Effect of mesh distortion on the accuracy of high order vorticity-velocity CFD approaches

The numerical solution of the incompressible Navier-Stokes equations offers an alternative to experimental analysis of fluid-structure interaction (FSI). We would save a lot of time and effort and help cut back on costs, if we are able to accurately model systems by these numerical solutions. These advantages are even more obvious when considering huge structures like bridges, high rise buildings or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the Kinematic Laplacian Equation (KLE) to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ordinary differential equations (ODE) time integration schemes, allowing us to tackle each problem as a separate module. The current algortihm for the KLE uses an unstructured quadrilateral mesh, formed by dividing each triangle of an unstructured triangular mesh into three quadrilaterals for spatial discretization. This research deals with determining a suitable measure of mesh quality based on the physics of the problems being tackled. This is followed by exploring methods to improve the quality of quadrilateral elements obtained from the triangles and thereby improving the overall mesh quality. A series of numerical experiments were designed and conducted for this purpose and the results obtained were tested on different geometries with varying degrees of mesh density.

Time-domain modeling of high-frequency electromagnetic wave propagation, overhead wires, and earth

Prediction of radiated fields from transmission lines has not previously been studied from a panoptical power system perspective. The application of BPL technologies to overhead transmission lines would benefit greatly from an ability to simulate real power system environments, not limited to the transmission lines themselves. Presently circuitbased transmission line models used by EMTP-type programs utilize Carson’s formula for a waveguide parallel to an interface. This formula is not valid for calculations at high frequencies, considering effects of earth return currents. This thesis explains the challenges of developing such improved models, explores an approach to combining circuit-based and electromagnetics modeling to predict radiated fields from transmission lines, exposes inadequacies of simulation tools, and suggests methods of extending the validity of transmission line models into very high frequency ranges. Electromagnetics programs are commonly used to study radiated fields from transmission lines. However, an approach is proposed here which is also able to incorporate the components of a power system through the combined use of EMTP-type models. Carson’s formulas address the series impedance of electrical conductors above and parallel to the earth. These equations have been analyzed to show their inherent assumptions and what the implications are. Additionally, the lack of validity into higher frequencies has been demonstrated, showing the need to replace Carson’s formulas for these types of studies. This body of work leads to several conclusions about the relatively new study of BPL. Foremost, there is a gap in modeling capabilities which has been bridged through integration of circuit-based and electromagnetics modeling, allowing more realistic prediction of BPL performance and radiated fields. The proposed approach is limited in its scope of validity due to the formulas used by EMTP-type software. To extend the range of validity, a new set of equations must be identified and implemented in the approach. Several potential methods of implementation have been explored. Though an appropriate set of equations has not yet been identified, further research in this area will benefit from a clear depiction of the next important steps and how they can be accomplished. Prediction of radiated fields from transmission lines has not previously been studied from a panoptical power system perspective. The application of BPL technologies to overhead transmission lines would benefit greatly from an ability to simulate real power system environments, not limited to the transmission lines themselves. Presently circuitbased transmission line models used by EMTP-type programs utilize Carson’s formula for a waveguide parallel to an interface. This formula is not valid for calculations at high frequencies, considering effects of earth return currents. This thesis explains the challenges of developing such improved models, explores an approach to combining circuit-based and electromagnetics modeling to predict radiated fields from transmission lines, exposes inadequacies of simulation tools, and suggests methods of extending the validity of transmission line models into very high frequency ranges. Electromagnetics programs are commonly used to study radiated fields from transmission lines. However, an approach is proposed here which is also able to incorporate the components of a power system through the combined use of EMTP-type models. Carson’s formulas address the series impedance of electrical conductors above and parallel to the earth. These equations have been analyzed to show their inherent assumptions and what the implications are. Additionally, the lack of validity into higher frequencies has been demonstrated, showing the need to replace Carson’s formulas for these types of studies. This body of work leads to several conclusions about the relatively new study of BPL. Foremost, there is a gap in modeling capabilities which has been bridged through integration of circuit-based and electromagnetics modeling, allowing more realistic prediction of BPL performance and radiated fields. The proposed approach is limited in its scope of validity due to the formulas used by EMTP-type software. To extend the range of validity, a new set of equations must be identified and implemented in the approach. Several potential methods of implementation have been explored. Though an appropriate set of equations has not yet been identified, further research in this area will benefit from a clear depiction of the next important steps and how they can be accomplished.

Design of high fidelity building energy monitoring system

Building energy meter network, based on per-appliance monitoring system, willbe an important part of the Advanced Metering Infrastructure. Two key issues exist for designing such networks. One is the network structure to be used. The other is the implementation of the network structure on a large amount of small low power devices, and the maintenance of high quality communication when the devices have electric connection with high voltage AC line. The recent advancement of low-power wireless communication makes itself the right candidate for house and building energy network. Among all kinds of wireless solutions, the low speed but highly reliable 802.15.4 radio has been chosen in this design. While many network-layer solutions have been provided on top of 802.15.4, an IPv6 based method is used in this design. 6LOWPAN is the particular protocol which adapts IP on low power personal network radio. In order to extend the network into building area without, a specific network layer routing mechanism-RPL, is included in this design. The fundamental unit of the building energy monitoring system is a smart wall plug. It is consisted of an electricity energy meter, a RF communication module and a low power CPU. The real challenge for designing such a device is its network firmware. In this design, IPv6 is implemented through Contiki operation system. Customize hardware driver and meter application program have been developed on top of the Contiki OS. Some experiments have been done, in order to prove the network ability of this system.

Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

BENEFICIATION OF HIGH-MgO SEDIMENTARY PHOSPHATE ORES

Dolomite [CaMg(CO3)2] is an intolerable impurity in phosphate ores due to its MgO content. Traditionally, the Florida phosphate industry has avoided mining high-MgO phosphate reserves due to the lack of an economically viable process for removal of dolomite. However, as the high grade phosphate reserves become depleted, more emphasis is being put on the development of a cost effective method for separating dolomite from high-MgO phosphate ores. In general, the phosphate industry demands a phosphate concentrate containing less than 1%MgO. Dolomite impurities have mineralogical properties that are very similar to the desired phosphate minerals (francolite), making the separation of the two minerals very difficult. Magnesium is primarily found as distinct dolomite-rich pebbles, very fine dolomite inclusions in predominately francolite pebbles, and magnesium substituted into the francolite structure. Jigging is a gravity separation process that attempts to take advantage of the density difference between the dolomite and francolite pebbles. A unique laboratory scale jig was designed and built at Michigan Tech for this study. Through a series of tests it was found that a pulsation rate of 200 pulse/minute, a stroke length of 1 inch, a water addition rate of 0.5gpm, and alumina ragging balls were optimum for this study. To investigate the feasibility of jigging for the removal of dolomite from phosphate ore, two high-MgO phosphate ores were tested using optimized jigging parameters: (1) Plant #1 was sized to 4.00x0.85mm and contained 1.55%MgO; (2) Plant #2 was sized to 3.40mmx0.85mm and contained 3.07% MgO. A sample from each plant was visually separated by hand into dolomite and francolite rich fractions, which were then analyzed to determine the minimum achievable MgO levels. For Plant #1 phosphate ore, a concentrate containing 0.89%MgO was achieved at a recovery of 32.0%BPL. For Plant #2, a phosphate concentrate containing 1.38%MgO was achieved at a recovery of 74.7%BPL. Minimum achievable MgO levels were determined to be 0.53%MgO for Plant #1 and 1.15%MgO for Plant #2.