Indiana University-Purdue University Indianapolis (IUPUI) / This thesis proposes an automated grid-based alignment system utilizing lasers and an array of light-detecting photodiodes. The intent is to create an inexpensive and scalable alignment system for pick-and-place robotic systems. The system utilizes the transformation matrix, geometry, and trigonometry to determine the movements to align the robot with a grid-based array of photodiodes. The alignment system consists of a sending unit utilizing lasers, a receiving module consisting of photodiodes, a data acquisition unit, a computer-based control system, and the robot being aligned. The control system computes the robot movements needed to position the lasers based on the laser positions detected by the photodiodes. A transformation matrix converts movements from the coordinate system of the grid formed by the photodiodes to the coordinate system of the robot. The photodiode grid can detect a single laser spot and move it to any part of the grid, or it can detect up to four laser spots and use their relative positions to determine rotational misalignment of the robot. Testing the alignment consists of detecting the position of a single laser at individual points in a distinct pattern on the grid array of photodiodes, and running the entire alignment process multiple times starting with different misalignment cases. The first test provides a measure of the position detection accuracy of the system, while the second test demonstrates the alignment accuracy and repeatability of the system. The system detects the position of a single laser or multiple lasers by using a method similar to a center-of-gravity calculation. The intensity of each photodiode is multiplied by the X-position of that photodiode. The summed result from each photodiode intensity and position product is divided by the summed value of all of the photodiode intensities to get the X-position of the laser. The same thing is done with the Y-values to get the Y-position of the laser. Results show that with this method the system can read a single laser position value with a resolution of 0.1mm, and with a maximum X-error of 2.9mm and Y-error of 2.0mm. It takes approximately 1.5 seconds to process the reading. The alignment procedure calculates the initial misalignment between the robot and the grid of photodiodes by moving the robot to two distinct points along the robot’s X-axis so that only one laser is over the grid. Using these two detected points, a movement trajectory is generated to move that laser to the X = 0, Y = 0 position on the grid. In the process, this moves the other three lasers over the grid, allowing the system to detect the positions of four lasers and uses the positions to determine the rotational and translational offset needed to align the lasers to the grid of photodiodes. This step is run in a feedback loop to update the adjustment until it is within a permissible error value. The desired result for the complete alignment is a robot manipulator positioning within ±0.5mm along the X and Y-axes. The system shows a maximum error of 0.2mm in the X-direction and 0.5mm in the Y-direction with a run-time of approximately 4 to 5 minutes per alignment. If the permissible error value of the final alignment is tripled the alignment time goes down to 1 to 1.5 minutes and the maximum error goes up to 1.4mm in both the X and Y-directions. The run time of the alignment decreases because the system runs fewer alignment iterations.

This thesis details the development, verification and validation of an unsteady unstructured high order (≥ 3) h/p Discontinuous Galerkin - Fourier solver for the incompressible Navier-Stokes equations on static and rotating meshes in two and three dimensions. This general purpose solver is used to provide insight into cross-flow (wind or tidal) turbine physical phenomena. Simulation of this type of turbine for renewable energy generation needs to account for the rotational motion of the blades with respect to the fixed environment. This rotational motion implies azimuthal changes in blade aero/hydro-dynamics that result in complex flow phenomena such as stalled flows, vortex shedding and blade-vortex interactions. Simulation of these flow features necessitates the use of a high order code exhibiting low numerical errors. This thesis presents the development of such a high order solver, which has been conceived and implemented from scratch by the author during his doctoral work. To account for the relative mesh motion, the incompressible Navier-Stokes equations are written in arbitrary Lagrangian-Eulerian form and a non-conformal Discontinuous Galerkin (DG) formulation (i.e. Symmetric Interior Penalty Galerkin) is used for spatial discretisation. The DG method, together with a novel sliding mesh technique, allows direct linking of rotating and static meshes through the numerical fluxes. This technique shows spectral accuracy and no degradation of temporal convergence rates if rotational motion is applied to a region of the mesh. In addition, analytical mappings are introduced to account for curved external boundaries representing circular shapes and NACA foils. To simulate 3D flows, the 2D DG solver is parallelised and extended using Fourier series. This extension allows for laminar and turbulent regimes to be simulated through Direct Numerical Simulation and Large Eddy Simulation (LES) type approaches. Two LES methodologies are proposed. Various 2D and 3D cases are presented for laminar and turbulent regimes. Among others, solutions for: Stokes flows, the Taylor vortex problem, flows around square and circular cylinders, flows around static and rotating NACA foils and flows through rotating cross-flow turbines, are presented.