Iteration schemes for rapid post‐stall aerodynamic prediction of wings using a decambering approach

Nonlinear aerodynamics of wings may be evaluated using an iterative decambering approach. In this approach, the effect of flow separation due to stall at any wing section is modeled as an effective reduction in section camber. The approach uses a wing analysis method for potential‐flow calculations and viscous airfoil lift curves for the sections as input. The calculation procedure is implemented using a Newton–Raphson iteration to simultaneously satisfy the boundary condition, which comes from potential‐flow wing theory, and drive the sectional operating points toward their respective viscous lift curves, as required for convergence. Of particular interest in this research is the calculation of the residuals during the Newton iteration. Unlike a typical implementation of the Newton iteration, the residual calculation is not performed via a straightforward function evaluation, but rather by estimating the target operating points on the input viscous lift curves. Estimation of these target operating points depends on the assumptions made in the cross‐coupling of the decambering at the different sections. This paper presents four residual calculation schemes for the decambering approach. The residual calculation schemes are compared against each other to assess computational speed and robustness. Decambering results are also compared with higher‐order computational fluid dynamics (CFD) solutions for rectangular and swept wings. Results from the best scheme compare well with the CFD solutions for the rectangular wing, motivating further development of the method. Poor predictions for the swept wings are traced to spanwise propagation of separated flow at stall, highlighting the limitations of the current approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Reliability of aerodynamic analysis using a moment method

In this study, a reliability analysis was performed for the aerodynamic analysis. Among various reliability analysis methods, the moment method was used and the results were compared with other methods. The reliability of aerodynamic analysis of a 2D airfoil, a 3D wing and a wing body configuration were considered. In the case of 2D airfoil, the reliability was computed by parameterising an airfoil shape using the PARSEC function and considering uncertainties of its shape. In the case of 3D wing and wing body configuration, it was computed by considering uncertainties of flow conditions.     

Analytical formulation of 2-D aeroelastic model in weak ground effect

This paper deals with the aeroelastic modeling and analysis of a 2-D oscillating airfoil in ground effect, elastically constrained by linear and torsional springs and immersed in an incompressible potential flow (typical section) at a finite distance from the ground. This work aims to extend Theodorsen theory, valid in an unbounded flow domain, to the case of weak ground effect, i.e., for clearances above half the airfoil chord. The key point is the determination of the aerodynamic loads, first in the frequency domain and then in the time domain, accounting for their dependence on the ground distance. The method of images is exploited in order to comply with the impermeability condition on the ground. The new integral equation in the unknown vortex distribution along the chord and the wake is solved using asymptotic expansions in the perturbation parameter defined as the inverse of the non-dimensional ground clearance of the airfoil. The mathematical model describing the aeroelastic system is transformed from the frequency domain into the time domain and then in a pure differential form using a finite-state aerodynamic approximation (augmented states). The typical section, which the developed theory is applied to, is obtained as a reduced model of a wing box finite element representation, thus allowing comparison with the corresponding aeroelastic analysis carried out by a commercial solver based on a 3-D lifting surface aerodynamic model. Stability (flutter margins) and response of the airfoil both in frequency and time domains are then investigated. In particular, within the developed theory, the solution of the Wagner problem can be directly achieved confirming an asymptotic trend of the aerodynamic coefficients toward the steady-state conditions different from that relative to the unbounded domain case. The dependence of flutter speed and the frequency response functions on ground clearance is highlighted, showing the usefulness of this approach in efficiently and robustly accounting for the presence of the ground when unsteady analysis of elastic lifting surfaces in weak ground effect is required.     

Extension of the problem of designing a wing airfoil with active flow controls to the case of systems involving a screen

The solution of the inverse boundary-value problem for a wing airfoil with slot air suction from the outer flow on its upper surface and control jet injection from its rear is generalized to include the case of the flow around such an airfoil in the presence of a screen. The complications due to the double connectivity of the flow region are overcome by means of introducing a fictitious flow beneath the screen. The solution is constructed using a numerical-analytical iteration procedure. Formulas for recalculating the aerodynamic characteristics and the velocity distribution over the airfoil surface to different flight regimes and suction-injection device operation regimes are derived. The effect of the injected jet energy, the airfoil-screen spacing, and the slope of the rectilinear airfoil undersurface on the aerodynamic and geometric characteristics of the airfoil, namely, the shape and the lift coefficient, is studied. The reliability of the results is confirmed by the results of calculations using the Fluent program.     

排翼布局飞行器气动性能的实验研究

通过低速低湍流度风洞实验,研究了利用排翼布局改善充气飞机采用大厚度翼型机翼带来的气动效率偏低问题。首先比较了采用不同厚度翼型的单翼与排式双翼布局的气动特性。在此基础上,为了优化排翼布局的气动特性,研究了给后翼安装偏转角对排翼布局气动特性的影响。同时,基于NACA0030翼型,设计了波纹型外形的充气机翼,比较了此外形下单翼和排翼布局气动性能的差异。实验结果表明,采用排翼布局能够改善采用厚翼型单翼布局的气动性能,而给后翼安装一定偏转角可以进一步提高排翼布局的升力和升阻比。采用波纹外形和光滑外形机翼模型的对比结果表明,波纹外形能够在大迎角时改善充气机翼的失速性能。分析认为,造成这一现象的流动机理是由于波纹型机翼在实验条件下提前由层流转捩为湍流,使失速推迟,流动分离现象有所减弱。     

Mathematical simulation of unsteady flow past a wing with jets

The various approximate approaches to the investigation of the unsteady aerodynamic characteristics of an airfoil with jet flap [1–3] are applicable only for an airfoil, low jet intensity, and low oscillation frequencies. In the present paper, the method of discrete vortices [4] is generalized to the case of unsteady flow past a wing with jets and arbitrary shape in plan. The problem is solved in the linear formulation; the conditions used are standard: no flow through the wing and jet, finite velocities at the trailing edges where there is no jet, and also a dynamical condition on the jet. The wing and jet are assumed to be thin and the medium inviscid and incompressible.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 139–144, May–June, 1982.     

Quasi‐steady aerodynamic analysis of propeller–wing interaction

A quasi‐steady scheme for the analysis of aerodynamic interaction between a propeller and a wing has been developed. The quasi‐steady analysis uses a 3D steady vortex lattice method for the propeller and a 3D unsteady panel method for the wing. The aerodynamic coupling is represented by periodic loads, which are decomposed into harmonics and the harmonic amplitudes are found iteratively. Each stage of the iteration involves the solution of an isolated propeller or wing problem, the interaction being done through the Fourier transform of the induced velocity field. The propeller analysis code was validated by comparing the predicted velocity field about an isolated propeller with detailed laser Doppler velocimeter measurements, and the quasi‐steady scheme by comparison with mean loads measured in a wing–propeller experiment. Comparisons have also been made among the fluctuating loads predicted by the present method, an unsteady panel scheme and a quasi‐steady vortex lattice scheme. Copyright © 1999 John Wiley & Sons, Ltd.     

Spectrographic analysis for the modal testing of nonlinear aeroelastic systems

The spectrograph is a signal-processing tool often used for the frequency domain analysis of time-varying signals. When the signal to be analyzed is a function of time, the spectrograph represents the frequency content of the signal as a sequence of power spectra that change with time. In this paper, the usefulness of the technique is demonstrated in its application to the analysis of the time history response of a nonlinear aeroelastic system. The aeroelastic system is modelled analytically as a two-dimensional, rigid airfoil section free to move in both the bending and pitching directions and possessing a rigid flap. The airfoil is mounted by torsional and translational springs attached at the elastic axis, and the flap is used to provide the forcing input to the system. The nonlinear system is obtained by introducing a freeplay type of nonlinearity in the pitch degree-of-freedom restoring moment. The airfoil is immersed in an aerodynamic flow environment, modelled using incompressible thin airfoil theory for unsteady oscillatory motion. The equations of motion are solved using a fourth-order Runge–Kutta numerical integration technique to provide time-history solutions of the response of the airfoil in the pitch and plunge directions. Time-histories are obtained for the nonlinear responses of the linear and nonlinear aeroelastic systems to a sine-sweep input. The time-histories are analyzed using the spectrographic technique, and the frequency content of the response is plotted directly as a function of the input frequency. Results show that the combination of the sine-sweep input with the spectrographic analysis permits a unique insight into the behavior of the nonlinear system with a minimum of testing. It is shown that the frequency of the nonlinear system response is a function of the input frequency and one other characteristic frequency that can be associated with the limit cycle oscillations of the same nonlinear system subject to a transient input.     

Mono‐block and non‐matching multi‐block structured mesh adaptation based on aerodynamic functional total derivatives for RANS flow

An enhanced goal‐oriented mesh adaptation method is presented based on aerodynamic functional total derivatives with respect to mesh nodes in a Reynolds‐Averaged Navier‐Stokes (RANS) finite‐volume mono‐block and non‐matching multi‐block‐structured grid framework. This method falls under the category of methods involving the adjoint vector of the function of interest. The contribution of a Spalart–Allmaras turbulence model is taken into account through its linearization. Meshes are adapted accordingly to the proposed indicator. Applications to 2D RANS flow about a RAE2822 airfoil in transonic, and detached subsonic conditions are presented for the drag coefficient estimation. The asset of the proposed method is patent. The obtained 2D anisotropic mono‐block mesh well captures flow features as well as global aerodynamic functionals. Interestingly, the constraints imposed by structured grids may be relaxed by the use of non‐matching multi‐block approach that limits the outward propagation of local mesh refinement through all of the computational domain. The proposed method also leads to accurate results for these multi‐block meshes but at a fraction of the cost. Finally, the method is also successfully applied to a more complex geometry, namely, a mono‐block mesh in a 3D RANS transonic flow about an M6 wing. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical simulation of thin airfoil stall by using a modified DES approach

The detached‐Eddy simulation (DES) method was applied to calculate pre‐ and post‐stall aerodynamic characteristics of airfoil stall. A discrepancy between numerical and experimental data was observed near the stall regime for the airfoil NACA64_A‐ 006 which is a thin airfoil stall type. The reason of this discrepancy and one possible way for improvement of the numerical model are discussed here. It is shown that the use of the Baldwin–Lomax model in the RANS region improves the DES results in this case. If the relevant factors (grid density, time step, turbulence model, etc.) are appropriately taken into account, the DES approach could reliably predict stall aerodynamical characteristics. Copyright © 2006 John Wiley & Sons, Ltd.     

Nonlinear characteristics of a thin wing in a shock-free flow around the nose

An effective means of controlling wing leading-edge stall at high angles of attack is deflection of the nose in order to assure shock-free entrance of the stream. A numerical method of computing the angles of nose deflection and the aerodynamic characteristics of a thin wing of arbitrary planform for a shock-free entrance of the steady ideal incompressible fluid stream is elucidated in this paper on the basis of nonlinear wing theory [1]. The problem is solved by the method of discrete vortices. In the computations, the wing and its wake, replaced by a vortex sheet, are modeled by a system of discrete vortices which are nonlinear segments with constant circulation along the length. The angles of deflection of the nose and the aerodynamic characteristics of the wing, including shunting of the free vortices shed from the side and trailing edges, are determined during the computation. Examples of an electronic digital computer are presented.     

An efficient method for nonlinear aeroelasticy of slender wings

This paper aims the nonlinear aeroelastic analysis of slender wings using a nonlinear structural model coupled with the linear unsteady aerodynamic model. High aspect ratio and flexibility are the specific characteristic of this type of wings. Wing flexibility, coupled with long wingspan can lead to large deflections during normal flight operation of an aircraft; therefore, a wing in vertical/forward-afterward/torsional motion using a third-order form of nonlinear general flexible Euler–Bernoulli beam equations is used for structural modeling. Unsteady linear aerodynamic strip theory based on the Wagner function is used for determination of aerodynamic loading on the wing. Combining these two types of formulation yields nonlinear integro-differentials aeroelastic equations. Using the Galerkin’s method and a mode summation technique, the governing equations will be solved by introducing a numerical method without the need to adding any aerodynamic state space variables and the corresponding equations related to these variables of the problem. The obtained equations are solved to predict the aeroelastic response of the problem. The obtained results for a test case are compared with those of some other works and show a good agreement between results.     

Chimera technique for transporting disturbances

The Chimera technique for moving grids is used to take into account nonhomogeneous unsteady inflow conditions in the simulation of aerodynamic flows. The method is applied to simulate the transport of a large‐scale vortex by a mean velocity field over a large distance, where it finally interacts with an airfoil. The Chimera approach allows one to resolve the vortex on a fine grid, whereas the unstructured background grid covering most of the computational domain can be much coarser. This method shows the same low numerical dissipation as a simulation on a globally fine grid. Several precursor tests are performed with a finite modified analytical Lamb–Oseen type vortex to study the influence of spatial and temporal resolution and the employed numerical scheme. Then, the interaction of an analytical vortex with a NACA0012 airfoil and with an ONERA‐A airfoil near stall is studied. Finally, a realistic vortex is generated by a ramping airfoil and is transported on a moving Chimera block and then interacts with a two‐element airfoil, which allows one to simulate a typical setup for a gust generator in aerodynamic facilities. Copyright © 2012 John Wiley & Sons, Ltd.     

Effect of uncertainty on the bifurcation behavior of pitching airfoil stall flutter

In this paper the effect of system parametric uncertainty on the stall flutter bifurcation behavior of a pitching airfoil is studied. The aerodynamic moment on the two-dimensional rigid airfoil with nonlinear torsional stiffness is computed using the ONERA dynamic stall model. The pitch natural frequency, a cubic structural nonlinearity parameter, and the structural equilibrium angle are assumed to be uncertain. The effect on the amplitude of the response, the bifurcation of the probability distribution, and the flutter boundary is considered. It is demonstrated that the system parametric uncertainty results already in 5% probability of pitching stall flutter at a 12.5% earlier position than the point where a deterministic analysis would predict unstable behavior. Probabilistic collocation is found to be more efficient than the Galerkin polynomial chaos method and Monte Carlo simulation for modeling uncertainty in the post-bifurcation domain.     

一种可用于机翼优化设计中的气动噪声预测模型

发展了一种可用于翼型/机翼外形设计中的气动噪声快速预测方法。相较于传统的半经验噪声预测方法,该方法以两方程非线性k-ε湍流模型模化雷诺应力的雷诺平均方程为背景,考虑了升力系数、三维流动效应以及机翼几何参数等因素对后缘噪声的影响。而相对于直接数值模拟或声类比拟方法,该方法虽不能准确预测噪声强度,但其计算量小,能给出不同翼型/机翼的相对总声压级,以及总声压级随升力系数的变化情况,易于应用于翼型/机翼气动外形优化设计中。通过计算分析二维NACA0012翼型几何参数或来流状态的改变所带来的气动噪声差异,与ANOPP软件及Brooks等计算结果进行对比,验证了该模型的可靠性。最后,计算分析二维、三维翼型/机翼气动噪声,凸显该方法在翼型/机翼气动外形优化设计中的应用价值。     

两种椭圆翼型高速气动特性实验研究

新概念旋转机翼飞机的主机翼既能高速旋转作为旋翼,又可锁定作为固定翼,所以只能使用特殊的前后对称翼型。针对主机翼翼型的这一特殊要求,对16％相对厚度,相对弯度分别为0％和3％的两种椭圆翼型的高速气动特性进行了风洞实验研究,试验分别在中国空气动力研究发展中心FL-21风洞和荷兰代尔夫特大学TST-27风洞进行,采用表面测压和尾排型阻测量技术。试验结果的对比分析表明,有弯度椭圆翼型的升力和力矩特性优于无弯度椭圆翼型,而阻力特性和最大升阻比劣于无弯度椭圆翼型。试验结果为旋转机翼飞机主机翼翼型的选取提供了参考。     

Design,manufacturing, and flight testing of a fixed wing micro air vehicle with Zimmerman planform

An optimized and comprehensive method is used to design and manufacture a fixed wing micro air vehicle (MAV) with Zimmerman planform. The design process includes four stages which are the specification of the flight mission, determination of the best aspect ratio, identification of the optimum wing loading and thrust loading values, and estimation of the weight of the structural components of the MAV. To do this, various statistical and analytical methods are utilized. Based on an aerodynamic analysis, the results show that an optimum aspect ratio that maximizes the performance of the Zimmerman MAV for a well-defined cruise speed is determined. Considering six possible flights, a constraint analysis is performed and an optimum wing loading value is determined. It is shown that the computational method is beneficial to determine the exact masses for the structural components including the wing, fuselage, and vertical tail. Using the 3D panel method, the determination of the shape of the reflexed airfoil for the MAV is successfully done by minimizing the drag force and the angle of attack to use less powerful motor and avoid any stall effect, respectively. A stability analysis is then performed to check the safe flight of the designed vehicle. During test flight, the results show that the designed Zimmerman MAV satisfies the pre-defined specification. The final characteristics of the manufactured MAV are: wingspan of 44 cm, weight of 450 g, aspect ratio of 1.51, cruise speed of 20 m/s, and flight endurance of 20 min.     

Efficient unsteady aerodynamic loads prediction based on nonlinear system identification and proper orthogonal decomposition

In the present work, an efficient surrogate-based framework is developed for the prediction of motion-induced surface pressure fluctuations and integral force and moment coefficients. The model construction is realized by performing forced-motion computational fluid dynamics (CFD) simulations, while the result is processed via the proper orthogonal decomposition (POD) to obtain the predominant flow modes. Subsequently, a nonlinear system identification is carried out with respect to the applied excitation and the resulting POD coefficients. For the input/output model identification task, a recurrent local linear neuro-fuzzy approach is employed in order to capture the linear and nonlinear characteristics of the dynamic system. Once the reduced-order model (ROM) is trained, it can substitute the flow solver within unsteady aerodynamic or aeroelastic simulation frameworks for a given configuration at fixed freestream conditions. For demonstration purposes, the ROM approach is applied to the LANN wing in high subsonic and transonic flow. Due to the characteristic lambda-shock system, the unsteady aerodynamic surface pressure distribution is dominated by nonlinear effects. Numerical investigations show a good correlation between the results obtained by the ROM methodology in comparison to the full-order CFD solution. In addition, the surrogate approach yields a significant speed-up regarding unsteady aerodynamic calculations, which is beneficial for multidisciplinary computations.     

A new frequency domain based approach for a nonlinear aeroelasticity analysis

In this paper, a new frequency-domain based approach for the investigation of aeroelasticity problems is introduced that is capable of handling both linear and nonlinear problems. This approach is based on coupling a conceptual method used in a structural dynamic analysis and an optimum equivalent linear frequency response function (OELF). Additionally, a new criterion for determining the flutter speed and the instability of nonlinear systems is introduced that is based on the condition number of the aeroelastic matrices. Due to the global nature of the condition number, the new criterion proves to be efficient and simple to use. To examine the efficiency of the new technique, a two-dimensional nonlinear airfoil with an unsteady aerodynamic model is considered.     

考虑几何非线性的复合材料机翼气动弹性分析

本文研究结构几何非线性与气动力非平面效应对大展弦比复合材料机翼的气动弹性行为的影响．将非线性有限元法与曲面涡格法结合,计算机翼静气动弹性变形;通过曲面偶极子格网法结合静气动弹性平衡位置处的结构切线刚度,建立气动弹性方程并求解得到机翼颤振速度．针对板模型机翼,分析了迎角对机翼几何非线性气动弹性特性的影响．结果表明：本文复合材料板模型机翼的颤振形式不受水平弯曲模态影响,属于经典弯扭颤振;在几何非线性的影响下,机翼扭转频率随结构变形增大而明显减小,颤振速度随迎角增大而减小．