Airfoil Shape Optimization Research Articles

Data-driven airfoil shape optimization framework for enhanced flutter performance

Data-driven airfoil shape optimization framework for enhanced flutter performance

Mathematical derivation of a unified equations for adjoint lattice Boltzmann method in airfoil and wing aerodynamic shape optimization

Unified equations of the adjoint lattice Boltzmann method (ALBM) are derived for five applicable objective functions in 2D/3D aerodynamic shape optimization problems. The derived equations include the adjoint equation, boundary condition, terminal condition and gradient of the cost function. In this research, firstly, these relations are extracted for each objective in details and then the general form of ALBM equations are presented for all defined practical aerodynamic objective function. Five applicable cost functions which are the most important objectives in optimization of aerodynamic geometries include desired pressure and viscous shear stress (VSS) inverse design, drag and moment at fixed lift and finally lift to drag ratio at fixed angle of attack. The new extracted relations are based on the circular and spherical function scheme, and are valid for viscous/inviscid, compressible/incompressible and 2D/3D flows in all continuous flow regimes. Proof of new extracted general relations have been performed by authors.

Aerodynamic shape optimization of NACA airfoils based on a novel unconstrained conjugate gradient algorithm

Airfoils are key factors in maximizing the efficiency of turbomachinery. The ideal configuration of the airfoil is engineered to produce significant lift while minimizing drag, all while adhering to specific structural limitations. In this investigation, an innovative algorithm based on unconstrained conjugate gradient techniques to optimize the aerodynamic shape of airfoils is proposed. NACA4412 and NACA2415 airfoils are chosen to be investigated in detail. Bézier parameterisation method is employed to define the design variables. Optimization is conducted utilizing a MATLAB code and the XFOIL panel method-based flow solver to attain the desired aerodynamic outcomes. The optimization process enhanced aerodynamic performance by increasing the lift-to-drag ratio and decreasing the angle of attack for maximum lift-to-drag ratio. An increase of 13.7 % in performance for the NACA 4412 airfoil and 32 % for the NACA 2415 airfoil was achieved. Comparisons with traditional methods demonstrated the efficiency and robustness of the proposed algorithm.

Fuel consumption and trailing-edge noise tradeoff studies via mission-based airfoil shape optimization

Aerodynamic drag is often used as a proxy for fuel consumption in aircraft design. However, the aeroacoustic byproduct of airfoil design, such as trailing-edge noise (TEN), is yet to be considered in aircraft applications, despite its inclusion in wind turbine designs. To explore the impact of TEN in airfoil design for aircraft, we establish a mission-based aerodynamic shape optimization framework. A surrogate-based detailed flight mission analysis (that can simulate a flight mission from takeoff to landing) is incorporated into the optimization framework to obtain realistic flight conditions during takeoff and landing—which are important to assess TEN metrics—and calculate accurate fuel consumption, where both are used to evaluate the objective function. To assess its effectiveness, we compare the results against those of the conventional single-point optimization. Not surprisingly, the mission-based optimization simultaneously reduces fuel consumption and TEN, while the single-point optima (performed at the low Mach region) reduce TEN at the expense of higher fuel consumption. This is due to the tradeoff between aerodynamic performance in the transonic region and aeroacoustic performance in the low Mach region, which cannot be properly analyzed without including flight mission analysis in the optimization loop.

Variable-Fidelity Surrogate Model-Based Airfoil Optimization at a Moderate Reynolds Number

Airfoil shape optimization for enhanced aerodynamic performance at a moderate Reynolds number is carried out using a novel technique for constrained optimization of expensive engineering functions. The proposed method is a co-kriging surrogate model using two levels of fidelity in conjunction with a gradient-free trust-region method to drive the model towards the global optimum. The methodology is first applied on a generic test function to demonstrate its efficiency. Later, the proposed optimization framework is applied on constrained airfoil shape optimization problems involving maximizing the lift-to-drag ratio, maximizing the endurance factor, and minimizing the drag coefficient of an Eppler E214 airfoil. The optimal lift-to-drag ratio and the endurance factor are found to be 13.25% and 16.05%, respectively, higher than the baseline airfoil. The optimal drag coefficient is 6.86% lower than the baseline airfoil. The flow transition is also delayed for the some of the optimal airfoils. The present results show that the proposed optimization methodology is successful in improving the aerodynamic characteristics in the sensitive low/moderate Reynolds number regime.

Optimization of Guide Vane Airfoil Shape of Pump Turbine Based on SVM-MDMR Model

Optimization of Guide Vane Airfoil Shape of Pump Turbine Based on SVM-MDMR Model

Natural laminar flow airfoil design via adjoint-based transition onset delay

This work is focused on the aerodynamic shape optimization (ASO) of airfoils with the aim of attaining natural laminar flow (NLF) designs. The two-equation Amplification Factor Transport (AFT) model is utilized for an accurate prediction of the transitional boundary layer flows. The NLF designs are achieved by utilizing two different objective functions. In the first approach, the conventional drag minimization problem is solved with a target lift coefficient. In addition, a second approach is proposed in this work that directly aims at delaying the transition onset on both the pressure and suction sides, thus expanding the natural laminar flow region around the airfoil. It is shown that by utilizing a sigmoid fitting of the turbulence index profile, the transition onset locations can be accurately predicted in a differentiable and smooth fashion, which is essential to the adjoint-based sensitivity analysis of the RANS solver. The efficacy of the proposed technique for NLF design has been tested for NACA 0012 and RAE 2822 airfoils at moderate lift coefficients. Results have shown that a significantly lower drag count can be achieved by delaying the transition onset locations compared to the case where only a drag minimization is sought. Additionally, the transition onset locations on both sides of the airfoil are delayed using our proposed technique which results in a significant expansion of the natural laminar flow region.

A Deep Learning Approach to Optimize Airfoil Shape for Reduced Trailing Edge Noise in Urban Air Mobility Rotors

The objective of this research is to optimize the airfoil shape of UAM VTOL rotors for trailing edge noise reduction. Our study focuses on employing deep learning techniques for airfoil shape optimization with an emphasis on noise reduction. We implement a neural network that combines a Variational Autoencoder and Generative Adversarial Networks to learn the representation of airfoil shapes. The generated airfoil shapes are then evaluated for aerodynamic performance using XFOIL and trailing edge noise using acoustic diffraction model. The optimization process employs a Particle Swarm Optimization algorithm to find optimal latent features for airfoil generation. The results show that the optimized airfoil shapes have improved aerodynamic performance and reduced noise levels compared to the airfoil VR-12 used in NASA's conceptual UAM. These findings demonstrate that our optimization process has the potential to reduce trailing edge noise while ensuring enhanced aerodynamic performance, which warrants further investigation.

Design-Variable Hypernetworks for Flowfield Emulation and Shape Optimization of Compressor Airfoils

Deep-learning-based flow emulators are used to predict the flowfield around parametrically defined airfoils and then used in place of Reynolds-averaged Navier–Stokes solvers in design optimization. The flow emulators are based on a) decoder convolutional neural networks, which generate solution snapshots in the computational domain, and b) design-variable hypernetworks, which provide pointwise predictions in physical space. The flow emulators are used to predict parametric subsonic and transonic compressor flows in an industrial design use case with baseline geometry corresponding to the NASA rotor 37. Both methods are effective in representing unseen subsonic airfoil flowfields, with mean errors less than 1%. The hypernetwork-based method generalizes more effectively under transonic conditions and is used in place of computational fluid dynamics (CFD) to drive shape optimization at varying rotor speeds. Under transonic conditions and at nominal speed, the emulator-driven optimization achieves the same optimal design as CFD in a reduced number of iterations at a fraction of the online computational cost while providing similarly performing designs at off-nominal conditions. It is remarked that once the emulator is trained once offline, it can be used online to conduct many different design optimizations, e.g., with different objective functions, constraints, and tradeoffs. These results establish the utility of design-variable hypernetworks as a viable emulation and optimization tool in practical industrial design.

Optimization of transonic low-Reynolds number airfoil based on genetic algorithm

A 2-D airfoil shape optimization in transonic low-Reynolds number regime is conducted. A Navier–Stokes flow solver with a transition model (k-ω SST γ-Reθ) is used to evaluate the fitness function. Single-point and multi-point formulations of the optimization results are compared. In addition, the effects of Mach number and angles of attack on aerodynamic characteristics of the optimized airfoils are investigated under low Reynolds number (Re = 17,000) and high-subsonic-flow ([Formula: see text]) conditions. The results show that the corresponding drag divergence Mach number curves of the conventional airfoil present almost a parallel shifting at the entire Mach number range. By contrast, the unconventional airfoil starts showing a significant drag reduction when Mach number is greater than 0.75. Besides, the maximum lift-to-drag ratio is highly influenced by the Mach number because of the formation, movement, type, and strength of a shock wave. In addition, the distinguishing difference in the conclusion between two airfoils is that the lift fluctuation of the conventional airfoil amplifies with the increase of the Mach number. However, the unconventional airfoil shows an opposite trend.

Evolutionary Airfoil Shape Optimization Coupling Parameterization Methods with Lagrangian Vortex Method

In the present paper, the evolutionary algorithm for single-objective optimization is developed using a genetic algorithm and employing polynomial-based (PARSEC) and radial basis function (RBF) functions for NACA 2412 airfoil parameterization. The determination of the objective functions, being aerodynamic coefficients, are performed using the Lagrangian vortex particle method. The results of the lift coefficient at the wide range of angle of attack using the vortex particle method shows a good agreement with experimental data listed in the literature. For the optimization results, the lift coefficient obtained from the PARSEC method is optimized to be larger for the whole range of angle of attack; while it still keeps the stall region at the upper surface of the airfoil to be the same as that of the original airfoil. In addition, the RBF method illustrates the lift coefficients larger at the range of angle of attack from -50 to 140 but stall occurs earlier than the original airfoil.

Airfoil shape optimization using genetic algorithm coupled deep neural networks

To alleviate the computational burden associated with the computational fluid dynamics (CFD) simulation stage and improve aerodynamic optimization efficiency, this work develops an innovative procedure for airfoil shape optimization, which is implemented through coupling the genetic algorithm (GA) optimizer with the aerodynamic coefficients prediction network (ACPN) model. The ACPN is established using a fully connected neural network with the airfoil geometry as the input and aerodynamic coefficients as the output. The results show that the ACPN's mean prediction accuracy for the lift and drag coefficient is high up to about 99.02%. Moreover, the prediction time of each aerodynamic coefficient is within 5 ms, four orders of magnitude faster compared to the CFD solver (3 min). Taking advantage of the fast and accurate prediction, the proposed ACPN model replaces the expensive CFD simulations and couples with GA to force the airfoil shape change to maximize the lift–drag ratio under multiple constraints. In terms of time efficiency, optimized airfoils can be fast obtained within 25 s. Even considering an extra 50 h spent on data preparing and 20 s for model training, the overall calculation cost is reduced by a remarkable 62.1% compared to the GA-CFD optimization method (5.5 days). Furthermore, the GA-ACPN model improves the lift–drag ratio with and without constraint by 51.4% and 55.4% for NACA0012 airfoil, respectively, while 50.3% and 60.0% improvement achieved by the GA-CFD optimization method. These results indicate that the GA-ACPN optimization approach significantly enhances the optimization efficiency and has great potential to address varying constraint optimization problems.

A reinforcement learning approach to airfoil shape optimization

Shape optimization is an indispensable step in any aerodynamic design. However, the inherent complexity and non-linearity associated with fluid mechanics as well as the high-dimensional design space intrinsic to such problems make airfoil shape optimization a challenging task. Current approaches relying on gradient-based or gradient-free optimizers are data-inefficient in that they do not leverage accumulated knowledge, and are computationally expensive when integrating Computational Fluid Dynamics (CFD) simulation tools. Supervised learning approaches have addressed these limitations but are constrained by user-provided data. Reinforcement learning (RL) provides a data-driven approach bearing generative capabilities. We formulate the airfoil design as a Markov decision process (MDP) and investigate a Deep Reinforcement Learning (DRL) approach to airfoil shape optimization. A custom RL environment is developed allowing the agent to successively modify the shape of an initially provided 2D airfoil and to observe the associated changes in aerodynamic metrics such as lift-to-drag (L/D), lift coefficient (Cl) and drag coefficient (Cd). The learning abilities of the DRL agent are demonstrated through various experiments in which the agent’s objective-maximizing L/D, maximizing Cl or minimizing Cd-as well as the initial airfoil shape are varied. Results show that the DRL agent is able to generate high performing airfoils within a limited number of learning iterations. The strong resemblance between the artificially produced shapes and those found in the literature highlights the rationality of the decision-making policy learned by the agent. Overall, the presented approach demonstrates the relevance of DRL to airfoil shape optimization and brings forward a successful application of DRL to a physics-based aerodynamics problem.

Multi-fidelity reinforcement learning framework for shape optimization

Deep reinforcement learning (DRL) is a promising outer-loop intelligence paradigm which can deploy problem solving strategies for complex tasks. Consequently, DRL has been utilized for several scientific applications, specifically in cases where classical optimization or control methods are limited. One key limitation of conventional DRL methods is their episode-hungry nature which proves to be a bottleneck for tasks which involve costly evaluations of a numerical forward model. In this article, we address this limitation of DRL by introducing a controlled transfer learning framework that leverages a multi-fidelity simulation setting. Our strategy is deployed for an airfoil shape optimization problem at high Reynolds numbers, where our framework can learn an optimal policy for generating efficient airfoil shapes by gathering knowledge from multi-fidelity environments and reduces computational costs by over 30\%. Furthermore, our formulation promotes policy exploration and generalization to new environments, thereby preventing over-fitting to data from solely one fidelity. Our results demonstrate this framework's applicability to other scientific DRL scenarios where multi-fidelity environments can be used for policy learning.

Study on Optimization Design of Airfoil Transonic Buffet with Reinforcement Learning Method

Transonic buffet is a phenomenon of large self-excited shock oscillations caused by shock wave-boundary layer interaction, which is one of the common flow instability problems in aeronautical engineering. This phenomenon involves unsteady flow, which makes optimal design more difficult. In this paper, aerodynamic shape optimization design is combined with reinforcement learning to address the problem of transonic buffet. Using the deep deterministic policy gradient (DDPG) algorithm, a reinforcement learning-based design framework for airfoil shape optimization was constructed to achieve effective suppression of transonic buffet. The aerodynamic characteristics of the airfoil were calculated by the computational fluid dynamics (CFD) method. After optimization, the buffet onset angles of attack of the airfoils NACA0012 and RAE2822 were improved by 2° and 1.2° respectively, and the lift-drag ratios improved by 83.5% and 30% respectively. Summarizing and verifying the optimization results, three general conclusions can be drawn to improve the buffet performance: (1) narrowing of the leading edge of the airfoil; (2) situating the maximum thickness position at approximately 0.4 times the chord length; (3) increasing the thickness of the trailing edge within a certain range. This paper established a reinforcement learning-based unsteady optimal design method that enables the optimization of unsteady problems, including buffet.

Airfoil Shape Optimization of a Horizontal Axis Wind Turbine Blade using a Discrete Adjoint Solver

In this study, airfoil shape optimization of a wind turbine blade is performed using the ANSYS Fluent Adjoint Solver. The aim of this optimization process is to increase the wind turbine output power, and the objective function is to maximize the airfoil lift to drag ratio (Cl/CD ). This study is applied to the NREL phase VI wind turbine, therefore, the S809 airfoil is used as a reference profile. First, for the validation of the applied numerical model, steady-state simulations are carried out for the S809 airfoil at various angles of attack. Then, the optimization is performed with the airfoil set at a fixed angle of attack, , considering three Reynolds numbers, Re =3 105,4.8 105 and 106. Next, computations are performed for the fluid flow around the optimized airfoils at angles of attack AOA= 6.1° ranging from 0° to 20°. The results show that (i) the lift to drag ratios of the optimized airfoils are significantly improved compared to the baseline S809 airfoil, (ii) this improvement is sensitive to the Reynolds number, and (iii) the Cl/CD ratios are also improved for another angle of attack values. Thereafter, the optimized airfoils are used for the design of the NREL Phase VI blade and the aerodynamic performances of this new wind turbine are assessed using the open-source code QBlade. These latter results indicate that when the blades are designed with the optimized airfoils, the wind turbine aerodynamic performances increase significantly. Indeed, at a wind speed of 10 m/s, the power output of the wind turbine is improved by about 38% compared to that of the original turbine.

Shape Optimization of an Asymmetric Airfoil for Low Wind Speed Region having Adjoint-Based Optimization Technique

The land needed to install wind turbines is shrinking as power generation from renewable energy sources increases significantly. A large number of studies are being conducted to maximize the power extraction from wind turbines in areas with low wind speeds. Wind turbine blades play a significant role in utilizing the maximum amount of energy from the wind. The aerodynamic performance of a wind turbine blade depends on the airfoil shape. The shape optimization of an asymmetric S2027 airfoil for a low wind speed region was investigated using the adjoint-based optimization technique. The primary objectives of this study were to maximize the lift coefficient, minimize the drag coefficient, and maximize the lift-to-drag ratio. The optimization is based on the adjoint method for Reynolds number variation in the range of 2 × 105 to 5 × 105 and an angle of attack variation from 0° to 12°. A two-dimensional Reynolds–Averaged Navier–Strokes Computational Fluid Dynamics model was created with all the operating parameters and used for optimization. The aerodynamic performance was validated experimentally. For each optimization function, approximately 16 shapes were obtained. The aerodynamic performance for each optimized shape was determined under different operating conditions. Different airfoil shapes with a specific chord, leading and trailing edges, and span arrangement was obtained. The drag coefficient was reduced by 2%–30%; the lift coefficient was improved by 2%–35%, and the lift-to-drag ratio was improved up to 40%.

Aeroacoustic airfoil shape optimization enhanced by autoencoders

Aeroacoustic noise is a major concern in wind turbine design that can be minimized by optimizing the airfoils that shape the rotating blades. To this end, we present a framework for airfoil shape optimization to reduce the trailing edge noise for the design of wind turbine blades. Far-field noise is evaluated using Amiet’s theory coupled with the TNO-Blake model to calculate the wall pressure spectrum and fast turn-around XFOIL simulations to evaluate the boundary layer parameters. The computational framework is first validated using a NACA0012 airfoil at 0° angle of attack. Particle swarm optimization is used to find the optimized airfoil configuration. The multi-objective optimization minimizes the A-weighted overall sound pressure level at various angles of attack, while ensuring enough lift and minimum drag. Furthermore, traditional shape optimization techniques show difficulties to converge to the optimum, when too many shape parameters are included in the optimization. For this reason, we compare classic parameterization methods to define the airfoil geometry (i.e., CST) to a machine learning method (i.e., a variational autoencoder). We observe that variational autoencoders can represent a wide variety of geometries, with only four encoded variables, leading to efficient optimizations, which result in improved optimal shapes. When compared to the baseline geometry, a NACA0012, the autoencoder-based optimized airfoil reduces by 3% (1.75 dBA) the overall sound pressure level (with decreased noise across the entire frequency range), while maintaining favorable aerodynamic properties in terms of lift and drag.

Deep-learning-based aerodynamic shape optimization of rotor airfoils to suppress dynamic stall

The use of computational fluid dynamics (CFD) to optimize the aerodynamic shape of rotor airfoils with the aim of suppressing dynamic stall is computationally expensive and inefficient. To address this issue, a surrogate model based on deep learning (DL) is employed to replace a CFD module of optimization process in this study. The optimization framework is demonstrated by optimizing a SC1095 rotor airfoil in subsonic flow. The airfoil shapes are parameterized using the class function/shape function transformation method, and an airfoil dataset for a deep neural network (DNN) is generated by Latin hypercube sampling. The surrogate model for predicting the aerodynamic coefficients of the airfoils is established by training the DNN, which can get the predicted results within a second. This surrogate model is then combined with the multi-island genetic algorithm for rotor airfoil optimization. Finally, the aerodynamic performance of a rotor with the optimized airfoil is investigated to verify the dynamic stall suppression effect. The results demonstrate that the peak drag and moment coefficients of the optimized airfoil can be reduced by 82.5% and 88.6%, respectively, compared with the baseline airfoil, while the lift coefficients increase during almost all of the pitching period. This means that the optimized airfoil has significantly improved dynamic stall characteristics. Moreover, by suppressing the dynamic stall, the rotor with the optimized airfoil achieves better aerodynamic performance than the baseline rotor. Statistical data show that our use of a DL-based surrogate model instead of the CFD module will reduce the optimization time by at least one order of magnitude.

GPU-Accelerated Infill Criterion for Multi-Objective Efficient Global Optimization Algorithm and Its Applications

In this work, a novel multi-objective efficient global optimization (EGO) algorithm, namely GMOEGO, is presented by proposing an approach of available threads’ multi-objective infill criterion. The work applies the outstanding hypervolume-based expected improvement criterion to enhance the Pareto solutions in view of the accuracy and their distribution on the Pareto front, and the values of sophisticated hypervolume improvement (HVI) are technically approximated by counting the Monte Carlo sampling points under the modern GPU (graphics processing unit) architecture. As compared with traditional methods, such as slice-based hypervolume integration, the programing complexity of the present approach is greatly reduced due to such counting-like simple operations. That is, the calculation of the sophisticated HVI, which has proven to be the most time-consuming part with many objectives, can be light in programed implementation. Meanwhile, the time consumption of massive computing associated with such Monte Carlo-based HVI approximation (MCHVI) is greatly alleviated by parallelizing in the GPU. A set of mathematical function cases and a real engineering airfoil shape optimization problem that appeared in the literature are taken to validate the proposed approach. All the results show that, less time-consuming, up to around 13.734 times the speedup is achieved when appropriate Pareto solutions are captured.