Arbitrary Airfoil Research Articles

A solver for subsonic flow around airfoils based on physics-informed neural networks and mesh transformation

Physics-informed neural networks (PINNs) have recently become a new popular method for solving forward and inverse problems governed by partial differential equations. However, in the flow around airfoils, the fluid is greatly accelerated near the leading edge, resulting in a local sharper transition, which is difficult to capture by PINNs. Therefore, PINNs are still rarely used to solve the flow around airfoils. In this study, we combine physical-informed neural networks with mesh transformation, using a neural network to learn the flow in the uniform computational space instead of physical space. Mesh transformation avoids the network from capturing the local sharper transition and learning flow with internal boundary (wall boundary). We successfully solve inviscid flow and provide an open-source subsonic flow solver for arbitrary airfoils. Our results show that the solver exhibits higher-order attributes, achieving nearly an order of magnitude error reduction over second-order finite volume method (FVM) on very sparse meshes. Limited by the learning ability and optimization difficulties of the neural network, the accuracy of this solver will not improve significantly with mesh refinement. Nevertheless, it achieves comparable accuracy and efficiency to second-order FVM on fine meshes. Finally, we highlight the significant advantage of the solver in solving parametric problems, as it can efficiently obtain solutions in the continuous parameter space about the angle of attack.

Empirical Rotor Broadband Noise Prediction Using CFD Boundary Layer Parameter Extraction

In this study, for small unmanned aerial vehicle aeroacoustic predictions, an in-house acoustic code was extended for broadband noise using the empirical Brooks–Pope–Marcolini (BPM) method. The acoustic code was coupled with a comprehensive analysis tool (FLIGHTLAB) or Reynolds-averaged Navier–Stokes (RANS) method to predict the noise from a DJI 9443 CF rotor. The effects of two input parameters of the BPM method on the broadband noise were investigated, including the effective angle of attack and boundary layer parameters. The empirical formula for the boundary layer parameters was replaced with predictions using two-dimensional RANS, allowing arbitrary airfoils other than NACA0012. The boundary layer parameters were also predicted using three-dimensional RANS to capture a three-dimensional flow effect, which can be dominant in modern propellers operating at high rotational speeds. As a result, the three-dimensional effect on the boundary layer was confirmed to conflict with the BPM method, which was developed based on a two-dimensional chordwise flow database. Finally, mid- and high-frequency noise spectra were predicted from the three-dimensional hybrid RANS/LES simulation to be combined with the BPM results, thus improving the noise spectra predictions at midrange frequencies.

Automated Mesh Generation and Solution Analysis of Arbitrary Airfoil Geometries

The current work presents a novel computational fluid dynamics mesh generation methodology, which is able to generate high-quality meshes around complex airfoil geometries, while also having a high degree of automation in order to reduce the required user effort. Points are distributed along the airfoil surface based on the airfoil’s geometric features; then, an advancing-front method is used to build a mesh which will capture the airfoil’s boundary layer. Existing unstructured mesh generation tools are integrated into the methodology to construct the off-body and background regions of the mesh. An advanced computational fluid dynamics solver is then used to compute the flow over the airfoils. Several airfoils are examined, demonstrating the combined mesh generation and flow solver’s ability to handle various geometries, multiple-element airfoils, and various flow conditions including transonic flow. The results generated by this methodology compare favorably to prior experimental and computational results, validating the methodology to be used later in other research and product development settings.

Model for Enhancing Turbulent Production in Laminar Separation Bubbles

Laminar separation bubbles are one of the main critical aspects of flows at low Reynolds numbers in the range of . The flow separates in the laminar regime, the turbulence developing inside the recirculation region enhances the momentum transport, and the flow can reattach. Models based on the Reynolds-averaged Navier–Stokes equations suffer two of main issues: the determination of the transition onset and the level of the pressure recovery downstream of the reattachment of the flow. A model addressing both issues is presented in this paper. It is based on the transition model for the transition detection. The production of the turbulent kinetic energy has been properly enhanced thanks to a correlation found between the necessary boosting of and the intermittency function behavior within the bubble. The low-Mach-number and Reynolds-number flows around the Selig–Donovan 7003, Eppler 387, and NACA 0015 airfoils are analyzed. The results are compared to experimental data and large-eddy simulations available in the literature. The model can be applied to the analysis of an arbitrary airfoil without need of preliminary calculation of the transition point within the bubble.

Insights into airfoil response to sinusoidal gusty inflow by oscillating vanes

Gust response is one of the classic topics in aerodynamics. Two different transfer functions, Sears and Atassi, have been used to model the unsteady lift responses of an airfoil experiencing a sinusoidal gust over the past few decades. However, a significant discrepancy against measured data has consistently been observed. Although the discrepancy at high frequencies was solved by a correct normalization of the lift response of an airfoil [Wei et al., “Insights into the periodic gust response of airfoils,” J. Fluid Mech. 876, 237 (2019)], totally opposite trends emerged between the experimental data and both functions at low frequencies. To clarify the observed discrepancy, both wind-tunnel experiments and numerical simulations are performed in this study to characterize the Sears and Atassi inflow conditions generated by oscillating grid vanes. A scaling law is established for fast determination of the oscillation parameters of the vanes required to generate a specific gust angle. The gust-angle phase shift between the empty-tunnel and test airfoil cases is quantified. A universal transfer function normalization method is proposed for arbitrary sinusoidal gusts and arbitrary airfoil shapes. The discrepancy between the measured and theoretical lift responses at low gust frequencies is found to be related to the dynamic effect of the highly turbulent wakes of the oscillating vanes as well as the large installation angle of the test airfoil.

A generalized method to extend airfoil polars over the full range of angles of attack

The accurate prediction of airfoil polars over the whole range of angles of attack and for different Reynolds numbers is pivotal to ensure an accurate prediction of wind turbine aerodynamic performance. In particular, modeling correctly the deep-stall and post-stall airfoil behavior is essential to reproduce reliable power and thrust curves for high wind conditions, especially as far as stall-controlled wind turbines are concerned. This need is even more urgent in vertical-axis wind turbines, in which the airfoils do experience a continuous variation of the angle of attack, exceeding the stall limit even in normal operating points.This paper presents a new method for extending an existing database of airfoil aerodynamic coefficients, e.g. in the common ranges of aeronautical references, over the ±180° range of angles of attack for an arbitrary airfoil shape. Moving from a few basic geometric data, as maximum thickness, camber and leading-edge radius, the whole curves of lift and drag coefficients are reconstructed starting from deep-stall conditions. The proposed correlation is compared to different models for the post-stall extrapolation of the airfoil behavior and experimental data, showing a good agreement with experimental polars for both symmetrical and cambered airfoils.

Aerodynamic Centers of Arbitrary Airfoils Below Stall

The aerodynamic center of an airfoil is commonly estimated to lie at the quarter-chord. This traditional estimate is based on thin airfoil theory, which neglects aerodynamic and geometric nonlinearities. Even below stall, these nonlinearities can have a significant effect on the location of the aerodynamic center. Here, a method is presented for accurately predicting the aerodynamic center of any airfoil from known lift, drag, and pitching-moment data as a function of angle of attack. The method accounts for aerodynamic and geometric nonlinearities, and it does not include small-angle, small-camber, and thin-airfoil approximations. It is shown that the aerodynamic center of an airfoil with arbitrary amounts of thickness and camber in an inviscid flow is a single, deterministic point, independent of angle of attack, and lies at the quarter-chord only in the limit as the airfoil thickness and camber approach zero. Furthermore, it is shown that, once viscous effects are included, the aerodynamic center is not a single point but is a function of angle of attack. Differences between this general solution and that predicted by the thin airfoil theory can be on the order of 3%, which is significant when predicting flutter speeds. Additionally, the results have implications for predicting the neutral point of a complete aircraft.

Prediction of Airfoil Trailing-Edge Noise Using Empirical Wall-Pressure Spectrum Models

This paper presents the predictions of airfoil turbulent boundary-layer trailing-edge noise using empirical wall-pressure spectrum models. Five empirical wall-pressure spectrum models were used. Input parameters for the wall-pressure spectrum models were obtained using the XFOIL panel code. A diffraction model was used to predict trailing-edge noise based on the empirically determined wall-pressure spectrum. This predictive method provided a fast evaluation of trailing-edge noise for arbitrary airfoil shapes with minimum flow input data. In total, 15 cases, including NACA 0012, DU96-W-180, NACA 64-418, and NACA 64-618 airfoils, were used to validate the trailing-edge noise prediction. Overall, it was found that one recently developed empirical wall-pressure spectrum model, named Lee’s model, provided the closest match with the measurement data. The detailed capabilities and limitations of each empirical wall-pressure spectrum model are discussed in terms of trailing-edge noise predictions.

Modeling and dynamic characterization of nonlinear non-smooth aeroviscoelastic systems

Abstract In this work, viscoelastic materials are adopted for handling aeroelastic features of typical section models with three degrees-of-freedom, which present non-smooth, free-play type nonlinearities in their control surface. A rotational viscoelastic damper is added to the resilient element associated to the control surface motion of the typical section. Equations of motion are derived accounting for the viscoelastic damper dependence on frequency and temperature. For this, a fractional derivatives-based viscoelasticity constitutive law is considered. Aerodynamic forces are introduced based on linear potential unsteady aerodynamics accounting for arbitrary airfoil motions. The aeroelastic behavior is investigated through time domain simulations, from which bifurcation diagrams are constructed. Numerical results show that the addition of viscoelastic damping can increase the flutter speed noticeably and reduce the amplitudes of limit cycle oscillations for the system under consideration. Another observed benefit provided by the viscoelastic damper is that undesirable subcritical behavior for the bifurcation onset can be eliminated or modified to have a supercritical character. The influence of temperature on the aeroviscoelastic behavior is also investigated. Using the proposed strategy, nonlinear instabilities can be controlled, improving the safety margins of aeroelastic systems.

An improved geometric parameter airfoil parameterization method

In the process of airfoil optimization, it is required to represent an airfoil with parameters, and the goal is to represent arbitrary airfoils with less parameters. In this paper, a new airfoil parameterization method is proposed, called the IGP method, which realized camber-thickness decoupling so that camber and thickness could be constructed respectively with fewer parameters compared to the previous methods. Also the IGP method is featured with clear physical meaning and consecution of parameter domain. The mathematical model is introduced. With this camber-thickness decoupling method, the definition and the domain of the control parameters was determined. To validate the feasibility, the most used airfoils were fitted and reconstructed by this method. Then according to the results of geometric and aerodynamic comparative analysis between original airfoils and fitted airfoils, the precision of the IGP method could meet the requirement of airfoil optimization.

Dynamic assessment of nonlinear typical section aeroviscoelastic systems using fractional derivative-based viscoelastic model

Nonlinear aeroelastic systems are prone to the appearance of limit cycle oscillations, bifurcations, and chaos. Such problems are of increasing concern in aircraft design since there is the need to control nonlinear instabilities and improve safety margins, at the same time as aircraft are subjected to increasingly critical operational conditions. On the other hand, in spite of the fact that viscoelastic materials have already been successfully used for the attenuation of undesired vibrations in several types of mechanical systems, a small number of research works have addressed the feasibility of exploring the viscoelastic effect to improve the behavior of nonlinear aeroelastic systems. In this context, the objective of this work is to assess the influence of viscoelastic materials on the aeroelastic features of a three-degrees-of-freedom typical section with hardening structural nonlinearities. The equations of motion are derived accounting for the presence of viscoelastic materials introduced in the resilient elements associated to each degree-of-freedom. A constitutive law based on fractional derivatives is adopted, which allows the modeling of temperature-dependent viscoelastic behavior in time and frequency domains. The unsteady aerodynamic loading is calculated based on the classical linear potential theory for arbitrary airfoil motion. The aeroelastic behavior is investigated through time domain simulations, and subsequent frequency transformations, from which bifurcations are identified from diagrams of limit cycle oscillations amplitudes versus airspeed. The influence of the viscoelastic effect on the aeroelastic behavior, for different values of temperature, is also investigated. The numerical simulations show that viscoelastic damping can increase the flutter speed and reduce the amplitudes of limit cycle oscillations. These results prove the potential that viscoelastic materials have to increase aircraft components safety margins regarding aeroelastic stability.

Aerodynamic Shape Optimization of Wind Turbine Blades Using a Parallel Genetic Algorithm

An aerodynamic shape optimization methodology based on Genetic Algorithm and Blade Element Momentum theory is developed for rotor blades of horizontal axis wind turbines Optimization studies are performed for the maximization of power production at a specific wind speed, rotor speed and rotor diameter. The potential flow solver with a boundary layer model, XFOIL, provides sectional aerodynamic loads. The sectional chord length, the sectional twist and the blade profiles at root, mid and tip regions of the blade are taken as design variables. The blade sections may be defined by the NACA four digit airfoil series or by arbitrary airfoil profiles defined by a Bezier curve. The sectional flow computations required by Genetic algorithm, which is inherently parallel, are performed in a parallel computing environment with 512 cores. Message Passage Interface (openMPI), is employed in parallel computations. Validation studies are first performed.

Unsteady Airfoil with Dynamic Leading- and Trailing-Edge Flaps

Unsteady Airfoil with Dynamic Leading- and Trailing-Edge Flaps

Unsteady Cascade Aerodynamics in the Time Domain

A linearized unsteady incompressible aerodynamic model for airfoil cascades is developed that is not restricted to harmonic motion at a constant interblade phase angle. This is accomplished by starting with the unsteady aerodynamic coefe cients generated by LINSUB, a semianalyticunsteady cascadeaerodynamics codethat assumes linearity in both space and time. An inverse Fourier transform is then performed to predict the unsteady aerodynamic forces on the airfoils due to an impulsive acceleration. This result, termed the cascade indicial function, is then convolved with the arbitrary motion of the blades to obtain the unsteady aerodynamic forces on the airfoils in the time domain. The aerodynamic damping predicted by the time domain model is shown to compare well to LINSUB results when the interblade phase angle is constant. Results demonstrating the ability of the model to handle arbitrary airfoil motion are also presented. Nomenclature

A Shock Loss Model for Supersonic Compressor Cascades

Loss models used in compression system performance prediction codes are often developed from the study of two-dimensional cascades. In this paper, compressible fluid mechanics has been applied to the changes in shock geometry that are known to occur with back pressure for unstarted operation of supersonic compressor cascades. This physics-based engineering shock loss model is applicable to cascades with arbitrary airfoil shapes. Predictions from the present method have been compared to measurements and Navier–Stokes analyses of the LO30-4 and L030-6 cascades, and very good agreement was demonstrated for unstarted operation. A clear improvement has been demonstrated over previously published shock loss models for unstarted operation, both in the accuracy of the predictions and in the range of applicability. The dramatic increase in overall loss with increasing inlet flow angle is shown to be primarily the result of increased shock loss, and much of this increase is caused by the detached bow shock. For a given Mach number, the viscous profile loss is nearly constant over the entire unstarted operating range of the cascade, unless a shock-induced boundary layer separation occurs near stall. Shock loss is much more sensitive to inlet Mach number than is viscous profile loss.

A Three-Dimensional Shock Loss Model Applied to an Aft-Swept, Transonic Compressor Rotor

An analysis of the effectiveness of a three-dimensional shock loss model used in transonic compressor rotor design is presented. The model was used during the design of an aft-swept, transonic compressor rotor. The demonstrated performance of the swept rotor, in combination with numerical results, is used to determine the strengths and weaknesses of the model. The numerical results were obtained from a fully three-dimensional Navier–Stokes solver. The shock loss model was developed to account for the benefit gained with three-dimensional shock sweep. Comparisons with the experimental and numerical results demonstrated that shock loss reductions predicted by the model due to the swept shock induced by the swept leading edge of the rotor were exceeded. However, near the tip the loss model underpredicts the loss because the shock geometry assumed by the model remains swept in this region while the numerical results show a more normal shock orientation. The design methods and the demonstrated performance of the swept rotor are also presented. Comparisons are made between the design intent and measured performance parameters. The aft-swept rotor was designed using an inviscid axisymmetric streamline curvature design system utilizing arbitrary airfoil blading geometry. The design goal specific flow rate was 214.7 kg/s/m2 (43.98 lbm/sec/ft2), the design pressure ratio goal was 2.042, and the predicted design point efficiency was 94.0. The rotor tip speed was 457.2 m/s (1500 ft/sec). The design flow rate was achieved while the pressure ratio fell short by 0.07. Efficiency was 3 points below prediction, though at a very high 91 percent. At this operating condition the stall margin was 11 percent.

Computational analysis of buffet alleviation in viscous transonic flow over a porous airfoil

RANSONIC flow past an airfoil at a high freestream Mach number is traditionally defined as consisting of large supersonic regions embedded within a subsonic flowfield. The pressure fluctuations initiated by the shock/boundary-layer interaction may excite intense levels of buffeting. 1 Therefore, to extend the buffet boundaries for a particular airfoil, a technique is required which is capable of controlling either the boundary layer, or alternatively, the shock strength. Boundary-layer control may be performed by employing either blowing or suction within the interaction region. Blowing has a twofold effect, namely, an increase in the boundary-layer thickness coupled with a reduction in the skin friction, whereas suction induces a contrasting decrease in boundary-layer thickness and increase in skin friction. Passive control of the shock/boundary-layer interaction is a technique which provides a combination of blowing and suction forward and aft of the shock, respectively, without the need for a pump. A passive control device (Fig. 1) consists of a porous region and plenum which are positioned at the interaction region. The static pressure rise across the shock wave results in the flow traveling through the plenum to the region of lower pressure forward of the shock position. The increased communication across the shock stimulates the development of a thicker boundary layer forward of the shock. This process effectively changes the airfoil's geometry in a manner which produces a weaker lambda shock system. Moreover, passive control's inherent damping characteristics have been shown experimentally25 to reduce the pressure fluctuations initiated by the shock/boundary-layer interaction and, therefore, delay buffet onset. In the present study, time-accurate flow over an 18%-thick porous circular-arc airfoil is computed in an attempt to ascertain whether passive control will damp, or even eliminate, the flow periodicity detected in the corresponding solid airfoil (CSA) computation,6 thus extending the airfoil's buffet boundary. The following sections briefly describe both the numerical procedure and the results. Numerical Model An explicit Navier-Stokes finite volume scheme MGENS has been developed which is capable accurately predicting viscous flow over an arbitrary airfoil using an orthogonal boundary conforming hyperbolic grid MGHYPR. A detailed description of both the

Field panel method with grid stretching technique for solving transonic potential flow around arbitrary airfoils

The Field Panel Method (FPM) with grid stretching technique, presented in this paper, was developed for solving transonic full potential flow around arbitrary airfoils at incidence. In this method, the total potential values are represented by boundary integrals together with a volume integral. The volume integral domain includes both inside and finite outside of the configuration and can be discretisized in a Cartesian grid which may penetrate into the configuration surface. Thus, we avoid the very difficult task of generating body-fitted grids around complex configurations. The boundary potential values are obtained by implementing a standard panel method (symmetrical singularity model), whereas the field potential values are estimated by solving the full potential equation (using AF3 scheme in a Cartesian grid) with approximate inner and proper outer boundary conditions. Furthermore, the grid stretching technique has been utilized that allows to capture the shock waves in a much better quality. It is also shown that both field grid and panel distribution have to be stretched at the same time. Results for transonic potential flows about NACA0012 and RAE2822 airfoils at different Mach numbers and incidences are obtained and compared with other numerical solutions. Great improvement in shock wave quality was achieved by using the present method.

Field panel method with grid stretching technique for solving transonic potential flow around arbitrary airfoils

Field panel method with grid stretching technique for solving transonic potential flow around arbitrary airfoils

On the Influence of Time‐Varying Flow Velocity on Unsteady Aerodynamics

The effects of a periodic free-stream velocity on the unsteady aerodynamics of an airfoil in incompressible flow are examined. Existing theories are reviewed, and their simplifications and limitations are properly identified. A new general aerodynamic theory for an airfoil undergoing a combination of harmonic pitching, plunging and fore-aft motion is presented. An extension to arbitrary free-stream velocity variations and arbitrary airfoil motion is also given. The theoretical results are validated against numerical predictions made by a modern Euler code.