Airfoil Optimization Research Articles

Steam turbine high-pressure reaction stages; new 3D vortices breakdown and airfoil optimization method

Steam turbine high-pressure reaction stages; new 3D vortices breakdown and airfoil optimization method

Optimizing Bionic Blades for Multi-blade Centrifugal Fans: Asymmetric Thickness Inspired by Carangiform Fish

Multi-blade centrifugal fans find wide application across various fields, with their internal airflow exhibiting complex turbulent behavior in three dimensions. Historically, blade optimization relied on constant thickness airfoils, limiting the effectiveness of optimization efforts. However, marine organisms have developed airfoil structures with highly efficient drag reduction, offering a novel approach to optimizing multi-blade centrifugal fans. This study proposes an airfoil optimization design method utilizing variable-thickness airfoils to maintain consistent pressure surface leading-edge parameters. By integrating the Non-dominated Sorting Genetic Algorithm II with biomimetic optimization design, performance improvements are achieved. The study constructs an asymmetric bionic blade using a Bezier curve to fit the mean camber line of the blade. Experimental testing validates the optimized fan's performance, demonstrating the effectiveness of the proposed design approach in reducing the unsteady interaction between the impeller and the volute tongue. This reduction significantly diminishes sound pressure fluctuations on the blade surface. Notably, at the maximum volume flow rate, the optimized fan featuring the asymmetric bionic blade exhibits a remarkable enhancement, with a 10.5% increase in volume flow rate and a notable 1.7 dB reduction in noise compared to the original fan configuration.

Adaptive Free-Form Deformation Parameterization Based on Spring Analogy Method for Aerodynamic Shape Optimization

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.

Experimental Optimization of the SG6043 Airfoil for Horizontal Axis Wind Turbines Using Schmitz Equations

This study presents the experimental optimization of the SG6043 airfoil for horizontal axis wind turbines (HAWTs) using the Schmitz equation, focusing on enhancing power output and elucidating the surface flow structure. Two blade models, M1 (conventional) and M2 (optimized), were designed and tested at rotational speeds of 400 rpm and 600 rpm across a range of tip speed ratios (TSR). The M2 model, optimized using Schmitz equations, demonstrated significantly improved performance compared to the M1 model at both rotational speeds. At 400 rpm, the maximum power coefficient (CP) for M1 was 0.274, while M2 reached 0.419, indicating a 52.91% improvement. At 600 rpm, M1 achieved a maximum CP of 0.293, whereas M2 attained 0.458, representing a 56.31% enhancement. The M2 model also showed superior performance at higher TSRs, with the highest percentage increase in CP recorded at 4.9 TSR, reaching 574.54%. Additionally, dynamic surface oil-flow visualization experiments were conducted to examine flow behavior on the blade surfaces. Results indicated better flow attachment in the M2 blade due to its optimized twist angle and chord length, particularly in the mid-section, leading to delayed flow separation. The reattachment observed on the suction side of the M2 model, following the laminar separation bubble (LSB), which was absent in the M1, contributed to its higher aerodynamic efficiency and overall power performance. These findings confirm that the optimized SG6043 airfoil design, guided by Schmitz equations, offers significant improvements in HAWT performance, particularly under varying operational conditions.

Airfoil Optimization Using Deep Learning Models and Evolutionary Algorithms for the Case Large-Endurance UAVs Design

This article presents the development of the AZTLI-NN network and the evaluation of this network as a set of evolutionary algorithms in airfoil optimization tasks. AZTLI-NN has the characteristic of predicting the aerodynamic coefficients of the airfoils in the form of images (graphs of the aerodynamic coefficients as a function of the angle of attack) from parameter vectors corresponding to the parameterization method CST. This feature allows the network to achieve good performance when generalizing the predictions of the aerodynamic coefficients, being on par with neural networks that have the aerodynamic coefficients encoded in the form of structured data, and has the ability to handle a wide range of usage airfoils in general aviation. In addition, a case of how AZTLI-NN together with an adaptive evolutionary algorithm and population size reduction methods achieve good performance in finding the airfoil that provides the highest possible endurance value is shown, so this work is considered as an option in the early stages of the design for the selection of airfoils in the design of large-endurance UAVs.

Multi-objective optimization of airfoils with integral tubular high-pressure tanks for hydrogen storage

Reducing the environmental impact of air transport is one of today's most important challenges in aviation industry and research. A promising key enabler is the use of hydrogen as an alternative to fossil fuels. The development of hydrogen-powered aircraft poses new engineering challenges due to its low volumetric energy density requiring high-pressure or cryogenic storage. If the volume in the wing shall be further used for storing hydrogen under high pressure, new demands arise to airfoil design. The present work focuses on this issue by presenting a multi-objective optimization approach aiming for airfoils with both low drag and high volume for internal tubular high-pressure tanks. This allows to directly address the new design objective and to find novel airfoil shapes providing the best compromise between aerodynamic efficiency and high storage volume for pressurized hydrogen. The resulting optimization problem is solved using Evolutionary Algorithms. For an efficient aerodynamic evaluation, the open source viscous-inviscid panel method XFOIL is used. An application example, based on the flight conditions of a general aviation aircraft, demonstrates the applicability of the method. Comparisons of the resulting aerodynamic characteristics obtained by XFOIL with RANS simulations confirm the feasibility of the results.

Blade Airfoil Optimization and Its Impact on Vertical Axis Wind Turbine Performance

Abstract Amidst the emergence of crises in petroleum prices and supply, the imperative for the development of clean energy has become increasingly apparent. Vertical axis wind turbines (VAWT), as a type of wind turbine, still grapple with challenges such as low wind energy utilization and sensitivity to dynamic wind speeds. This study focuses on optimizing the airfoil of a two-dimensional vertical axis wind turbine and analyzes the performance variations in a three-dimensional model. Following the optimization, the average power coefficients of the dual-blade two-dimensional VAWT increased by 7.9% and 4%, respectively, while those of the dual-blade three-dimensional model rose by 7.9% and 1.2%. However, the performance of the three-dimensional model was compromised due to the influence of tip vortices, resulting in inferior performance compared to the two-dimensional model. Both three-dimensional optimized blade designs exhibited a substantial reduction in the flow separation region downstream and improved pressure distribution fluctuations caused by the shedding of tip vortices, leading to decreased pressure differentials. Along the spanwise section, the power coefficient gradually decreased from the central segment to the tip segment. Notably, the power coefficient of the optimized blades at the tip segment increased significantly, accompanied by an augmented pressure differential between the upper and lower surfaces. This augmentation contributed to a significant enhancement in lift, thereby facilitating the rotation of the vertical axis wind turbine.

Blade height impact on self-starting torque for Darrieus vertical axis wind turbines

Self-starting torque (TSelf-starting) presents a significant challenge for Darrieus vertical axis wind turbines (DVAWTs), often necessitating external assistance to initiate rotation. This study addresses the issue by optimizing airfoil design, employing embossed blades (EBs), and adjusting blade height (H) to reduce TSelf-starting. From an analysis of 43 rotors at a chord-based Reynolds number (Rec) of 45,192, national advisory committee for aeronautics (NACA) 0015, NACA4412, and NACA4415 rotors were selected for their superior power coefficients (Cp). These rotors were optimized using double-multiple streamtube theory (DMST) and particle swarm optimization (PSO), focusing on the thickness-to-chord ratio (TCR). Among them, the NACA0015-Opt rotor achieved the highest Cp, demonstrating its effectiveness in enhancing DVAWT efficiency. This study also investigates the effect of H on the performance of EBs, comparing H of 35 cm and 75 cm. Experimental findings reveal that combining airfoil optimization with EBs, along with an increased H, leads to a substantial decrease in TSelf-starting. Specifically, higher H enhance the aerodynamic performance of EBs by improving airflow over the blade surface, further reducing drag and contributing to a significant reduction in TSelf-starting. At a H of 75 cm, the embossed blade Darrieus vertical axis wind turbine (EB-DVAWT) equipped with the optimized NACA0015-Opt rotor required 15.92 %, 17.04 %, 18.12 %, 21.23 %, 52.06 %, 49.23 %, 51.25 %, 35.20 %, 14.12 %, and 9.09 % less TSelf-starting at wind velocities (U∞) of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 9.5 m/s, respectively, compared to the baseline smooth blade Darrieus vertical axis wind turbine (SB-DVAWT) with the original NACA0015 rotor.

Surrogate based design space exploration and exploitation for an efficient airfoil optimization under uncertainties using transition models

The pursuit of sustainable, zero-emission air travel is heavily dependent on the creation of energy-efficient aircraft. Key strategies for achieving this sustainability in aviation include reducing fuel consumption through low-drag designs harnessing laminar flow. However, designing aircraft with laminar flow characteristics is complex due to their sensitivity to environmental and operational factors. This study tackles the challenge of developing energy-efficient aircraft by using computational fluid dynamics models and sophisticated optimization techniques that account for uncertainty. Our approach demonstrates the effectiveness of surrogate-based optimization and uncertainty quantification in optimizing airfoil drag for a natural laminar airfoil (NLF) design. We use surrogate models, trained with data from detailed airfoil simulations, which include a boundary layer code coupled with a linear stability method and a newly developed transition transport model. Transition location predicted using transition models facilitate an accurate drag prediction used in the optimization process. The accuracy of these surrogate models is enhanced through active sampling strategies. Our robust optimization method considers uncertainties in environmental and operational conditions, offering a deeper insight into their effects on crucial design parameters. Unlike traditional deterministic aerodynamic design optimization, our findings highlight the efficacy and precision of uncertainty-based optimization in achieving robust NLF airfoil designs over large (exploration mode) and small (exploitation mode) design spaces. Investigating design space parameterization based on the size of design variables reveals significant differences in optimal airfoil configurations. The optimized designs we propose favor delayed transition, in contrast to deterministic designs which often result in significant loss of laminarity when facing uncertainties. This study represents a significant advancement in aerospace engineering, providing a practical and effective methodology for creating energy-efficient airfoil designs. The application of these advanced optimization and uncertainty quantification techniques shows great potential for the wider field of aerospace engineering, paving the way for more resilient and robust aircraft designs.

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.

Novel airfoil for improved supersonic aerodynamic performance

PurposeThis study aims to validate the linear flow theory with computational fluid dynamics (CFD) simulations and to propose a novel shape for the airfoil that will improve supersonic aerodynamic performance compared to the National Advisory Committee for Aeronautics (NACA) 64a210 airfoil.Design/methodology/approachTo design the new airfoil shape, this study uses a convex optimization approach to obtain a global optimal shape for an airfoil. First, modeling is conducted using linear flow theory, and then numerical verification is done by CFD simulations using ANSYS Fluent. The optimization process ensures that the new airfoil maintains the same cross-sectional area and thickness as the NACA 64a210 airfoil. This study found that an efficient way to obtain the ideal airfoil shape is by using linear flow theory, and the numerical simulations supported the assumptions inherent in the linear flow theory.FindingsThis study’s findings show notable improvements (from 4% to 200%) in the aerodynamic performance of the airfoil, especially in the supersonic range, which points to the suggested airfoil as a potential option for several fighter aircraft. Under various supersonic conditions, the optimized airfoil exhibits improved lift-over-drag ratios, leading to improved flight performance and lower fuel consumption.Research limitations/implicationsThis study was conducted mainly for supersonic flow, whereas the subsonic flow is tested for a Mach number of 0.7. This study would be extended for both subsonic and supersonic flights.Practical implicationsConvex optimization and linear flow theory are combined in this work to create an airfoil that performs better in supersonic conditions than the NACA 64a210. By closely matching the CFD results, the linear flow theory's robustness is confirmed. This means that the initial design phase no longer requires extensive CFD simulations, and the linear flow theory can be used quickly and efficiently to obtain optimal airfoil shapes.Social implicationsThe proposed airfoil can be used in different fighter aircraft to enhance performance and reduce fuel consumption. Thus, lower carbon emission is expected.Originality/valueThe unique aspect of this work is how convex optimization and linear flow theory were combined to create an airfoil that performs better in supersonic conditions than the NACA 64a210. Comprehensive CFD simulations were used for validation, highlighting the optimization approach's strength and usefulness in aerospace engineering.

A design optimization method for rarefied and continuum gas flows

A design optimization method applicable to both rarefied and continuum gas flows with good efficiency is proposed in the framework of gas-kinetic theory. The method follows the methodology of topology optimization where the areas of gas and solid are marked by the material density, based on which a fictitious porosity model is used to reflect the effect of the solid on the gas and mimic the diffuse boundary condition on the gas-solid interface. The formula of this fictitious porosity model is modified to make the model work well from the free-molecular flow regime to the continuum flow regime. To find the optimized material density, a gradient-based optimizer is adopted and the design sensitivity is obtained by the continuous adjoint method. To solve the primal kinetic equation and the corresponding adjoint equation, efficient multiscale numerical schemes are constructed. Several airfoil optimization problems are solved to demonstrate the performance of the present design optimization method in wide ranges of flow speed and gas rarefaction. It is found that the thickness of the optimized airfoil first increases and then decreases as the Knudsen number increases, and on the supersonic condition the optimized airfoil has quite different shapes of leading edge for different degrees of gas rarefaction.

A comparison between 2D DeepCFD, 2D CFD simulations and 2D/2C PIV measurements of NACA 0012 and NACA 6412 airfoils

In this study, fluid flow predictions using three different methods were compared: DeepCFD, an artificial intelligence code; computational fluid dynamics (CFD) using Ansys Fluent and OpenFOAM; and two-dimensional, two-component particle image velocimetry (PIV) measurements. The airfoils under investigation were the NACA 0012 with a 10° angle of attack and the NACA 6412 with a 0° angle of attack. To train DeepCFD, 763, 2585, and 6283 OpenFOAM simulations based on primitives were utilized. The investigation was conducted at a free stream velocity of 10 m/s and a Reynolds number of 82000. Results show that once the DeepCFD network is trained, prediction times are negligible, enabling real-time optimization of airfoils. The mean absolute error between CFD and DeepCFD, with 6283 trained primitives, for NACA 0012 predictions resulted in velocity components Ux = 1.08 m/s, Uy = 0.43 m/s, and static pressure p = 4.57 Pa. For NACA 6412, the corresponding mean absolute errors are Ux = 0.81 m/s, Uy = 0.59 m/s, and p = 7.5 Pa. Qualitative agreement was observed between PIV measurements, DeepCFD, and CFD. Results are promising that artificial intelligence has the potential for real-time fluid flow optimization of NACA airfoils in the future. The main goal was not just to train a network specifically for airfoils, but also for variant shapes. Airfoils are used since they are highly sophisticated in fluid dynamics and experimental data was available.

Biomimetic Airfoil Optimization to Supplement Flight Efficiency in Unmanned Aerial Vehicles

Biomimetic Airfoil Optimization to Supplement Flight Efficiency in Unmanned Aerial Vehicles

Aerodynamic performance optimization of a UAV's airfoil at low-Reynolds number and transonic flow under the Martian carbon dioxide atmosphere

Unmanned aerial vehicles (UAV) on Mars operate in a thin atmosphere of carbon dioxide, where the flow Reynolds number and local sound velocity are significantly reduced compared to the Earth's atmosphere because of low gas density and temperature. Therefore, a Mars UAV with a rotary-wing design can operate in a state of low-Reynolds number (Re = 1-5 × 104) and transonic flow (Matip = 0.7–1.2), where flow separation and shock waves occur simultaneously. The interaction between flow separation and shock waves not only makes the entire flow field more complex but also seriously affects the aerodynamic performance of the airfoil, thereby reducing the payload of UAVs, which previous aircraft designs based on the thick atmospheric environment of the Earth have not considered. Therefore, in this study, a numerical simulation method is used to conduct airfoil optimization research on a characteristic airfoil under low-Reynolds number transonic flow (Re = 33200, Ma = 0.85) conditions to acquire additional insight, improve aerodynamic performance of the airfoil, and enhance the payload. The results were compared with the optimization results of subsonic flow (Re = 19500, Ma = 0.50). The Hicks-Henne bump functions method was selected for airfoil parameterization, and non-dominated sorting genetic algorithms (NSGA)-Ⅱ were used for optimization. Through an analysis of the pressure coefficient (Cp), surface friction coefficient (Cf), and density gradient, the number and intensity of oblique shock waves on the upper and lower surfaces were observed to significantly affect the aerodynamic performance of airfoils under low-Reynolds number flow. The changes in flow separation and transition positions do not directly affect the aerodynamic performance but weaken the oblique shock wave intensity induced by the separation point or directly transform strong shock waves into weaker compression waves because of the absence of flow separation. The optimization results for both subsonic and transonic flow point to a thinner overall shape with a flatter surface with the drag greatly reduced due to the disappearance of shock waves on the lower surface, which significantly improves aerodynamic performance. Compared with the original airfoil, at Ma = 0.85, this design can increase the lift coefficient (Cl) by at least 124 % and lift drag ratio (Cl/Cd) by 177 %.

Random flutter analysis of a novel binary airfoil with fractional order viscoelastic constitutive relationship

The fractional order model emerges naturally when the integer order model fails to meet practical requirements and finds extensive applications in engineering practice. However, there is still limited research on the random flutter of fractional order viscoelastic binary airfoils. This study aims to explore the random flutter of such airfoils under the influence of Gaussian white noise excitation by utilizing the pth moment Lyapunov exponent. Firstly, a two-degree-of-freedom fractional order stochastic dynamic equation is established for the viscoelastic binary airfoil through the introduction of fractional order damping. The singular perturbation method is then employed to derive the pth moment Lyapunov exponent of the system. An approximate analytical solution of the pth moment Lyapunov exponent is obtained through Fourier series expansion, which exhibits good agreement with numerical results obtained from Monte Carlo simulations. Subsequently, a comprehensive analysis is conducted to examine the impacts of fractional order, airflow velocity, noise intensity, and key structural parameters on the stochastic flutter of the fractional order viscoelastic binary airfoil. The findings indicate that compared with the typical binary airfoil model, the flutter speed of the fractional-order viscoelastic binary airfoil is significantly increased, the stability of the system is highly sensitive to the natural frequency of the system, and the fractional-order factor has a positive effect on the stochastic stability of the binary airfoil before the critical value. The above research results can guide the design optimization of the fractional-order viscoelastic airfoil.

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.

Selecting the Optimal Airfoil for Automotive Rear Wings: Performance Assessment

Selecting the Optimal Airfoil for Automotive Rear Wings: Performance Assessment

Inverse design optimization of the compressor cascade airfoil assisted by active subspace approach

Inverse design optimization of the compressor cascade airfoil assisted by active subspace approach

Efficient geometric parametrization of blades cross-sections by means of B-splines

Optimization and enhancement of rotor blade design are critical to improving the productivity of the wind energy industry. Airfoil geometry is a key factor that makes airfoil design and optimization a common task for aerodynamicists. Ensuring proper airfoil parametrization is essential. It serves as the first step in aerodynamic optimization, where the efficiency is directly related to the geometric complexity. This research presents a cost-effective and robust method for fitting airfoils using B-splines. We take into account factors such as computational cost, resource requirements, and accuracy. In this work, we present a method for minimizing the geometric distances between target points and a B-spline curve. We streamline the fitting process, create a computational Python package, and explore different approaches, objective functions, algorithms, and error tolerance settings. The work concludes that it is highly recommended to use an iterative fitting process, to adequately represent common airfoils with B-splines. Moreover, the accuracy and the computational cost can be managed subject to the minimization algorithm used, and the technique utilized for the objective cost calculation. The fitting procedure we develop in this study gives the smallest number of variables capable of accurately representing a desired airfoil.