State of the Art in the Optimisation of Wind Turbine Performance Using CFD

Wind energy has received increasing attention in recent years due to its sustainability and geographically wide availability. The efficiency of wind energy utilisation highly depends on the performance of wind turbines, which convert the kinetic energy in wind into electrical energy. In order to optimise wind turbine performance and reduce the cost of next-generation wind turbines, it is crucial to have a view of the state of the art in the key aspects on the performance optimisation of wind turbines using Computational Fluid Dynamics (CFD), which has attracted enormous interest in the development of next-generation wind turbines in recent years. This paper presents a comprehensive review of the state-of-the-art progress on optimisation of wind turbine performance using CFD, reviewing the objective functions to judge the performance of wind turbine, CFD approaches applied in the simulation of wind turbines and optimisation algorithms for wind turbine performance. This paper has been written for both researchers new to this research area by summarising underlying theory whilst presenting a comprehensive review on the up-to-date studies, and experts in the field of study by collecting a comprehensive list of related references where the details of computational methods that have been employed lately can be obtained

Hybrid Intelligent Optimization Methods for Engineering Problems

The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients of these increments are essential to search the yield space. However, the landscape of yield is not a simple one and mostly multi-modal. Another issue is differentiability. Engineering design problems are usually nonlinear and they sometimes exhibit discontinuous derivatives for the objective and constraint functions. Due to these difficulties, non-gradient-based algorithms have become more popular in recent decades. Genetic algorithms (GA) and particle swarm optimization (PSO) algorithms are popular, non-gradient based algorithms. Both are population-based search algorithms and have multiple points for initiation. A significant difference from a gradient-based method is the nature of the search methodologies. For example, randomness is essential for the search in GA or PSO. Hence, they are also called stochastic optimization methods. These algorithms are simple, robust, and have high fidelity. However, they suffer from similar defects, such as, premature convergence, less accuracy, or large computational time. The premature convergence is sometimes inevitable due to the lack of diversity. As the generations of particles or individuals in the population evolve, they may lose their diversity and become similar to each other. To overcome this issue, we studied the diversity concept in GA and PSO algorithms. Diversity is essential for a healthy search, and mutations are the basic operators to provide the necessary variety within a population. After having a close scrutiny of the diversity concept based on qualification and quantification studies, we improved new mutation strategies and operators to provide beneficial diversity within the population. We called this new approach as multi-frequency vibrational GA or PSO. They were applied to different aeronautical engineering problems in order to study the efficiency of these new approaches. These implementations were: applications to selected benchmark test functions, inverse design of two-dimensional (2D) airfoil in subsonic flow, optimization of 2D airfoil in transonic flow, path planning problems of autonomous unmanned aerial vehicle (UAV) over a 3D terrain environment, 3D radar cross section minimization problem for a 3D air vehicle, and active flow control over a 2D airfoil. As demonstrated by these test cases, we observed that new algorithms outperform the current popular algorithms. The principal role of this multi-frequency approach was to determine which individuals or particles should be mutated, when they should be mutated, and which ones should be merged into the population. The new mutation operators, when combined with a mutation strategy and an artificial intelligent method, such as, neural networks or fuzzy logic process, they provided local and global diversities during the reproduction phases of the generations. Additionally, the new approach also introduced random and controlled diversity. Due to still being population-based techniques, these methods were as robust as the plain GA or PSO algorithms. Based on the results obtained, it was concluded that the variants of the present multi-frequency vibrational GA and PSO were efficient algorithms, since they successfully avoided all local optima within relatively short optimization cycles

A comparative analysis of nature-inspired optimization approaches to 2d geometric modelling for turbomachinery applications

A vast variety of population-based optimization techniques have been formulated in recent years for use in different engineering applications, most of which are inspired by natural processes taking place in our environment. However, the mathematical and statistical analysis of these algorithms is still lacking. This paper addresses a comparative performance analysis on some of the most important nature-inspired optimization algorithms with a different basis for the complex high-dimensional curve/surface fitting problems. As a case study, the point cloud of an in-hand gas turbine compressor blade measured by touch trigger probes is optimally fitted using B-spline curves. In order to determine the optimum number/location of a set of Bezier/NURBS control points for all segments of the airfoil profiles, five dissimilar population-based evolutionary and swarm optimization techniques are employed. To comprehensively peruse and to fairly compare the obtained results, parametric and nonparametric statistical evaluations as the mathematical study are presented before designing an experiment. Results illuminate a number of advantages/disadvantages of each optimization method for such complex geometries’ parameterization from several different points of view. In terms of application, the final appropriate parametric representation of geometries is an essential, significant component of aerodynamic profile optimization processes as well as reverse engineering purposes

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

Multi-level Systems Modeling and Optimization

This research combines the disciplines of system-of-systems (SoS) modeling, platform-based design, optimization and evolving design spaces to achieve a novel capability for designing solutions to key aeronautical mission challenges. A central innovation in this approach is the confluence of multi-level modeling (from sub-systems to the aircraft system to aeronautical system-of-systems) in a way that coordinates the appropriate problem formulations at each level and enables parametric search in design libraries for solutions that satisfy level-specific objectives. The work here addresses the topic of SoS optimization and discusses problem formulation, solution strategy, the need for new algorithms that address special features of this problem type, and also demonstrates these concepts using two example application problems - a surveillance UAV swarm problem, and the design of noise optimal aircraft and approach procedures

A high-lift optimization methodology for the design of leading and trailing edges on morphing wings

Data Availability Statement - The experimental data presented in Figure 10 and Figure 11 are available in Reference [2] “Axelson, J.A.; Stevens, G.L. Investigation of a Slat in Several Different Positions on a NACA 64A010 Airfoil for a Wide Range of Subsonic Mach Numbers. Technical Note 3129; Ames Aeronautical Laboratory: Moffett Field, CA, USA, March 1954.”Morphing offers an attractive alternative compared to conventional hinged, multi-element high lift devices. In the present work, morphed shapes of a NACA 64A010 airfoil are optimized for maximum lift characteristics. Deformed shapes of the leading and trailing edge are represented through Bezier curves derived from locally defined control points. The optimization process employs the fast Foil2w in-house viscous-inviscid interaction solver for the calculation of aerodynamic characteristics. Transitional flow results indicate that combined leading and trailing edge morphing may increase maximum lift in the order of 100%. A 60–80% increase is achieved when morphing is applied to leading edge only—the so-called droop nose—while a 45% increase is obtained with trailing edge morphing. Out of the stochastic optimization algorithms tested, the Genetic Algorithm, the Evolution Strategies, and the Particle Swarm Optimizer, the latter performs best. It produces the designs of maximum lift increase with the lowest computational cost. For the optimum morphed designs, verification simulations using the high fidelity MaPFlow CFD solver ensure that the high lift requirements set by the optimization process are met. Although the deformed droop nose increases drag, the aerodynamic performance is improved ensuring the overall effectiveness of the airfoil design during take-off and landing

Airfoil Optimisation with a Genetic Algorithm

In this Master Thesis, an airfoil optimisation using a Genetic Algorithm is developed. This project has been proposed by myself and done with the guidance and supervision of professor Manel Soria. The main idea of the project is to develop from scratch an algorithm capable of finding the optimal airfoil for specific flow conditions, such as the angle of attack, the Reynolds number, and the Mach number. The objective is to create a useful tool for aerospace engineering students so they can use it on their projects and designs during the college years. The work has a first theoretical part about Genetic Algorithms, in which the basic concepts needed to understand the current project are explained. Then, the implementation of the algorithm is fully explained and all the intern processes of the genetic algorithm can be consulted. Several validations of the code have also been made. The Genetic Algorithm created uses crossovers and mutations. The airfoil parametrisation used has been the PARSEC parametrisation and the computation of the aerodynamic coefficients is done with XFOIL. The whole code is written in C language and the analysis and graphs of the results are done with MATLAB and XFLR5. Finally, the algorithm is tested with two real design cases, an airfoil for a heavy lifter aircraft that participated in the Air Cargo Challenge 2017 in Stuttgart, and an airfoil for a glider that flew in the Paper Air Challenge 2015 in ESEIAAT, Terrasa. The results and improvements offered by the algorithm are compared with the results that the designers of these aircraft obtained manually during the design process

User-preference based evolutionary algorithms for many-objective optimisation

Evolutionary Algorithms (EA) have enjoyed great success in finding solutions for multi-objective problems that have two or three-objectives in the past decade. The majority of these Evolutionary Multi-objective Optimisation (EMO) algorithms explored the decision-space using the selection pressure governed methods that are based on dominance relation. Although these algorithms are effective locating solutions for multi-objective problems, they have not been very successful for problem instances having more than three objectives, usually named as many-objective problems. The main reason behind this shortcoming is the fact that the dominance comparison becomes ineffective as the number of objectives increases. In this thesis, we incorporate some user-preference methods into EMO algorithms to enhance their ability to handle many-objective problems. To this end, we introduce a distance metric derived from user-preference schemes such as the reference point method and light beam search found in multi-criteria decision making. This distance metric is used to guide the EMO algorithm to locate solutions within certain areas of the objective-space known as preferred regions. In our distance metric approach, the decision maker is allowed to specify the amount of spread of solutions along the solution front as well. We name this distance metric based EMO algorithm as d-EMO, which is a generalised framework that can be constructed using any EA. This distance metric approach is computationally less expensive as it does not rely on dominance ranking methods, but very effective in solving many-objective problems. One key issue that remains to be resolved is that there are no suitable metrics for comparing the performance of these user-preference EMO algorithms. Therefore, we introduce a variation of the normalised Hyper-Volume (HV) metric suitable for comparing user-preference EMO algorithms. The key feature in our HV calculation process is to consider only the solutions within each preferred region. This methodology favours user-preference EMO algorithms that have converged closely to the Pareto front within a preferred region. We have identified two real-world engineering design problems in optimising aerofoil and lens designs, and formulated them as many-objective problems. The optimisation process of these many-objective problems is computationally expensive. Hence, we use a reference point PSO algorithm named MDEPSO to locate solutions effectively in fewer function evaluations. This PSO algorithm is less prone to getting stuck in local optimal fronts and still retains its fast convergence ability. In MDEPSO, this feature is achieved by generating leader particles using a differential evolution rule rather than picking particles directly from the population or an external archive. The main feature of the optimisation process of these aerofoil and lens design problems is the derivation of reference points based on existing designs. We illustrate how these existing designs can be used to either obtain better or new design solutions that correspond to various requirements. This process of deriving reference points based on existing design models, and integrating them into a user-preference EMO framework is a novel approach in the optimisation process of such computationally expensive engineering design problems

Two-Dimensional-Based Hybrid Shape Optimisation of a 5-Element Formula 1 Race Car Front Wing under FIA Regulations

Front wings are a key element in the aerodynamic performance of Formula 1 race cars. Thus, their optimisation makes an important contribution to the performance of cars in races. However, their design is constrained by regulation, which makes it more difficult to find good designs. The present work develops a hybrid shape optimisation approach to obtain an optimal five-element airfoil front wing under the FIA regulations and 17 design parameters. A first baseline design is obtained by parametric optimisation, on which the adjoint method is applied for shape optimisation via Mesh Morphing with Radial Basis Functions. The optimal front wing candidate obtained outperforms the parametric baseline up to a 25% at certain local positions. This shows that the proposed and tested hybrid approach can be a very efficient alternative. Although a direct 3D optimisation approach could be developed, the computational costs would be dramatically increased (possibly unaffordable for such a complex five-element front wing realistic shape with 17 design parameters and regulatory constraints). Thus, the present approach is of strong interest if the computational budget is low and/or a fast new front wing design is desired, which is a frequent scenario in Formula 1 race car design.The authors want to acknowledge the financial support from the Ramón y Cajal 2021 Excellence Research Grant action from the Spanish Ministry of Science and Innovation (FSE/AGENCIA ESTATAL DE INVESTIGACIÓN), the UMA18-FEDERJA-184 grant, and the Andalusian Research, Development and Innovation Plan (PAIDI—Junta de Andalucia) fundings. Partial funding for open access charge: Universidad de Málag