Two-dimensional Airfoil Sections Research Articles

HLPW-4/GMGW-3: High-Order Discretization Technology Focus Group Workshop Summary

This paper summarizes the High-Order Technical Focus Group (HO-TFG) submissions for the joint 4th AIAA High Lift Prediction (HLPW-4) and 3rd Geometry and Mesh Generation Workshop (GMGW-3). The goal of the workshop was to assess the state-of-the-art in mesh generation and computational fluid dynamics software. The Common Research Model High-Lift (CRM-HL) variant served as the primary focus of the workshop, and a two-dimensional airfoil section from the CRM-HL was used as a verification test case. The HO-TFG was tasked with generating high-order curved meshes for both geometries, and computing high-order solutions using both Reynolds-averaged Navier–Stokes and scale-resolving formulations. While limited by computational resources, the final results demonstrate the potential of higher-order methods to increase solution accuracy with a lower degree-of-freedom count relative to second-order discretizations.

Vortex Shedding Lock-In due to Pitching Oscillation of a Wind Turbine Blade Section at High Angles of Attack

The unsteady flow around a pitching two-dimensional airfoil section (NREL S809) has been simulated using unsteady RANS with the transition SST turbulence model. This geometry is chosen to represent a wind turbine blade in a standstill configuration. The Reynolds number is Re=106 based on a chord length of 1 m. A prescribed sinusoidal pitching motion has been applied at a fixed amplitude of 7° for a range of high angles of attack 30°<α<150°. At these incidences, the airfoil will behave more like a bluff body and may experience periodic vortex shedding. It is well known that, in bluff body flows, oscillations can lead to a lock-in (lock-in) of the vortex shedding frequency, fv, with the body’s motion frequency, fp. In order to investigate the susceptibility of airfoil to lock-in, the frequency ratio r (r=fp/fv0) has been varied around r=1. The lock-in region boundaries have been proposed, and an analysis of the effect of the oscillation amplitude has been conducted. The lock-in map obtained suggests that, for the vibration amplitude considered, the risk of vortex-induced vibration is more significant in the regions of α≈40° and α≈140°, i.e., for shallower characteristic lengths. Finally, a lumped parameter wake oscillator model has been proposed for pitching airfoils. This simple model is in qualitative agreement with the CFD results.

A transformation-based formulation of an airfoil cloak using Joukowski mapping

Since its introduction in 2006, the transformation approach to cloaking has been extensively explored for electromagnetic and acoustic fields, due to its intuitive nature as well as the methodology. In this approach, the construction of invisibility cloaks consists of exploiting a change of coordinates to create a void region within a finite space while keeping the outer boundary of the considered space unchanged. Such changes in physical coordinates can be interpreted as a transformation of material properties related to electromagnetics and acoustics, given the invariance of the respective field equations to coordinate change. Based on the transformation, properties of an invisibility cloak can be inferred using available formulae. To this date, this approach has been successfully applied to various two-dimensional geometries including circular and square cylinders. In this work, as an extension, the authors present initial results obtained for the cloaking of a two-dimensional airfoil section. They take advantage of the mapping properties of the well-known Joukowski transformation, a complex mapping that is used in aerodynamics applications.

Aeroelastic Dynamic Response and Control of an Aeroelastic System with Hysteresis Nonlinearities

A state feedback control law based on the sliding mode control method is derived for the aeroelastic response and flutter suppression of a two-dimensional airfoil section with hysteresis nonlinearity in pitch. An observer is constructed to estimate the unavailable state variables of the system. With the control law designed, nonlinear effect of time delay between the control input and actuator is investigated by a numerical approach. The closed-loop system including the observer and nonlinear controller is asymptotically stable. The simulation results show that the observer can give precise estimations for the plunge displacement and the velocities in pitch and plunge and that the controller is effective for flutter suppression. The time delay between the control input and actuator may jeopardize the control performance and cause high-frequency vibrations.

Multi-objective optimization of lean and sweep angles for stator and rotor blades of an axial turbine

The axial turbine is one of the most challenging components of gas turbines for industrial and aerospace applications. With the ever-increasing requirement for high-aerodynamic performance blades, three-dimensional aerodynamic shape optimization is of great importance. In this research, the rear part of a gas turbine consisting of a one-stage axial turbine is optimized numerically. A useful optimization algorithm is presented to improve the efficiency and/or pressure ratio of the axial turbine with two different objective functions. The three-dimensional blade-shape optimization is employed to study the effects of the turbine stator and rotor lean and sweep angles on the turbine performance. The investigation is carried out at the turbine design speed. By coupling a verified computational fluid dynamics simulation code with the genetic algorithm, an automated design procedure is prepared. Geometry candidates for the optimization algorithm are generated by re-stacking of the two-dimensional airfoil sections. Three-dimensional, turbulent, and compressible flow field is numerically investigated via a Navier–Stokes solver to calculate various objective functions. Experimental results of the gas turbine are used for specifying the boundary conditions and validation of the simulation results. The proposed method results in 1.3% and 1.5% improvements in the turbine stage efficiency in design speed and reduced mass parameter at choke condition, respectively.

탄성 플랩을 갖는 2차원 날개 단면 공력 특성 전산해석

이 연구에서는 탄성 플랩이 뒷전에 장착된 2차원 날개 단면의 공력 특성을 전산 해석하였다. EDISON_CFD는 날개 주위의 비압축성 난류 유동을 시뮬레이션 하기 위해 이용되었으며, MIDAS_IT는 전산 해석 결과로 얻어진 압력 하중 하에서 탄성 플랩의 변위를 구조해석 하기 위해 사용되었다. EDISON_CFD와 MIDAS_IT의 반복 계산 절차를 이용하여, 플랩의 변위가 수렴되면 해석을 종료하여, 날개 단면에 작용하는 공력을 분석하였다. 양항비의 추정 결과 일정 받음각 이내에서 플랩의 유리한 효과가 나타날 것으로 예상된다.

Gust Response Parameter Optimization of Two-Dimensional Airfoil Section

Taking the two-dimensional airfoil section model with two degrees of freedom as the object, this paper develops a multi-parameter optimization method, which regards the minimum system response under the given gust disturbances as the objective function and gives the expression describing the state space form of response sensitivity in which the matrix parameter sensitivity solution obtained by CVD method, further more, the Newton iteration method based on the sensitivity is adopted to realize the parameter optimization. By the simulated calculation of numerical examples and comparing with the conventional method, the optimization method has the advantage of better calculation efficiency and robustness and being used for aircraft design.

Flutter control based on ultrasonic motor for a two-dimensional airfoil section

This paper presents how to use an ultrasonic motor, which features high torque at low speed, small size and low weight, as an actuator in the flutter control of a two-dimensional airfoil section. The paper begins with the design of a two-dimensional airfoil model with the piecewise-linear torsional stiffness in pitch direction and a control surface driven by an ultrasonic motor. Then, it gives the experimental modeling of the airfoil section and the servo, composed of the control surface and the ultrasonic motor, as well as the identification of system parameters through the use of a simple approach of nonlinear least squares estimation. Afterwards, the paper presents the dynamic equation of the aeroservoelastic equation based on Theodorsen's aerodynamic load, and the numerical simulations for the sub-optimal control of flutter. Finally, the paper outlines the experimental study of the flutter control of the airfoil section in a wind tunnel test, where the critical flutter speed of controlled system could be increased by 13.4%, and the flutter was effectively suppressed when the flow speed exceeded the critical flutter speed of the uncontrolled system.

Nonlinear instabilities of a non-self-similar boundary layer on an airfoil: Experiments, DNS, and theory

Transition prediction of a laminar boundary layer developing on a two-dimensional airfoil section at pure subsonic speeds is still a challenge, because the commonly used semi-empirical prediction tools are mainly based on results derived from the linear stability theory (LST). This approach completely neglects non-linear interactions at later stages of the transition development and therefore provides limited accuracy for cases when the non-linear part has significant length in comparison to the linear stage. Nevertheless, the later one can be of significant importance for airfoil design. The onset and further development of non-linear, in general resonant wave interactions is depending on the pre-history of the boundary layer and the specific linear and non-linear stability characteristics driven by the pressure gradient, which varies in streamwise direction for typical airfoil sections. The variation of the pressure gradient leads to a non self-similar boundary layer development connected with a continuous change of the resonance conditions for wave interactions. The present paper is devoted to the detailed experimental, numerical and theoretical study of weakly nonlinear subharmonic resonant interactions of Tollmien–Schlichting waves in such a two-dimensional non self-similar boundary layer on an airfoil. The experimental approach is based on phase locked hot-wire measurements under controlled disturbance conditions in a low turbulence wind tunnel at a Reynolds number of Re=0.7×10 6. Direct numerical simulations (DNS) based on the vorticity–velocity formulation of the complete Navier–Stokes equations are utilized to provide a detailed comparison for the test cases. The results of weakly non-linear theory (WNT) enabled a profound understanding of the underlying physical mechanisms observed in the experiments and simulations. The joint study provides a complete set of data, starting from the base flow and stability characteristics up to non-linear disturbance development with different involved wave triplets. The phase synchronization mechanism is investigated in detail as well as the resonance efficiency for tuned cases with respect to the exact subharmonic frequency. In general, a good agreement between the experiment, DNS and WNT is found. The essential non-self-similarity of the airfoil boundary layer does not prevent strong resonant interactions and in accordance with investigations in self-similar flows, rapid, close to double-exponential amplification of subharmonic modes is observed. At the resonant stage, the phase-synchronization condition is shown to be satisfied, which provides equal phase speeds for all involved modes. For tuned cases, the initial phase relation between fundamental and subharmonic modes can lead, partly, to a suppression of the subharmonic wave amplification. Variation of the fundamental wave frequency shows that the integral resonance efficiency is significantly decreased with the reduction of the frequency. This effect is explained as a frequency dependence of the nonlinear coupling coefficients as well as the detuning of the subharmonic-fundamental phase speed associated mainly with the base-flow non-self-similarity. Depending on the frequency content of the initial disturbances this can lead to a direct influence on the corresponding transition position.

Modeling of Aerodynamically Generated Noise From Wind Turbines

A semiempirical acoustic generation model based on the work of Brooks, Pope, and Marcolini [NASA Reference Publication 1218 (1989)] has been developed to predict aerodynamic noise from wind turbines. The model consists of dividing the blades of the wind turbine into two-dimensional airfoil sections and predicting the total noise emission as the sum of the contribution from each blade element. Input is the local relative velocities and boundary layer parameters. These quantities are obtained by combining the model with a Blade Element Momentum (BEM) technique to predict local inflow characteristics to the blades. Boundary layer characteristics are determined from two-dimensional computations of airfoils. The model is applied to the Bonus 300 kW wind turbine at a wind speed of 8 m/s. Comparisons of total noise spectra show good agreement with experimental data.

Aeroelastic analysis of a non-linear airfoil based on unsteady vortex lattice model

Recent years have witnessed a successful model of unsteady vortex lattice to predict the limit cycle oscillations of an airfoil section. The aerodynamic model is usually in the form of discrete time, and hence, is not convenient for the analysis of non-linear aeroelastic systems. In this paper, the aerodynamic model of unsteady vortex lattice is formulated in continuous time domain and expressed in a dimensionless form. The order of aerodynamic model is greatly reduced in terms of a few aerodynamic eigenmodes to describe the unsteady vortex. Meanwhile, a static correction is included in the modal reduction to take the effects of truncated higher aerodynamic modes into account. The accuracy of the reduced-order model of aerodynamics is compared with Theodorsen's model. Using the modified aerodynamic model, the aeroelastic analysis of a two-dimensional airfoil section with combined non-linearity of freeplay and cubic stiffening in pitch is made. The numerical results indicate that the modified aerodynamic model is capable of predicting the flow about airfoil accurately and detecting the complex non-linear aeroelastic behaviors.

Airfoil inverse design and optimization by means of viscous-inviscid techniques

Abstract This paper deals with airfoil design aimed at optimizing rotor blade aerodynamic performances. Although the statements presented in this study are quite general, particular attention has been given to the design of two-dimensional airfoil sections for wind turbine rotors. Analytical and numerical tools are briefly mentioned. Aspects of viscous flows are discussed, along with boundary layer control, turbulent transition, drag reduction and accuracy in C L max prediction. Outstanding is the design of a thin low-drag airfoil having rather low C L max , and of a thick section having high C L max . The design of the outboard and mean airfoil sections is also presented.

Comparison of Measured and Predicted Transonic Flow Around an Airfoil

ATWO-DIMENSIONAL numerical solution using an inviscid time marching method has been compared with interferometric data obtained from image plane holograms. This has been done over the whole blade profile including the trailing edge shock region, but a particularly detailed analysis has been made of the leading edge. The data obtained show isodensity/iso-Mach contours (AM=0.03), with a spacing of typically 50 /mi between them. It was found that a highly refined grid size of similar resolution was required to compute an accurate solution. Contents Description of Flow The two-dimensional airfoil section which was based upon a NACA 0010-34 profile1 was mounted at zero incidence in the center of the tunnel on two supports from below. These were located within the tunnel flow, causing a 12% blockage of the throat area beneath the blade. It may be thought that such a large blockage would generate three-dimensional effects; previous oil flow and pressure measurements show this not to be the case.1 They also show that despite a 5-mmthick sidewall boundary layer the flow on the upper surface of the blade is two-dimensional for 90% of its span. As a result of the partial blockage of the blade at the leading edge, the stagnation point has moved toward the pressure surface. The flow is seen to accelerate around the leading edge up to a maximum speed of M=1.25 (Fig. 1). This can be compared with the computed flow solutions shown in Figs. 2-4. The flow remains attached around the leading edge and subsequently decelerated to a minimum Mach number of 1.06 at 10% of the blade chord. The suction surface of the blade then behaves in a more conventional manner, the supersonic flow being accelerated by the convex surface of the blade profile up to M= 1.26. It is also noted that the boundary-layer thickness at the trailing edge is 2 mm. This thickness has not been taken into account in the inviscid calculations. Optical System The optical system used in this experiment was similar to that applied previously2 to turbine cascade, image plane holography. The interferometric fringes formed in the

Effects of Masts on the Aerodynamics of Sail Sections

The effects of the addition of masts of varying geometries to two different sail-like two-dimensional airfoil sections were determined by water tunnel tests. Thirteen different mast-sail combinations were tested with four of the sections retested at a different time to confirm repeatability of the data. The results were found to be best presented and best understood by means of graphs of drag coefficient versus lift coefficient for fixed values of d/c(mast diameter/sail chord). The additional drag caused by the addition of a mast was found to be substantial, especially as the ratio d/cbecame relatively large. Results were found to be insensitive to changes in Reynolds number of a factor of two for d/cless than 0.3 for round masts, and 0.2 for elliptical masts (d for an elliptical mast is taken as the diameter of a circle having the same cross-sectional area). Elliptical masts with d/c greater than 0.3 gave results which exhibited a sensitivity to Reynolds number and which, over a limited range of lift coefficients, gave an unexpectedly high value of the ratio of lift coefficient/drag coefficient.

Discrete vortex method of two-dimensional jet flaps.

A jet flap theory is developed with the aid of a classical cooformal mapping of airfoils onto unit circles and the method is free of any restrictions on the amount of airfoil thickness, camber or angle of attack. The jet sheet is supposed to be infinitesimally thin and is approximated by a finite number of discrete vortices placed on a stagnation streamline. The strengths of vortices are determined by an iterative procedure which is set up between the transformed and the physical plane. Any one of the classical incompressible airfoil theories, such as Theodorsen and Garrick's direct method or LighthilPs inverse one, can be applied to determine the mapping function of airfoils onto unit circles. The present approximation will converge to the exact incompressible potential flow theory of two-dimensional airfoil sections with infinitesimally thin jet flaps, if the number of vortices is increased and the distances between the adjacent vortices decreased indefinitely. Furthermore, the classical Blasius formulae are modified for jet flaps with discrete vortex approximations; and lift, drag and moment of airfoils are obtained. An example of an elliptical section of 12.5% thickness chord ratio with jet flaps shows a fair agreement with Dimmock's experimental data. With the aid of Theodorsen and Garrick's direct and author's inverse method several more examples are worked out.

Inverse method of designing two-dimensional transonic airfoil sections.

The approximate compressible theory of two-dimensional airfoil sections at transonic speeds is obtained by means of the method of integral relations and quasi-linearization. The theory is an inverse method in which airfoil sections are obtained from prescribed velocity distributions which are assumed to be shock free at design Mach numbers. In order to decrease the number of strips necessary to keep the accuracy of results, the singularity of equations at stagnation points is removed analytically and the remaining regular parts of equations are transformed into a two-point boundary value problem of a system of nonlinear ordinary differential equations by means of the method of integral relations; and these equations are integrated through using quasi-linearization and the Runge-Kutta-Gill numerical method. Application of quasi-linearization admits the use of as many strips as one wishes and the accuracy of results can be improved without limit. An iterative cycle is set up to make the resulting profiles close when the pressure distributions are arbitrarily prescribed. Examples of airfoil sections designed with a four strip method and an experimental pressure distribution are presented. The rate of convergence of quasi-linearization is shown to be high.