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The research presented here provides a basis for understanding the hydrodynamics of surfboard fin geometries. While there have been select studies on fins there has been little correlation to the shape of the fin and its corresponding hydrodynamic performance. This research analyzes how changing the planform shape of a surfboard fin effects its performance and flow field. This was done by isolating the taper and sweep distribution of a baseline geometry and varying each parameter individually whilst maintaining a constant span and surface area. The baseline surfboard fin was used as a template in Matlab to generate a set of x and y coordinates that defined the outline of the fin shape. These coordinates were then altered by changing either the sweep or taper distribution and resulted in new, unique planform shapes. The new shapes were used to generate 3D models with the NACA 0006 foil as the cross-section hydrofoil. After the geometry was modeled, each fin was meshed and simulated in CFD for incidence angles ranging from 0o to 20o and a fin Reynolds Number of 3.51x105. When the sweep distribution was changed, there was a direct correlation to vortex formation off the leading edge. Increasing the sweep generated a stronger vortex that persisted for higher angles of attack and resulted in higher moments but increased drag. Changing the taper distribution was not as influential. The tapered fin set showed similar flow fields and body forces to each other. Making a fin more rectangular had slight decreases in drag but made the shape more prone to separation.

The utility of computational fluid dynamics (CFD) for solving problems of engineering interest has experienced rapid growth due to the improvements in both memory capacity and processing speed of computers. While the capability now exists for the solution of the Navier-Stokes equations about complex and complete aircraft configurations, the bottleneck within the process is the time consuming task of properly generating a mesh that can accurately solve the governing partial differential equations (PDEs). This thesis explored two numerical techniques that attempt to circumvent the difficulty associated with the meshing process by solving a simplified form of the continuity equation within a meshless framework. The continuity equation reduces to the full potential equation by assuming irrotational flow. It is a nonlinear PDE that can describe flows for a wide spectrum of Mach numbers that do not exhibit discontinuities. It may not be an adequate model for the detailed analysis of a complex flowfield since viscous effects are not captured by this equation, but it is an appealing alternative for the aircraft designer because it can provide a quick and simple to implement estimate of the aerodynamic characteristics during the conceptual design phase. The two meshless methods explored in this thesis are the Dual Reciprocity Method (DRM) and the Generalized Finite Difference Method (GFD). The Dual Reciprocity Method was shown to have the capability to solve for the two-dimensional subcritical compressible flow over a Circular Cylinder and the non-lifting flow for a NACA 0012 airfoil. Unfortunately these solutions were obtained with the requirement of a priori knowledge of the solution to tune a parameter necessary for proper convergence of the algorithm. Due to the shortcomings of applying the Dual Reciprocity Method, the Generalized Finite Difference Method was also investigated. The GFD method solves a PDE in differential form and can be thought of as a meshless form of a standard finite difference scheme. This method proved to be an accurate and general technique for solving the previously mentioned cases along with the lifting flow about a NACA 0012 airfoil. It was also demonstrated that the GFD method could be formulated to discretize the full potential equation with second order accuracy. Both solution methods offer their own set of unique advantages and challenges, but it was determined that the GFD Method possessed the flexibility necessary for a meshless technique to become a viable aerodynamic design tool.

A direct, simple, and accurate way to measure skin friction by oil-film laser interferometry has been developed by various researchers. Equations and methods were developed to correct measurement errors arising from three-dimensional effects and pressure gradients. The oil-film, dual-beam laser interferometer was constructed to measure the skin friction around a wing-body junction in a three-dimensional, turbulent boundary layer with pressure gradients. The flow was dominated by the formation of a junction vortex generated at the nose of the wing-body. The oil-film skin friction results were compared with previous skin-friction measurements for the flow obtained by hot-wire measurements. The skin friction values agreed within approximately 8% between the two methods. The effects and benefits of scanning laser interferometry and alternative beam directions were investigated and discussed. The effect of dirt contamination on the data is also discussed. Methods to improve the data quality are presented. / Master of Science

Fundamental intuition of aerodynamics begins with understanding steady flow, a time- independent flow state. A fluid region undergoing steady flow consists of constant properties such as pressure and velocity at different positions in the flow field. This time-independent principle is crucial for beginning a foundation of understanding aerodynamics; however, analyzing this state of flow was beyond the limit at my university's Fundamentals of Aerodynamics course. There was minimal education on time-dependent unsteady flow, which created a vacuum on my understanding of how flow can be analyzed with time. The purpose of writing this thesis is to create a framework for aspiring learners of aerodynamics to better comprehend unsteady flow, including myself. The basis for developing an understanding of unsteady flow is accomplished by analyzing the aerodynamics of a simple two-dimensional zero-thickness flat plate, using a numerical method called Discrete Vortex Method under steady and unsteady conditions. Constructing a numerical method for steady and unsteady flow requires a software to compute enormous quantities of linear equations, therefore a combination of numerous arguments, functions, and loops were developed on MATLAB written in the C/C++ languages. Results from the numerical methods will be compared with the experimental and theoretical results from Katz & Plotkin (2001). The Steady Discrete Vortex Method was a basis for calculating the circulation of the flat plate at varying angles of attack and freestream velocities. The Unsteady Discrete Vortex Method derived much of the self-induced calculations in the body-fixed coordinate system. At the same time, a time-stepping method was developed to calculate the coordinates as the flat plate and shed vortices translated from the origin of an additional frame of reference called the inertial coordinate system. A wake vortex is shed from the trailing-edge of the flat plate at each time step iv to model vorticity shed from a body in motion. The flat plate undergoes sudden acceleration and plunging maneuvers to demonstrate further effects of unsteady aerodynamic conditions. The results from the flat plate undergoing sudden acceleration with a Reynolds number of 68,435.8 was an increasing proportionality between the lift and circulation of the steady and unsteady case until reaching a constant trend as time increases, demonstrating the nature of low-speed flow reaching a steady state after a given period. The results from the flat plate undergoing plunging with a Reynolds number of 106,759.8 demonstrate a sinusoidal trend in the normal force experienced as the flat plate traverses in its sinusoidal plunging translation like that observed in the theoretical results. This thesis intends to expand on the understanding of unsteady aerodynamics by developing a numerical method that can alter its dependent factors to visualize the effects of changing specific parameters on pressure and force acting on the two-dimensional body.

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Aerodynamic topology optimization is a useful tool in the aerodynamic design pro-cess, especially when looking for marginal gains within a design. One example isa turboprop racer concept aircraft that is designed with the goal of breaking worldspeed records. An optimization framework was developed with the intention of laterbeing applied to this design. In the early design stages, the optimization frameworkmust focus on quicker methods of drag estimation, such as a panel codes. The largenumber of design variables in topology optimization can exponentially increase func-tion evaluations and thus computational cost. A vorticity-based panel solver wasproven out for this application to reduce the computational cost while keeping theaccuracy of the results similar to that of traditional CFD solvers in conditions with-out prominent flow separation. The framework developed here includes geometryparameterization, function evaluation scripting, and post-processing, which are allrun within the optimization algorithm. The designs used to validate the solver arewing-fuselage systems of various sailplane configurations with existing experimentaldata. These sailplane designs were also used as the initial geometry to demonstratethe framework. A parametric optimum was found to reduce drag by 9%, but it mustbe noted that this method does have certain trade offs and limitations.