Aeroelastic Dynamics Research Articles

Modelling and analysis of two-dimensional static and dynamic aeroelasticity of Fish Bone Active Camber morphing aerofoils

As a continuous and smooth morphing concept for aerofoils, the Fish Bone Active Camber (FishBAC) concept has demonstrated significant aerodynamic efficiency improvements over traditional hinged flaps. In this paper, to investigate the static and dynamic aeroelasticity of FishBAC aerofoils, an unsteady two dimensional coupled fluid-structure interaction model is developed, which includes the structural response of the FishBAC spine, skin, stringers, tendons and actuator, coupled to an unsteady aerodynamics model. The structural dynamic model is Timoshenko beam-theory-based, while the aerodynamic model is based on Peters’ unsteady model. The static and dynamic aeroelasticity is studied after the model is validated. Results show that the increase in pulley rotational angle reduces the zero-lift angle of attack, while keeping the slope between the lift coefficient and angle of attack the same. A shorter morphing region closer to the trailing edge is beneficial for generating larger lift coefficient with the same tendon moment and angle of attack. Flutter occurs with the increase of the air speed. When the morphing end position is fixed at 0.9 chord, increasing the morphing length reduces the critical flutter speed significantly, with the second bending mode tending to drive instability. With the same morphing length, moving the morphing region closer to the leading edge increases the critical flutter speed, and the unstable mode changes from the second mode into the first mode.

Analysis of the Dynamic Behavior, Buckling, and Aeroelasticity of a thin Composite Plate with the Effect of General and Local Geometric Defects

Analysis of the Dynamic Behavior, Buckling, and Aeroelasticity of a thin Composite Plate with the Effect of General and Local Geometric Defects

Analysis of the Aeroelastic Dynamics of Lightweight Flexible Variations of the SNL-NRT Turbine

Current trends show that wind turbines are growing in size to meet a rising demand for renewable energy generation, and their upscaled rotors have inherently become more flexible to maintain a proportionally lighter design. This is because larger rotors must be less massive relative to their diameter to minimize the levelized cost of energy (LCOE), which means that blades that are notably less stiff are produced as a result. These structural changes to blades are often reflected in their compromised aeroelastic stability and amplified deformation during operation, which has the potential to decrease the blade’s expected lifetime and the performance of the machine overall. Variations in blade flexibility are also known to influence vortex-wake structures downstream of the turbine, causing patterns of velocity deficit to evolve in ways that affect the performance of other turbines in the farm. This research explores how the increased flexibility of modern utility-scale wind turbine blades influences rotor aeroelastic behavior and interactions with farm flow. High-fidelity simulations of Sandia National Laboratories’ (SNL) National Rotor Testbed (NRT) wind turbine are presented. Flexible variations of the NRT baseline blade are simulated in a variety of realistic operational conditions typically expected at the SNL’s SWiFT facility in Lubbock, Texas. Solutions are then compared to investigate how specific changes to the structural properties of the NRT baseline blade’s design and construction can influence its aeroelastic response at the rotor and the evolution of the turbine’s wake.

Characterization of Oscillatory Response of Light-Weight Wind Turbine Rotors under Controlled Gust Pulses

Given the industry-wide trend of continual increases in the size of utility-scale wind turbines, a point will come where reductions will need to be made in terms of the weight of the turbine’s blades to ensure they can be as long as needed without sacrificing structural stability. One such technique that may be considered is to decrease the material used for the shell and spar cap. While this will solve the weight issue, it creates a new one entirely—less material for the shell and spar cap will in turn create blades that are more flexible than what is currently used. This article aims to investigate how the oscillatory response of light-weight wind turbine rotors is affected by these flexibility changes. The object of our study is the Sandia National Lab National Rotor Testbed (SNL-NRT) wind turbine, which the authors investigated in the course of a research project supported by SNL. Using a reduced-order characterization (ROC) technique based on controlled gust pulses, introduced by the authors in a previous work, the aeroelastic dynamics of the NRT’s original baseline blade design and several of its flexible variations were studied via numerical simulations employing the CODEF multiphysics suite. Results for this characterization are presented and analyzed, including a generalization of the ROC of the SNL-NRT oscillatory dynamics to larger machines with geometrical similarity. The latter will prove to be valuable in terms of extrapolating results from the present investigation and other ongoing studies to the scale of current and future commercial machines.

Conditions for simulation of transonic flutter of aerodynamic control surfaces of supersonic aircraft in wind tunnels

The transonic flutter of the aerodynamic control surfaces of supersonic and hypersonic aircraft refers to those phenomena of dynamic aeroelasticity, the assessment of whichin a flight experiment is dangerous. Since there is still no universally accepted mathematical model of the occurrence of this phenomenon, tests of dynamic-like models in wind tunnels can be classified as basic and safe methods for evaluating the characteristics of transonic flutter. Therefore, the substantiation of the conditions for modeling transonic flutter, which allow the transfer of the results of blowing of dynamic-like models in wind tunnels to full-scale aircraft designs, remains an actual scientific problem.The article proposes one of the possible approaches to justifying the conditions for modeling transonic flutter of aerodynamic control surfaces in wind tunnels, which is based on the analysis of a nonlinear mathematical model of the occurrence of this phenomenon.Based on the analysis of this mathematical model, it was determined that, in addition to the conditions for modeling transonic flutter in wind tunnels, which are due to the geometric similarity of the system "carrying aerodynamic surface – aerodynamic control surface", additional conditions for modeling this phenomenon should be the following dimensionless quantities of nature and model:- amplitudes of oscillations of nature and model;- numbers M at which transonic flutter occurs;- logarithmic decrements of oscillations of aerodynamic control surfaces;- Strouhal numbers;- ratio of gas density to material density of aerodynamic control surfaces;- the adiabatic index k=1.405, that is, the working body in the wind tunnel should be air.Blowing of dynamically similar models must be carried out in wind tunnels of a continuous type, subject to conditions (s-1).

Geometrically nonlinear effects in wing aeroelastic dynamics at large deflections

This paper investigates geometrically nonlinear effects due to nonlinear kinematics and follower aerodynamics in the aeroelastic dynamics of a very flexible wing. The test case is the Pazy wing, a benchmark wing model for geometrically nonlinear aeroelastic studies involving large deflections in low-speed flow. The work builds on a low-order model of the wing composed of a geometrically nonlinear beam coupled with potential flow thin airfoil theory. Nonfollower aerodynamics underestimates static deflections by up to 10%, whereas linear kinematics overestimates them by up to 50%. At low static deflections, the wing hump mode flutter mechanism is driven by three-dimensional unsteady aerodynamic effects. As static deflections increase, the flutter onset and offset speeds are driven by curvature effects that can only be captured by nonlinear kinematics, which reduce the natural frequencies associated with torsion and in-plane bending motions. Follower aerodynamics shrinks the hump mode instability region and shifts it to 1–4% lower flow speeds with no change in the flutter frequency, the qualitative trends, and the amplitude of limit-cycle oscillations. Overall, nonlinear kinematics is the primary geometrical nonlinearity influencing the wing aeroelastic behavior: the modal and stability scenarios with and without follower aerodynamics collapse onto the same curves when presented as functions of the tip deflection. However, geometrical nonlinearities alone miss the subcritical nature of the hump mode flutter mechanism, which is attributed to aerodynamic stall and its interaction with large deflections. This work expands the growing literature on the aeroelastic dynamics of very flexible wings and will ease future studies considering aerodynamic nonlinear effects.

A study of nonlinear aeroelastic response of a long flexible blade for the horizontal axis wind turbine

As long flexible blades in large wind turbines are prone to excessive bending deformations, there are failures in dynamic analyses under linear (small deflection) conditions. Thus, a large deflection blade model is developed here to study the dynamic response. The updated Lagrangian equation is used to derive the large deflection blade model from the Euler–Bernoulli beam. Then, the nonlinear aeroelastic dynamics equations of the blade are established using blade element momentum (BEM) theory, and time-domain simulations are performed using the nonlinear Newmark and Newton–Raphson methods. The effects of structural vibrations and aerodynamic damping are considered throughout the process. Finally, the nonlinear model is applied to the DTU 10 MW wind turbine. The results show that under steady and below-rated wind speeds, the flapwise deflection of the nonlinear blade is smaller than that of the linear blade. However, this phenomenon is the opposite for above-rated wind speeds. Under a step wind, the model responds quickly to the blade’s flexible deformation. Under turbulence, the linear results are consistent with the DNVGL Bladed 4.3 results, indicating that the nonlinear blade based on the linear Euler–Bernoulli beam is reliable. Meanwhile, the flapwise deflection for both blades fluctuates slightly when turbulent speeds are lower than the rated speed (0–5 s and 41–50 s), which is distinct from the steady-state analysis. In the aeroelastic coupling analysis, responses that consider vibration feedback are significantly smaller than those without feedback, and a nonlinear blade is significantly more affected in the flapping direction than a linear blade. Finally, the aerodynamic performance of large wind turbines is negatively affected by certain turbulent wind speeds.

Structure health inspection for aging transport aircraft

Purpose This study aims to present a diagnosis method to inspect the structure health for aging transport aircraft based on the postflight data in severe clear-air turbulence at transonic flight. The purpose of this method development is to assist certificate holder of aircraft maintenance factory as a complementary tool for the structural maintenance program to ensure that the transport aircraft fits airworthiness standards. Design/methodology/approach In this study, the numerical approach to analyze the characteristics of flight dynamic and static aeroelasticity for two four-jet transport aircraft will be presented. One of these two four-jet transport aircraft is an aging one. Another one is used to demonstrate the order of magnitude of the static aeroelastic behaviors. The nonlinear unsteady aerodynamic models are established through flight data mining and the fuzzy-logic modeling technique based on postflight data. The first and second derivatives of flight dynamic and static aeroelastic behaviors, respectively, are then estimated by using these aerodynamic models. Findings Although the highest dynamic pressure of aging aircraft is lower, the highest absolute value of static aeroelastic effects response to the wing of aging aircraft is about 3.05 times larger than normal one; the magnitude variations of angles of attack are similar for both aircrafts; the highest absolute value of the static aeroelastic effects response to the empennage of aging aircraft is about 29.67 times larger than normal one in severe clear-air turbulence. The stabilizer of aging aircraft has irregular deviations with obvious jackscrew assembly problems, as found in this study. Research limitations/implications A lack of the measurement data of vertical wind speed sensor on board to verify the estimated values of damping term is one of the research limitations of this study. This research involved potential problem monitoring of structure health for transport aircraft in different weights, different sizes and different service years. In the future research, one can consider more structural integrity issues for other types of aircraft. Practical implications It can be realized from this study that the structure of aging transport aircraft may have potential safety threat. Therefore, when the airline managed aging transport aircraft, it ought to be conducted comprehensive and in-depth inspections to reduce such safety risks and establish a complete set of safety early warning measures to deal with the potential problem of aircraft aging. Social implications It can be realized that the structure of aging transport aircraft has potential safety threat. The airline managed aging transport aircraft; it should conduct comprehensive and in-depth inspections to reduce safety risks and establish a complete set of safety early warning measures. Originality/value This method can be used to assist airlines to monitor aging transport aircraft as a complementary tool of structural maintenance program to improve aviation safety, operation and operational efficiency.

About revising the computational dynamic scheme of an unmanned aerial vehicle based on the results of ground-based modal test operations in the aeroelasticity problems

The problem of revising the computational dynamic scheme of an unmanned aerial vehicle (UAV), based on the results of ground-based modal test operations, in order to study the UAV flutter and to assess the aeroelastic stability of an UAV with an automatic control system (ACS), is considered. It is noted that at the design stage, when there is no UAV prototype or its units yet, the determination of modal characteristics, specifically natural frequencies, modes and generalized masses, is carried out using the computational dynamic scheme developed according to the design documentation. However, the similar computations, performed even with the use of modern finite-element software systems, do not give sufficiently precise values of the parameters of the UAV design elastic-mass schematization. In this regard, it is relevant and important to specify the parameters of the design schematization in conformity with data of ground test operations for UAV prototypes. The provisions, allowing us to achieve satisfactory results when revising the UAV computational dynamic scheme, are made. The criteria of revising are considered. The features of revising the computational dynamic scheme, while studying the flutter and aeroelastic stability of the ACS-fitted UAV, are presented. It is noted that along with the provisions that are universal for dynamic aeroelasticity problems, specifically for flutter, and related to compensating of natural frequencies, modes and coefficients of structural damping for the UAV model according to the results of ground modal tests. In the problems of aeroelastic stability study of the UAV equipped with the ACS, it is also crucial to correct the UAV body transfer function from the section, corresponding to the axis of controls rotation, to the section where ACS sensors are installed. This is because the UAV hull is an integral part of the UAV stabilization loop and significantly affects its stability margin. The example of revising the computational dynamic scheme of a maneuverable cruciform UAV is given.

Aeroelastic characteristics of inflatable reentry vehicle in transonic and supersonic regions

As an emerging space return technology, the inflatable reentry vehicle provides a new technical solution for deep space exploration, recovery of target spacecraft, and freight transport of space products. Aimed at the serious structural failure of inflatable reentry vehicle induced by the aeroelastic effect in transonic and supersonic flows, a fluid-solid coupling approach considering the effect of the inflation gas is established. The proposed model comprehensively considers the nonlinear factors of flexible inflatable film and the feedback of structural deformation on flow field. Based on this model, the static and dynamic aeroelastic problems under transonic and supersonic conditions are carefully studied. The obtained results reveal that the depressed deformations of flexible skin hinder the flow near surface and aggravate the degree of stagnation and heat dissipation, causing the surface temperature and pressure field significantly growing compared to the case of undeformed situation. Under action of the dynamic aeroelasticity, the violent low-frequency vibration induced by the turbulent wake occurs on the vehicle, which is more serious at the transonic stage condition (about Ma 0.8) or asymmetric incoming flow. The performed research indicates that the effects of the static and dynamic aeroelasticity should be fully taken into account in the design process of inflatable reentry vehicles, giving insightful guidance for engineering practice.

Design of Stability Augmentation Systems for Flexible Aircraft Using Projective Control

There are many challenges related to the design and operation of flexible aircraft. Flight control law design for improving handling qualities is one of them because the major problem in the design of controllers then concerns aeroservoelastic stability. To deal with this difficulty, methodologies for flight control law design considering the aeroelastic dynamics of the aircraft are being pursued. In this paper, a static output-feedback-based stability augmentation system is proposed and designed to improve the handling qualities and the structural dynamics decoupling of a flexible aircraft. The design is based on the projective control technique, which allows preserving in the closed-loop system the eigenstructure of certain modes of interest whose dynamic characteristics stem from an optimal state feedback solution. An experimental prototype of a flexible aircraft that mimics a high-altitude long-endurance airplane, called X-HALE, is considered in the case studies. Robustness analysis based on classical and disk-based stability margins, and nonlinear simulations of gusts and turbulent flight conditions evaluated and confirmed the effectiveness of the proposed controller.

Flutter Analysis of Last Stage Steam Turbine Power Plant Blade Through Transient Blade Row Simulation

Flutter phenomena becomes significant in response with turbomachinery design trends that prioritize efficiency. Especially in later stages of steam turbines, the slender profile of the blade becomes more prone to unstable dynamic aeroelasticity. Predicting the potential of flutter on a turbine blade can be done by constructing aeroelastic stability curve with evaluation of aerodynamic damping value under different rotor blade position, relative to the stator blade (inter blade phase angle). In this study, combination of steady Computational Fluid Dynamics (CFD), structural Finite Element Analysis (FEA) and transient blade row CFD was carried out using ANSYS 2019 R2 with the end goal of constructing aeroelastic stability curve and analysing the flutter risk of a 350 MW last stage steam turbine blade. At inter blade phase angle position of -180°, -70°, 0°, 77° and 180°, the system are exhibits positive aerodynamic damping values which indicates low to none flutter potential.

Energy approach to transonic flutter and LCO with shock waves movement

The paper briefly describes the main features of the used mathematical model of aerodynamic forces in transonic flow. The model is based on the Euler equations in various approximations, the boundary layer theory and viscous-inviscid interaction. Structural elastic deformations are described by equations in modal coordinates. The algorithm for computation of dynamic aeroelasticity characteristics in transonic flow has been developed on the base of energy method.The problem of transonic self-oscillations and their relationship with the pressure distribution peculiarities and shock waves motion is numerically investigated using the CAST wing section as example. The dependence of aeroelastic stability characteristics on the distributed work of aerodynamic forces along the wing chord is shown. An approach to the creation of a numerical modeling methodology is developed for LCO processes in the time domain.

ДИНАМІЧНА РЕАКЦІЯ ТА СТІЙКІСТЬ ПОШКОДЖЕНОЇ КОНСТРУКЦІЇ ТРАНСПОРТНОГО ЛІТАКА

In the process of designing and operating the aircraft, it is important to determine the ultimate state of the structure, taking into account the dynamic load of the structure and its stability. The ultimate state of the structure is characterized by damage, in which the structure still retains the ability to withstand without catastrophic destruction of the maximum operating load. The main method of studying the stability of the structure is the dynamic method. It allows us to investigate the perturbed motion of a structure as a nonconservative system for some initial perturbation. The monotonic departure of the system from the equilibrium position or its oscillations with increasing amplitudes indicate the instability of the structure. The paper analyzes the effect of damage to the aircraft structure on its dynamic stability based on the determination of the dynamic response of the aircraft to some non-stationary perturbation, for example, on the action of a turbulent atmosphere. The method of computational analysis is used to study the dynamic stability of the structure. The basis of this method is mathematical modeling (MM) of the operation of the aircraft in the form of a system of equations of motion and deformation of the structure. The problem of dynamic aeroelasticity is considered - the behavior of the elastic damaged structure of the aircraft in the air flow to the initial perturbation. On the basis of computer simulation, the dynamic stability of the elastic structure, its oscillating or quasi-static (aperiodic) deformation motion within the flight range of the aircraft is estimated. On the basis of parametric researches the limits of instability of a design at the set damages for typical operating conditions are estimated. The relevance of the direction focused on the creation and advanced operation of MM aircraft - their mathematical backups in the process of design and operation of aircraft due to the complexity and limited capabilities of ground experimental installations and flight experiment. It is noted that the condition for the application of this method is the formed MM operation of the aircraft and the availability of information on the mass-inertial, stiffness and aerodynamic characteristics of the aircraft.

LPV modeling and controller design for body freedom flutter suppression subject to actuator saturation

In recent years, the Active Flutter Suppression (AFS) employing Linear Parameter-Varying (LPV) framework has become a hot spot in the research field. Nevertheless, the flutter suppression technique is facing two severe challenges. On the one hand, due to the fatal risk of flight test near critical airspeed, it is hard to obtain the accurate mathematical model of the aeroelastic system from the testing data. On the other hand, saturation of the actuator may degrade the closed-loop performance, which was often neglected in the past work. To tackle these two problems, a new active controller design procedure is proposed to suppress flutter in this paper. Firstly, with the aid of LPV model order reduction method and State-space Model Interpolation of Local Estimates (SMILE) technique, a set of high-fidelity Linear Time-Invariant (LTI) models which are usually derived from flight tests at different subcritical airspeeds are reduced and interpolated to construct an LPV model of an aeroelastic system. And then, the unstable aeroelastic dynamics beyond critical airspeed are ‘predicted’ by extrapolating the resulting LPV model. Secondly, based on the control-oriented LPV model, an AFS controller in LPV framework which is composed of a nominal LPV controller and an LPV anti-windup compensator is designed to suppress the aeroelastic vibration and overcome the performance degradation caused by actuator saturation. Although the nominal LPV controller may have superior performance in linear simulation in which the saturation effect is ignored, the results of the numerical simulations show that the nominal LPV controller fails to suppress the Body Freedom Flutter (BFF) when encountering the actuator saturation. However, the LPV anti-windup compensator not only enhances the nominal controller’s performance but also helps the nominal controller to stabilize the unstable aeroelastic system when encountering serious actuator saturation.

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.

Aeroelastic oscillations of a pitching flexible wing with structural geometric nonlinearities: Theory and numerical simulation

This paper focuses on the derivation of an analytical model of the aeroelastic dynamics of an elastically mounted flexible wing. The equations of motion obtained serve to help understand the behaviour of the aeroelastic wind tunnel setup in question, which consists of a rectangular wing with a uniform NACA 0012 airfoil profile, whose base is free to rotate rigidly about a longitudinal axis. Of particular interest are the structural geometric nonlinearities primarily introduced by the coupling between the rigid body pitch degree-of-freedom and the continuous system. A coupled system of partial differential equations (PDEs) coupled with an ordinary differential equation (ODE) describing axial-bending-bending-torsion-pitch motion is derived using Hamilton's principle. A finite dimensional approximation of the system of coupled differential equations is obtained using the Galerkin method, leading to a system of coupled nonlinear ODEs. Subsequently, these nonlinear ODEs are solved numerically using Houbolt's method. The results that are obtained are verified by comparison with the results obtained by direct integration of the equations of motion using a finite difference scheme. Adopting a linear unsteady aerodynamic model, it is observed that the system undergoes coalescence flutter due to coupling between the rigid body pitch rotation dominated mode and the first flapwise bending dominated mode. The behaviour of the limit cycle oscillations is primarily influenced by the structural geometric nonlinear terms in the coupled system of PDEs and ODE.

Development of Efficient Dynamic Aeroelasticity Model for High Fidelity Pointing Accuracy Assessment of VLBI Earth-Based Radio Antennas

Modern Earth-based radio antennas of very-long-baseline interferometry system are furnished with robust control systems for their pointing control. Their pointing accuracy is critical to the quality of the radio wave-front captured. External disturbances, particularly those of wind gusts, produce a non-negligible dynamic aeroelastic response that degrades its pointing accuracy, and yet are not mitigated by the antenna’s control system. In this paper, a high fidelity and efficient dynamic aeroelastic model of an earth-based antenna is developed which is used to study the effects of wind gusts on the antenna’s pointing accuracy. Model order reduction of the antenna structural model is carried out using Craig–Bampton method taking into consideration the dominant modal characteristics of the antenna. The aerodynamic forces are approximated using the 2D Doublet-Lattice Method. The Davenport Spectrum is used to model aerodynamic turbulences near the earth surface. The developed dynamic aeroelastic model is employed to investigate the effects of discrete and random gusts on the pointing accuracy of the antenna. It is found that the deviation in the pointing angle is more prominent in the z (azimuth) direction and it displays a quadratic dependency with respect to the mean wind speed. This behavior is attributed to the inertial component of the aeroelastic response solution represented by the gravitational field acting on the center of gravity of the main reflector and the counterweights. The developed efficient aeroelastic model can be integrated into the antenna control system for its response prediction and mitigation.

Reduced order nonlinear aeroelasticity of swept composite wings using compressible indicial unsteady aerodynamics

Nonlinear dynamic aeroelasticity of composite wings in compressible flows is investigated. To provide a reasonable model for the problem, the composite wing is modeled as a thin walled beam (TWB) with circumferentially asymmetric stiffness layup configuration. The structural model considers nonlinear strain displacement relations and a number of non-classical effects, such as transverse shear and warping inhibition. Geometrically nonlinear terms of up to third order are retained in the formulation. Unsteady aerodynamic loads are calculated according to a compressible model, described by indicial function approximations in the time domain. The aeroelastic system of equations is augmented by the differential equations governing the aerodynamics lag states to derive the final explicit form of the coupled fluid-structure equations of motion. The final nonlinear governing aeroelastic system of equations is solved using the eigenvectors of the linear structural equations of motion to approximate the spatial variation of the corresponding degrees of freedom in the Ritz solution method. Direct time integrations of the nonlinear equations of motion representing the full aeroelastic system are conducted using the well-known Runge–Kutta method. A comprehensive insight is provided over the effect of parameters such as the lamination fiber angle and the sweep angle on the stability margins and the limit cycle oscillation behavior of the system. Integration of the interpolation method employed for the evaluation of compressible indicial functions at any Mach number in the subsonic compressible range to the derivation process of the third order nonlinear aeroelastic system of equations based on TWB theory is done for the first time. Results show that flutter speeds obtained by the incompressible unsteady aerodynamics are not conservative and as the backward sweep angle of the wing is increased, post-flutter aeroelastic response of the wing becomes more well-behaved.

Effects of rotational motion on dynamic aeroelasticity of flexible spinning missile with large slenderness ratio

Abstract The structural rigidity of a spinning missile with large slenderness ratio is usually small, and the structural deformation and rate should not be ignored. Furthermore, rotational motion makes the aeroelasticity more complicated. Therefore, unsteady Euler equations and generalized dynamic aeroelastic equations are coupled simultaneously to simulate the dynamic aeroelastic response of a spinning missile with large slenderness ratio using rigid-motion mesh and radial-basis-function (RBF) morphing mesh techniques. The unsteady Euler equations are solved by computational fluid dynamics (CFD) technique by the in-house code. The Coriolis term and centrifugal loading term due to rotational motion are both considered in the generalized dynamic aeroelastic equations. The rigid-motion mesh and RBF morphing mesh techniques are both based on unstructured mesh, and the rigid-motion mesh is adopted to treat the rigid motion due to rotational motion, while the RBF morphing mesh is employed for flexible structural deformation caused by aeroelasticity. Numerical results of aeroelastic case are well agreed with the experimental results, which validates the numerical method. A missile model with X-X configuration is constructed to investigate the effects of rotational motion on dynamic aeroelasticity. The dynamic aeroelastic responses of the missile with and without rotational motion are simulated, respectively. Comparison results show that the lateral modes and longitudinal modes are coupled together because of rotational motion. In addition, the structural natural frequencies are changed due to rotational motion. In the end, detailed numerical analysis of the generalized dynamic aeroelastic equations used in this paper indicates the mechanism by which the rotational motion leads to the coupling of lateral modes and longitudinal modes and changes the structural natural frequencies.