NACA0012 Airfoil Research Articles

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.

A deep neural network reduced order model for unsteady aerodynamics of pitching airfoils

A machine learning framework is developed to compute the aerodynamic forces and moment coefficients for a pitching NACA0012 airfoil incurring in light and deep dynamic stall. Four deep neural network frameworks of increasing complexity are investigated: two multilayer perceptrons and two convolutional neural networks. The convolutional framework, in addition to the standard mean squared error loss, features an improved loss function to compute the airfoil loads. In total, five models are investigated of increasingly complexity. The convolutional model, coupled with the loss function based on force and moment coefficients and embedding the attention mechanism, is found to robustly and efficiently predict pressure and skin friction distributions over the airfoil over the entire pitching cycle. Periodic conditions are implemented to grant the physical smoothness of the model output both in space and time. An analysis of the training dataset point distributions is performed to point out the effects of adopting low discrepancy sequences, such as Latin hypercube, Sobol', and Halton, compared to random and uniform sequences. The current model shows improved performances in predicting forces and pitching moment in a broad range of operating conditions.

Double distribution function-based lattice Boltzmann flux solver for simulation of compressible viscous flows

In this work, a double distribution function-based lattice Boltzmann flux solver (LBFS) is proposed for simulating compressible viscous flows. This approach utilizes the double distribution function compressible lattice Boltzmann model and employs Chapman–Enskog expansion analysis to connect the lattice Boltzmann equation (LBE) with the Navier–Stokes (N–S) equations. Unlike conventional computational fluid dynamics methods that compute inviscid and viscous fluxes separately, the present method simultaneously evaluates both types of fluxes at the cell interface by locally reconstructing the solution of the LBE. Recognizing the significance of considering the non-equilibrium part of distribution functions for viscous flows, a straightforward method is introduced to calculate this component. This facilitates the derivation of computational expressions for macroscopic conservative variables and fluxes in the N–S equations. To validate the accuracy and stability of the present numerical scheme, various benchmark problems, including shock tube problem, Couette flow, lid-driven cavity flow, and flow around the NACA0012 airfoil, are tested. The obtained numerical results are compared with analytical solutions or existing reference data, confirming the capability of the proposed LBFS to deliver accurate and stable numerical results for compressible flows. Moreover, this method demonstrates effectiveness in handling viscous flow problems on non-uniform grids and with curved boundaries.

Research on Active Flow Control Method of NACA0012 Airfoil with Traveling Wave Structure

Research on Active Flow Control Method of NACA0012 Airfoil with Traveling Wave Structure

Experimental comparison of a NACA0021 airfoil in large plunging and surging motions at 90 ◦ angle of attack

The topic of vortex-induced vibrations on a wind turbine blade has recently gained much attention due to its growing size and flexibility. To address this concern, a wind tunnel test was conducted to study the forced plunging and surging motion of a NACA0021 airfoil at 90° angle of attack. Results indicate that vortex lock-in occurred for a motion amplitude of one chord length even for a small frequency ratio (between motion frequency and static Strouhal frequency) of 0.39. Analysis of the drag coefficient, derived from the phase-averaged Particle Image Velocimetry (PIV) data, shows that a plunging airfoil experiences higher average loading than a surging airfoil, which is deemed to be more harmful considering the higher loading in the crossflow-direction due to the variation of effective angle of attack.

Entropy damping and Bulk Viscosity based artificial compressibility methods on dynamically distorting grids

Artificial Compressibility Methods (ACM) rely on an artificial equation that links the pressure and velocity fields to model incompressible flows. These hyperbolic/parabolic equations can rapidly converge to a ‘nearly’ divergence-free flow field in contrast to the methods based on the elliptic pressure Poisson equation. We compare the computational efficacy of two ACMs, namely, the Bulk Viscosity ACM (BVACM) and Entropically Damped Artificial Compressibility (EDAC) recently proposed in the literature. The methods implemented in the in-house high-order finite difference solver, COMPSQUARE, are validated for the test cases of a 2D doubly periodic shear layer (DPSL), a 3D Taylor Green Vortex (TGV), and 2D/3D NACA0012 airfoil pitching about the quarter chord. The efficacy of these methods was also tested on static and dynamic grids using conservative metrics. Although both ACMs yield competitive results, the divergence of the velocity field is found to be more prominent in the highly unsteady regions. BVACM resulted in (a) a superior divergence-free velocity field and (b) 20−38% higher maximum stable time than the EDAC, thereby increasing the computational speed. A higher value of the bulk viscosity coefficient, A, although ensures a stringent divergence-free velocity field, is shown to have minimal effect on the flow statistics and reduce the maximum stable time step. The parabolic–hyperbolic nature of the governing equations and the lack of dual time-stepping in BVACM and EDAC ensures that both these methods are highly scalable on massively parallel architectures. Since the energy equation is no longer required to compute the velocity field, both EDAC and BVACM approaches are found to be 8−10% faster than the weakly compressible Navier–Stokes simulations under the low-Mach number limit.

Turbulence model study for aerodynamic analysis of the leading edge tubercle wing for low Reynolds number flows

A turbulence model study was performed to analyze the flow around the Tubercle Leading Edge (TLE) wing. Five turbulence models were selected to evaluate aerodynamic force coefficients and flow mechanism by comparing with existing literature results. The selected models are realizable k-ε, k-ω Shear Stress Transport (SST), (γ−Reθ) SST model, Transition k-kl-ω model and Stress- ω Reynolds Stress Model (RSM). For that purpose, the TLE wing model was developed by using the NACA0021 airfoil profile. The wing model is designed with tubercle wavelength of 0.11c and amplitude of 0.03c. Numerical simulation was performed at chord-based Reynolds number of Rec = 120,000. The Computational Fluid Dynamic (CFD) simulation reveals that among the selected turbulence models, Stress- ω RSM estimated aerodynamic forces (i.e. lift and drag) coefficients closest to that of the experimental values followed by realizable k-ε, (γ−Reθ) SST model, k-ω SST model and k-kl-ω model. However, at a higher angle of attacks i.e. at 16° & 20° k-ω SST model predicted closest drag and lift coefficient to that of the experimental values. Additionally, the critical observation of pressure contour confirmed that at the lower angle of attack Stress- ω RSM predicted strong Leading Edge (LE) suction followed by realizable k-ε, (γ−Reθ)SST model, k-ω SST model and k-kl-ω model. Thus, the superiority of Stress- ω RSM in predicting the aerodynamic force coefficients is shown by the flow behavior. In addition to this pressure contours also confirmed that k-kl-ω model failed to predict tubercled wing aerodynamic performance. At higher angles of attacks k-ω SST model estimated aerodynamic force coefficients closest to that of the experimental values, thus k-ω SST model is used at 16° & 20° AoAs. The observed streamline behavior for different turbulence models showed that the Stress- ω RSM model and k-kl-ω model failed to model flow behavior at higher AoAs, whereas k-ω SST model is a better approach to model separated flows that experience strong flow recirculation zone.

Experimental Parametric Study on Flow Separation Control Mechanisms around NACA0015 Airfoil Using a Plasma Actuator with Burst Actuation over Reynolds Numbers of 105–106

Dielectric barrier discharge plasma actuators (DBD-PAs) have the potential to improve the performance of fluid machineries such as aircrafts and wind turbines by preventing flow separation. In this study, to identify the multiple flow control mechanisms in high Reynolds number flow, parametric experiments for an actuation parameter F+ with a wide range of Re values (105–106) for NACA0015 airfoil was conducted. We conducted wind tunnel tests by applying a DBD-PA to the flow field around a wing model at the leading edge. Lift characteristics, turbulent kinetic energy in the flow field, shear layer height, and the separation point of the boundary layer were evaluated based on pressure distributions on the wing surface and velocity of the flow field, with the effect of DBD-PA on the post-stall flow around the wing and the mechanism behind the increase in the lift coefficient CL analyzed based on these evaluation results. The following phenomena contributed to the increase in CL: (1) increase in turbulent kinetic energy; (2) increase in circulation; and (3) acceleration of the flow near the leading edge. Thus, this study effectively investigated the dependence of the increase in lift on F+ and the lift-increasing mechanism for a wide range of Re values.

An Improved Boundary Element Method for Predicting Half-Space Scattered Noise Combined with Permeable Boundaries

The boundary element method is widely used in practical engineering problems, especially in the field of acoustics. For flow-induced noise, the main target of acoustic calculations is to solve the wave equation with the flow field information. However, the sound field distribution of noncompact structures in half-space is especially complex because of the strong scattering effect, while the object surface boundary integration often brings a large workload and generates numerical singularities. In this paper, an improved boundary element method for predicting the aeroacoustic noise of noncompact structures is proposed, which can consider the characteristic distribution of sound field induced by complex structures in half-space. The smooth permeable boundary surrounding the object is used as the integration boundary, while the scattering effect of the ground boundary is investigated by combining the mirror Green’s function method, and the numerical prediction of aeroacoustic noise is carried out for the dipole source and NACA0012 airfoil in half-space. Numerical results show that the far-field noise obtained by using the permeable surface is consistent with that obtained by integrating the direct object boundary under the influence of ground boundary scattering. The mirror image Green’s function method is able to finely capture the ground scattering effect, which has a significant effect on the sound field as the frequency increases.

Aerodynamic design optimization of a NACA 0012 airfoil: An introductory adjoint discrete tool for educational purposes

The adjoint method is a powerful tool in high-fidelity aerodynamic shape optimization, providing an efficient means to compute derivatives of a target function with respect to various design variables. This paper delves into the discrete adjoint method. It offers a theoretical exploration of its implementation as an innovative tool for calculating partial derivatives (sensitivities) related to objective functions and design variables, specifically applied to a subsonic NACA0012 airfoil. The study conducts a qualitative evaluation using a designated test case, considering specified Mach number and Reynolds number values of 0.297 and 6,667 million, respectively. The Spalart-Allmaras turbulence model is employed to enhance computational cost efficiency. The results affirm the efficacy of the introduced tool, DAFoam, showcasing its ability to generate optimal geometries. The achieved performance optimization is evidenced by minimizing the drag coefficient value (CD) to an impressive 0.0131. While this research does not delve into the post-processing of sensitivity calculations, it acknowledges the potential for future investigations. The primary objective and novelty of this study is to provide the elementary background of the state of the art test case (NACA0012) within the subsonic regime, introducing the pioneer discrete adjoint aerodynamic optimization methodology (DAFoam) with the potential to explore its higher order capabilities in other aerodynamic related studies. Furthermore, it caters the educational needs of both graduate students and engineers in this exciting field. By presenting this cutting-edge methodology, it contributes to future advancements for the aerodynamicists in terms of optimal solutions.

An experimental investigation on the flow control of the partially stepped NACA0012 airfoil at low Reynolds numbers

An experimental study of flow control around a NACA0012 airfoil modified with fully and partially step geometry was conducted at Reynolds numbers of 6 × 104 and 1.2 × 105. Partially step geometries, the location of the step on the airfoil, and Reynolds number are varied to show their effect on aerodynamic performance and flow structures on the airfoil. Experimental results show that fully and partially step geometries are effective for flow control around the airfoil and aerodynamic performance enhancement. The maximum increase in lift coefficient is approximately 46%, and the stall angle is shifted about 1° by the SM4 model at Re of 6x104 while the step geometry is on the pressure side. For a Reynolds number of 1.2 × 105, the highest increase in the lift-to-drag ratio of the airfoil is observed about 17.1 at an angle of attack of 6° by the SM2 model when step geometry is placed on the pressure side of the airfoil. In the event of partially or fully stepped at the pressure side of the model, step flow structures, including the reattachment line, recirculation zone, and corner eddy, are obtained. However, even though the step geometry is at the suction surface of the model, the formation of a laminar to turbulent transition is observed. The overall results suggest that the partially stepped geometry length, Reynolds number, and step location side on the airfoil have an important role in flow control to improve aerodynamic performance for various angles of attack.

Modification in airfoil’s tonal noise using periodic suction-blowing excitation

This paper examines the modifications in the flow and sound fields due to the application of a periodic suction-blowing excitation strip on the top and bottom surfaces of a NACA0012 airfoil. The flow and sound fields have been directly computed (DNS approach) by solving unsteady, two-dimensional compressible Navier–Stokes equations using physical dispersion relation preserving schemes. The flow approaches the airfoil at a Reynolds number of 5000 and 5o angle of attack. In the no-excitation case, the sound is mainly created by the lift and drag dipole equivalent sources associated with vortex shedding. However, the application of suction-blowing excitation results in two additional sound sources: monopole-equivalent sound sources due to fluid movement in and out of the airfoil surface and the drag dipole-equivalent sound sources due to periodic change in the airfoil’s effective cross-sectional area. The combined effects of these sound sources result in significant mitigation of sound on the suction side of the airfoil. The excitation amplitude and forcing frequency effects on sound field modifications have been studied in depth. Beats of sound have been observed when the forcing frequency is close to the excitation frequency.

Stall characteristics of wavy leading-edge airfoil in subsonic and transonic airflows

Based on the bioinspired wavy leading-edge, the stall characteristics of the NACA0012 airfoil are optimized. In this paper, the semicircle plus line segment is used to obtain the wavy leading edge. The aerodynamic forces of the airfoil are measured by a high-precision balance, and the detailed flow features of the airfoil are obtained by the oil flow tests. Then, combined with numerical simulation, the optimization mechanism is obtained. The operating conditions are as follows: Mach number ranging from 0.4 to 0.8, and angle of attack ranging from −4° to 25°. The results show that in high speed airflows, compared with the basic airfoil, the lift coefficient of the wavy leading-edge airfoil does not decrease sharply with the increase of the angle of attack, and the drag coefficient of the wavy leading-edge airfoil is similar to the basic airfoil; among the three types of airfoils studied, the larger wavy leading-edge feature size has better aerodynamic characteristics; combined with the numerical simulation results, it can be seen that the stall mechanism of airfoils varies at different Mach numbers. The wavy leading-edge generate streamwise vortex. The streamwise vortices increase energy transport in the boundary layer. Therefore, the separation zone moves toward the trailing edge of the airfoil, and the stall characteristics of the airfoil are optimized.

The optimization method of wing plasma ice shape regulation based on quantitative assessment of flight risk

Plasma ice shape regulation is a technology which uses plasma actuator to regulate the continuous ice into safer intermittent ice by its significant thermal effect with limited energy. Whether plasma ice shape regulation could reduce flight risk is a new problem under the wing with continuous ice. The 3D printed ice shapes were arranged on the leading edge of the wing based on NACA0012 airfoil, aiming to simulate the configuration after ice shape regulation. And the aerodynamic parameters were obtained by wind tunnel experiments. The experimental results showed that the ratio of signal regulation ice width d\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d$$\\end{document} to chord length of the wing bA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b_{A}$$\\end{document} determined the aerodynamic characteristics, and the aerodynamic characteristics changed better compared with configuration of the continuous ice. However, the flight risk of the wing under given regulation ratio is unknown. Based on the straight and swept wing after regulating, the flight safety boundaries were simulated by the reachable set method. Further, a method of quantitative assessment of flight risk is proposed. Quantitative values of risk were calculated. The results show that the flight risk all decreases from level 2 to level 4 compared with configuration of the continuous ice when d/bA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d/b_{A}$$\\end{document} equals 0.15 under conditions of swept and straight wing.

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.

Numerical simulation of two-dimensional plain flap ground effect based on NACA4412 airfoil

Based on the NACA4412 airfoil, by solving a two-dimensional unsteady Reynolds-averaged N-S equation and using the k-ωSST model, this paper analyzes the influence of near-ground altitude change on different configuration flow fields under moving ground conditions and explores the variation law of wing pressure coefficient at different near-ground altitudes. The results show that the attraction of the upper airfoil is weakened by the GE (ground effect), the pressure of the lower airfoil is increased, and the upper and lower airfoils influence the lift change of the airfoil. With the decrease of near-ground altitude, at a certain AOA (angle of attack), the greater the flap angle is, the faster the suction loss on the upper wing surface is and the slower the pressure increases on the lower wing surface, and the lower the near-ground altitude corresponding to the minimum lift coefficient is. With the decrease of near-ground altitude, at a certain flap angle, the greater the AOA is, the faster the suction loss on the upper wing surface is and the slower the pressure increases on the lower wing surface, and the lower the near-earth altitude corresponding to the minimum lift coefficient is.

Experimental study on rooftop flow field of building based on the operation of vertical-axis wind turbines

Vertical-axis wind turbines (VAWTs) demonstrate good adaptability for harnessing wind energy on the building rooftops. However, knowledge gaps still exist in the understanding of the wind resources on the rooftop, the operation of VAWTs, and its effect on the wind field. To add new knowledge on this subject, the operation of wind turbines modeled by the NACA0018 airfoil on the rooftop of a building is experimentally studied via wind tunnel. The results indicate that flow above the rooftop of building shows an obvious speed reduction due to the blunt body effect of the turbines, and the turbulence intensities are dramatically enhanced. The different tip-speed ratios, wind directions, and installation locations of wind turbine have significant effect on flow field on the roof. Due to the flow characteristics above the rooftop, the power spectral density of the fluctuating wind speed exhibits high energy below the top position of the VAWT on the rooftop. Additionally, the wind profiles and probability distribution of the wake of VAWTs on the rooftop are analyzed and mathematically fitted for quantifying wind field characteristics rooftop turbines on the roof. For the VAWTs investigated in this study, the impacts of the operation of VAWTs on the wind field are non-negligible on the roof of building. The findings of this study will provide valuable insights for the optimal placement of VAWTs and utilization of wind energy on the rooftops.

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.

Numerical simulation of the effect of helicopter flight advance ratio and lift rate on rotor aerodynamic noise

To study the aerodynamic noise characteristics of helicopter rotors under different flight states, this paper combined with the FW-H calculation equation, adopted NACA0012 airfoil and ROBIN fuselage to form a helicopter model and used FLUENT software to simulate different flight states of the helicopter. The influence of the two flight parameters, advance ratios, and lift rates, on the aerodynamic noise characteristics of the rotor, is studied. The results show that with the increase of helicopter advance ratio, the aerodynamic noise generated by the rotor becomes larger, and the effect of helicopter lift rate on the aerodynamic noise of the rotor is not obvious.

Orca hydrofoil shape optimization using Bezier curve and Artificial Neural Network – Multiple objective Genetic Algorithm for low flow velocity

Tidal energy is a clean and predictable power source that is commonly harnessed by using horizontal axis tidal turbines. The power generating process of tidal turbines is influenced by various elements, one of which is the hydrofoil performance. This includes the lift coefficient, drag coefficient, and lift-to-drag ratio. This study introduces the utilization of the Orcinus Orca hydrofoil for horizontal axis tidal turbines. The Orcinus Orca geometry is obtained by modified the NACA0021 airfoil. Subsequently, Bezier curve parameterization is employed to make a smooth hydrofoil profile. The study further deploy an Artificial Neural Network coupled with a Multi-Objective Genetic Algorithm, specifically targeting optimization of the hydrofoil shape optimization at a low flow velocity, specifically at an inlet velocity of 0.5 m/s. The aim of this optimization is to augment the lift coefficient and diminish the drag coefficient in order to amplify the lift to drag ratio. The findings reveal a significant enhancement in performance, as the optimized Orcinus Orca hydrofoil exhibits a remarkable increase of 42.78 % and 27.93 % compared to the original Orcinus Orca and the Bezier-modified Orcinus Orca hydrofoils, respectively.