Search Results (19)

An aircraft that has been carefully optimized for a single flight condition will tend to perform poorly at other flight conditions. For aircraft such as long-haul airliners, this is not necessarily a problem, since the cruise condition so heavily dominates a typical mission. However, other aircraft, such as Unmanned Aerial Vehicles (UAVs), may be expected to perform well at a wide range of flight conditions. Morphing systems may be a solution to this problem, as they allow the aircraft to adapt its shape to produce optimum performance at each flight condition. This study proposes an aerodynamic optimization framework for morphing airfoils by integrating Principal Component Analysis (PCA) for geometric dimensionality reduction and deep learning (DL) for surrogate modeling, alongside an optimization-guided data augmentation strategy. By employing PCA, the geometric dimensionality of airfoil surfaces is reduced from 24 to 18 design variables while preserving 100% shape fidelity, thus establishing a compressed morphing parameterization space. A Multi-Island Genetic Algorithm (MIGA) efficiently explores the reduced design space, while iterative retraining of the surrogate model enhances prediction accuracy, particularly in high-performance regions. Additionally, Shapley Additive Explanation (SHAP) analysis reveals interpretable correlations between principal component modes and aerodynamic performances. Experimental results show that the optimized airfoil achieves a 54.66% increase in low-speed cruise lift-to-drag ratio and 10.90% higher climb lift compared to the baseline. Overall, the proposed framework not only enhances the adaptability of morphing airfoils across various low-speed flight conditions but also facilitates targeted surrogate refinement and efficient data acquisition in high-performance regions. Full article

The aerodynamic optimization of the airfoil of vertical-axis wind turbines (VAWTs) is limited by the time-consuming nature of computational fluid dynamics (CFD), resulting in difficulty in the efficient implementation of multi-parameter optimization. In response to this challenge, this study constructed a collaborative optimization framework based on the Kriging surrogate model and the multi-island genetic algorithm (MIGA). Based on the NACA 0015 airfoil, 13 geometric variables (including 12 Bernstein polynomial coefficients and 1 installation angle) were defined through the Classification and Shape Transformation (CST) parameterization method. Through sensitivity analysis, seven key parameters were screened as design variables. Seventy training samples and ten validation samples were generated via Latin hypercube sampling to construct a high-precision Kriging surrogate model (R² = 0.91368). The optimized results show that the power coefficient of the new airfoil increases by 14.2% under the condition of the tip velocity ratio (TSR > 1.5), and the average efficiency of the entire working condition increases by 9.8%. The drag reduction mechanism is revealed through pressure cloud maps and velocity field analysis. The area of the high-pressure zone at the leading edge decreases by 23%, and the flow separation phenomenon at the trailing edge is significantly weakened. This research provides an engineering solution that takes into account both computational efficiency and optimization accuracy for the VAWT airfoil design. Full article

This paper explores the application of multidisciplinary design optimization to the blades in horizontal-axis wind turbines. The aerodynamics and structural performance of blades are considered in the optimization framework. In the aerodynamic discipline, class function/shape function transformation-based parameterized modeling is used to express the airfoil. The Wilson method is employed to obtain the aerodynamic shape of the blade. Computational fluid dynamics numerical simulation is performed to analyze the aerodynamics of the blade. In the structural discipline, the materials and ply lay-up design are studied. Finite element method-based modal analysis and static structural analysis are conducted to verify the structural design of the blade. A collaborative optimization framework is set up on the Isight platform, employing a genetic algorithm to find the optimal solution for the blade’s aerodynamics and structural properties. In the optimization framework, the design variables refer to the length of the blade chord, twist angle, and lay-up thickness. Additionally, Kriging surrogate models are constructed to reduce the numerical simulation time required during optimization. An optimal Latin hypercube sampling method-based experimental design is employed to determine the samples used in the surrogate models. The optimized blade exhibits improved performance in both the aerodynamic and the structural disciplines. Full article

To address the issues of tedious optimization processes, insufficient fitting accuracy of surrogate models, and low optimization efficiency in drone propeller airfoil design, this paper proposes an aerodynamic optimization method for propeller airfoils based on DBO-BP (Dum Beetle Optimizer-Back-Propagation) and NSWOA (Non-Dominated Sorting Whale Optimization Algorithm). The NACA4412 airfoil is selected as the research subject, optimizing the original airfoil at three angles of attack (2°, 5° and 10°). The CST (Class Function/Shape Function Transformation) airfoil parametrization method is used to parameterize the original airfoil, and Latin hypercube sampling is employed to perturb the original airfoil within a certain range to generate a sample space. CFD (Computational Fluid Dynamics) software (2024.1) is used to perform aerodynamic analysis on the airfoil shapes within the sample space to construct a sample dataset. Subsequently, the DBO algorithm optimizes the initial weights and thresholds of the BP neural network surrogate model to establish the DBO-BP neural network surrogate model. Finally, the NSWOA algorithm is utilized for multi-objective optimization, and CFD software verifies and analyzes the optimization results. The results show that at the angles of attack of 2°, 5° and 10°, the test accuracy of the lift coefficient is increased by 45.35%, 13.4% and 49.3%, and the test accuracy of the drag coefficient is increased by 12.5%, 39.1% and 13.7%. This significantly enhances the prediction accuracy of the BP neural network surrogate model for aerodynamic analysis results, making the optimization outcomes more reliable. The lift coefficient of the airfoil is increased by 0.04342, 0.01156 and 0.03603, the drag coefficient is reduced by 0.00018, 0.00038 and 0.00027, respectively, and the lift-to-drag ratio is improved by 2.95892, 2.96548 and 2.55199, enhancing the convenience of airfoil aerodynamic optimization and improving the aerodynamic performance of the original airfoil. Full article

An adaptive Free-Form Deformation parameterization method based on a spring analogy is presented for aerodynamic shape optimization problems. The proposed method effectively incorporates the gradients of the objective and constraint functions, achieving automatic control point adjustment based on variances in design variable components. To evaluate the performance of the adaptive FFD parameterization method, two 2D airfoil optimization design problems are examined. The optimization of the RAE2822 airfoil with 12, 18 and 24 design variables demonstrates superior results for the adaptive method compared to uniform parameterization. The adaptive method requires fewer iterations and achieves lower objective function values. Additionally, the optimization design from NACA0012 to RAE2822 airfoil with 18 design variables shows that the adaptive parameterization method achieves a lower drag coefficient while satisfying the optimization objective. This validates the method’s capability to finely adjust airfoil shapes and capture more optimal design points by exerting stronger control over local shapes. The proposed adaptive FFD parameterization method proves highly effective for optimizing aerodynamic shapes, offering stability and efficiency in the early stages of optimization, even with a limited number of design variables. Full article

An airfoil shape parameterization that can generate a compact design space is highly desirable in practice. In this paper, a compact airfoil parameterization is proposed by incorporating deep learning into the PAERO parameterization method based on the thin-airfoil theory. Following the PAERO parameterization, the mean camber line is represented by a number of aerodynamic performance parameters, which can be used to narrow down the design space according to the thin-airfoil theory. In order to further reduce the design space, the airfoil thickness distribution is represented by data-driven generative models, which are trained by the thickness distributions of existing airfoils. The trained models can automatically filter out the physically unreasonable airfoil shapes, resulting in a highly compact design space. The test results show that the proposed method is significantly more efficient and more robust than the widely used CST parameterization method for airfoil optimization. Full article

For the analysis of low-speed incompressible fluid dynamics with turbulence around airfoils, we developed a finite element formulation based on a stabilized pressure and velocity formulation. To shape the optimization of bidimensional airfoils, this formulation is applied using machine learning (TensorFlow) and public domain global optimization algorithms. The goal is to maximize the lift-over-drag ratio by using the class-shape function transformation (CST) parameterization technique and machine learning. Specifically, we propose equal-order stabilized three-node triangles for the flow problem, standard three-node triangles for the approximate distance function (ADF) required in the turbulence stage, and stabilized three-node triangles for the Spalart–Allmaras turbulence model. The backward Euler time integration was employed. An implicit time-integration algorithm was adopted, and a solution was obtained using the Newton–Raphson method. This was made possible in the symbolic form via Mathematica with the AceGen package. Three benchmarks are presented, with Reynolds numbers up to $1\times {10}^7$, demonstrating remarkable robustness. After the assessment of the new finite element, we used machine learning and global optimization for four angles of attack to calculate airfoil designs that maximized $C_L/C_D$. Full article

This paper shows a series of tools that help in the research of morphing micro air vehicles (MAVs). These tools are aimed at generating parametric CAD models of wings in a few seconds that can be used in aerodynamic studies, either via CFD directly using the model obtained or via wind tunnel through rapid prototyping with 3D printers. It also facilitates the analysis of morphing wings by allowing for the continuous parametric deformation of the airfoils and the wing geometry. In addition, one of the tools greatly simplifies the purely experimental design of this type of vehicle, allowing the transfer of experimental measurements to the computer, generating virtual models with the same deformation as the physical model. This software has two fundamental parts. The first one is the parameterization of the airfoils, for which the CST (Class-Shape Transformation) method will be used. CST coefficients can be modified according to the actuator variable that changes the wing geometry. The second part is the generation of a three-dimensional parametric model of the wing. We used OpenCASCADE technology in its Python version called PythonOCC, which enables the generation of geometries with good surface quality for typical and non-standard wing shapes. Finally, the use of this software for the study of a morphing aircraft will be shown, as well as improvements that could be incorporated in the future to increase its capabilities for the design and analysis of MAVs. Full article

This study presents a novel approach to parameterize the geometry of a morphing trailing-edge flap that allows its aerodynamics to be optimized while capturing the expected structural behavior of the flap. This approach is based on the finite frame element method, whereby the initial flap surface is defined as a structure with constraints that are similar to those of a morphing flap with passive skin. The initial shape is modified by placing a series of distributed loads on the surface. The finite frame element method is modified with rigid rotation corrections to maintain the initial element length without requiring nonlinear calculations and to achieve accurate surface-length results by only solving the linear FEM equations twice. The proposed method enables the shape of the morphing flaps to be rapidly formulated while maintaining the initial upper surface-length and trailing-edge angle. The constraints are inherently integrated into the algorithm, eliminating the need for unnecessary feasibility checks during the aerodynamic optimization. By using the proposed airfoil parameterization method, a case study was conducted by using a genetic algorithm to optimize the lift-to-drag ratio of the NACA 23012 airfoil flap starting at 0.7c with 10 degrees of deflection. The optimizer resulted in a structurally feasible morphing flap that achieved a 10% increase in the lift-to-drag ratio in the optimized angle of attack range. Full article

The aim of this work is to implement an innovative parameterization and fitting procedure for the definition of a mathematical model useful to describe a wide range of airfoils. They are partitioned into three sections: central box, leading edge, and trailing edge. Each section is mathematically represented by two opposed, uniform, non-rational B-spline curves, describing the upper and lower airfoil segments’ perimeter. A novel approach is used to ensure both the desired continuity between two adjacent segments (up to 2nd derivatives) and sufficient model versatility and flexibility while managing a limited number of parameters, defining tangent and curvature vectors as scale factor variables. These parameters allow for a variable separation approach during the geometric fitting procedure that can be carried out considering two nested optimization processes, one based on a genetic algorithm and the other on a numerical gradient evaluation of the objective function. The representation method has been verified against different airfoils, comparing the geometric and aerodynamic properties of the input and model-based generated profile. To show the mathematical model’s capabilities and possible applications, a comparison between existing and proposed airfoil approximation methods has been provided together with examples of “global” and “local” morphing and CFD analyses of the resulting airfoils. Full article

The conventional method of optimizing the aerodynamic performance of an airfoil heavily depends on the confines of the design space. The design variables create a non-normalized space that is fragmented into several different clusters of airfoils. An approach that is data-driven and deforms airfoils over a Grassmannian submanifold is utilized in the work that is being presented here. The affine deformation, which includes camber and thickness, can be uncoupled from the method that is currently in use, and the operations that are performed on the airfoil shape can be made smooth enough to prevent unreasonable shapes from being produced. The CST method is also a part of the current study so that a comparison can be made between the two. A new method to describe the airfoil geometries over the Grassmannian space was generated using a dataset that contained 7007 different shapes of airfoils. These two methods are used to parameterize the subsonic (NACA0012) and transonic (RAE2822) airfoils, and the new method cuts the number of design variables from twelve to six, resulting in a reduction in overall complexity. The findings demonstrate that the new method maintains a high degree of consistency regardless of the flow conditions. Full article

An aerodynamic optimization for a Droop-Nose Leading-Edge (DNLE) morphing of a well-known UAV, the UAS-S45, is proposed, using a novel Black Widow Optimization (BWO) algorithm. This approach integrates the optimization algorithm with a modified Class-Shape Transformation (CST) parameterization method to enhance aerodynamic performance by minimizing drag and maximizing aerodynamic endurance at the cruise flight condition. The CST parameterization technique is used to parameterize the reference airfoil by introducing local shape changes and provide skin flexibility to obtain various optimized morphing airfoil configurations. The optimization framework uses an in-house MATLAB algorithm, while the aerodynamic calculations use the XFoil solver with flow transition estimation criteria. These results are validated with a CFD solver utilizing the Transition $\left(\gamma -R{e}_{\theta }\right)$ Shear Stress Transport (SST) turbulence model. Numerical studies verified the effectiveness of the optimization strategy, and the optimized airfoils have shown a significant improvement in overall aerodynamic performance by up to 12.18% drag reduction compared to the reference airfoil, and an increase in aerodynamic endurance of up to 10% for the UAS-S45 optimized airfoil configurations over its reference airfoil. These results indicate the importance of leading-edge morphing in enhancing the aerodynamic efficiency of the UAS-S45 airfoil. Full article

This paper presents an adjoint-based shape optimization framework and its demonstration in a conjugate heat transfer problem in a turbine blading. The gradient of the objective function is computed based on the continuous adjoint method, which also includes the adjoint to the turbulence model. Differences in the gradient resulting from making the frozen turbulence assumption are discussed. The developed software was used to optimize both the blade shape of the internally cooled linear C3X turbine blade and the position of cooling channels aiming at (a) minimum total pressure drop of the hot gas flow and (b) minimum highest temperature within the blade. A two-step optimization procedure was used. A free-form parameterization tool, based on volumetric NURBS, controls the blade airfoil contour, while the cooling channels are free to move following changes in the coordinates of their centers. Geometric and flow constraints are included in the performed optimizations, keeping the cooling channels away from the airfoil sides and retaining the turbine inlet capacity and flow turning. Full article

This paper presents the parameterization and optimization of two well-known airfoils. The aerodynamic shape optimization investigation includes the subsonic (NREL S-821) and transonic airfoils (RAE-2822). The class shape transformation is employed for parametrization while the genetic algorithm is used for optimization purposes. The absolute scheme of the optimization process is carried out for the minimization of the drag coefficient and maximization of lift to drag ratio. In-house MATLAB code is incorporated with a genetic algorithm to calculate the drag coefficient and lift to drag ratio of the resulting optimized airfoil. The panel method is utilized in genetic algorithm optimization code to calculate pressure distribution, lift coefficient, and lift to drag ratio for optimized airfoil shapes and validates with XFOIL and NREL experimental data. Furthermore, CFD analysis is conducted for both the original (NREL S-821) and optimized airfoil obtained. The present method shows that the optimized airfoil achieved an improvement in lift to drag ratio by 7.4% and 15.9% of S-821 and RAE-2822 airfoil, respectively, by the panel technique method and provides high design desirable stability parameters. These features significantly improve the overall aerodynamic performance of the newly optimized airfoils. Finally, the improved aerodynamics results are reported for the design of turbulence modeling and NREL phase II, Phase III, and Phase VI HAWT blades. Full article

Sustainability has become one of the most significant considerations in everyday work, including energy production. The fast-growing trend of wind energy around the world has increased the demand for efficient and optimized airfoils, which has paved the way for energy harvesting systems. The present manuscript proposes an aerodynamically optimized design of the well-known existing NREL S809 airfoil for performance enhancement of the blade design for wind turbines. An integrated code, based on a genetic algorithm, is developed to optimize the asymmetric NREL S809 airfoil by class shape transformation (CST) and the parametric section (PARSEC) parameterization method, analyzing its aerodynamic properties and maximizing the lift of the airfoil. The in-house MATLAB code is further incorporated with XFOIL to calculate the coefficient of lift, coefficient of drag and lift-to-drag ratio at angles of attack of 0° and 6.2° by the panel technique and validated with National Renewable Energy Laboratory (NREL) experimental results provided by The Ohio State University (OSU). On the other hand, steady-state CFD analysis is performed on an optimized S809 airfoil using the Reynolds-averaged Navier–Stokes (RANS) equation with the K–ω shear stress transport (SST) turbulent model and compared with the experimental data. The present method shows that the optimized airfoil by CST is predicted, with an increment of 11.8% and 9.6% for the lift coefficient and lift-to-drag ratio, respectively, and desirable stability parameters obtained for the design of the wind turbine blades. These characteristics significantly improve the overall aerodynamic performance of new optimized airfoils. Finally, the aerodynamically improved results are reported for the design of the NREL Phase II, Phase III and Phase VI HAWT blades. Full article