Aeroelastic inverse: Estimation of aerodynamic loads during large amplitude limit cycle oscillations

This paper presents an algorithm to compute the aerodynamic forces and moments of an aeroelastic wing undergoing large amplitude heave and pitch limit cycle oscillations. The technique is based on inverting the equations of motion to solve for the lift and moment experienced by the wing. Bayesian inferencing is used to estimate the structural parameters of the system and generate credible intervals on the lift and moment calculations. The inversion technique is applied to study the affect of mass coupling on limit cycle oscillation amplitude. Examining the force, power, and energy of the system, the reasons for amplitude growth with wind speed can be determined. The results demonstrate that the influence of mass coupling on the pitch–heave difference is the driving factor in amplitude variation. The pitch–heave phase difference not only controls how much aerodynamic energy is transferred into the system but also how the aerodynamic energy is distributed between the degrees of freedom.     

Subcritical, nontypical and period-doubling bifurcations of a delta wing in a low speed wind tunnel

Limit Cycle Oscillations (LCOs) involving Delta wings are an important area of research in modern aeroelasticity. Such phenomena can be the result of geometric or aerodynamic nonlinearity. In this paper, a flexible half-span Delta wing is tested in a low speed wind tunnel in order to investigate its dynamic response. The wing is designed to be more flexible than the models used in previous research on the subject in order to expand the airspeed range in which LCOs occur. The experiments reveal that this wing features a very rich bifurcation behavior. Three types of bifurcation are observed for the first time for such an aeroelastic system: subcritical bifurcations, period-doubling/period-halving and nontypical bifurcations. They give rise to a great variety of LCOs, even at very low angles of attack. The LCOs resulting from the nontypical bifurcation display Hopf-type behavior, i.e. having fundamental frequencies equal to one of the linear modal frequencies. All of the other LCOs have fundamental frequencies that are unrelated to the underlying linear system modes.     

PrandtlPlane Joined Wing: Body freedom flutter,limit cycle oscillation and freeplay studies

Dynamic aeroelastic behavior of a joined-wing PrandtlPlane configuration is investigated herein. The baseline model is obtained from a configuration previously designed by partner universities through several multidisciplinary optimizations and ad hoc analyses, including detailed studies on the layout of control architecture. An equivalent structural model has then been adopted to qualitatively retain similar aeroelastic properties.Flutter and post-flutter regimes, including limit cycle oscillations (LCOs), are studied. A detailed analysis of the energy transfer between fluid and structure is carried out; the areas in which energy is extracted from the fluid are identified to gain insights on the mechanism leading to the aeroelastic instability. Starting from an existing design of control surfaces on the baseline configuration, freeplay is also considered and its effects on the aeroelastic stability properties of the joined-wing system are investigated for the first time.Both cantilever and free flying configurations are analyzed. Fuselage inertial effects are modeled and the aeroelastic properties are studied considering plunging and pitching rigid body modes. For this configuration a positive interaction between elastic and rigid body modes yields a flutter-free design (within the range of considered airspeeds).To understand the sensitivity of the system and gain insight, fuselage mass and moment of inertia are selectively varied. For a fixed pitching moment of inertia, larger fuselage mass favors body freedom flutter. When the moment of inertia is varied, a change of critical properties is observed. For smaller values the pitching mode becomes unstable, and coalescence is observed between pitching and the first elastic mode. Increasing pitching inertia, the above criticality is postponed; meanwhile, the second elastic mode becomes unstable at progressively lower speeds. For larger inertial values “cantilever” flutter properties, having coalescence of first and second elastic modes, are recovered.     

Transonic limit cycle oscillation behavior of an aeroelastic airfoil with free-play

The limit cycle oscillation (LCO) behaviors of an aeroelastic airfoil with free-play for different Mach numbers are studied. Euler equations are adopted to obtain the unsteady aerodynamic forces. Aerodynamic and structural describing functions are employed to deal with aerodynamic and structural nonlinearities, respectively. Then the flutter speed and flutter frequency are obtained by V-g method. The LCO solutions for the aeroelastic airfoil obtained by using dynamically linear aerodynamics agree well with those obtained directly by using nonlinear aerodynamics. Subsequently, the dynamically linear aerodynamics is assumed, and results show that the LCOs behave variously in different Mach number ranges. A subcritical bifurcation, consisting of both stable and unstable branches, is firstly observed in subsonic and high subsonic regime. Then in a narrow Mach number range, the unstable LCOs with small amplitudes turn to be stable ones dominated by the single degree of freedom flutter. Meanwhile, these LCOs can persist down to very low flutter speeds. When the Mach number is increased further, the stable branch turns back to be unstable. To address the reason of the stability variation for different Mach numbers at small amplitude LCOs, we find that the Mach number freeze phenomenon provides a physics-based explanation and the phase reversal of the aerodynamic forces will trigger the single degree of freedom flutter in the narrow Mach number range between the low and high Mach numbers of the chimney region. The high Mach number can be predicted by the freeze Mach number, and the low one can be estimated by the Mach number at which the aerodynamic center of the airfoil lies near its elastic axis. Influence of angle of attack and viscous effects on the LCO behavior is also discussed.     

Numerical study of the dependence of the critical flutter speed and time of a plate on rheological parameters

The nonlinear flutter of some aircraft elements is modeled. A viscoelastic model is used. Numerical algorithms for solving integro-differential equations are developed. The critical flutter speed and time for a viscoelastic plate are determined __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 97–104, June 2008.     

On the role of thickness ratio and location of axis of rotation in the flat plate motions

Wind tunnel experiments were performed to characterize the flow-induced rotations and pitching of various flat plates as a function of the thickness ratio and the location of the axis of rotation. High-resolution telemetry, laser tachometer, and hotwire were used to get time series of the plates motions and the signature of the wake flow at a specific location. Results show that small axis offset can induce high-order modes in the plate rotation due to torque unbalance, and can trigger self-initiated pitching. The spectral decomposition of the flow velocity in the plate wake reveals the existence of a dominating high-frequency mode that corresponds to a static-like vortex shedding occurring at the maximum plate pitch. The associated characteristic length scale is the projected width at maximum pitching angle. The increase of the plate thickness ratio implies lower angular velocity in rotation cases. A simple model based on aerodynamic forces is used to explain the linear relation between pitching frequency and wind speed, the pitching frequency increase with axis offset, and the onset of pitching.     

Limit cycle oscillations of two-dimensional panels in low subsonic flow

Limit cycle oscillations of a two-dimensional panel in low subsonic flow have been studied theoretically and experimentally. The panel is clamped at its leading edge and free at its trailing edge. A structural non-linearity arises in both the bending stiffness and the mass inertia. Two-dimensional incompressible (linear) vortex lattice aerodynamic theory and a corresponding reduced order aerodynamic model were used to calculate the linear flutter boundary and also the limit cycle oscillations (that occur beyond the linear flutter boundary).     

Wind tunnel and full-scale study of wind effects on a super-tall building

This paper presents the analyzed results from a combined wind tunnel and full-scale study of the wind effects on a super-tall building with a height of 420 m in Hong Kong. In wind tunnel tests, mean and fluctuating forces and pressures on the building models for the cases of an isolated building and the building with the existing surrounding condition are measured by the high-frequency force balance technique and synchronous multi-pressure sensing system under two typical boundary layer wind flow fields. Global and local wind force coefficients and structural responses are presented and discussed. A detailed study is conducted to investigate the influences of incident wind direction, upstream terrain conditions and interferences from the surroundings on the wind loads and responses of the high-rise structure. On the other hand, full-scale measurements of the wind effects on the super-tall building have been performed under typhoon conditions. The field data, such as wind speed, wind direction, structural acceleration and displacement responses have been simultaneously and continuously recorded during the passage of 12 typhoons since 2008. Analysis of the field measured data is carried out to investigate the typhoon effects on the super-tall building. Finally, the model test results are compared with the full-scale measurements for verification of the wind tunnel test techniques. The comparative study shows that the wind tunnel testing can provide reasonable predictions of the structural resonant responses. The resonant displacement responses are comparable to the background displacement responses so that the contribution of the background responses to the total displacement responses should not be underestimated. The outcome of the combined wind tunnel and full-scale study is expected to be useful to engineers and researchers involved in the wind-resistant design of super-tall buildings.     

Numerical study of flow-induced oscillations of two rigid plates elastically hinged at the two ends of a stationary plate in a cross-flow

The flow-induced oscillation (FIO) of bluff bodies is commonly encountered in the fluid structure interaction (FSI) problems. In this study, we use an unstructured moving grid strategy and simulate the FIO of two rigid plates, which are elastically hinged at the two ends of a fixed flat plate in a cross-flow. We use a hybrid finite-element-volume (FEV) method in an arbitrary Lagrangian–Eulerian (ALE) framework to study FIO of the two hinged plates. The current simulations are carried out for wide ranges of flow Reynolds number (50–175), spring stiffness coefficient, and the two hinged plates' moment of inertia magnitudes. The influences of these parameters are investigated on the magnitudes of maximum deflection angle, the amplitude of oscillation, the total lift and drag coefficients, and so on. The study is also carried out in the transition period to describe the in-phase and out-of-phase angular oscillations occurring for the two elastically hinged plates with respect to each other. After the transition period, the two hinged plates eventually arrive to a similar periodic oscillation; however, with some phase lags. We find that the achieved phase lag is equal to the phase lag between the two pairs of flow vortices, which are alternatively shed into the flow from the upper and lower hinged plates. Similar to past FIO problems, the current model also exhibits two important lock-in and phase-switch FSI phenomena; however, in angular directions. There is a phase jump of approximately 170° between the aerodynamic lift coefficient and angular oscillations of hinged plates, which nearly occurs in the middle of lock-in region. Indeed, our literature review shows that this is the first time to report the phase-switch phenomenon in angular oscillations of three-element bluff bodies in a FSI problem.     

Vibration characteristics and flutter analysis of a composite laminated plate with a store

The effects of an external store on the flutter characteristics of a composite laminated plate in a supersonic flow are investigated. The Dirac function is used to formulate the interaction between the plate and the store. The first-order piston theory is used to describe the aerodynamic load. The governing equation of the composite laminated plate with an external store is established based on the Hamilton principle. The mode shapes are constructed by the admissible functions which are a set of characteristic orthogonal polynomials generated directly by the Gram-Schmidt process, and the boundary constraint is modeled as the artificial springs. The frequency and mode shapes of the plate under different boundaries are determined by the Rayleigh-Ritz method. The validity of the proposed approach is confirmed by comparing the results with those obtained from the finite element method (FEM). The effects of the mounting position, the center of gravity position and the mounting points spacing of the external store on the flutter boundary are discussed for both the simply supported and cantilever plates, respectively, which correspond to the two installation sites of the external store, i.e., the belly and wings of the aircraft.     

On the aeroelastic transient behaviour of a streamlined bridge deck section in a wind tunnel

The study deals with the transient behaviour of a two degrees of freedom bridge deck section in a wind tunnel under the effect of an initial excitation. Response of the bridge deck section subjected to an initial mechanical excitation and excitation by an upstream gust is investigated separately. Experiments are conducted with three different frequency ratios between the plunge and pitch degrees of freedom. This experimental study shows that transient growth of energy occurs for wind velocities below the onset of flutter, reaching a level higher than 5 times the level of the initial excitation. In high wind conditions, this means that statistical or spectral computation techniques might underestimate the motion amplitude reached by a flexible bridge deck. This emphasises the importance of using temporal techniques under such circumstances.     

Influence of friction and asymmetric freeplay on the limit cycle oscillation in aeroelastic system: An extended Hénon’s technique to temporal integration

Nonlinear effects such as friction and freeplay on the control surfaces can affect aeroelastic dynamics during flight. In particular, these nonlinearities can induce limit cycle oscillations (LCO), changing the system stability, and because of this it is essential to employ computational methods to predict this type of motion during the aircraft development cycle. In this context, the present article presents a matrix notation for describing the Hénon’s method used to reduce errors when considering piecewise linear nonlinearities in the numerical integration process. In addition, a new coordinate system is used to write the aeroelastic system of equations. The proposal defines a displacement vector with generalized and physical variables to simplify the computational implementation of the Hénon’s technique. Additionally, the article discusses the influence of asymmetric freeplay and friction on the LCO of an airfoil with control surface. The results show that the extended Hénon’s technique provides more accurate LCO predictions, that friction can change the frequency and amplitude of these motions, and the asymmetry of freeplay is important to determine the LCO behavior.     

Experimental investigations on the dynamic behavior of a 2-DOF airfoil in the transitional Re number regime based on digital-image correlation measurements

The present paper investigates the fluid–structure interaction (FSI) of a wing with two degrees of freedom (DOF), i.e., pitch and heave, in the transitional Reynolds number regime. This 2-DOF setup marks a classic configuration in aeroelasticity to demonstrate flutter stability of wings. In the past, mainly analytic approaches have been developed to investigate this challenging problem under simplifying assumptions such as potential flow. Although the classical theory offers satisfying results for certain cases, modern numerical simulations based on fully coupled approaches, which are more generally applicable and powerful, are still rarely found. Thus, the aim of this paper is to provide appropriate experimental reference data for well-defined configurations under clear operating conditions. In a follow-up contribution these will be used to demonstrate the capability of modern simulation techniques to capture instantaneous physical phenomena such as flutter. The measurements in a wind tunnel are carried out based on digital-image correlation (DIC). The investigated setup consists of a straight wing using a symmetric NACA 0012 airfoil. For the experiments the model is mounted into a frame by means of bending and torsional springs imitating the elastic behavior of the wing. Three different configurations of the wing possessing a fixed elastic axis are considered. For this purpose, the center of gravity is shifted along the chord line of the airfoil influencing the flutter stability of the setup. Still air free-oscillation tests are used to determine characteristic properties of the unloaded system (e.g. mass moment of inertia and damping ratios) for one (pitch or heave) and two degrees (pitch and heave) of freedom. The investigations on the coupled 2-DOF system in the wind tunnel are performed in an overall chord Reynolds number range of $9.66\times 10^3\le \text{Re}\le 8.77\times 10^4$. The effect of the fluid-load induced damping is studied for the three configurations. Furthermore, the cases of limit-cycle oscillation (LCO) as well as diverging flutter motion of the wing are characterized in detail. In addition to the DIC measurements, hot-film measurements of the wake flow for the rigid and the oscillating airfoil are presented in order to distinguish effects originating from the flow and the structure.     

Experimental and computational studies of low cycle fatigue crack nucleation in a polycrystal

Low cycle fatigue tests were carried out on a model ‘two-dimensional’ polycrystalline nickel-base alloy; that is, a directionally solidified material with near prismatic grains. Grain morphology and orientation were determined using electron back scatter diffraction (EBSD), and polycrystal plasticity analyses carried out for the characterised microstructure with, in principle, identical conditions to the experiment tests.     

Effects of suction or blowing on the velocity and temperature distribution in the flow past a porous flat plate of a power-law fluid

An analysis is made of the steady flow of a non-Newtonian fluid past an infinite porous flat plate subject to suction or blowing. The incompressible fluid obeys Ostwald-de Waele power-law model. It is shown that steady solutions for velocity distribution exist only for a pseudoplastic (shear-thinning) fluid for which the power-law index n satisfies 0<n<1 provided that there is suction at the plate. Velocity at a point is found to increase with increase in n. No steady solution for velocity distribution exists when there is blowing at the plate. The solution of the energy equation governing temperature distribution in the flow of a pseudoplastic fluid past an infinite porous plate subject to uniform suction reveals that temperature at a given point near the plate increases with n but further away, temperature decreases with increase in n. A novel result of the analysis is that both the skin-friction and the heat flux at the plate are independent of n.