Airfoil Shape Research Articles

The reproduction of 2-D non-synoptic wind field in an actively controlled wind tunnel

This work mainly discusses the simulation of 2-D non-synoptic wind field in a novel actively controlled wind tunnel. The vibrating fins with airfoil shape are installed at the downstream of multiple fans in the updated active wind tunnel, which will work with fans simultaneously to generate 2-D non-synoptic flow. The fins mainly control the vertical flow while the fans control the along-wind flow, and the input signal of equipment can be adjusted in a predefined way. Then, based on Banach fixed-point theorem, the input signal of fans and fins is constantly updated by an iteration-based method to derive the generated wind characteristics to approach the different target values within an acceptable error range. According to the degree of interference between the longitudinal and the vertical wind characteristics, different iteration strategies are proposed for different wind fields. Two typical non-synoptic wind fields are taken as application examples: irregular turbulence spectra in typhoons and non-stationary winds in mountainous terrains. After iterations, both case studies were generated appropriately in the active tunnel. The simulated wind fields are crucial for wind-resistant design of wind-sensitive structures under non-synoptic wind climates.

Exploring a bio-inspired passive flow control strategy for wind turbines: Experimental characterization of the aerodynamics of a wind turbine blade section possibly equipped with leading-edge tubercles

Focusing on a bio-inspired passive flow control strategy with a potential application to wind turbines, this study consists of an experimental characterization of the aerodynamics of a representative wind turbine blade section to be possibly equipped with leading-edge tubercles. A total of five airfoils are tested in a low-speed wind tunnel, their aerodynamic characteristics being explored over a wide range of flow conditions by the means of load measurements and wall-flow visualizations. Results reveal that the leading-edge tubercles alter differently the airfoil's aerodynamics, depending on their specific design (amplitude and wavelength) as well as on the flow conditions (speed and incidence). The magnitude of these effects is seen to vary with the tubercles' amplitude and/or wavelength, ultimately leading to an optimal trade-off between pre- and post-stall regimes being offered by an intermediate amplitude-to-wavelength ratio. Second, the aerodynamic benefits/penalties induced by the leading-edge tubercles are explored through wall-flow visualizations; The tubercled airfoils exhibit pairs of counter-rotating vortices, whose characteristics are driven by the tubercles' design, the airfoil shape, and/or the flow conditions. Overall, these vortex pairs are more prominent for large-amplitude and/or small-wavelength tubercles, each design altering the near-wall flow and, thus, the aerodynamic performances in a specific fashion.

Machine Learning Based Predictions of Airfoil Aerodynamic Coefficients for Reynolds Number Extrapolations

This study investigates the application of various machine learning (ML) algorithms for predicting two critical aerodynamic coefficients, i.e. the maximum lift coefficient (C l max ) and the minimum drag coefficient (C d min ), for wind turbine airfoils at any given Reynolds number. We propose to use clustering techniques to group similar airfoil shapes and use the created partitions to predict unseen airfoil properties utilizing their similarity. Here, we also represent airfoils in the PARSEC low dimensional space, rather than high dimensional airfoil points space, to remedy the small number of training data. For this purpose, an extended experimental airfoil database is created and used for training models based on five different ML algorithms. We observe that the Decision Tree Ensemble (DTE), Random Forest (RF) and multi-layer perceptron (MLP) models emerge as the most effective predictors for C l max and C d min . Testing these two ML models on three additional airfoil cases not included in the training database shows that the C l max prediction performance is generally reasonable, with error levels being around 5% on average. In contrast, the prediction error levels for C d min are usually higher, with an average of around 15%.

Physics-Informed Machine Learning Using Low-Fidelity Flowfields for Inverse Airfoil Shape Design

Physics-informed neural networks (PINNs) are a class of scientific machine learning that utilizes differential equations in loss formulations to model physical quantities. Despite recent developments, complex phenomena such as high-Reynolds-number (high-Re) flow remain a modeling challenge without the use of high-fidelity inputs. In this study, a low-fidelity-influenced physics-informed neural network (LF-PINN) is proposed as a surrogate aerodynamic analysis model for inverse airfoil shape design at Re=1.0×106. The LF-PINN is developed in a hybrid approach using low-fidelity flowfields approximated from a viscous-inviscid coupled airfoil analysis tool (mfoil) and physics residuals from the steady, incompressible, two-dimensional Navier–Stokes (NS) equations. The approach is designed to alleviate offline computational costs by avoiding high-fidelity simulations and sustain predicting accuracy using corrections by the physics residuals. The LF-PINN is able to correct the low-fidelity flowfield quantities toward the ground truth, with a mean improvement of about 19% in pressure and about 5% in total velocity based on Euclidean distance comparisons. Evaluation of the airfoil surface pressure coefficient Cp distributions shows corrections by the LF-PINN at the suction peak, which largely contributes to lifting forces. Inverse airfoil shape design is conducted using target Cp distributions in the objective function, whereby the LF-PINN can approach the expected target shapes while reducing online computational time by at least an order of magnitude compared to direct airfoil analysis tools.

Numerical Study of Transonic Buffet on SC(2)-0518 and OAT15A with Vortex Generators

Predicting the transonic buffet and its onset is important for ascertaining the performance limits of an aircraft at its critical angle of attack. Additionally, a physical understanding of the buffet suppression technique is important for preventing shock wave oscillations. In this study, we conducted zonal detached-eddy simulations to numerically investigate the effects of vortex generators (VGs) on buffet suppression and to discuss the differing flow characteristics of the SC(2)-0518 and OAT15A supercritical airfoils when the chordwise position of the VGs is varied. The results for both airfoils equipped with VGs demonstrated significant suppression of large-scale lift oscillations across all calculation steps. VGs placed at 10% of the chord (10%c) from the leading edge produced higher time-averaged lift coefficients for both airfoils, with the OAT15A airfoil showing a particularly notable 2.5% improvement in lift coefficient, leading to a 0.82% increase in L/D ratio. The visualized results indicated that the interaction between the shock wave and VGs leads to variations in the separation point, depending on the VG chordwise position. This separation is affected by the aerodynamic characteristics of the airfoil shapes and the wake induced by the VGs, ultimately resulting in changes to the lift coefficient.

Numerical investigation of nitrogen spontaneous condensation over airfoils in cryogenic wind tunnel

Cryogenic wind tunnels (CWT) provide the aerodynamic tests that occur at high Reynolds numbers by operating under cryogenic environment to meet the requirements of hypersonic flight simulation. However, condensation in cryogenic environment near the limited condition destroys the reliability of the test measurement results. Accordingly, research on condensation in CWT is imperative for devising effective control strategies. This study introduces a transonic non-equilibrium condensation model, tailored to evaluate the complex phenomena of nitrogen condensation over airfoils. The model was applied to assess condensation effects on the NACA 0012–64 airfoil and the RAE 2822 airfoil under various operating conditions. Furthermore, the study examined the effect of the angle of attack and airfoil shape on the condensation process. The result show that nitrogen condensation near the airfoil is observable only under operating conditions within the pre-condensation zone. Operating conditions of CWT can be tailored to prevent condensation with specific airfoil profiles. The effect of condensation on the pressure coefficient includes advancing the position of the pressure jump and increasing the pressure coefficient of the airfoil intermediate region, particularly within the 20 %–70 % chord length span on the airfoil's upper surface. This primarily affects the measurement of lift coefficients in CWT. In the operating conditions of this study, the lift coefficient exhibits a maximum deviation of 31.4 %, and the drag coefficient shows a maximum deviation of 2.4 %. The transonic spontaneous condensation model offers an approach to evaluate condensation's impact on airfoil tests within CWT. The findings introduce a methodological framework for effectively controlling condensation phenomena.

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.

Prediction of the Influence of the Inlet End-Wall Boundary Layer on the Secondary Flow of a Low Pressure Turbine Airfoil Using RANS and Large-Eddy Simulations

Abstract This paper analyzes the effect of the inlet end-wall boundary layer on the secondary flow of a low pressure turbine airfoil cascade at Reynolds number 2 × 105 using RANS and implicit large-eddy simulations (LES). The results are compared against experimental data obtained at two low-speed linear cascade facilities, one located at the Whittle Laboratory of the University of Cambridge and the other at the Polytechnic University of Madrid. The RANS turbulence model is the k−ω−γ−Reθt and no sub-grid scale model has been used in the LES. An unstructured mesh of hexahedra and prisms is used, with high order elements used in the boundary layer region to better describe the airfoil shape in the LES. Two inlet end-wall boundary layers that produce different secondary flow patterns are analyzed: a laminar thin velocity profile and a turbulent thick velocity profile with several inlet turbulent intensities. The agreement between LES numerical predictions and experimental measurements of the position and intensity of the secondary vortices is very good for both cases. RANS simulations are much cheaper in terms of computational cost and reasonably predict most of the flow features, except when the inlet turbulence is low and turbulent transition prediction becomes critical. The effect of the inlet velocity profiles and inlet turbulence on the secondary flow structure is quite pronounced. The velocity profile thickness determines the spanwise penetration of the passage vortex, and different inlet turbulence intensities modify its mixing. Higher inlet turbulence intensities lead to a decrease of the secondary losses due to the passage vortex and an increase of end-wall losses.

Effect of the shape of flapping airfoils on aerodynamic forces

The rapid exhaustion of fossil fuels and the ozone depletion caused by the excessive usage of the fossil fuels has prompted researchers to look towards bioinspired designs for both propulsion and energy extraction purposes. Limited amount of work has been done to present the effects of airfoil shape on the aerodynamic forces on flapping foils. In this paper, we examine in detail the effect of airfoil camber and its position on flapping foil performance in both energy extraction and propulsion regimes. We also examine the effect of reflex camber on flapping foil performance in both flow regimes. In total, 42 airfoils are analyzed using the NACA 4 and 5-series cross-sections. The man objective of this research is to identify a trend, between airfoil shape and aerodynamic forces. The database created as a result will be used in the future work for designing a hydrokinetic turbine and a bio-inspired unmanned aerial vehicle. The results from the numerical simulations indicate that the airfoil shape has significant effects on the time averaged drag force on the airfoil in both flow regimes. However, the time averaged lift force remains negligible for all cases.

Resolvent model for aeroacoustics of trailing edge noise

This study presents a physics-based, low-order model for the trailing edge (TE) noise generated by an airfoil at low angle of attack. The approach employs incompressible resolvent analysis of the mean flow to extract relevant spanwise-coherent structures in the transitional boundary layer and near wake. These structures are integrated into Curle’s solution to Lighthill’s acoustic analogy to obtain the scattered acoustic field. The model has the advantage of predicting surface pressure fluctuations from first principles, avoiding reliance on empirical models, but with a free amplitude set by simulation data. The model is evaluated for the transitional flow (Re=5e4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {Re} = 5e4$$\\end{document}) around a NACA0012 airfoil at 3 deg angle of attack, which features TE noise with multiple tones. The mean flow is obtained from a compressible large eddy simulation, and spectral proper orthogonal decomposition (SPOD) is employed to extract the main hydrodynamic and acoustic features of the flow. Comparisons between resolvent and SPOD demonstrate that the physics-based model accurately captures the leading coherent structures at the main tones’ frequencies, resulting in a good agreement of the reconstructed acoustic power with that of the SPOD (within 4 dB). Discrepancies are observed at high frequencies, likely linked to nonlinearities that are not considered in the resolvent analysis. The model’s directivity aligns well with the data at low Helmholtz numbers, but it fails at high frequencies where the back-scattered pressure plays a significant role in directivity. This modeling approach opens the way for efficient optimization of airfoil shapes in combination with low-fidelity mean flow solvers to reduce TE noise.Graphical abstract

Convolutional Neural Networks-Based For Predicting Aerodynamic Coefficient Of Airfoils At Ultra-Low Reynolds Number

Many applications, including airplane design, wind turbines, and heat transmission, use symmetric or asymmetric airfoils. Engineers employ these airfoil shapes to optimize performance and efficiency. Each airfoil has a unique set of aerodynamic coefficients that must be calculated to maximize the airfoil design. Engineers utilize numerous ways to calculate coefficients, such as lift and drag. One of the methods is the prediction method, which effectively reduces time and cost. This study's training dataset is obtained from particle-based numerical computation using the Lattice Boltzmann Method (LBM). Then, Convolutional Neural Networks (CNN) are used as a prediction method to get the aerodynamic coefficients of airfoils for lift and drag based on two different Reynolds numbers. In CNN, airfoil geometry representation is essential. The Signed Distance Function (SDF) was used to convert airfoil geometry into RGB pictures. On the other hand, the SDF method cannot explain different flow conditions; in this case, it is represented by the Reynolds number (Re). Therefore, we propose a Text-based Watermarking Method (TWM) to differentiate between Re = 500 and Re = 1000. Each airfoil representation was trained and tested to generate each prediction model using a modified LeNet-5. The computation results show that using CNN with TWM on SDF to define the Reynolds numbers could predict the lift and drag coefficients with varying angles of attack. Future research can focus on generalizations to different aerodynamic aspects and practical applications in complex scenarios.

Numerical Investigation and Optimization of a Morphing Airfoil Designed for Lower Reynolds Number

A novel concept of morphing airfoils, capable of changing camber and thickness, is proposed. A variable airfoil shape, defined by six input parameters, is achieved by allowing the three spinal points (at fixed axial positions) to slide vertically, while the upper and lower surfaces are determined by the lengths of the three corresponding ribs that are perpendicular to the spine. Thus, it is possible to find the most appropriate geometric configuration for a wide range of possible operating conditions often present with contemporary unmanned aerial vehicles. Shape optimizations for different Reynolds numbers and different cost functions are performed by coupling a genetic algorithm with simple panel method flow calculations. The obtained airfoils are presented and compared, whereas the proposed concept is validated by more advanced flow simulations. It appears that improvements in aerodynamic performance of nearly 20% can be expected at Re ranging from 0.05 × 106 to 0.1 × 106. The proposed methodology shows promise and can be applied to different types of lifting surfaces, including wing, tail or propeller blade segments. To check the viability of this method for producing airfoils that can be used in a practical sense, structural analysis of one of the obtained geometries using a simplified 1D finite element method as well as a more detailed 3D analysis are performed. The model is then 3D-printed on a fused deposition modeling (FDM) printer with a polyethylene terephthalate glycol (PETG) filament, and the capability of the airfoil to adequately morph between the two desired geometries is experimentally shown.

A Hermite-type collocation mesh-free approach for simulating incompressible viscous fluid flows

In this work, a novel Hermite-type mesh-free model for incompressible viscous fluid flows is proposed, as a way, to overcome the numerical difficulties experienced by solving under weak or strong formulation the pure stream-function Navier–Stokes equation. In this model a dimensionless virtual domain is utilized, in order to make an accurate dimensionless shape-functions of the recently developed Hermite-type collocation Weighted Least Square approximation, by using dimensionless scale parameters. Then, a Jacobian transformation matrix is built to express the shape-functions spatial derivatives from the virtual to the considered domain. The resolution of the obtained nonlinear algebraic system is performed by the High Order Continuation Method. Numerical tests were investigated on incompressible viscous isothermal fluid flows in lid-driven cavity, backward-facing step, sudden expansions and around various obstacle shapes. They show the advantages of the proposed model compared to the reference Hermite-type collocation models used for pure stream-function equation and the weak Galerkin procedures as Finite Element Method and Element Free Galerkin method, in term of computation accuracy, number of degree of freedom, implementation simplicity and computation time. The numerical and experimental results of literature confirm the validity and capability of the proposed dimensionless model to simulate fluid flows in a expended-lengths inflow–outflow geometry and around obstacles of circular, inclined elliptical and Joukowski airfoil shapes.

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

Optimizing the Performance of different Airfoils at Various Angles of Attack through CFD Simulation

This study specifically examines the NACA 0012, NACA 4412, and NACA 2412 airfoil profiles using ANSYS FLUENT. By simulating the flow over these airfoils, we can comprehensively explore the impact of the angle of attack on lift and drag coefficients. Notably, the study reveals that the angle of attack directly influences lift force, with a critical angle beyond which the aircraft may stall. Thus, the research underscores the importance of maintaining an optimal angle of attack to avoid turbulence and optimize aircraft performance. The aerodynamics of airfoil shapes play a crucial role in the performance and safety of aircraft. Understanding airflow characteristics over airfoils, particularly concerning the critical angle of attack, is paramount in achieving optimal lift while avoiding stalling. This paper delves into the shift of the separation point on the upper surface of most airfoil shapes, emphasizing the shift from the trailing edge to the leading edge as the angle of attack increases. Stalling becomes a critical concern beyond the critical angle of attack, necessitating comprehensive research to enhance aircraft performance and safety.

Computational fluid dynamics analysis on performance assessment of Darrieus-type vertical axis wind turbine using NACA0016, NACA0019 and NACA0020 airfoil sections

The efficiency of a vertical-axis wind turbine is remarkably less than a horizontal-axis wind turbine and consequently, the most important challenge of the former one is to enhance its aerodynamic performance. An earlier study shows that the selection of an efficient airfoil shape is an important criterion for enhancing the overall performance of a wind turbine. The objective of the present work is to perform the two-dimensional Computational Fluid Dynamics simulation of Darrieus Vertical axis wind turbine using NACA0016, NACA0019 and NACA0020 airfoils which are neither too thick nor too thin. Furthermore, the performance of these three airfoils is compared with two established airfoils, namely NACA0015 and NACA0018. The result reveals that the overall power coefficient of NACA0019 airfoils resulting from the CFD simulation is significantly higher than that of NACA0015. Therefore, the NACA0019 airfoil may be considered one of the effective alternative airfoils for the Darrieus VAWT. Highlights Simulation of vertical axis wind turbine using NACA0016, NACA0019 and NACA0020 airfoils Unsteady URANS studies are carried out to investigate the performance of the airfoils Among the blade profiles studied in this work, NACA 0019 offers superior fluid mechanical performance

Simulation Analysis and Experimental Study on Airfoil Optimization of Low-Velocity Turbine

By combining computational fluid dynamics (CFD) and surrogate model method (SMM), the relationship between turbine performance and airfoil shape and flow characteristics at low flow rate is revealed. In this paper, the flow velocity tidal energy airfoil model is designed based on the Kriging model, and the original airfoil with a relative thickness of 12% and a relative curvature of 2.5% is obtained. The parameter optimization is carried out by setting the 4th CST equations through the surrogate model; the maximum lift-drag ratio is the optimization goal, the optimization design variable is 10, the maximum number of iterations is 100, and the maximum number of sub-optimization iterations is 200. The results show that the hydrodynamic performance of the airfoil with thinner thickness and more curvature is better, the maximum thickness part is shifted forward by 4.58%, and the lift-drag ratio is improved by 4.03%. The flow field and the efficiency are more stable, which provides an engineering reference for the optimal design of hydraulic turbine airfoils under low flow velocity. It supplements the research on the performance of turbine blades in low velocity.

Quantification and reduction of uncertainty in aerodynamic performance of GAN-generated airfoil shapes using MC dropouts

Generative adversarial network (GAN) models are widely used in mechanical designs. The aim in the airfoil shape design is to obtain shapes that exhibits the required aerodynamic performance, and conditional GAN is used for that aim. However, the output of GAN contains uncertainties. Additionally, the uncertainties of labels have not been quantified. This paper proposes an uncertainty quantification method to estimate the uncertainty of labels using Monte Carlo dropout. In addition, an uncertainty reduction method is proposed based on imbalanced training. The proposed method was evaluated for the airfoil generation task. The results indicated that the uncertainty was appropriately quantified and successfully reduced.

A de-icing experimental investigation of blade airfoil for wind turbines based on external hot air method

Wind turbines operating in cold and wet climates are prone to icing on the surface of their blades. It is necessary to develop effective de-icing methods for wind turbine blades. The commonly used blade de-icing method is heating, which includes the blade internal hot air method and the surface heating method. Recently, the use of external heat sources for blade de-icing has also received attention, such as the use of steam, infrared, and hot air, etc. In this research, the external hot air de-icing method for wind turbine blade was studied by experiments. A de-icing experimental system based on external hot air method was designed and established. The de-icing test was carried out on a blade segment with NACA0018 airfoil. The initial ice shape of blade airfoil was obtained by using an icing wind tunnel. The de-icing experiments were set up with four hot air temperatures and four hot air velocities. The deicing process was recorded by a high-speed camera, and the temperature changes on the blade surface are measured by an infrared thermal instrument. Furthermore, the de-icing time, de-icing area, de-icing rate and de-icing energy efficiency under different conditions were calculated and analyzed. According to the results, the external hot air method can effectively perform blade de-icing. The temperature and speed of the hot air have a significant impact on the de-icing process. Under the condition of this test, the maximum de-icing energy efficiency reached as 6.33 % at hot air temperature of 35 °C and velocity of 9 m/s. This study can provide a reference for solving the wind turbine blade icing problem by using external hot air de-icing method.

Use of an optical profilometer to measure the aerodynamic shape and the twist of a wind turbine blade

This study introduces a metrological approach to measure the aerodynamic shape and the twist of a wind turbine blade. The optical profilometer measurement technique used is laser triangulation. A camera records the image of a line projected onto a section of the blade and, by reconstructing the airfoil shape, the twist angular position of the profile with respect to the axial line of the blade is determined. This methodology is applied to test different sections of a Wortmann FX 63-137 airfoil with a length of 1700 mm. The results of the aerodynamic shape and twist angle are quantitatively verified by comparing them with the ideal or design values. The reconstruction process achieved a resolution of 0.06 mm, and measurement errors in the twist angular position were less than 0.1°. The presented method is efficient, accurate, and low cost to evaluate the blade profiles of low-power wind turbines. However, due to its easy implementation, it is expected to be able to measure any full-scale wind blade profile up to several meters in length.