Wings In Subsonic Flow Research Articles

An Improved Approach for Reducing the Dimensionality of Wing Aerodynamic Optimization Considering Longitudinal Stability

The wing aerodynamic shape optimization is a typical high-dimensional problem with numerous independent design variables. Researching methods to reduce the dimensionality of optimization from the perspective of aerodynamic characteristics is necessary. One traditional aerodynamic-based approach decouples the wing’s camber and thickness according to the thin airfoil theory, but it has limitations due to unclear application scope and effectiveness. This paper proposes an improved approach that determines the values of certain thickness variables based on a data-driven aerodynamic characteristics model before optimization, which considers longitudinal stability. By reducing the number of design variables, the dimensionality of optimization is decreased effectively. The derivation of the improved approach is accomplished through the design of experiments, parametric modeling, computational fluid dynamics, and sensitivity analysis. The effectiveness of the improved approach is validated by applying it to the aerodynamic optimization of an ONERA-M6 wing in subsonic flow based on the surrogate-based optimization algorithm. The results demonstrate that the improved approach significantly accelerates the optimization process while maintaining global effectiveness.

On the Incipient Indicial Lift of Thin Wings in Subsonic Flow: Acoustic Wave Theory with Unsteady Three-Dimensional Effects

Enhanced approximate expressions for the incipient indicial lift of thin wings in subsonic potential flow are presented in this study, featuring explicit analytical corrections for the unsteady downwash. Lifting-line and acoustic-wave theories form the basis of the method, within an effective synthesis of the governing physics, which grants a consistent generalised framework and unifies previous works. The unsteady flow perturbation consists of a step-change in angle of attack or a vertical sharp-edged gust. The proposed model is successfully evaluated against numerical results in the literature for the initial airload development of elliptical and rectangular wings with a symmetric aerofoil, considering several aspect ratios and Mach numbers. While nonlinear downwash and compressibility terms demonstrate marginal (especially for the case of a travelling gust), both linear and nonlinear geometrical effects from a significant taper ratio, sweep angle or curved leading-edge are found to be more important than linear downwash corrections (which are crucial for the circulation growth at later times instead, along with linear compressibility corrections). The present formulae may then be used as a rigorous reduced-order model for validating higher-fidelity tools and complex simulations in industrial practice, as well as for estimating parametric sensitivities of unsteady aerodynamic loads within the preliminary design of aircraft wings in the subsonic regime.

Nonlinear dynamics of Z-shaped morphing wings in subsonic flow

Morphing wing aircraft have generated increasing interest in recent years owing to their ability to alter the shape and configuration of the wings to retain optimum flight performance under different flight conditions. However, while theoretical approaches have greatly advanced our understanding of the nonlinear vibrational characteristics of morphing wings during the morphing process, little effort has been made to verify the results of theoretical studies based on corresponding experimental results. The present work addresses this issue by first investigating the nonlinear dynamic behaviors of Z-shaped morphing wings during the morphing process in subsonic flow based on thin airfoil theory under ideal incompressible fluid conditions. First, the steady aerodynamic lift on the morphing wing is derived and the nonlinear partial differential equations governing the morphing wing motion are established. The influence of the folding angle on the nonlinear responses of the morphing wing is investigated via numerical simulations. Then, the aeroelastic characteristics of the morphing wing, including the flutter displacements of edge points on the outer plate of the wing, are investigated using the computational fluid dynamics module in ANSYS. Finally, the results of theoretical analysis are verified by experiments conducted with a corresponding Z-shaped morphing wing model.

Multifidelity Sensitivity Study of Subsonic Wing Flutter for Hybrid Approaches in Aircraft Multidisciplinary Design and Optimisation

A comparative sensitivity study for the flutter instability of aircraft wings in subsonic flow is presented, using analytical models and numerical tools with different multidisciplinary approaches. The analyses build on previous elegant works and encompass parametric variations of aero-structural properties, quantifying their effect on the aeroelastic stability boundary. Differences in the multifidelity results are critically assessed from both theoretical and computational perspectives, in view of possible practical applications within airplane preliminary design and optimisation. A robust hybrid strategy is then recommended, wherein the flutter boundary is obtained using a higher-fidelity approach while the flutter sensitivity is computed adopting a lower-fidelity approach.

Extension of analytical indicial aerodynamics to generic trapezoidal wings in subsonic flow

Analytical indicial aerodynamic functions are calculated for several trapezoidal wings in subsonic flow, with a Mach number 0.3 ≤ Ma ≤ 0.7. The formulation herein proposed extends well-known aerodynamic theories, which are limited to thin aerofoils in incompressible flow, to generic trapezoidal wing planforms. Firstly, a thorough study is executed to assess the accuracy and limitation of analytical predictions, using unsteady results from two state-of-the-art computational fluid dynamics solvers as cross-validated benchmarks. Indicial functions are calculated for a step change in the angle of attack and for a sharp-edge gust, each for four wing configurations and three Mach numbers. Then, analytical and computational indicial responses are used to predict dynamic derivatives and the maximum lift coefficient following an encounter with a one-minus-cosine gust. It is found that the analytical results are in excellent agreement with the computational results for all test cases. In particular, the deviation of the analytical results from the computational results is within the scatter or uncertainty in the data arising from using two computational fluid dynamics solvers. This indicates the usefulness of the developed analytical theories.

Semi-analytical static aeroelastic analysis and response of flexible subsonic wings

A semi-analytical model for the combined static aeroelastic analysis and response of flexible subsonic wings is presented. Based on a general variational formulation, the proposed aeroelastic models allow any arbitrary distribution of the flexible wing’s physical properties and provide with a continuous solution of the wing’s displacement along the span, as suitable for parametric optimisation studies within preliminary wing design. Numerical results which provide sound insights on the behaviour of a flexible wing in subsonic flow are obtained and critically discussed for all aeroelastic models, with respect to the most relevant aerodynamic and structural parameters as well as the computational efficiency. Different degrees of fidelity are considered for the aerodynamic modelling and the formulated modified strip theory is shown to be an excellent compromise between the lower complexity of standard strip theory and the higher accuracy of lifting line theory. The modified strip theory is hence suggested as a general and effective steady aerodynamic tool for the multidisciplinary design and optimisation of flexible wings in the subsonic regime.

English

The third article of this series continues to deal with the calculation of the aerodynamic unsteady forces on lifting surfaces. Here we present how the theory of oscillating wing in subsonic flow can be applied to the aerodynamic response to certain kinds of wing motions or gusts.

Aeroelastic Stability and Response of Composite Swept Wings in Subsonic Flow Using Indicial Aerodynamics

In this study, the aeroelastic stability and response of an aircraft swept composite wing in subsonic compressible flow are investigated. The composite wing was modeled as an anisotropic thin-walled composite beam with the circumferentially asymmetric stiffness structural configuration to establish proper coupling between bending and torsion. Also, the structural model consists of a number of nonclassical effects, such as transverse shear, material anisotropy, warping inhibition, nonuniform torsional model, and rotary inertia. The finite state form of the unsteady aerodynamic loads have been modeled based on the indicial aerodynamic theory and strip theory in the subsonic compressible flow. Novel Mach dependent exponential approximations of the indicial aerodynamic functions have been developed. The extended Galerkin’s method was used to construct the mass, stiffness, and damping matrices of the nonconservative aeroelastic system. Eigen analysis of the system was performed to obtain the aeroelastic instability (divergence and flutter) boundaries. Also, solving the equations of motion in the time domain leads to the aeroelastic response of wing in different flight speeds. The obtained results are compared with the available results in the literature, which reveals an excellent agreement. The numerical results obtained in this article seek to clarify the effects of geometrical and material couplings and flight Mach number on the aeroelastic instability and response of composite wings in subsonic compressible flow.

Aeroelastic Investigation of Composite Plate Wing in Subsonic Flow

Aeroelastic phenomena including divergence and flutter are investigated for composite plate wing without sweep angle. Suitable derivations of aerodynamic loads have been developed for calculating both flutter speed (UF) and divergence speed (UD). Equivalent plate method is used for structural modeling of composite plate wing. Approximate solutionsfrom the linearized formulation are obtained for studying steady and unsteady aerodynamic loadings on harmonically oscillating wing in subsonic flow. The wing is divided into element panels on which lift distributions are represented by concentrated lift forces. The pressure coefficient distribution is calculated at root chord using steady and unsteady aerodynamic modeling. The span wise distribution of lift coefficient is calculated from the pressure coefficient. The numerical results for both UF and UD show good agreement with previous works. Finally a parametric study of the effect of composite fiber’s orientation on both UF and UD is carried out.

Asymptotic Analysis of Passive Nonlinear Suppression of Aeroelastic Instabilities of a Rigid Wing in Subsonic Flow

We study theoretically passive suppression of aeroelastic instabilities of a rigid wing in subsonic flow with an essentially nonlinear attachment. The analysis is performed by constructing a reduced-order model, applying complexification/averaging and slow-fast partition of the dynamics. The resulting slow-flow dynamics is then analyzed by singular perturbation. We fully recover computational and experimental results for this system reported in previous works and prove the existence of trivial/nontrivial stable attractors as well as relaxation oscillations in the slow-flow dynamics. These, in turn, correspond to complete/partial instability suppression, and (periodic or quasi-periodic) strongly modulated responses in the full-order dynamics. Moreover, we demonstrate the existence of Shilnikov bifurcations in the dynamics. The analysis of the slow-flow dynamics is confirmed by numerical simulations of the full-order system. The methodology developed in this work can be used in a predictive capacity when ap...

이차원 타원형 날개꼴의 실속제어에서 간헐제트 브로잉의 효과

이차원 타원형 날개꼴에서 펄스제트 브로잉에 의한 박리 제어 효과에 대하여 연구하였다. 박리 유동의 능동제어기술 개발을 위하여 압축공기를 사용하는 연속제트/간헐제트 엑츄에이터를 설계제작하여 타원형 날개 풍동 실험 모델에 장착하였다. 아음속 유동에서 날개 주위 유동장의 PIV 측정과 유동의 가시화을 통하여 간헐제트 브로잉의 타원형 날개의 실속제어 효과와 실용성에 대해 실험연구를 수행하였다. PIV 실험 결과 제트 브로잉에 의해 난류 후류 영역과 박리 버블의 크기를 현저하게 감소시킴으로써 박리제어가 가능함을 보였다. 간헐제트는 연속제트보다 박리제어에 보다 효과적이었다. 간헐제트의 주파수를 증가시키면 보다 높은 받음각에 이르기까지 난류 박리 후류를 효과적으로 억제할 수 있었다. This paper explored the effects of separation control through the use of pulsating jet blowing on a two dimensional elliptical airfoil. To develop an active control technique of flow separation, a flow control actuator utilizing continuous/pulsed jet of pressurized air was designed and installed in a wind tunnel testing model of elliptic wing. PIV measurement and flow visualization of the wing near field were conducted to access the feasibility and effectiveness of the pulsed jet blowing on controlling the stall of the elliptical wing in subsonic flow. PIV experimental results show that separation control can provide significant reduction in turbulent flow wake and separation bubbles by jet blowing. The pulsating jet blowing is more effective on the separation control than continuous one. Increased jet frequency suppressed the turbulent separated flow wake effectively at even higher AOAs.

Ｌａｔｅｒａｌ Ｂｌｏｗｉｎｇによる次世代ＳＳＴ用改良アロー翼の亜音速領域における空力特性向上の研究

An experimental study on the improvement of aerodynamic characteristics of a modified arrow wing by applying lateral blowing in subsonic flow has been conducted. The modified arrow wing, which is one of the baseline configurations of the proto-type of next-generation SST, is selected for the experiments. The testing model is the combination of a body of a circular cylinder and ogive and a modified arrow wing with aspect ratio of 1.91. The lateral blowing is realized by injecting a pair of sonic jets parallel to the trailing edge of the wing. The experiments have been conducted in the transonic wind tunnel of ISAS under the testing conditions of free-stream Mach number M∞=0.3, 0.4 and 0.5, Reynolds number Re=4.77×106∼7.34×106, angle of attack α=−15°∼30° and jet momentum coefficient Cμ=0.0124∼0.0312. The results show that the CL and L/D is increased by lateral blowing while CD is slightly increased for positive α. The results suggest that the lateral blowing can be useful for the improvement of aerodynamic characteristics of the arrow wing in subsonic flow.

Experimental study of the turbulent boundary layer on a transport wing in subsonic flow

The upper-surface boundary layer on a transport wing model was extensively surveyed with miniature yaw probes at a subsonic cruise condition. Significant variation in flow direction with distance from the surface was observed near the trailing edge, everywhere except at the wing root and tip. Values of streamwise displacement thickness, normalized by the local chord, were maximum at the highly loaded midsemispan stations. The data are intended to provide a test case for computational fluid dynamics code validation.

Measurements on an oscillating 70-deg delta wing in subsonic flow

A series of low-speed wind tunnel tests on a 70-deg sharp leading-edged delta wing at both static and dynamic conditions were performed to investigate the aerodynamic forces and moments. Forces and moments were obtained from a six-component internal strain-gauge balance. Large amplitude dynamic motion was produced by sinusoidally oscillating the model over a range of reduced frequencies. Static results compared well with previous experimental findings. Significant Reynolds number effects were present in the experimental measurements. Reynolds number effects are reduced, but still present when a sharper leading-edge delta wing was tested. Large hysteresis loops and a delay in dynamic stall were seen in the dynamic data. Dynamic forces and moments were a strong function of reduced frequency. Nonzero sideslip created complex rolling moment and lift behavior due to asymmetric vortex bursting.

Numerical and experimental determination of secondary separation on delta wings in subsonic flow

A quasi-three-dimensional boundary layer method for conical inviscid flows is presented. The model was developed to characterize the flow fields over slender delta wings, particularly the shed vortex sheet. A steady, incompressible, laminar boundary layer is assumed and a solution is obtained with the Smith (1966) finite difference code. Predictions are compared with oil flow patterns and surface pressure measurements for 74 and 80 deg delta wings at 0-20 deg angles of attack. The model is capable of accurately predicting the secondary separation lines. Inviscid velocities derived from panel methods lead, however, to inaccurate pressure distributions.

The theory of oscillating thick wings in subsonic flow. Lifting line theory

On the basis of the fundamental solutions method developped by the author in some previous papers, in this paper a theory of oscillating thick wings in subsonic flow is given. In this way the representation of the general solution for arbitrary wings and the integral equation of the problem are obtained. The known solutions for the stationary motion and the plane problem are regained as particular cases. General solutions and integral equations for the incompressible fluid and for the two and three dimensional motion at Mach number one are also put into evidence. In the last part of the paper the theory of oscillating lifting line is given.

ダブルストリップ法による亜音速流中の非定常く形翼の圧力分布計算

An improved numerical method is presented for calculating the load distribution on oscillating rectangular wings in subsonic flow. The wing is divided into many chordwise strips. In the strips containing control point, the kernel function is treated in the form of expansion series and spanwise integration is performed first to get a chordwise logarithmic singularity. Through accurate evaluation the singularity, present method gives quick convergence and excellent computational efficiency to other current methods.

Induced drag and lift of wing by the piecewise continuous kernel function method

T piecewise continuous kernel function method is extended to compute induced drag on three dimensional wings in subsonic flow The method was used to compute induced drag and lift on a wide number of wings, and the results compared very well with other existing methods Trie method was applied to compare induced drag and lift of nontwisted planar swept forward and back wings with the equivalent M or W type configuration It was found that the spanwise load distribution and the induced drag are in fluenced by the sweep angle of the lifting surface. Fur therrriore, it was found that the spanwise pressure distribution of the M wing type offers some advantages that can be used to improve the configuration performance characteristics as one wishes

A new solution method for lifting surfaces in subsonic flow

A simple method for calculating the unsteady aerodynamic loadings on harmonically oscillating thin wings in subsonic flow has been developed. The method is based on a concept of concentrated lift forces. The wing is divided into the element surfaces on which lift distributions are represented by single concentrated lift forces. Since the procedure does not include any quadratures, it can be applied easily to calculate the unsteady aerodynamic loadings on complex planform wings even when they have partial span control surfaces. Numerical calculations are carried out for various wing geometries and compared with other analyses and experiments.

Doublet lattice method — schemes for CPU time reduction

Two simple techniques — CTSA and SILT — to reduce the CPU time in using the doublet lattice method to calculate the steady or unsteady airloads on wings in subsonic flow are discussed in this paper. These are based on the fact that some of the elements in the aerodynamic influence matrix are repeatedly occurring and the far off panels have negligible contribution to the downwash at a given panel. The methods are illustrated through an example of a rectangular wing oscillating in bending mode. It is shown that the application of CTSA leads to a CPU time reduction of the order of 50% without any loss of accuracy. However, SILT could be used only at the cost of some accuracy in the final results, and time reduction is comparatively small as compared to that obtained with CTSA.