Performance enhancement of wing-based piezoaeroelastic energy harvesting through freeplay nonlinearity

We investigate experimentally how controlled freeplay nonlinearity affects harvesting energy from a wing-based piezoaeroelastic energy harvesting system. This system consisits of a rigid airfoil which is supported by a nonlinear torsional spring （freeplay） in the pitch degree of freedom and a linear fiexural spring in the plunge degree of freedom. By attaching a piezoelectric material （PSI-5A4E） to the plunge degree of freedom, we can convert aeroelastic vibrations to electrical energy. The focus of this study is placed on the effects of the freeplay nonlinearity gap on the behavior of the harvester in terms of cut-in speed and level of harvested power. Although the freeplay nonlinearity may result in subcritical Hopf bifurcations （catastrophic for real aircrafts）, harvesting energy at low wind speeds is beneficial for designing piezoaeroelastic systems. It is demonstrated that increasing the freeplay nonlinearity gap can decrease the cut-in speed through a subcritical instability and gives the possibility to harvest energy at low wind speeds. The results also demonstrate that an optimum value of the load resistance exists, at which the level of the harvested power is maximized.

APPLICATION OF HYBRID GENETIC ALGORITHM IN AEROELASTIC MULTIDISCIPLINARY DESIGN OPTIMIZATION OF LARGE AIRCRAFT

The genetic/gradient-based hybrid algorithm is introduced and used in the design studies of aeroelastic optimization of large aircraft wings to attain skin distribution,stiffness distribution and design sensitivity.The program of genetic algorithm is developed by the authors while the gradient-based algorithm borrows from the modified method for feasible direction in MSC/NASTRAN software.In the hybrid algorithm,the genetic algorithm is used to perform global search to avoid to fall into local optima,and then the excellent individuals of every generation optimized by the genetic algorithm are further fine-tuned by the modified method for feasible direction to attain the local optima and hence to get global optima.Moreover,the application effects of hybrid genetic algorithm in aeroelastic multidisciplinary design optimization of large aircraft wing are discussed,which satisfy multiple constraints of strength,displacement,aileron efficiency,and flutter speed.The application results show that the genetic/gradient-based hybrid algorithm is available for aeroelastic optimization of large aircraft wings in initial design phase as well as detailed design phase,and the optimization results are very consistent.Therefore,the design modifications can be decreased using the genetic/gradient-based hybrid algorithm.

Stiffness Distribution and Aeroelastic Performance Optimization of High-Aspect-Ratio Wings

The relationship between stiffness distribution and aeroelastic performance for a beam-frame model and a3-D model is investigated based on aeroelastic optimization of global stiffness design for high-aspect-ratio wings.The sensitivity information of wing spanwise stiffness distribution with respect to the twist angle at wing tip,the vertical displacement at wing tip,and the flutter speed are obtained using a sensitivity method for both models.Then the relationship between stiffness distribution and aeroelastic performance is summarized to guide the design procedure.By using the genetic/sensitivity-based hybrid algorithm,an optimal solution satisfying the strength,aeroelastic and manufacturing constraints is obtained.It is found that the summarized guidance is well consistent with the optimal solution,thus providing a valuable design advice with efficiency.The study also shows that the aeroelastic-optimization-based global stiffness design procedure can obtain the optimal solution under multiple constraints with high efficiency and precision,thereby having a strong application value in engineering.

Aeroelastic modeling of wind loading on a cable-net supported glass wall

Wind loading study on a cable-net supported glass wall is conducted by means of wind tunnel tests. An equiva- lent aeroelastic model is designed and constructed. Response of displacements of the wall is measured and analyzed. In order to design a glass wall under wind loading, the ＂wind- vibration factor＂ is estimated and discussed. In fact, the mech- anism of wind acting on the wall is commonly known not only as positive pressure, but also as negative pressure caused by the flow separation on the corners of the building. Due to the diffidence in the mechanism of wind acting, two typi- cal response cases are classified. The results show that the dynamic response of the structure caused by the negative pressure is stronger than that of the positive pressure case. To determine the aerodynamic wind loading on a flexible part of structure on a building, wind tunnel study may be useful and play an important role.

A modified airfoil-based piezoaeroelastic energy harvester with double plunge degrees of freedom

In this letter, a piezoaeroelastic energy harvester based on an airfoil with double plunge degrees of freedom is proposed to additionally take advantage of the vibrational energy of the airfoil pitch motion. An analytical model of the proposed energy harvesting system is built and compared with an equivalent model using the well-explored pitch-plunge configuration. The dynamic response and average power output of the harvester are numerically studied as the flow velocity exceeds the cut-in speed （flutter speed）. It is found that the harvester with double-plunge configuration generates 4%-10% more power with varying flow velocities while reducing 670 of the cut-in speed than its counterpart.

The Effect of Composite Flexures on Aeroelastic Stability of a Hingeless Rotor Blade

The effects of ply orientation angle of composite flexures on stability of hingeless rotor blade system are studied.The composite hingeless rotor blade system is simplified as a hub,a flap flexure and a lag flexure.pitch bearing and main blade.The kinematics formulations are inferred by employing the moderate deflection beam theory.The shear deformation and warping related to torsion are considered.The quasi-steady strip theory with dynamic inflow effects is applied to obtain the aerodynamic loads acting on the blade.Based on these.the set of finite element formulations of a hingeless rotor blade system is worked out.The numerical results show that the ply angle of the composite flexures has great effects on the aeroelastic stability of rotor blade.

Semi-analytical method for calculating aeroelastic effect of profiled rod flying at high velocity

The key technique of a kinetic energy rod(KER) warhead is to control the flight attitude of rods. The rods are usually designed to different shapes. A new conceptual KER named profiled rod which has large L/D ratio is described in this paper. The elastic dynamic equations of this profiled rod flying at high velocity after detonation are set up on the basis of Euler-Bernoulli beam, and the aeroelastic deformation of profiled rod is calculated by semi-analytical method for calculating the vibration characteristics of variable cross-section beam. In addition, the aeroelastic deformation of the undeformed profiled rod and the aeroelastic deformation of deformed profiled rod which is caused by the detonation of explosive are simulated by computational fluid dynamic and finite element method(CFD/FEM), respectively. A satisfactory agreement of these two methods is obtained by the comparison of two methods. The results show that the semi-analytical method for calculating the vibration characteristics of variable cross-section beam is applied to analyze the aeroelastic deformation of profiled rod flying at high velocity.

Electroaeroelastic Modeling and Analysis for Flow Energy Piezoelectric Harvester

An electroaeroelastic model for wind energy harvesting using piezoelectric generators is presented.The flow field is mapped in detail.The force which the fluid flow exerts on the generator is formulated.The output voltage levels generated from the mechanical strain within the piezoelectric elements are determined.An analytical model is developed with consideration of the interactions between the fluid,solid and electric.Various analytical results are obtained,such as flow velocity contour and pressure contour for the flow,moving trajectories,stress contour and output voltage of the harvester.A prototype is fabricated and tested.The simulation result is close to the experimental result.The model developed in this paper can predict the performance and behavior of different energy harvesters.And it also can be used as a design tool for optimizing the performance of the harvester.

Optimal Control of Aeroelastic StochasticVibration of Aerocraft

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Control-Oriented Modeling and Simulation on Rigid-Aeroelasticity Coupling for Hypersonic Vehicle

Since the subsystems of aerodynamics,propulsion,structure and so on in hypersonic vehicles involve characteristics of nonlinearity,strong coupling and uncertainty,and typical hypersonic vehicles adopt slender-body and wave-rider layout with widely-used lightweight materials,the accuracy of the modeling with a conventional rigid-body assumption is challenged.Therefore,a nonlinear mathematical longitudinal model of a hypersonic vehicle is established with its geometry provided to estimate aerodynamic force and thrust using hypersonic aerodynamics and quasi-one-dimensional flow with heat added and capture vehicle aeroelasticity using a single free-free Bernoulli-Euler beam model.Then the static and dynamic properties of the rigid and rigid-aeroelasticity coupling model are compared via theoretical analysis and numerical simulation under the given flight condition.Finally,a LQR controller for rigid model is designed and the comparable results are obtained to explain the aerolasticity influence on the control effect.The simulation results show that the aeroelasticity mode of slender-body hypersonic vehicles affects short period mode significantly and it cannot be simply neglected.

Aeroelastic Responses for Wind Turbine Blade Considering Bend-Twist Coupled Effect

The Euler-Bernoulli beam model coupled with the sectional properties obtained by the variational asymptotic beam sectional analysis(VABS)method is used to construct the blade structure model.Combined the aerodynamic loads calculated by unsteady blade element momentum model with a dynamic inflow and the dynamic stall correction,the dynamics equations of blade are built.The Newmark implicit algorithm is used to solve the dynamics equations.Results of the sectional properties and blade structure model are compared with the multi-cell beam method and the ANSYS using shell elements.It is proved that the method is effective with high precision.Moreover,the effects on the aeroelastic response caused by bend-twist coupling are analyzed.Torsional direction is deflected toward the upwind direction as a result of coupling effects.The aerodynamic loads and the displacement are reduced.

Nonlinear aeroelastic coupled trim and stability analysis of rotor-fuselage

Based on the Hamilton principle and the moderate deflection beam theory, discretizing the helicopter blade into a number of beam elements with 15 degrees of freedora, and using a quasi-steady aero-model, a nonlinear coupled rotor/fuselage equation is established. A periodic solution of blades and fuselage is obtained through aeroelastic coupled trim using the temporal finite element method （TEM）. The Peters dynamic inflow model is used for vehicle stability. A program for computation is developed, which produces the blade responses, hub loads, and rotor pitch controls. The correlation between the analytical results and related literature is good. The converged solution simultaneously satisfies the blade and the vehicle equilibrium equations.

Effects of Thermo-Mechanical Loads on Aeroelastic Instabilities of Metallic and Composite Panels

Panel flutter phenomena can be strongly affected by thermal loads,and so a refined aeroelastic model is presented.Higher-order shell theories are used as structural models.The aerodynamic forces are described using the Piston theory.The temperature is considered uniform over the thickness of the panel.The aero-thermo-elastic model is derived in the framework of the Carrera unified formulation(CUF),therefore the matrices are expressed in a compact form using the″fundamental nuclei″.Composite and sandwich structures are considered and different boundary conditions are taken into account.The effects of the thermal load on the aeroelastic behavior are investigated.

Recent Progress on Aeroelasticity of High-Performance Morphing UAVs

The high-performance morphing aircraft has become a research focus all over the world.The morphing aircraft,unlike regular unmanned aerial vehicles(UAVs),has more complicated aerodynamic characteristics,making itmore difficultto conduct its design,model analysis,and experimentation.This paper reviews the recent process and the current status of aeroelastic issues,numerical simulations,and wind tunnel test of morphing aircrafts.The evaluation of aerodynamic characteristics,mechanism,and relevant unsteady dynamic aerodynamicmodeling throughout the morphing process are the primary technological bottlenecks formorphing aircrafts.The unstable aerodynamic forces have a significant impact on the aircraft handling characteristics,control law design,and flight safety.In the past,the structural analysis of morphing aircrafts,flight dynamics modeling,computational mesh morphing technology,and aerodynamic calculation were performed in promoting the development of next generation UAVs,with nonlinear dynamic challenges includingtransonic aeroelastic problems and high angle of attack aeroelastic problems.At present,many facets of these difficulties,together with the accompanying numerical simulation studies,remain under-explored.In addition,wind tunnel experiments face significant challenges in the dynamic morphing process.Finally,dynamic unsteady aerodynamic characteristics in the continuous morphing process still need to be verified by more related experiments.

Numerical Simulation Research on Static Aeroelastic Effect of the Transonic Aileron of a High Aspect Ratio Aircraf

The static aeroelastic effect of aircraft ailerons with high aspect ratio at transonic velocity is investigated in this paper by the CFD/CSD fluid-structure coupling numerical simulation.The influences of wing static aeroelasticity and the‘scissor opening’gap width between aileron control surface and the main wing surface on aileron efficiency are mainly explored.The main purpose of this paper is to provide technical support for the wind tunnel experimental model of aileron static aeroelasticity.The results indicate that the flight dynamic pressure has a great influence on the static aeroelastic effect of ailerons,and the greater the dynamic pressure,the lower the aileron efficiency.Aileron deflection causes asymmetric elastic deformation of the main wing surfaces of the left and right wings.The torque difference caused by the load distribution on the main wing surface offsets the rolling torque generated by the aileron.This results in a significant reduction in aileron efficiency,and it is noticeable that it is not the elastic deformation of the aileron itself or the reduction in effective deflection that leads to the reduction in rolling control efficiency.Under typical transonic conditions,the rolling control torque of the aileron can be reduced by more than 25%,in the range of 2.5–10 mm,and the‘scissor opening’gap width of the aileron has almost no influence on its static aeroelastic effect.

Aeroelastic Analysis of a Transonic Fan Blade with Low Hub-to-Tip Ratio including Mistuning Effects

This paper presents a comprehensive investigation of aeroelastic stability for a high aft-swept transonic fan blade with low hub-to-tip ratio. The evolution of the blade’s aeroelastic stability in the first bending modes is studied. A 3D flutter computation representing today’s industry standard is performed. Steady state flow field and motion-induced unsteady pressures acting on the blade have been determined by a 3D Reynolds-Averaged Navier-Stokes (RANS) equations with a standard k-ε turbulence model. A weakly coupled (one-way) method has been employed to describe the interaction between fluid and structure. The results of aerodynamic damping indicate a significant shock-driven risk. To increase the flutter margin by a viable method, a statistical mistuned aeroelastic stability investigation has been performed. It has been found that alternately intentional mistuning with a small blade frequency offset stabilizes the system effectively. However, as the standard deviation of random mistuning reaches some critical values, the introduction of alternately intentional mistuning does not provide any additional stabilizing effects.

Review of Proper Orthogonal Decomposition Method Applied to Computational Aeroelasticity

Over the recent years there has been an increased trend in the use of Reduced Order Models （ROM） for modeling the coupled aeroelastic system. Of all the ROM models, the Proper Orthogonal Decomposition Method （POD） has been the most widely used, reason being the relative simplicity of implementation and the physical insight that it offers towards the physical problem. In this paper we begin by briefly recalling the recent work using POD for the computational aeroelasticity followed by the mathematical formulation. Mathematical formulation is important as it provides understanding of how POD method works. Implementation issues related to the POD method are presented next. Since POD is an empirical technique therefore, it is marred by the robustness issues as is the case with all the ROMs. In the end the variations of POD method, developed over the years are presented along with the most recent trend of using hybrid ROM.

Oscillation quenching and physical explanation on freeplay-based aeroelastic airfoil in transonic viscous flow

Limit Cycle Oscillation(LCO)quenching of a supercritical airfoil(NLR 7301)considering freeplay is investigated in transonic viscous flow.Computational Fluid Dynamics(CFD)based on Navier-Stokes equations is implemented to calculate transonic aerodynamic forces.A loosely coupled scheme with steady CFD and an efficient graphic method are developed to obtain the aerodynamic preload.LCO quenching phenomenon is observed from the nonlinear dynamic aeroelastic response obtained by using time marching approach.As the airspeed increases,LCO appears then quenches,forming the first LCO branch.Following the quenching region,LCO occurs again and sustains until the divergence of the response,forming the second LCO branch.The quenching of LCOs was addressed physically based on the aerodynamic preload and the linear flutter characteristic.An“island”of stable region is observed in the flutter boundary,i.e.the flutter speed versus the mean Angle of Attack(AoA).The LCO quenches when the aerodynamic preload crosses this stable region with the increasing of airspeed.The LCO quenching of this model in transonic flow is essentially induced by destabilizing effect from aerodynamic preload,since the flutter speed is sensitive to AoA due to aerodynamic nonlinearity.

Static aeroelasticity of the propulsion system of ion propulsion unmanned aerial vehicles

“Ionic wind”generators are used as the main propulsion system in ion propulsion unmanned aerial vehicles(UAVs).Owing to the large size and poor stiffness of the electrode array in the propulsion system,the electrode array is prone to deformation under the flight load.In this work,the thrust characteristics and static aeroelastic properties of“ionic wind”propulsion systems were analyzed in detail.The simulation model for an“ionic wind”propulsion system was established by coupling a two-dimensional gas discharge model with a gas dynamics model.The influences of electrode voltage,spacing,size,and shape on the performance of the propulsion system were investigated.The fluid-solid interaction method was used to solve static aeroelastic characteristics under deformation.The aerodynamic and thrust performances of the elastic state and the rigid state were compared.It was found that the operating voltage,the distance between two electrodes,and the emitter radius had greater impacts on the thrust of the propulsion system.The propulsion system had a small contribution to the lift but a large contribution to the drag.In the elastic state,the lift coefficient accounted for 12.2%,and the drag coefficient accounted for 25.8%.Under the action of the downwash airflow from the wing,the propulsion system formed an upward moment around the center of mass,which contributed greatly to the pitching moment derivative of the whole aircraft.In the elastic state,the pitching moment derivative accounted for 29.7%.After elastic deformation,the thrust action point moved upward by 28.7 mm.Hence,the no lift pitching moment is reduced by 0.104 N$m,and the pitching moment coefficient is reduced by 0.014,causing a great impact on the longitudinal trimming of the whole aircraft.

Static aeroelastic analysis of very flexible wings based on non-planar vortex lattice method

A rapid and efficient method for static aeroelastic analysis of a flexible slender wing when considering the structural geometric nonlinearity has been developed in this paper. A non-planar vortex lattice method herein is used to compute the non-planar aerodynamics of flexible wings with large deformation. The finite element method is introduced for structural nonlinear statics analysis. The surface spline method is used for structure/aerodynamics coupling. The static aeroelastic characteristics of the wind tunnel model of a flexible wing are studied by the nonlinear method presented, and the nonlinear method is also evaluated by comparing the results with those obtained from two other methods and the wind tunnel test. The results indicate that the traditional linear method of static aeroelastic analysis is not applicable for cases with large deformation because it produces results that are not realistic. However, the nonlinear methodology, which involves combining the structure finite element method with the non-planar vortex lattice method, could be used to solve the aeroelastic deformation with considerable accuracy, which is in fair agreement with the test results. Moreover, the nonlinear finite element method could consider complex structures. The non-planar vortex lattice method has advantages in both the computational accuracy and efficiency. Consequently, the nonlinear method presented is suitable for the rapid and efficient analysis requirements of engineering practice. It could be used in the preliminary stage and also in the detailed stage of aircraft design.