Unsteady aerodynamic reduced-order modeling of an aeroelastic wing using arbitrary mode shapes

Computational fluid dynamics (CFD) based unsteady aerodynamic reduced-order model (ROM) can offer significant improvements to the efficiency of transonic aeroelastic analysis. To construct a ROM based on mode shapes, one run of CFD solver is needed to compute aerodynamic responses corresponding to mode excitations. When mode shapes change with structure, another run of the CFD solver is required to construct the new ROM. The typically large computational cost associated with repeated runs of the CFD solver impedes the application of existing unsteady aerodynamic reduced-order modeling methods to transonic aeroelastic design optimization and aeroelastic uncertainty analysis. This paper demonstrates a method that can replace the CFD solver used in the process of existing unsteady aerodynamic reduced-order modeling. It can produce aerodynamic responses corresponding to mode excitations for arbitrary mode shapes within a few seconds. Computational cost can be reduced by two orders of magnitude using the mode excitations and the corresponding aerodynamic responses computed by the method to construct the ROMs used for flutter analyses in aeroelastic design optimization or aeroelastic uncertainty analysis in transonic regime compared with the existing unsteady aerodynamic reduced-order modeling methods. Results show that the method can accurately produce the aerodynamic responses corresponding to the mode excitations and predict the flutter characteristics of AGARD 445.6 wings root-attached in three different ways.     

Experimental study on interaction of aerodynamics with flexible wings of flapping vehicles in hovering and cruise flight

Flapping wings are promising lift and thrust generators, especially for very low Reynolds numbers. To investigate aeroelastic effects of flexible wings (specifically, wing’s twisting stiffness) on hovering and cruising aerodynamic performance, a flapping-wing system and an experimental setup were designed and built. This system measures the unsteady aerodynamic and inertial forces, power usage, and angular speed of the flapping wing motion for different flapping frequencies and for various wings with different chordwise flexibility. Aerodynamic performance of the vehicle for both no wind (hovering) and cruise condition was investigated. Results show how elastic deformations caused by interaction of inertial and aerodynamic forces with the flexible structure may affect specific power consumption. This information was used here to find a more suitable structural design. The best selected design in our tests performs up to 30% better than others (i.e., less energy consumption for the same lift or thrust generation). This measured aerodynamic information could also be used as a benchmarking data for unsteady flow solvers.     

The aerodynamic forces and pressure distribution of a revolving pigeon wing

The aerodynamic forces acting on a revolving dried pigeon wing and a flat card replica were measured with a propeller rig, effectively simulating a wing in continual downstroke. Two methods were adopted: direct measurement of the reaction vertical force and torque via a forceplate, and a map of the pressures along and across the wing measured with differential pressure sensors. Wings were tested at Reynolds numbers up to 108,000, typical for slow-flying pigeons, and considerably above previous similar measurements applied to insect and hummingbird wing and wing models. The pigeon wing out-performed the flat card replica, reaching lift coefficients of 1.64 compared with 1.44. Both real and model wings achieved much higher maximum lift coefficients, and at much higher geometric angles of attack (43°), than would be expected from wings tested in a windtunnel simulating translating flight. It therefore appears that some high-lift mechanisms, possibly analogous to those of slow-flying insects, may be available for birds flapping with wings at high angles of attack. The net magnitude and orientation of aerodynamic forces acting on a revolving pigeon wing can be determined from the differential pressure maps with a moderate degree of precision. With increasing angle of attack, variability in the pressure signals suddenly increases at an angle of attack between 33° and 38°, close to the angle of highest vertical force coefficient or lift coefficient; stall appears to be delayed compared with measurements from wings in windtunnels.     

Passage of a subsonic flow around V-shaped wings

In view of the problems involved in the design of hypersonic aircraft great interest has arisen in recent years as to the behavior of wings in fast supersonic flows. Two main approaches have been used: a study of hypersonic flow around traditional wings, and a search for new configurations with optimum aerodynamic properties. Aerodynamic [1, 2], heat-transfer [3], and stability investigations (for V-shaped wings in super- and hypersonic flows) belong to the latter category. Before attaining supersonic flight the aircraft has to overcome the range of subsonic velocities. In this connection it is important to study flow around V-shaped wings at M < 1. Little research has been devoted to flow around such configurations at subsonic velocities, principal attention having been directed at the study of rapid flow around aircraft configurations with V-shaped wings or tails. The results of analytical and numerical calculations allowing for the interference of transient aerodynamic forces acting on a V-shaped and mutiple-fin tail group in combination with the fuselage were presented in [4, 5]. An experimental study of V-shaped wings as regards the influence of the wing dihedral angle on the aerodynamic characteristics of a model aircraft was presented in [6, 7].Translated from Zhurnal Prikladnoi Mekhaniki i Technicheskoi Fiziki, No. 4, pp. 102–106, July–August, 1975.     

Effects of camber angle on aerodynamic performance of flapping-wing micro air vehicle

This study investigates the unsteady aerodynamic characteristics of the cambered wings of a flapping-wing micro air vehicle (FW-MAV) in hover. A three-dimensional fluid–structure interaction solver is developed for a realistic modeling of large-deforming wing structure and geometry. Cross-validation is conducted against the experimental results obtained also in the present study to establish more accurate analyses of cambered wings. An investigation is carried out on the unsteady vortex structures around the wings caused by the passive twisting motion. A parametric study is then conducted to evaluate the aerodynamic performance with respect to the camber angle at three different flapping frequencies including normal operating conditions. The camber angles producing the largest thrust and highest propulsive efficiency are estimated at each flapping frequency, and their effects on aerodynamic performance are analyzed in terms of the stroke phase. The timing and magnitude of the passive twisting motion, which are dependent on the camber angle at the operating frequency, greatly affects the unsteady vortex structure. Consequently, the camber angle designed at the operating frequency plays a key role in enhancing the aerodynamic performance of FW-MAVs.     

Engine Modeling for Small-Disturbance-CFD Related to Aircraft Flutter Investigations

Aeroelastic behavior of aircraft is significantly affected by the presence of engines mounted under the wings. Powered engines influence the unsteady aerodynamics on the one hand and lead to additional unsteady forces due to thrust vector oscillations on the other hand. This work focuses on the incorporation of aerodynamic engine effects into a small disturbance CFD framework to enhance the modeling accuracy of unsteady aerodynamics of aircraft. The effects are numerically modeled by mimicking physically reasonable flow conditions at the intake and nozzle planes of the engine nacelle. Subsequently, the influence of the engine effects on the flutter behavior of an aircraft is studied employing the small-disturbance-CFD-based flutter analysis. The basis for the investigation is the Common Research Model, which represents a modern transonic commercial airliner with a cruise Mach number of 0.85. Two configurations are considered: aircraft with passive engines represented by flow-through nacelles and aircraft with powered engines, where the novel small disturbance engine model is applied. The results are compared in terms of the flutter trends and the predicted flutter boundary. Furthermore, the impact of the modal induced thrust oscillations on the aeroelastic behavior of the aircraft is discussed.     

Experimental investigation of the effect of chordwise flexibility on the aerodynamics of flapping wings in hovering flight

Ornithopters or mechanical birds produce aerodynamic lift and thrust through the flapping motion of their wings. Here, we use an experimental apparatus to investigate the effects of a wing's twisting stiffness on the generated thrust force and the power required at different flapping frequencies. A flapping wing system and an experimental set-up were designed to measure the unsteady aerodynamic and inertial forces, power usage and angular speed of the flapping wing motion. A data acquisition system was set-up to record important data with the appropriate sampling frequency. The aerodynamic performance of the vehicle under hovering (i.e., no wind) conditions was investigated. The lift and thrust that were produced were measured for different flapping frequencies and for various wings with different chordwise flexibilities. The results show the manner in which the elastic deformation and inertial flapping forces affect the dynamical behavior of the wing. It is shown that the generalization of the actuator disk theory is, at most, only valid for rigid wings, and for flexible wings, the power P varies by a power of about 1.0  of the thrust T. This aerodynamic information can also be used as benchmark data for unsteady flow solvers.     

A simulation-based study on longitudinal gust response of flexible flapping wings

Winged animals such as insects are capable of flying and surviving in an unsteady and unpredictable aerial environment. They generate and control aerodynamic forces by flapping their flexible wings. While the dynamic shape changes of their flapping wings are known to enhance the efficiency of their flight, they can also affect the stability of a flapping wing flyer under unpredictable disturbances by responding to the sudden changes of aerodynamic forces on the wing. In order to test the hypothesis, the gust response of flexible flapping wings is investigated numerically with a specific focus on the passive maintenance of aerodynamic forces by the wing flexibility. The computational model is based on a dynamic flight simulator that can incorporate the realistic morphology, the kinematics, the structural dynamics, the aerodynamics and the fluid–structure interactions of a hovering hawkmoth. The longitudinal gusts are imposed against the tethered model of a hovering hawkmoth with flexible flapping wings. It is found that the aerodynamic forces on the flapping wings are affected by the gust, because of the increase or decrease in relative wingtip velocity or kinematic angle of attack. The passive shape change of flexible wings can, however, reduce the changes in the magnitude and direction of aerodynamic forces by the gusts from various directions, except for the downward gust. Such adaptive response of the flexible structure to stabilise the attitude can be classified into the mechanical feedback, which works passively with minimal delay, and is of great importance to the design of bio-inspired flapping wings for micro-air vehicles.     

主动控制翼板抑制悬索桥颤振的研究

主动控制翼板是一种新型桥梁气动措施。本文基于非定常气动力理论，推演了安装主动控制翼板后作用在整个桥梁主梁单位长度上气动力表达式，从增加系统扭转阻尼的角度，研究了翼板主动扭转振动参数的选取。在此基础上，对某大跨悬索桥方案进行了二自由度颤振分析，结果表明：合理选取翼板的主动扭转振动参数，主动控制翼板能够有效地提高该桥的颤振稳定性。     

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.     

Experimental study of wings undergoing active root flapping and pitching

This paper presents the results of experiments carried out on mechanical wings undergoing active root flapping and pitching in the wind tunnel. The objective of the work is to investigate the effect of the pitch angle oscillations and wing profile on the aerodynamic forces generated by the wings. The experiments were repeated for a different reduced frequency, airspeed, flapping and pitching kinematics, geometric angle of attack and wing sections (one symmetric and two cambered airfoils). A specially designed mechanical flapper was used, modelled on large migrating birds. It is shown that, under pitch leading conditions, good thrust generation can be obtained at a wide range of Strouhal numbers if the pitch angle oscillation is adjusted accordingly. Consequently, high thrust was measured at both the lowest and highest tested Strouhal numbers. Furthermore, the work demonstrates that the aerodynamic forces can be sensitive to the Reynolds number, depending on the camber of the wings. Under pitch lagging conditions, where the effective angle of attack amplitude is highest, the symmetric wing was affected by the Reynolds number, generating less thrust at the lowest tested Reynolds value. In contrast, under pure flapping conditions, where the effective angle of attack amplitude was lower but still significant, it was the cambered wings that demonstrated Reynolds sensitivity.     

Numerical study of gas-cyclone airflow: an investigation of turbulence modelling approaches

A numerical study of unsteady single-phase vortical flow inside a cyclone is presented. Two different geometric configurations have been considered, with the goal of assessing several different turbulence modelling approaches for this class of problem. The models investigated include three Reynolds-averaged Navier–Stokes models: a commonly used two-equation eddy-viscosity model, a differential Reynolds stress model (DRSM) and an eddy-viscosity model sensitised to rotational and curvature (RC) effects which was recently developed and implemented into a commercial CFD (computational fluid dynamics) code by the authors. Results were also obtained using large eddy simulation (LES). The computational results are analysed and compared with available experimental data. The RC-sensitised eddy-viscosity model shows significant improvement over the standard eddy-viscosity model. The RC-sensitised model, DRSM and LES model predictions of the mean flowfield are in good agreement with the experimental data. The results suggest that curvature- and rotation-sensitive eddy-viscosity models may provide a practical alternative to more computationally intensive approaches.     

Using a Proper Orthogonal Decomposition representation of the aerodynamic forces for stochastic buffeting prediction

High-performance aircraft often suffer from the consequences of tail buffeting at moderate subsonic Mach numbers and medium to high angles of attack. The impact of the aircraft’s highly unsteady flow field on the tails can result in significant structural fatigue and degraded handling qualities. Various methods have been developed to predict tail buffeting. Stochastic response methods are among frequently used approaches. For such methods the size of the excitation data set can become an issue, especially when the auto- and cross-spectra of all available excitation signals on the configuration are considered. The present paper demonstrates how to modify stochastic tail buffeting prediction methods using Proper Orthogonal Decomposition (POD). The approach is based on the modal decomposition of the aerodynamic buffet excitation data set. It notably reduces the computational effort for structural response and loads prediction with limited losses in accuracy while using all power- and cross-spectra of the reduced dataset. The method was applied to the computational buffeting prediction for a generic configuration with double-delta wing and horizontal tail plane (HTP) over a wide range of angles of attack. It was shown that the POD-modes of the aerodynamic buffet excitation resembled the characteristics of configuration’s complex vortical flow field. The predicted structural response and loads converged well with increasing number of POD-modes. With the presented approach, the computational effort of stochastic tail buffeting prediction has been reduced by orders of magnitude compared to the case with the full aerodynamic buffet excitation data set.     

Mechanism of unsteady aerodynamic heating with sudden change in surface temperature

The characteristics and mechanism of unsteady aerodynamic heating of a transient hypersonic boundary layer caused by a sudden change in surface temperature are studied. The complete time history of wall heat flux is presented with both analytical and numerical approaches. With the analytical method, the unsteady compressible boundary layer equation is solved. In the neighborhood of the initial and final steady states, the transient responses can be expressed with a steady-state solution plus a perturbation series. By combining these two solutions, a complete solution in the entire time domain is achieved. In the region in which the analytical approach is applicable, numerical results are in good agreement with the analytical results, showing reliability of the methods. The result shows two distinct features of the unsteady response. In a short period just after a sudden increase in the wall temperature, the direction of the wall heat flux is reverted, and a new inflexion near the wall occurs in the profile of the thermal boundary layer. This is a typical unsteady characteristic. However, these unsteady responses only exist in a very short period in hypersonic flows, meaning that, in a long-term aerodynamic heating process considering only unsteady surface temperature, the unsteady characteristics of the flow can be ignored, and the traditional quasi-steady aerodynamic heating prediction methods are still valid.     

Numerical study of steady supersonic separated flow past spatial lifting systems

At the present, spatial lifting systems are usually calculated numerically using linear approximation. However, the practical application of such systems at moderate and large angles of incidence requires new approaches that allow for various nonlinear effects such as large disturbances, flow separation, and jumps in entropy across shock waves. The existing investigations [3, 4] generally cover only simple systems (bodies of revolution, wings, and so on). Here, a numerical method is proposed for investigating supersonic flows past complicated spatial systems. The method extends and continues the well-known methods widely used to solve analogous problems in subsonic aerodynamics [5, 6]. Some examples of the computation of the aerodynamic parameters for flows past wings and spatial lifting systems are also given.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 142–148, May–June, 1993.     

Investigation on the planform and kinematic optimization of bio-inspired nano air vehicles for hovering applications

Wing shape and kinematics of flapping wing nano air vehicles are two important factors in their design process. These factors require an optimal design in terms of decreasing the needed aerodynamic power. Since, insects are regarded as the best natural flier in hovering flight, seven of their wings are considered in order to determine the best wing shape for hovering applications. Because of the difference in the original bio-inspired shape of these wings, two scenarios are studied, namely, considering the same wingspan and same wing surface. Using the quasi-steady approximation to model the aerodynamic loads and a basic gradient approach to optimize the kinematics of the wing, the optimum Euler angles, required aerodynamic power, and hence the best wing shape for each scenario are analytically determined. The results show that the wing shape and surface strongly impact the aerodynamic characteristics and performances of the chosen wing shapes. It is demonstrated that the twisted parasite wing shape is a good candidate to minimize the required aerodynamic power during hovering. The strategy used in this analysis can be used to evaluate the performance of any realistic wing shape design and could provide a guideline for selecting the best wing shape and kinematics for flapping wing nano air vehicles with hovering capabilities.     

A check on the energy method of predicting blade transonic stall flutter

An improved structural dynamic model of an oscillating blade in two degrees of freedom is combined with an unsteady aerodynamic model for the transonic flow about a cascade with separation, which results in a coupled system. The system is solved in an iterative way between the two models. As a check on the current energy methods, the stall flutter boundaries for two real rotors are predicted by using the present method and the results are compared with the experiments and those predicted by using an energy method.     

Smoke visualization of free-flying bumblebees indicates independent leading-edge vortices on each wing pair

It has been known for a century that quasi-steady attached flows are insufficient to explain aerodynamic force production in bumblebees and many other insects. Most recent studies of the unsteady, separated-flow aerodynamics of insect flight have used physical, analytical or numerical modeling based upon simplified kinematic data treating the wing as a flat plate. However, despite the importance of validating such models against living subjects, few good data are available on what real insects actually do aerodynamically in free flight. Here we apply classical smoke line visualization techniques to analyze the aerodynamic mechanisms of free-flying bumblebees hovering, maneuvering and flying slowly along a windtunnel (advance ratio: −0.2 to 0.2). We find that bumblebees, in common with most other insects, exploit a leading-edge vortex. However, in contrast to most other insects studied to date, bumblebees shed both tip and root vortices, with no evidence for any flow structures linking left and right wings or their near-wakes. These flow topologies will be less efficient than those in which left and right wings are aerodynamically linked and shed only tip vortices. While these topologies might simply result from biological constraint, it is also possible that they might have been specifically evolved to enhance control by allowing left and right wings to operate substantially independently. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Method of calculating unsteady aerodynamic characteristics of a lifting surface at high subsonic speed

A method is presented for calculating the unsteady aerodynamic characteristics of harmonically oscillating thin wings traveling at high subsonic speed. The medium is assumed ideal. The aerodynamic coefficients are expressed in terms of the rotational derivatives, which are determined for a Strouhal number of zero. The calculation of the rotational derivatives of the aerodynamic coefficients in a compressible medium reduces to the conversion of the corresponding characteristics of a transformed wing, determined in an incompressible medium for altered boundary conditions. To calculate the aerodynamic characteristics of the transformed wing in the incompressible medium we use a technique based on replacement of the lifting surface by a system of discrete unsteady vortices. The problem is solved in general form, and together with the new relations for the rotational derivatives with dots we derive the known formulas for the rotational derivatives without dots.     

Numerical simulation of flapping‐wing insect hovering flight at unsteady flow

A computational fluid dynamics (CFD) analysis was conducted to study the unsteady aerodynamics of a virtual flying bumblebee during hovering flight. The integrated geometry of bumblebee was established to define the shape of a three‐dimensional virtual bumblebee model with beating its wings, accurately mimicking the three‐dimensional movements of wings during hovering flight. The kinematics data of wings documented from the measurement to the bumblebee in normal hovering flight aided by the high‐speed video. The Navier–Stokes equations are solved numerically. The solution provides the flow and pressure fields, from which the aerodynamic forces and vorticity wake structure are obtained. Insights into the unsteady aerodynamic force generation process are gained from the force and flow‐structure information. The CFD analysis has established an overall understanding of the viscous and unsteady flow around the virtual flying bumblebee and of the time course of instantaneous force production, which reveals that hovering flight is dominated by the unsteady aerodynamics of both the instantaneous dynamics and also the past history of the wing. A coherent leading‐edge vortex with axial flow and the attached wingtip vortex and trailing edge vortex were detected. The leading edge vortex, wing tip vortex and trailing edge vortex, which caused by the pressure difference between the upper and the lower surface of wings. The axial flow, which include the spanwise flow and chordwise flow, is derived from the spanwise pressure gradient and chordwise pressure gradient, will stabilize the vortex and gives it a characteristic spiral conical shape. Copyright © 2006 John Wiley & Sons, Ltd.