Airfoil Chord Research Articles

Horizontal walls effect on the subsonic flow around airfoil by the image method

The aim of this work consists in developing a new numerical method and a calculation program making it possible to determine the effect of one and two horizontal walls on the distribution of the pressure ratio, and the aerodynamics coefficients of a subsonic flow around airfoils. The model is considered for the perfect gas. The calculation is presented by adding the effect of one and two walls on the discretization of the airfoils boundary to obtain a closed surface. The method is called by the image method. So for the case of the existence of one wall, we will see a single image of the main airfoil, and in the case of two walls, we will have an infinity of images. The equation system is obtained by considering the effect of all images using alternating digital series, whose convergence is ensured numerically. We therefore obtain a large system of equations, the resolution of which is done by the Khaletski method to obtain the velocities and pressure. The application is made for some practical interest’s airfoils. Since the airfoils boundary is given by tabulated values, the cubic spline interpolation is used to obtain an analytical equation of the upper and the lower surfaces. The comparison is made with the case of open air flow by extending the distance between the walls and the airfoil chord towards infinity.

Improvement of the airfoil lift and drag characteristics using plasma-efficient flow control

Flow control is studied to improve the aerodynamic performance of an aerofoil. A strategy for maintaining the near-wall flow structure with a given spatial scale, developed within the framework of interdisciplinary research, is used. The proposed active flow control method is based on the application of spanwise arrays of mechanical, thermal, or plasma vortex generators. The latter are found most versatile and efficient for the formulated goal. Aerodynamic coefficients measured in the specified wind tunnel are discussed for the 12.5% supercritical airfoil model. The model is controlled by the spanwise array of pulsating high-voltage plasma discharges. This multi-actuator system provides a sufficient number of control parameters such as pulse duration and repetition rate, the distance between the neighboring actuators (space scale of generated disturbances), and the plasma array location along the airfoil chord. Measurements in a range of Reynolds numbers of Rec=(3-7)x105 showed growth of a maximal lift coefficient CLmax up to 10% and the stall angle by 1.5°-3.5° accompanied by drag reduction up to 7%.

Effect of Airfoil thickness on low-frequency gust-airfoil interaction noise

Interaction between turbulence and an airfoil is a significant aerodynamic noise source for many engineering applications when turbulence in the wake of upstream blades interacts with the leading edge of downstream blades. Modeling the oncoming turbulence as harmonic gusts is a common approach to studying the noise generated by turbulence-airfoil interaction. The airfoil can be considered a compact noise source, resulting in a dipole-like sound directivity pattern when the acoustic wavelength of gust-airfoil interaction is much larger than the airfoil chord length. However, the interaction becomes more complex when the acoustic wavelength is comparable to or smaller than the airfoil chord, as the airfoil cannot be treated as a compact source anymore and multiple lobes appear in the radiated sound directivity. This paper studies airfoil thickness effects using a computational aeroacoustics approach based on the spectral/hp element method for low-reduced frequency gusts. It is found that the sound pressure decreases with the increase of thickness for low reduced frequency gusts. To reveal its mechanism, a semi-analytical method and the convective FW-H equation are used for low reduced frequency to analyze the radiated noise. The interaction between sound sources on the airfoil surface is crucial for the thickness effect.

Optimizing a vertical axis wind turbine with helical blades: Application of 3D CFD and Taguchi method

Vertical axis wind turbines (VAWT) with helical blades are being interested in urban areas due to the low dependency on the wind direction and also due to low noise production. In spite of good self-starting and smooth operation as the advantages of this type of turbine, its optimizing has not been reported in literature yet and is the subject of this research. A primary investigation by 3D computational fluid dynamics (CFD) to simulate the air flow about the above type of VAWT in the first step showed the importance of three design variables of tip speed ratio, helical angle, and airfoil chord length. However, in the second step, CFD runs were very time consuming and costly. For considering five values for each design variable, 53=125 cases had to be simulated by 3D CFD. Thus, by the use of Taguchi method and with definition of an orthogonal array named L-25, the number of required 3D CFD simulations reduced from 125 to 25. Then, the optimum values of variables were obtained as 1.33 for the tip speed ratio, 30 degrees for the helical angle, and 0.4 m for the airfoil chord length. At the optimum point, the average power coefficient increased to 0.17542. The presented research is novel for optimizing VAWT with helical blades.

Development of a control co-design optimization framework with aeroelastic-control coupling for floating offshore wind turbines

Sequential design optimization is frequently used to design floating offshore wind turbines. This method simplifies the design problem by implementing each of the disciplines successively and independently with the direct/dynamic coupling between them neglected. However, if the coupling between disciplines is strong, the global optimum may not be found by sequential design. Control co-design optimization is an approach that integrates all physics in a single optimization formulation to achieve the global optimum. However, it is challenging to achieve due to the highly complex system-control coupling in floating offshore wind turbines. This paper describes a control co-design optimization framework developed for floating offshore wind turbines. In particular, the blade airfoil chord and twist distributions are parameterized to change aerodynamics while the blade structural characteristics can be updated. The rotor speed and blade pitch controllers are tuned automatically based on the properties of the new plant model. For demonstration, a 10 MW reference wind turbine is used in the case study. The annual energy production is maximized, and the blade mass is minimized. The blade shape and control parameters are optimized simultaneously, subject to constraints on geometric design variables, fatigue loads, ultimate loads, and blade deflection. To solve this high-dimensional, nonlinear, and constrained problem, a genetic algorithm is used, and the Pareto front of the design space is found. The design solutions on the Pareto front showed an improvement in the blade mass and annual energy production. These design alternatives also showed reduced structural ultimate and fatigue loads, and generator torque. This revealed the potential of control co-design to reach a better performance than the sequential method.

Effects of Leading-Edge Blowing Control and Reduced Frequency on Airfoil Aerodynamic Performances

Abstract Airfoil leading-edge fluid-blowing control is computationally studied to improve aerodynamic efficiency. The fluid injection momentum coefficient Cμ (the ratio of injection to incoming square velocities times the slot's width to airfoil's half chord length) varies from 0.5% to 5.4%. Both static and dynamic conditions are investigated for a NACA0018 airfoil at low speed and Reynolds number of 250 k based on the airfoil's chord length. The airfoil is dynamically pitched at a reduced frequency (the pitching tangential speed to the freestream speed ratio), varying between 0.0078 and 0.2. Reynolds-averaged Navier–Stokes (RANS) and unsteady RANS (URANS) is used in the simulations as based on the Transition SST and Spalart–Allmaras models, generally achieving good agreement with experimental results in lift and drag coefficients and in the pressure coefficient distributions along the airfoil. It is found that oscillating the airfoil can delay stall, as expected, in dynamic stall (DS). Leading-edge blowing control can also significantly delay stall both in static and dynamic conditions as long as sufficient momentum is applied to the control. On the other hand, for a small Cμ such as 0.5%, the leading-edge control worsens the performance and hastens the appearance of stall in both static and dynamic conditions. The airfoil's oscillation reduces the differences between pitch-up and pitch-down aerodynamic performances. Detailed analysis of vorticity, pressure, velocity, and streamline contours is given to provide plausible explanations and insight to the flow.

On the investigation of the aerodynamics performance and associated flow physics of the optimized tubercle airfoil

In the present study, the evolutionary multi-objective optimization is employed to design the optimum amplitude and wavelength of sinusoidal leading-edge tubercles for the NACA0012 (National Advisory Committee for Aeronautics) airfoil to improve its aerodynamic performance at Reynolds number of 5.0 × 104 than that of the NACA0012 smooth leading-edge or baseline airfoil. Here, the optimum tubercle is found to have an amplitude of 11.71% and a wavelength of 25% of the baseline airfoil chord, respectively. Through a combination of in-house water tunnel experiments and numerical simulations, it is additionally established that the optimized tubercle airfoil exhibits superior lift and reduced drag characteristics compared to the baseline airfoil, particularly in the post-stall high angle of attack regime. Furthermore, it is noticed that the optimized tubercle design enhances the gap between large separation regions or stall cells along the tubercle airfoil span during the post-stall regime. Consequently, a more pronounced attached flow regime is developed between the consecutive stall cells, contributing to the tubercle airfoil's improved aerodynamic characteristics compared to the baseline airfoil. Our investigations also revealed that the formation and arrangement of the stall cells on the tubercle airfoil span are associated with a biased wake mechanism similar to the one observed in the wake of side-by-side arranged circular cylinders.

Multi-objective optimization study on the performance of double Darrieus hybrid vertical axis wind turbine based on DOE-RSM and MOPSO-MODM

The Double Darrieus Vertical Axis Wind Turbine (DD-VAWT) effectively enhances wind energy efficiency at low tip speed ratios. In this study, the multi-objective optimization method is constructed for DD-VAWT. The optimization objective is to enhance the power coefficient as well as reduce the maximum instantaneous torque coefficient, while decision variables include the inner ring wind turbine diameter, inner ring wind turbine height, inner ring wind turbine blade airfoil chord length and inner and outer ring wind turbine phase angle. Firstly, the computational fluid hydrodynamics model of DD-VAWT is established and validated by experimental data from the literature. Then, the regression model between critical structural parameters and power coefficients, maximum instantaneous torque coefficients is constructed using response surface analysis. Finally, the multi-objective particle swarm optimization algorithm is used to optimize the objective and the optimal solution is selected from the Pareto frontier solution. This work provides a direction to improve the operating performance of DD-VAWT at low tip speed ratios as well as contributes to energy saving and emission reduction.

Freestream turbulence effects on low Reynolds number NACA 0012 airfoil laminar separation bubble and lift generation

Laminar separation bubbles (LSB's) over the suction surface of a wing at low Reynolds number (O(104)−O(106) based on the airfoil chord length) can significantly affect the aerodynamic performance of the wing, and pose a unique challenge for the predictive capabilities of simulation tools due to their high sensitivity to flow environments and wing surface conditions. In this work a series of two-dimensional (2D) and three-dimensional (3D) low-order, and high-order accurate unstructured-grid-based numerical methods with varying model fidelity levels were used to study LSB physics over a NACA 0012 airfoil both in a clean freestream and in a turbulent freestream at a chord-based Reynolds number of 12,000. Lift production and time-averaged flow fields were compared with available experimental results. A major discovery is that in clean freestream flow a 3D high-order numerical scheme is necessary to capture LSB physics. This is due to the sensitivity of LSB-induced laminar-turbulent transition to flow conditions and boundary geometry at low Reynolds number. In freestream flows with moderate background turbulence (∼5%), 2D simulations failed to capture subtle 3D flow physics due to their intrinsic limitation, but can reasonably predict time-averaged airfoil performance. Similarity and distinction between freestream vortex-LSB interaction in 2D and eddy-LSB interaction in 3D were explained. The role of the Kelvin-Helmholtz instability and Klebanoff modes in the transition of 3D airfoils were shown to be critical for understanding laminar-turbulent transition and LSB formation on airfoils in clean and turbulent freestreams.

Research on energy harvesting characteristics of a flapping foil with trailing edge jet flap

Flapping foils offer a potential means for extracting hydrokinetic energy from ocean and river flows by utilizing a combined pitching and heaving motion of the airfoil. In this paper, the effectiveness of trailing edge active flow control in enhancing the energy harvesting performance of the conventional flapping foil is examined through numerical simulations. In this approach, an injections slot is opened at the trailing edge of the flapping foil, from which a high velocity jet is discharged into ambient water. Since the water jet is issued vertically downwards perpendicular to the airfoil surface, it operates like a Gurney flap and thus is known as jet flap in aeronautics. Parametric studies show that the optimal injection position should be as far as possible from the leading edge of the flapping foil. In addition, it is also found when the width of the exit slot of jet equals to 2.6 % of the airfoil chord and the momentum coefficient of jet is 0.02, the flapping foil with the jet flap can increase the maximum net energy harvesting efficiency obtained after deducting the energy consumption for the flow control from 39.22 % to 47.6 % compared to its baseline counterpart, indicating the effectiveness of this method. Furthermore, the dynamic mode decomposition (DMD) method is also adopted to reveal the spatial-temporal features of the coherent structures in the wake flow behind the proposed flapping foil in an attempt to gain a deep understanding of the underlying flow mechanism involved in promoting its energy harvesting performance.

Performance optimization of vertical axis wind turbine based on Taguchi method, improved differential evolution algorithm and Kriging model

ABSTRACT The capability of vertical axis wind turbine (VAWT) is influenced by its input parameters. In this paper, for the three-bladed VAWT with the NACA0018 airfoil, three important input parameters, i.e. tip speed ratio (TSR), airfoil chord length (C), and pitch angle (β), are selected to explore their impact on the capability of the VAWT, and then to find the best combination of them. Firstly, 16 sets of experiments are determined according to the Taguchi method and are evaluated using the 2D computational fluid dynamics (CFD) numerical simulation, and further studied with the Analysis of Variance. The consequence shows that the TSR and pitch angle are more critical to the performance of the VAWT. In order to obtain the optimal configuration of these parameters, an intelligent method is further proposed. Firstly, a certain number of design schemes are extracted in the selected space through Latin hypercube sampling (LHS), and then the torque coefficient (C m ) of each design scheme was obtained by 2D CFD simulation, the Kriging model is used to establish the correlation among the input parameters and their corresponding torque coefficient. Finally, the improved differential evolution algorithm (JADE) is used to tackle the Kriging model to get the optimal input parameter values. The results show that when the rotor diameter (D) is 2.5 m, the optimal parameters are TSR is 2.6, C is 0.227 m and β is −2.47°, the performance of the VAWT is further improved by about 4.5% compared with the optimal values obtained by the Taguchi method.

Reduction of rotorcraft BVI using synthetic jets; computational studies using LES

In rotorcraft, the blade-vortex interaction (BVI) has been recognized as one of the main sources of noise and vibrations, affecting its aerodynamics performance and stability. Active and passive flow control techniques, for the reduction of BVI, have been investigated. The passive flow control techniques have proved to be inefficient due to the complex aerodynamics of rotorcraft. Thus, active flow control techniques has become of particular interest. In the present research we propose a novel approach, for the reduction of rotorcraft’s noise and vibrations due to BVI. The main idea of this approach is to inject air at the leading-edge of the blade to alter the characteristics (strength and core size) of the incoming vortex and thus, minimize the noise and vibrations associated with BVI. Computational studies are carried out using the large-eddy simulation (LES) with the dynamic Smagorisky sub-grid scale model. The computations are carried out for a flow of Reynolds number R e = 1.3 × 10 6 , based on the chord of NACA0012 airfoil and free-stream velocity. The studies show that injecting air at the leading edge of the blade, the influence of blade-vortex interaction on the aerodynamic coefficients is significantly reduced. Higher reduction of BVI effect, on the aerodynamic coefficients, was achieved with the increase of the speed of the synthetic jet. The reduction of the BVI, also, leads to the reduction of the vibrations.

Control of flow separation over an aerofoil by external acoustic excitation at a high Reynolds number

The effectiveness of acoustic excitation as a means of flow control at high Reynolds number turbulent flows is investigated numerically by using improved delayed detached eddy simulations (IDDES). Previous studies on low Reynolds number laminar flows have shown that acoustic excitation can substantially suppress flow separation for specific effective frequency and amplitude ranges. However, the effect of acoustic excitation on higher Reynolds number turbulent flow separation has not yet been explored due to limitations on appropriate fidelity computational methods or experimental facility constraints. Therefore, this paper addresses this research gap. A NACA0015 airfoil profile at 1 × 106 Reynolds number based on the airfoil chord length is used for the investigations. Acoustic excitation is applied to the baseline flow field in the form of transient boundary conditions at the computational domain inlet. A parametric study revealed that the effective sound frequency range shows a Gaussian distribution around the frequency of the dominant disturbances in the baseline flow. A maximum of ∼43% increase in lift-to-drag ratio is observed for the most effective excitation frequency F+=1.0 at a constant excitation amplitude of Am=1.8%. The effect of excitation amplitude follows an asymptotic trend with a maximum effective excitation amplitude above which the gains are not significant. A fully reattached flow is observed for the highest excitation level considered (Am=10%) that results in ∼120% rise in airfoil lift-to-drag coefficient. Overall, the findings of the current work demonstrate the higher Reynolds number effectiveness of acoustic excitation on separated turbulent flows, thereby paving the way for application in realistic flow scenarios observed in aircraft and gas turbine engine flow fields.

Investigation of the effect of critical structural parameters on the aerodynamic performance of the double darrieus vertical axis wind turbine

Double Darrieus Vertical Axis Wind Turbine (DD-VAWT) can efficiently capture wind energy at low tip speed ratios. In this work, the laws governing the effects of critical structural parameters, such as diameter of inner ring wind turbine, height of inner ring wind turbine, inner ring wind turbine blade airfoil chord length, and phase angle of inner and outer ring wind turbine, on the power performance and aerodynamic load are investigated. The power coefficient increases from 0.1670 to 0.2403 when the diameter of the inner ring wind turbine decreases from 1600 mm to 400 mm. The power coefficient increases from 0.1755 to 0.2135 when the height of the inner ring wind turbine increases from 600 mm to 1200 mm. The power coefficient increases from 0.1773 to 0.2135 when the chord length of the inner ring wind turbine blade airfoils increases from 0.15 m to 0.3 m. The power coefficient decreases from 0.2135 to 0.1976 when the phase angle of the inner and outer wind turbine is increased from 0° to 135°. Finally, based on Taguchi's experiments and grey correlation analysis, it is known that the most influential weight on the power coefficient and the maximum instantaneous torque coefficient is the airfoil chord length of the inner ring wind turbine blades, and the least is the phase angle of the inner and outer ring wind turbines. This work provides a reference for enhancing the DD-VAWT's performance.

Noise generation mechanisms of a micro-tube porous trailing edge

The noise generation and flow characteristics of a forced-transitioned NACA 0012 airfoil with a micro-tube porous trailing edge and its solid counterpart have been numerically investigated. The near-field flow dynamics and far-field noise predictions are obtained using compressible large-eddy simulations and the Ffowcs-William and Hawkings acoustic analogy, respectively. The computed far-field noise levels agree with experimental data, showing that the micro-tube structure reduces low-frequency trailing-edge noise without noticeably altering the noise directivity but induces additional high-frequency noise along the direction perpendicular to the airfoil chord. An in-depth analysis of the trailing-edge flow and surface pressure fields reveals that the noise reduction is largely linked to the ‘cross-jet-like’ flow permeation through the micro-tube structures. The interaction between the flow permeation and the boundary layer turbulence leads to a reduction in the strength of the Reynolds-stress source term in the pressure-side flow field and a reduction in the magnitude of the source terms in Amiet’s trailing-edge noise model. Spectral proper orthogonal decomposition is performed to identify flow structures that are spatially and temporally coherent within the micro-tube geometries and to link the flow features to the attenuation in noise scattering efficiency. The effect of the micro-tube structure on the wavenumber–frequency spectra of the trailing-edge surface pressure field is quantitatively analysed. Additional high-energy regions exist in the wavenumber–frequency spectra of the porous trailing edge, resulting from the turbulent eddies that permeate through the micro-tubes. Further, the high-frequency noise increase mechanism is identified as the acoustic dipole noise arising from interactions of edge-induced flow separation with the suction-side surface.

Fluid dynamic design of a vertical axis wind turbine rotor under low wind speed

The design of the rotor geometry of a vertical axis wind turbine (VAWT) type H, for power generation at low wind speeds, is presented. The computational simulation allowed us to establish that the NACA 0018 profile offers a better ratio of lift and drag coefficients in contrast to NACA 0021 and NACA 0025, so this geometry was selected as the working profile. Then, to generate a power of 30W, the dimensions of the airfoil chord, the radius, and the rotor's height were found from the blade tip speed ratio (TSR) values and the power coefficient. The results obtained indicate that the appropriate dimensions of the rotor at low-speed conditions are, a diameter of 2 m, a height of 2.16 m, and several blades of 3, for a rotation speed of 9 rad/s. Finally, an agreement was found between the angular velocity calculated theoretically, for the proposed rotor dimensions, and that obtained from the ANSYS-CFD simulation.

A novel approach to performance improvement of a VAWT using plasma actuators

The numerous advantages of Vertical-Axis Wind Turbines (VAWTs) have made them suitable for urban areas compared to other types of wind turbines; however, the occurrence of phenomena such as vortices and flow separation around the blades which have adverse effects on the turbine performance, indicates the necessity of using control methods to improve the behavior of the flow around the blades. This study numerically examines the effect of different installation positions and activation timing of plasma actuators and presents new strategies for flow control and turbine performance improvement. The model presented by Shyy et al. was used for the numerical modeling of the plasma actuator. The results showed that applying actuators in ten different positions from 10% to 90% of the airfoil chord length on the outer and inner edges of the blades, can lead to an increase in the turbine production power; however, the high-power consumption of the actuator clarifies the necessity of reducing the actuator activity time to smaller azimuthal intervals. The results revealed that applying the actuators under the optimal combined strategy in a 90° interval, increases the turbine power coefficient by 29.2%, while it leads to the lowest power consumption of the actuator.

Towards smart blades for vertical axis wind turbines: different airfoil shapes and tip speed ratios

Abstract. Future wind turbines will benefit from state-of-the-art technologies that allow them to not only operate efficiently in any environmental condition but also maximise the power output and cut the cost of energy production. Smart technology, based on morphing blades, is one of the promising tools that could make this possible. The present study serves as a first step towards designing morphing blades as functions of azimuthal angle and tip speed ratio for vertical axis wind turbines. The focus of this work is on individual and combined quasi-static analysis of three airfoil shape-defining parameters, namely the maximum thickness t/c and its chordwise position xt/c as well as the leading-edge radius index I. A total of 126 airfoils are generated for a single-blade H-type Darrieus turbine with a fixed blade and spoke connection point at c/2. The analysis is based on 630 high-fidelity transient 2D computational fluid dynamics (CFD) simulations previously validated with experiments. The results show that with increasing tip speed ratio the optimal maximum thickness decreases from 24 %c (percent of the airfoil chord length in metres) to 10 %c, its chordwise position shifts from 35 %c to 22.5 %c, while the corresponding leading-edge radius index remains at 4.5. The results show an average relative improvement of 0.46 and an average increase of nearly 0.06 in CP for all the values of tip speed ratio.

Assessment of Turbulence Models for Unsteady Separated Flows Past an Oscillating NACA 0015 Airfoil in Deep Stall

This paper provides 2D Computational Fluid Dynamics (CFD) investigations, using OpenFOAM package, of the unsteady separated fully turbulent flows past a NACA 0015 airfoil undergoing sinusoidal pitching motion about its quarter-chord axis in deep stall regime at a reduced frequency of 0.1, a free stream Mach number of 0.278, and at a Reynolds number, based on the airfoil chord length, , of . First, eighteen 2D steady-state computations coupled with the SST model were carried out at various angles of attack to investigate the static stall. Then, the 2D Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations of the flow around the oscillating airfoil about its quarter-chord axis were carried out. Three eddy viscosity turbulence models, namely the Spalart-Allmaras, Launder-Sharma , and SST were considered for turbulence closure. The results are compared with the experimental data where the boundary layer has been tripped at the airfoil’s leading-edge. The findings suggest that the SST performs best among the other two models to predict the unsteady aerodynamic forces and the main flow features characteristic of the deep stall regime. The influence of moving the pitching axis downstream at mid chord was also investigated using URANS simulations coupled with the SST model. It was found that this induces higher peaks in the nose-down pitching moment and delays the stall onset. However, the qualitative behavior of the unsteady flow in post-stall remains unchanged. The details of the flow development associated with dynamic stall were discussed

The aerodynamic analysis of iced and clean NACA 4410 and 0012 airfoils

AbstractThe aims of the work is to develop a numerical iced airfoil; quarter round forward ice was tested on NACA 4410 and NACA 0012 airfoils at zero and non-zero angles of attack, and Reynolds numbers equal to (2∙105, 2.4∙105) based on airfoil chord and Mach number 0.04. The two-dimensional steady-state momentum equations with the continuity equation have been solved applying a finite volume method to examine the turbulent flow over a clean and iced airfoil. The cambered airfoil NACA 4410 spends less power than the unsymmetrical airfoil at the same angle of attack. The reported numerical results demonstrated that for airfoil NACA 4410, the drag was increased by 40%, and the lift was reduced by 22%. However, for airfoil NACA 0012, the drag was increased by 43%, and the lift was decreased by 21%.