Mathematical models

Boundary layers are regions where turbulence develops easily. In the case where the flow occurs on a surface showing a certain degree of roughness, turbulence eddies will interact with the roughness elements and will produce an acoustic field. This thesis aims at predicting this type of noise with the help of the Computational Fluid Dynamics (CFD) simulation of a wall jet using the Reynolds Average Navier-Stokes (RANS) equations. A frequency spectrum is reconstructed using a representation of the turbulence with uncorrelated sheets of vorticity. Both aerodynamic and acoustic results are compared to experimental measurements of the flow. The CFD simulation of the flow returns consistent results but would benefit from a refinement of the grid. The surface pressure spectrum presents a slope in the high frequencies close to the experimental spectrum. The far field noise spectrum has a 5dB difference to the experiments.

Radar rainfall estimates have become a decision making tool for scientists, engineers and water managers in their tasks for developing hydrologic models, water supply planning, restoration of ecosystems, and flood control. In the present study, the utility of a power function for linking the rain gauge and radar estimates has been assessed. Mean daily rainfall data from 163 rain gauges installed within the South Florida Water Management District network have been used and their records from January 1st, 2002 to October 31st, 2007 analyzed. Results indicate that the power function coefficients and exponents obtained by using a non-linear optimization formulation, show spatial variability mostly affected by type of rainfall events occurring in the dry or wet seasons, and that the linear distance from the radar location to the rain gauge has a significant effect on the computed values of the coefficients and exponents.

A computational tool has been developed by integrating National Renewable Energy Laboratory (NREL) codes, Sandia National Laboratories' NuMAD, and ANSYS to investigate a horizontal axis composite ocean current turbine. The study focused on the design, analysis, and life prediction of composite blade considering random ocean current, cyclic rotation, and hurricane-driven ocean current. A structural model for a horizontal axis FAU research OCT blade was developed. Following NREL codes were used: PreCom, BModes, ModeShape, AeroDyn and FAST. PreComp was used to compute section properties of the OCT blade. BModes and ModeShape calculated the mode shapes of the blade. Hydrodynamic loading on the OCT blade was calculated by modifying the inputs to AeroDyn and FAST. These codes were then used to obtain the dynamic response of the blade, including blade tip displacement, normal force (FN) and tangential force (FT), flap and edge bending moment distribution with respect to blade rotation.

A sudden expansion combustor (SUE) is analyzed using computation fluid dynamics (CFD). CO emissions and NOx emissions are computed for various operating conditions of the SUE combustor using a can type and an annular type geometrical configurations. The goal of this thesis is to see if the SUE combustor is a viable alternative to conventional combustors which utilize swirlers. It is found that for the can type combustor the NOx emissions were quite low compared to other combustor types but the CO emissions were fairly high. The annular combustor shows better CO emissions compared to the can type, but the CO emissions are still high compared to other combustors. Emissions can be improved by providing better mixing in the primary combustion zone. The SUE combustor design needs to be further refined in order for it to be a viable alternative to conventional combustors with swirlers.

In recent years, a plethora of wireless applications such as Bluetooth and Ultra-wide band (UWB) radio have emerged. This drastic increase has overly congested the spectrum. So, new networks such as cognitive radios that can solve the spectrum congestion have emerged. But in such networks, interference is introduced at the physical layer. We study and develop an interference model capable of capturing the intrinsic characteristics of the coexistence of such wireless applications. We investigate the effect of interference using device isolation probability or outage probability in presence Rayleigh and Nakagami-m fading at the physical layer and the impact of lognormal shadowing. We assume that the devices are either deterministically placed or randomly distributed according to a Poisson point process. We derive explicit expressions for the isolation probability and outage probability that give insight into how these channel impairments affect communication in these applications. We use computer simulations to validate our analytical results.

This study assesses the viability of using a towfish mounted ADV for quantifying water velocity fluctuations in the Florida Current relevant to ocean current turbine performance. For this study a motion compensated ADV is operated in a test flume. Water velocity fluctuations are generated by a 1.3 cm pipe suspended in front of the ADV at relative current speeds of 0.9 m/s and 0.15 m/s, giving Reynolds numbers on the order of 1000. ADV pitching motion of +/- 2.5 [degree] at 0.3 Hz and a heave motion of 0.3 m amplitude at 0.2 Hz are utilized to evaluate the motion compensation approach. The results show correction for motion provides up to an order of magnitude reduction in turbulent kinetic energy at frequencies of motion while the IMU is found to generate 2% error at 1/30 Hz and 9% error at 1/60 Hz in turbulence intensity.

In essay I, I empirically examine theoretical inferences of real options models regarding the effects of business risk on the pricing of firms engaged in corporate control transactions. This study shows that the risk differential between the merging firms has a significant effect on the risk dynamic of bidding firms around control transactions and that the at-announcement risk dynamic is negatively related to that in the preannouncement period. In addition, the relative size of the target, the volatility of bidder cash flows, and the relative growth rate of the bidder have significant explanatory power in the cross-section of announcement returns to bidding firm shareholders as does the change in the cost of capital resulting from the transaction. Essay II provides an empirical analysis of a second set of real options models that theoretically examine the dynamics of financial risk around control transactions as well as the link between financial leverage and the probability of acquisition. In addition, I present a comparison of the financial risk dynamics of firms that choose an external growth strategy, through acquisition, and those that pursue an internal growth strategy through capital expenditures that are unrelated to acquisition.

Simulating the exact chaotic turbulent flow field about any geometry is a dilemma between accuracy and computational resources, which has been continuously studied for just over a hundred years. This thesis is a complete walk-through of the entire process utilized to approximate the flow ingested by a Sevik-type rotor based on solutions to the Reynolds Averaged Navier-Stokes equations (RANS). The Multiple Reference Frame fluid model is utilized by the code of ANSYS-FLUENT and results are validated by experimental wake data. Three open rotor configurations are studied including a uniform inflow and the rotor near a plate with and without a thick boundary layer. Furthermore, observations are made to determine the variation in velocity profiles of the ingested turbulent flow due to varying flow conditions.

This thesis proposes a sensor approach for quantifying the hydrodynamic performance of Ocean Current Turbines (OCT), and investigates the influence of sensor-specific noise and sampling rates on calculated turbine performance. Numerical models of the selected sensors are developed, and then utilized to add stochastic measurement error to numerically-generated, non-stochastic OCT data. Numerically-generated current velocity and turbine performance measurements are used to quantify the relative influence of sensor-specific error and sampling limitations on sensor measurements and calculated OCT performance results. The study shows that the addition of sensor error alters the variance and mean of OCT performance metric data by roughly 7.1% and 0.24%, respectively, for four evaluated operating conditions. It is shown that sensor error results in a mean, maximum and minimum performance metric to Signal to Noise Ration (SNR) of 48.6% and 6.2%, respectively.

Submerged turbines which harvest energy from ocean currents are an important potential energy resource, but their harsh and remote environment demands an automated system for machine condition monitoring and prognostic health monitoring (MCM/PHM). For building MCM/PHM models, vibration sensor data is among the most useful (because it can show abnormal behavior which has yet to cause damage) and the most challenging (because due to its waveform nature, frequency bands must be extracted from the signal). To perform the necessary analysis of the vibration signals, which may arrive rapidly in the form of data streams, we develop three new wavelet-based transforms (the Streaming Wavelet Transform, Short-Time Wavelet Packet Decomposition, and Streaming Wavelet Packet Decomposition) and propose modifications to the existing Short-TIme Wavelet Transform. ... The proposed algorithms also create and select frequency-band features which focus on the areas of the signal most important to MCM/PHM, producing only the information necessary for building models (or removing all unnecessary information) so models can run on less powerful hardware. Finally, we demonstrate models which can work in multiple environmental conditions. ... Our results show that many of the transforms give similar results in terms of performance, but their different properties as to time complexity, ability to operate in a fully streaming fashion, and number of generated features may make some more appropriate than others in particular applications, such as when streaming data or hardware limitations are extremely important (e.g., ocean turbine MCM/PHM).