Probabilistic design optimization of horizontal axis wind turbine rotors

Considerable interest in renewable energy has increased in recent years due to the concerns raised over the environmental impact of conventional energy sources and their price volatility. In particular, wind power has enjoyed a dramatic global growth in installed capacity over the past few decades. Nowadays, the advancement of wind turbine industry represents a challenge for several engineering areas, including materials science, computer science, aerodynamics, analytical design and analysis methods, testing and monitoring, and power electronics. In particular, the technological improvement of wind turbines is currently tied to the use of advanced design methodologies, allowing the designers to develop new and more efficient design concepts. Integrating mathematical optimization techniques into the multidisciplinary design of wind turbines constitutes a promising way to enhance the profitability of these devices. In the literature, wind turbine design optimization is typically performed deterministically. Deterministic optimizations do not consider any degree of randomness affecting the inputs of the system under consideration, and result, therefore, in an unique set of outputs. However, given the stochastic nature of the wind and the uncertainties associated, for instance, with wind turbine operating conditions or geometric tolerances, deterministically optimized designs may be inefficient. Therefore, one of the ways to further improve the design of modern wind turbines is to take into account the aforementioned sources of uncertainty in the optimization process, achieving robust configurations with minimal performance sensitivity to factors causing variability. The research work presented in this thesis deals with the development of a novel integrated multidisciplinary design framework for the robust aeroservoelastic design optimization of multi-megawatt horizontal axis wind turbine (HAWT) rotors, accounting for the stochastic variability related to the input variables. The design system is based on a multidisciplinary analysis module integrating several simulations tools needed to characterize the aeroservoelastic behavior of wind turbines, and determine their economical performance by means of the levelized cost of energy (LCOE). The reported design framework is portable and modular in that any of its analysis modules can be replaced with counterparts of user-selected fidelity. The presented technology is applied to the design of a 5-MW HAWT rotor to be used at sites of wind power density class from 3 to 7, where the mean wind speed at 50 m above the ground ranges from 6.4 to 11.9 m/s. Assuming the mean wind speed to vary stochastically in such range, the rotor design is optimized by minimizing the mean and standard deviation of the LCOE. Airfoil shapes, spanwise distributions of blade chord and twist, internal structural layup and rotor speed are optimized concurrently, subject to an extensive set of structural and aeroelastic constraints. The effectiveness of the multidisciplinary and robust design framework is demonstrated by showing that the probabilistically designed turbine achieves more favorable probabilistic performance than those of the initial baseline turbine and a turbine designed deterministically

Low speed aerofoil optimization

Aerofoil shape has a significant influence on aircraft performance. Multiple methodologies can be applied, such as direct design, inverse design or performance design. With the improvement of computer technology there has been a continuing trend of automating this process by using performance­based methods and formal optimisation algorithms. Parametrization formulations of aerofoils have continually advanced, some examples are B­Spline, Class Shape Functions, Hicks­Henne functions and Bezier­PARSEC 3333. Main comparisons of parametrizations have focussed on morphology, design space and aerodynamic consistency. In the present work, the parametrizations mentioned are applied to aerofoil optimisation and their results compared for different numbers of design variables, in order to ascertain optimisation differences. Performance design optimisation is used in a multi­point approach with an aggregated objective function using weights that are determined using the aircraft design data, to maximize the score for the competition Air Cargo Challenge (ACC2019 and ACC2022), using XFOIL for aerodynamic analysis and particle swarm optimisation (PSO) under a modified version of the XOPTFOIL tool. The initial aerofoil was obtained by iterative inverse design during previous works, the optimisation includes the flap chord and deflection angle for the different selected lift coefficient conditions as design variables. The initial population is bounded between maximum and minimum limits set by the initial aerofoil design variables and an initial perturbation. The aerofoil is constrained by minimum and maximum thicknesses, a minimum trailing edge angle and a specified trailing edge thickness. Several additional restrictions are also imposed on the aerofoil to avoid unneeded analysis of a geometry with an expected non converged solution in XFOIL. These include the angles’ maximum, minimum and difference values of the two points closest to the leading edge, the maximum angle between any three consecutive points and the number of curvature sign reversals at the upper surface and lower surface of the aerofoil. To deal with the constraints and restrictions a penalty function is used, each penalty being normalised by a maximum set value. To ensure that these do not unduly constrain the domain exploration of the optimisation, a dynamic limit to the penalties is used. During the optimisation, this limit decreases linearly with the iterations. From two case studies, it was possible to demonstrate the tool ability to optimize aerofoils. In the first case, utilisation of B­Splines achieved better results relative to the other methods. In the second case, the dynamic limit, consistency method and XFOIL convergence recuperation method are studied. This last one has the greatest influence on optimisation.A topologia de perfis aerodinâmicos tem uma influência significativa no desempenho de aeronaves. Múltiplas metodologias podem ser aplicadas para definir perfis, tais como projeto direto, projeto inverso ou projeto por desempenho. Com o desenvolvimento da tecnologia computacional, tem havido uma tendência contínua para automatizar o projeto de perfis utilizando projeto por desempenho e algoritmos de otimização formais. A parametrização de perfis tem avançado lado a lado, alguns exemplos são B­Spline, funções de tipo morfológicas, funções de Hicks­Henne e Bezier­PARSEC 3333. As principais comparações entre estes métodos têm­se focado na morfologia, espaço de projeto e consistência aerodinâmica. No presente trabalho, os tipos de parameterização mencionados são utilizados para otimização de perfis e uma comparação é feita para diferentes números de variáveis com o objetivo de avaliar diferenças para a otimização. Projeto por desempenho é utilizado numa abordagem multi­ponto nesta dissertação, com uma função objetivo de agregação de pesos determinados via dados de projeto da aeronave, para maximizar a pontuação para a competição Air Cargo Challenge (ACC2019 e ACC2022), através do uso da ferramenta XFOIL para análise aerodinâmica e otimização por enxame de partículas sobre uma versão modificada da ferramenta XOPTFOIL. O perfil inicial foi obtido via projeto inverso de forma iterativa durante trabalhos anteriores. A otimização inclui a corda do flap e o ângulo de deflexão para diferentes condições de voo como variáveis de projeto. A população inicial é delimitada por limites máximos e mínimos determinados através das variáveis de projeto do perfil inicial e uma perturbação inicial. O perfil é constrangido pelas máxima e mínima espessuras, um ângulo de bordo de fuga mínimo e uma espessura de bordo de fuga fixa. Outras restrições adicionais são também impostas ao perfil para evitar a análise desnecessária de geometrias cujo solução do XFOIL não converge. Estas incluem os ângulos máximos, mínimos e a diferença dos dois pontos mais próximos ao bordo de ataque, o ângulo máximo entre quaisquer três pontos ao longo do perfil e o número máximo de mudanças de sinal da curvatura do perfil na superfície superior e inferior. Para lidar com estes constrangimentos e restrições utilizou­se uma função de penalidade com valores normalizados. De forma a garantir que estas não restringem o domínio de exploração da otimização, um limite dinâmico é aplicado à função penalidade. Este diminui linearmente durante a otimização. A partir de dois casos de estudo é possível demonstrar a capacidade de otimização da ferramenta. No primeiro, o uso de B­Splines alcançou melhores resultados comparativamente aos outros métodos. No segundo, o limite dinâmico, método para consistência e método de recuperação de convergência para a ferramenta XFOIL são estudados. Tendo este último o maior efeito na optimização

Evolutionary optimization of aerofoil profile

This thesis deals with the heuristic optimization of an F1A free flight airfoil. The goal is to generate an airfoil that is better than the ones currently in use. We implemented three optimization algorithms, differential evolution (DE), Firework algorithm (FA) and Particle swarm optimization (PSO). Currently used airfoils, called LDA (Low-drag airfoil) are able to obtain high speed in the phase of climbing but in the free flight phase they fly poorly compared to their predecessors. With the help of optimization methods we aim to find an airfoil that performs both tasks well. All heuristic algorithms were developed in java programming language using a customized JMetal library. Each airfoil is presented with two Bézier curves, one for the upper and one for the lower half of the foil. This kind of presentation gives us more freedom and control, but it comes at a price - the software may generate irregular shapes due to randomness. That is why it is important to pay attention to structural constraints (i.e. airfoil thickness). Airfoils are evaluated using Xfoil [3] which calculates the characteristics of an airfoil. Our experiments show that L/D ratio is not a good indicator of airfoil quality and one has to take into account other parameters as well. A multi-objective criteria function would therefore be advisable

Facilitating the Use of Optimisation in the Aerodynamic Design of Axial Compressors

There is commercial pressure to design axial compressors exhibiting high levels of performance more quickly. This is despite the performance of these machines approaching an asymptote in recent years, with further gains becoming increasingly difficult to achieve. One tool that can be used to help is optimisation, effectively harnessing the speed of computational analysis to accelerate the design process and unlock additional performance improvements. The greatest potential for optimisation exists at the preliminary design stage, however, current methodologies struggle when applied at this early point in the design process due to inadequate problem formulations, an inability to fulfil the role of enhancing designer understanding and a lack of high-fidelity analysis due to computational cost. The goal of this thesis is to facilitate the use of optimisation in the preliminary aerodynamic design of axial compressors by developing an improved methodology that overcomes these limitations. The multiple dominance relations (MDR) formulation enables a larger number of performance parameters to be incorporated in a way that accurately reflects the desires of the designer. This is implemented within a Tabu Search (TS) that is capable of providing interpretable design development information to enhance designer understanding. The combined MDRTS algorithm, overcoming the limitations associated with formulation and understanding, outperforms existing methods when applied to analytic, aerofoil and six-stage axial compressor test cases, generating computational savings of up to 80%. Multi-fidelity techniques are used to accelerate the search by conducting analysis on a "need-to-know'' basis. Computational savings of over 70% are observed compared to the single-fidelity version of the algorithm across the analytic, aerofoil and six-stage axial compressor test cases, enabling high-fidelity analysis to be employed in a computationally efficient manner. The resultant methodology represents a novel and inherently flexible multi-level multi-fidelity optimisation technique. Application to an N-stage axial compressor test case, in which the optimiser is given control over the number of stages in the machine, demonstrates the capabilities of the accelerated MDRTS approach. The complex design space is effectively navigated, generating computational savings of over 90% compared to existing methodologies and producing designs that are more likely to be of interest to the designer. Interpretable design development information is also provided for this problem to enhance designer understanding. These results show that the improved methodology successfully facilitates the use of optimisation in the preliminary aerodynamic design of axial compressors, overcoming the problems associated with formulation, understanding and speed that limit existing approaches

Advanced Techniques for Design and Manufacturing in Marine Engineering

Modern engineering design processes are driven by the extensive use of numerical simulations; naval architecture and ocean engineering are no exception. Computational power has been improved over the last few decades; therefore, the integration of different tools such as CAD, FEM, CFD, and CAM has enabled complex modeling and manufacturing problems to be solved in a more feasible way. Classical naval design methodology can take advantage of this integration, giving rise to more robust designs in terms of shape, structural and hydrodynamic performances, and the manufacturing process.This Special Issue invites researchers and engineers from both academia and the industry to publish the latest progress in design and manufacturing techniques in marine engineering and to debate the current issues and future perspectives in this research area. Suitable topics for this issue include, but are not limited to, the following:CAD-based approaches for designing the hull and appendages of sailing and engine-powered boats and comparisons with traditional techniques;Finite element method applications to predict the structural performance of the whole boat or of a portion of it, with particular attention to the modeling of the material used;Embedded measurement systems for structural health monitoring;Determination of hydrodynamic efficiency using experimental, numerical, or semi-empiric methods for displacement and planning hulls;Topology optimization techniques to overcome traditional scantling criteria based on international standards;Applications of additive manufacturing to derive innovative shapes for internal reinforcements or sandwich hull structures

Linear and non-linear deformations of a wind turbine blade considering warping and all aeroelastic load couplings

The structural dynamics behavior of the blade of a horizontal axis wind turbine that reacts to the different components of the aerodynamic loading were studied by many researchers using different approaches and assumptions. In the present research, the author considered all the extensional, torsional and flexural loadings acting on the blade with their couplings, variable airfoil cross sections with warping effects, shear deflection, rotary inertia and with or without blade\u27s pretwist for both the linear small deformation case and the nonlinear large deformation case. To the best knowledge of the author the simultaneous inclusion of all these factors has not been done before. The assumed modes method was used, in which displacements are assumed to be an expansion of products of time-step dependent constants and polynomial functions of x (where x is the coordinate along the length of the blade) that satisfy the boundary conditions at the fixed end where x=0 (hub of the blade) and at the free end where x=L (tip of the blade). The mass matrix, linear and nonlinear stiffness matrices and the load vector (function of time step) of the dynamic equations of motion are deduced from the Lagrange equations of motion that were derived step by step. The steps of the linear and nonlinear Newmark implicit iteration schemes used for solving the linear and nonlinear dynamic equations of motion respectively were explained in detail. Numerical implementation examples for both linear and nonlinear cases were demonstrated for a 14m long blade with and without pretwisting that has specific material and geometrical properties and a decreasing NACA4415 airfoil cross section from hub to tip. For both of the linear and nonlinear examples, the aerodynamic loadings (lift, drag and pitch moment) and the nonlinear stiffness matrices were computed at each time step utilizing a time dependent set of parameters such as angle of attack, material and air density, wind and blade speed, flow angle, yaw and pitch angles. Then the unknown displacements u,v and w in the directions of x, y and z axes respectively, the bending rotations Θ 1 and Θ 2 about the y and z axes respectively and the torsional rotation Φ about the x axis, were solved using the linear and nonlinear Newmark implicit iteration schemes. The linear case displacement result plots are shown to agree with the work of Younsi et al. The nonlinear case displacement result plots are shown to agree with the Ls-Dyna code

Identifying preferred solutions for multi-objective aerodynamic design optimization

 Aerodynamic designers rely on high-fidelity numerical models to approximate, within reasonable accuracy, the flow around complex aerodynamic shapes. The ability to improve the flow field behaviour through shape modifications has led to the use of optimization techniques. A significant challenge to the application of evolutionary algorithms for aerodynamic shape optimization is the often excessive number of expensive computational fluid dynamic evaluations required to identify optimal designs. The computational effort is intensified when considering multiple competing objectives, where a host of trade-off designs are possible. This research focuses on the development of control measures to improve efficiency and incorporate the domain knowledge and experience of the designer to facilitate the optimization process. A multi-objective particle swarm optimization framework is developed, which incorporates designer preferences to provide further guidance in the search. A reference point is projected on the objective landscape to guide the swarm towards solutions of interest. This point reflects the preferred compromise and is used to focus all computing effort on exploiting a preferred region of the Pareto front. Data mining tools are introduced to statistically extract information from the design space and confirm the relative influence of both variables and objectives to the preferred interests of the designer. The framework is assisted by the construction of time-adaptive Kriging models, for the management of high-fidelity problems restricted by a computational budget. A screening criterion to locally update the Kriging models in promising areas of the design space is developed, which ensures the swarm does not deviate from the preferred search trajectory. The successful integration of these design tools is facilitated through the specification of the reference point, which can ideally be based on an existing or target design. The over-arching goal of the developmental effort is to reduce the often prohibitive cost of multi-objective design to the level of practical affordability in aerospace problems. The superiority of the proposed framework over more conventional search methods is conclusively demonstrated via a series of experiments and aerodynamic design problems

Validation of morphine wing methodologies on an unmanned aerial system and a wind tunnel technology demonstrator

To increase the aerodynamic efficiency of aircraft, in order to reduce the fuel consumption, a novel morphing wing concept has been developed. It consists in replacing a part of the wing upper and lower surfaces with a flexible skin whose shape can be modified using an actuation system placed inside the wing structure. Numerical studies in two and three dimensions were performed in order to determine the gains the morphing system achieves for the case of an Unmanned Aerial System and for a morphing technology demonstrator based on the wing tip of a transport aircraft. To obtain the optimal wing skin shapes in function of the flight condition, different global optimization algorithms were implemented, such as the Genetic Algorithm and the Artificial Bee Colony Algorithm. To reduce calculation times, a hybrid method was created by coupling the population-based algorithm with a fast, gradient-based local search method. Validations were performed with commercial state-of-the-art optimization tools and demonstrated the efficiency of the proposed methods. For accurately determining the aerodynamic characteristics of the morphing wing, two new methods were developed, a nonlinear lifting line method and a nonlinear vortex lattice method. Both use strip analysis of the span-wise wing section to account for the airfoil shape modifications induced by the flexible skin, and can provide accurate results for the wing drag coefficient. The methods do not require the generation of a complex mesh around the wing and are suitable for coupling with optimization algorithms due to the computational time several orders of magnitude smaller than traditional three-dimensional Computational Fluid Dynamics methods. Two-dimensional and three-dimensional optimizations of the Unmanned Aerial System wing equipped with the morphing skin were performed, with the objective of improving its performances for an extended range of flight conditions. The chordwise positions of the internal actuators, the spanwise number of actuation stations as well as the displacement limits were established. The performance improvements obtained and the limitations of the morphing wing concept were studied. To verify the optimization results, high-fidelity Computational Fluid Dynamics simulations were also performed, giving very accurate indications of the obtained gains. For the morphing model based on an aircraft wing tip, the skin shapes were optimized in order to control laminar flow on the upper surface. An automated structured mesh generation procedure was developed and implemented. To accurately capture the shape of the skin, a precision scanning procedure was done and its results were included in the numerical model. High-fidelity simulations were performed to determine the upper surface transition region and the numerical results were validated using experimental wind tunnel data

NURBS-Enhanced Finite Element Method (NEFEM)

The development of NURBS-Enhanced Finite Element Method (NEFEM) is revisited. This technique allows a seamless integration of the CAD boundary representation of the domain and the finite element method (FEM). The importance of the geometrical model in finite element simulations is addressed and the benefits and potential of NEFEM are discussed and compared with respect to other curved finite element techniques.Peer ReviewedPostprint (published version

Contribution to the definition of non deterministic robust optimization in aeronautics accounting with variable uncertainties

Shape optimization is a largely studied problem in aeronautics. It can be applied to many disciplines in this field, namely efficiency improvement of engine blades, noise reduction of engine nozzles, or reduction of the fuel consumption of aircraft. Optimization for general purposes is also of increasing interest in many other fields. Traditionally, optimization procedures were based on deterministic methodologies as in Hamalainen et al (2000), where the optimum working point was fixed. However, not considering what happens in the vicinity of the defined working conditions can produce problems like loose of efficiency and performance. That is, in many cases, if the real working point differs from the original, even a little distance, efficiency is reduced considerably as pointed out in Huyse and Lewis (2001). Non deterministic methodologies have been applied to many fields (Papadrakakis, Lagaros and Tsompanakis, 1998; Plevris, Lagaros and Papadrakakis, 2005). One of the most extended nondeterministic methodologies is the stochastic analysis. The time consuming calculations required on Computational Fluid Dynamics (CFD) has prevented an extensive application of the stochastic analysis to shape optimization. Stochastic analysis was firstly developed in structural mechanics, several years ago. Uncertainty quantification and variability studies can help to deal with intrinsic errors of the processes or methods. The result to consider for design optimization is no longer a point, but a range of values that defines the area where, in average, optimal output values are obtained. The optimal value could be worse than other optima, but considering its vicinity, it is clearly the most robust regarding input variability. Uncertainty quantification is a topic of increasing interest from the last few years. It provides several techniques to evaluate uncertainty input parameters and their effects on the outcomes. This research presents a methodology to integrate evolutionary algorithms and stochastic analysis, in order to deal with uncertainty and to obtain robust solutions