to a power law. Results show that gray matter areas exhibit a signal reduction with variable decay trends in the range of diffusion sensitivity values used here. This suggests that gray matter microstructure features are pictured by the orientationally-averaged signal in the high diffusion sensitivity regime and, as theoretically suggested, neurite curvature might play a role in characterizing the signal decay. These preliminary results may prove useful in the development of models for the interpretation of the diffusion signal and the design of acquisition strategies that aim to study the high diffusion sensitivity regime.