Numerous hydrodynamic theories may be used to predict the performance of marine propellers. The goal of this thesis is to investigate and implement a lifting line theory as a program written in FORTRAN and to test its capabilities on some Wageningen B-Series propellers. Special attention is given to the validation of the routines involved in the implementation of the theory. Difficulties were experienced in obtaining results that accurately reflect the published experimental results, and some discussion is included regarding possibilities for the sources of these errors. Also discussed are the results of other lifting line codes and their respective differences from the current implementation.

This work focuses on the development of efficient methods for wing shape optimization for morphing wing technologies. Existing wing shape optimization processes typically rely on computational fluid dynamics tools for aerodynamic analysis, but the computational cost of these tools makes optimization of all but the most basic problems intractable. In this work, we present a set of tools that can be used to efficiently explore the design spaces of morphing wings without reducing the fidelity of the results significantly. Specifically, this work discusses automatic differentiation of an aerodynamic analysis tool based on lifting line theory, a light-weight gradient-based optimization framework that provides a parallel function evaluation capability not found in similar frameworks, and a modification to the lifting line equations that makes the analysis method and optimization process suitable to wings of arbitrary aspect ratio. The toolset discussed is applied to several wing shape optimization problems. Additionally, a method for visualizing the design space of a morphing wing using this toolset is presented. As a result of this work, a light-weight wing shape optimization method is available for analysis of morphing wing designs that reduces the computational cost by several orders of magnitude over traditional methods without significantly reducing the accuracy of the results.

Computational fluid dynamics (CFD) analysis was performed in order to compare the solutions of oscillating wings with Prandtl’s lifting-line theory. Quasi-steady and steady-periodic simulations were completed using the CFD software Star-CCM+. The simulations were performed for a number of frequencies in a pure plunging setup. Additional simulations were then completed using a setup of combined pitching and plunging at multiple frequencies. Results from the CFD simulations were compared to the quasi-steady lifting-line solution in the form of the axial-force, normal-force, power, and thrust coefficients, as well as the efficiency obtained for each simulation. The mean values were evaluated for each simulation and compared to the quasi-steady lifting-line solution. It was found that as the frequency of oscillation increased, the quasi-steady lifting-line solution was decreasingly accurate in predicting solutions.

This master thesis shows, how can be the modified lifting line theory used for preliminary glider design an for wing loads determination. It is shown, that relatively accurate results can be obtained at less computational cost in comparison with CFD methods

The FanWing propulsion system is a novel propulsion system which aerodynamically behaves as a hybrid between a helicopter and a fixed wing aircraft, and if the knowledge base with regards to this novel concept can be fully explored, there could be a new class of aircraft developed. In the current research, only 2D CFD studies have been done for the FanWing, hence the 3D lift characteristics of the FanWing have been unknown thus far, at least in the theoretical domain. Therefore, it was proposed to develop a modified Prandtl's Lifting Line Theory numerical solution and a CFD solution, comparing the results of each. A new variable was introduced into the classical Lifting Line Theory solution, αi,FW, to account for the additional lift produced by the FanWing as opposed to a traditional airfoil. This variable, αi,FW, is a function of the wing angle and the velocities taken at three-quarter chord length on the FanWing. The introduction of this variable was informed by other papers which superimposed velocities when developing Lifting Line Theory for unconventional airfoil planforms. After introducing a correction factor, the numerical model aligned with the 3D CFD results where LLT assumptions were valid. For the 3D simulation, it was observed that the lift per unit span rapidly increases from quarter span to wingtip, which is different from traditional wing planforms. This study provides a valuable first step towards documenting the 3D lift characteristics of the novel FanWing propulsion system.

A combined wing and propeller model is presented as a low-cost approach to preliminary modeling of slipstream effects on a finite wing. The wing aerodynamic model employs a numerical lifting-line method utilizing the 3D vortex lifting law along with known 2D airfoil data to predict the lift distribution across a wing for a prescribed upstream flowfield. The propeller/slipstream model uses blade element theory combined with momentum conservation equations. This model is expected to be of significant importance in the design of tail-sitter vertical take-off and landing (VTOL) aircraft, where the propeller slipstream is the primary source of air flow past the wings in some flight conditions. The algorithm is presented, and results compared with published experimental data.

Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Computational Aeroelasticity is a complex research field which combines structural and aerodynamic analyses to describe a vehicle in flight. This thesis investigates the feasibility of including such an analysis in the development of control systems for unmanned aerial vehicles within the Electronic Systems Laboratory at the Department of Electrical and Electronic Engineering at Stellenbosch University. This is done through the development of a structural analysis algorithm using the Finite Element Method, an aerodynamic algorithm for Prandtl’s Lifting Line Theory and experimental work. The experimental work was conducted at the Low-Speed Wind Tunnel at the Department of Mechanical and Mechatronic Engineering. The structural algorithm was applied to 20-noded hexahedral elements in a winglike structure. The wing was modelled as a cantilever beam, with a fixed and a free end. Natural frequencies and deflections were verified with the experimental model and commercial software. The aerodynamic algorithm was applied to a Clark-Y airfoil with a chord of 0:1m and a half-span of 0:5m. This profile was also used on the experimental model. Experimental data was captured using single axis accelerometers. All postprocessing of data is also discussed in this thesis. Results show good correlation between the structural algorithm and experimental data. / AFRIKAANSE OPSOMMING: Numeriese Aeroelastisiteit is ’n komplekse navorsingsveld waar ’n vlieënde voertuig deur ’n strukturele en ’n aerodinamiese analise beskryf word. Hierdie tesis ondersoek die toepaslikheid van hierdie tipe analise in die ontwerp van beheerstelsels vir onbemande voertuie binne die ESL groep van die Departement Elektriese en Elektroniese Ingenieurswese by Stellenbosch Universiteit. Die ondersoek bevat die ontwikkeling van ’n strukturele algoritme met die gebruik van die Eindige Element Methode, ’n aerodinamiese algoritme vir Prandtl se Heflynteorie en eksperimentele werk. Die eksperimentele werk is by die Department Meganiese en Megatroniese Ingensierswese toegepas in die Lae-Spoed Windtonnel. Die strukturele algoritme maak gebruik van ’n 20-nodus heksahedrale element om ’n vlerk-tipe struktuur op te bou. Die vlerk is vereenvouding na ’n kantelbalk met ’n vasgeklemde en ’n vrye ent. Natuurlike frekwensies en defleksies is met die eksperimentele werk en kommersiële sagteware geverifieer. Die aerodinamiese algoritme is op ’n Clark-Y profiel met 0:1m koord lengte en ’n halwe vlerk length van 0:5m geïmplementeer. Die profiel is ook in die eksperimentele model gebruik. Die eksperimentele data is met eendimensionele versnellingsmeters opgeneem. Al die verdere berekeninge wat op ekperimentele data gedoen is, word in die tesis beskryf. Resultate toon goeie korrelasie tussen die strukturele algoritme en die eksperimentele data.

Research into advanced wind turbine design has shown that load alleviation strategies like bend-twist coupled blades and coned rotors could reduce costs. However these strategies are based on nonlinear aero-structural dynamics providing additional benefits to components beyond the blades. These innovations will require Multi-disciplinary Design Optimization (MDO) to realize the full benefits. This research expands the MDO capabilities of Horizontal Axis Wind Turbines. The early research explored the numerical stability properties of Blade Element Momentum (BEM) models. Then developed a provincial scale wind farm siting models to help engineers determine the optimal design parameters. The main focus of this research was to incorporate advanced analysis tools into an aero-elastic optimization framework. To adequately explore advanced designs with optimization, a new set of medium fidelity analysis tools is required. These tools need to resolve more of the physics than conventional tools like (BEM) models and linear beams, while being faster than high fidelity techniques like grid based computational fluid dynamics and shell and brick based finite element models. Nonlinear beam models based on Geometrically Exact Beam Theory (GEBT) and Variational Asymptotic Beam Section Analysis (VABS) can resolve the effects of flexible structures with anisotropic material properties. Lagrangian Vortex Dynamics (LVD) can resolve the aerodynamic effects of novel blade curvature. Initially this research focused on the structural optimization capabilities. First, it developed adjoint-based gradients for the coupled GEBT and VABS analysis. Second, it developed a composite lay-up parameterization scheme based on manufacturing processes. The most significant challenge was obtaining aero-elastic optimization solutions in the presence of erroneous gradients. The errors are due to poor convergence properties of conventional LVD. This thesis presents a new LVD formulation based on the Finite Element Method (FEM) that defines an objective convergence metric and analytic gradients. By adopting the same formulation used in structural models, this aerodynamic model can be solved simultaneously in aero-structural simulations. The FEM-based LVD model is affected by singularities, but there are strategies to overcome these problems. This research successfully demonstrates the FEM-based LVD model in aero-elastic design optimization. / Graduate / 0548 / pilot.mm@gmail.com

This thesis contributes to the state of the art in integrated design of insect-scale piezoelectric actuated flapping wing vehicles through the development of novel theoretical models for flapping wing aerodynamics and piezoelectric actuator dynamics, and integration of these models into a closed form design process. A comprehensive literature review of available engineered designs of miniature rotary and flapping wing vehicles is provided. A novel taxonomy based on wing and actuator kinematics is proposed as an effective means of classifying the large variation of vehicle configurations currently under development. The most successful insect-scale vehicles developed to date have used piezoelectric actuation, system resonance for motion amplification, and passive wing pitching. A novel analytical treatment is proposed to quantify induced power losses in normal hover that accounts for the effects of non uniform downwash, wake periodicity and effective flapping disc area. Two different quasi-steady aerodynamic modelling approaches are undertaken, one based on blade element analysis and one based on lifting line theory. Both approaches are explicitly linked to the underlying flow physics and, unlike a number of competing approaches, do not require empirical data. Models have been successfully validated against experimental and numerical data from the literature. These models have allowed improved insight into the role of the wing leading-edge vortex in lift augmentation and quantification of the comparative contributions of induced and profile drag for insect-like wings in hover. Theoretical aerodynamic analysis has been used to identify a theoretical solution for the optimum planform for a flapping wing in terms of chord and twist as a function of span. It is shown that an untwisted elliptical planform minimises profile power, whereas a more highly tapered design such as that found on a hummingbird minimises induced power. Aero-optimum wing kinematics for hovering are also assessed. It is shown that for efficient flight the flapping velocity should be constant whereas for maximum effectiveness the flapping velocity should be sinusoidal. For both cases, the wing pitching at stroke reversal should be as rapid as possible. A dynamic electromechanical model of piezoelectric bending actuators has been developed and validated against data obtained from experiments undertaken as part of this thesis. An expression for the electromechanical coupling factor (EMCF) is extracted from the analytical model and is used to understand the influence of actuator design variables on actuator performance. It is found that the variation in EMCF with design variables is similar for both static and dynamic operation, however for light damping the dynamic EMCF will typically be an order of magnitude greater than for static operation. Theoretical contributions to aerodynamic and electromechanical modelling are integrated into a low order design method for propulsion system sizing. The method is unique in that aside from mass fraction estimation, the underlying models are fully physics based. The transparency of the design method provides the designer with clear insight into effects of changing core design variables such as the maximum flapping amplitude, wing mass, transmission ratio, piezoelectric characteristics on the overall design solution. Whilst the wing mass is only around 10% of the actuator mass, the effective wing mass is 16 times the effective actuator mass for a typical transmission ratio of 10 and hence the wing mass dominates the inertial contribution to the system dynamics. For optimum aerodynamic effectiveness and efficiency it is important to achieve high flapping amplitudes, however this is typically limited by the maximum allowable field strength of the piezoelectric material used in the actuator.

Two models of a self-stabilizing hydrofoil system is developed where the effects from the struts and hydrofoil give torques for angular rotations. Lifting line theory for the hydrofoil which can twist is used. Nonlinear versions of the models are also developed and compared to find that the linear models use valid approximations. Backward Differentiation Formula is used to get numerical solutions, and eigenvalues of linear system matrices are used to get stability regions. The models did not accurately capture what has been seen in testing. / Två modeller för ett självstabiliserande bärplanssystem utvecklas där effekter från stöttor och bärplan ger vridmoment för vinkelrotationer. Lyftande linjeteori för det skevande bärplanet används. Icke-linjära versioner av modellerna tas också fram och jämförs för att finna att de linjära modellerna använder giltiga approximationer. Backward Differentiation Formula används för att fram numeriska lösningar, och egenvärden i det linjära systemetsmatriser används för att hitta stabilitetsregioner. Modellerna fångade inte korrekt vad som har setts i testning.