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An overview of automatic mesh generation is presented and the need for a specialized mesh generation program for triax domes is discussed. The method of generation of the triax dome geometry, the terminology, the dome members and loading conditions and its modelling with ABAQUS is explained briefly. Development of an automatic mesh generation program, its structure and functions, the limitations and desirable extensions are also discussed. The program generates nodal coordinate and element connectivity data and also has mesh refinement features. All the necessary data required for modelling the triax dome with ABAQUS is generated automatically by the program. The model of an existing triax dome at Raleigh, North Carolina, is generated by the mesh generation program and is analyzed for stresses and displacements using the ABAQUS finite element analysis program. / Master of Science

A fully automated Cartesian/Quad grid generator and laminar flow solver have been developed for external flows by using C++. After defining the input geometry by nodal points, adaptively refined Cartesian grids are generated automatically. Quadtree data structure is used in order to connect the Cartesian cells to each other. In order to simulate viscous flows, body-fitted quad cells can be generated optionally. Connectivity is provided by cut and split cells such that the intersection points of Cartesian cells are used as the corners of quads at the outmost row. Geometry based adaptation methods for cut, split cells and highly curved regions are applied to the uniform mesh generated around the geometry. After obtaining a sufficient resolution in the domain, the solution is achieved with cellcentered approach by using multistage time stepping scheme. Solution based grid adaptations are carried out during the execution of the program in order to refine the regions with high gradients and obtain sufficient resolution in these regions. Moreover, multigrid technique is implemented to accelerate the convergence time significantly. Some tests are performed in order to verify and validate the accuracy and efficiency of the code for inviscid and laminar flows.

In this thesis, an approach is presented for the generation of grids suitable for the simulation of high Reynolds number viscous flows in complex three-dimensional geometries. The automatic and reliable generation of such grids is today on the biggest bottlenecks in the industrial CFD simulation environment. In the proposed approach, unstructured tetrahedral grids are employed for the regions far from the viscous boundaries of the domain, while semi-structured layers of high aspect ratio prismatic and hexahedral elements are used to provide the necessary grid resolution inside the boundary layers and normal to the viscous walls. The definition of the domain model is based on the STEP ISO standard and the topological information contained in the model is used for applying the hierarchical grid generation parameters defined by the user. An efficient, high-quality and robust algorithm is presented for the generation of the unstructured simplicial (triangular of tetrahedral) part of the grid. The algorithm is based on the Delaunay triangulation and the internal grid points are created following a centroid or frontal approach. For the surface grid generation, a hybrid approach is also proposed similar to the volume. Semi-structured grids are generated on the surface grid (both on the edges and faces of the domain) to improve the grid resolution around convex and concave ridges and corners, by aligning the grid elements in the directions of high solution gradients along the surface. A method is also developed for automatically setting the grid generation parameters related to the surface grid generation based on the curvature of the surface in order to obtain an accurate and smooth surface grid. Finally, a semi-structured prismatic/hexahedral grid generation algorithm is presented for the generation of the part of grid close to the viscous walls of the domain. The algorithm is further extended with improvements meant to increase the grid quality around concave and convex ridges of the domain, where the semi-structured grids are known to be inadequate. The combined methodology is demonstrated on a variety of complex examples mainly from the automotive and aeronautical industry.

Shape optimization is an important step in many design processes. With the growing use of Computer Aided Engineering in the design chain, it has become very important to develop robust and efficient shape optimization algorithms. The field of Computer Aided Optimal Shape Design has grown substantially over the recent past. In the early days of its development, the method based on small shape perturbation to probe the parameter space and identify an optimal shape was routinely used. This method is nothing but an educated trial and error method. A key development in the pursuit of good shape optimization algorithms has been the advent of the adjoint method to compute the shape sensitivities more formally and efficiently. While undoubtedly, very attractive, this method relies on very sophisticated and advanced mathematical tools which are an impediment to its wider use in the engineering community. It that spirit, it is the purpose of this thesis to propose a new shape optimization algorithm based on more intuitive engineering principles and numerical procedures. In this thesis, the new shape optimization procedure which is proposed is based on the generation of a body-fitted mesh. This process maps the physical domain into a regular computational domain. Based on simple arguments relating to the use of the chain rule in the mapped domain, it is shown that an explicit expression for the shape sensitivity can be derived. This enables the computation of the shape sensitivity in one single solve, a performance analogous to the adjoint method, the current state-of-the art. The discretization is based on the Finite Difference method, a method chosen for its simplicity and ease of implementation. This algorithm is applied to the Laplace equation in the context of heat transfer problems and potential flows. The applicability of the proposed algorithm is demonstrated on a number of benchmark problems which clearly confirm the validity of the sensitivity analysis, the most important aspect of any shape optimization problem. This thesis also explores the relative merits of different minimization algorithms and proposes a technique to “fix” meshes when inverted element arises as part of the optimization process. While the problems treated are still elementary when compared to complex multiphysics engineering problems, the new methodology presented in this thesis could apply in principle to arbitrary Partial Differential Equations.

The development and numerical implementation of a three-dimensional Particle-In-Cell (PIC) methodology on unstructured Voronoi-Delauney tetrahedral grids is presented. Charge assignment and field interpolation weighting schemes of zero- and first-order are formulated based on the theory of long-range constraints for three-dimensional unstructured grids. The algorithms for particle motion, particle tracing, particle injection, and loading are discussed. Solution to Poisson's equation is based on a finite-volume formulation that takes advantage of the Voronoi-Delauney dual. The PIC methodology and code are validated by application to the problem of current collection by cylindrical Langmuir probes in stationary and moving collisionless plasmas. Numerical results are compared favorably with previous numerical and analytical solutions for a wide range of probe radius to Debye length ratios, probe potentials, and electron to ion temperature ratios. A methodology for evaluation of the heating, slowing-down and deflection times in 3D PIC simulations is presented. An extensive parametric evaluation is performed and the effects of the number of computational particles per cell, the ratio of cell-edge to Debye length, and timestep are investigated. The unstructured PIC code is applied to the simulation of Field Emission Array (FEA) cathodes. Electron injection conditions are obtained from a Field Emission microtip model and the simulation domain includes the FEA cathode and anode. Currents collected by the electrodes are compared to theoretical values. Simulations show the formation of the virtual cathode and three-dimensional effects under certain injection conditions. The unstructured PIC code is also applied to the simulation of a micro-Retarding Potential Analyzer. For simple cases the current at the collector plate is compared favorably with theoretical predictions. The simulations show the complex structure of the potential inside the segmented microchannel, the phase space of plasma species and the space-charge effects not captured by the theory.

The present study utilizes the ultrasonic travel time technique to diagnose grid generated turbulence. Ultrasonic flow metering technology relies on the measurement and computation of small perturbations in the travel time of acoustic ultrasonic waves through the dynamic medium. The statistics of the travel time variations of ultrasonic waves that are caused by turbulence probably affect the performance of ultrasonic flow meters. Motivation for the study stems from the large travel time variations observed in typical ultrasonic flow and circulation meters. Turbulent flow data was collected downstream of a grid introduced in a uniform flow in the wind tunnel using ultrasonic techniques. Grid turbulence is well defined in literature, and is nearly homogeneous and isotropic. The experimental investigation was performed under well-controlled laboratory conditions. The grid mesh sizes varied from 0.25-0.5in, and flow velocities from 0-20m/s. The ultrasonic transducers were of 100 kHz working frequency; and all of the data was collected with them oriented perpendicular to the mean flow. Path lengths were increased from 2-10in; and the data acquisition and control system featured a very high speed data acquisition card with an analog to digital converter that enabled excellent resolution of ultrasonic signals. Experimental data was validated by comparison to other studies. The work aims to investigate the influence of the grid-generated turbulent flow on acoustic wave propagation, in terms of the variance of the travel time. The effect of turbulence on acoustic wave propagation was observed. The experimental data was used to compute average travel times, acoustic travel time variances, and standard deviation amplitude fluctuations. The data was collected in the region estimated to be homogeneous and isotropic. Average travel time data support the assumption that only the large (as compared to the wavelength ) turbulent inhomogeneities influence acoustic wave propagation. Variance data confirm the presence of a non-linear trend in the acoustic travel times with increasing path length. Amplitude fluctuations data confirm a correlation between areas of caustic formation and large amplitude fluctuations.

This dissertation presents a technique for the solution of incompressible equivalents to planar steady subsonic potential flows. Riemannian geometric formalism is used to develop a gauge transformation of the length measure followed by a curvilinear coordinate transformation to map a subsonic flow into a canonical Laplacian flow with the same boundary conditions. The method represents the generalization of the methods of Prandtl-Glauert and Karman-Tsien and gives exact results in the sense that the inverse mapping produces the subsonic full potential solution over the original airfoil, up to numerical accuracy. The motivation for this research was provided by the analogy between linear potential flow and the special theory of relativity that emerges from the invariance of the wave equation under Lorentz transformations. Whereas elements of the special theory can be invoked for linear and global compressibility effects, the question posed in this work is whether other techniques from relativity theory could be used for effects that are nonlinear and local. This line of thought leads to a transformation leveraging Riemannian geometric methods common to the general theory of relativity. The dissertation presents the theory and a numerical method for practical solutions of equivalent incompressible flows over arbitrary profiles. The numerical method employs an iterative approach involving the solution of the incompressible flow with a panel method and the solution of the coordinate mapping to the canonical flow with a finite difference approach. This method is demonstrated for flow over a circular cylinder and over a NACA 0012 profile. Results are validated with subcritical full potential test cases available in the literature. Two areas of applicability of the method have been identified. The first is airfoil inverse design leveraging incompressible flow knowledge and empirical data for the potential field effects on boundary layer transition and separation. The second is aerodynamic testing using distorted models.