Static Aeroelastic Analysis Research Articles

Wing optimization for static aeroelastic effect

Abstract An aeroelastic analysis module based on the VLM model and FE model with non-linear static analysis was developed to calculate the lift and deformation of a wing in a cruise case. The traditional static aeroelastic analysis method focuses on compensation of loss of lift by adjusting wing root AoA (angle of attack). To improve the aeroelastic property, integrated static aeroelastic optimization was developed, which compensates for the loss lift by adjusting a series of sectional AoA instead of only wing root AoA. Compared with traditional static aeroelastic analysis, the manufacture wing optimized by integrated static aeroelastic optimization is closer to the initial design wing.

High-fidelity fluid-structure interaction applied to static aeroelasticity in transonic flows

Transonic flows at high Reynolds numbers can lead to high dynamic pressures and, consequently, to aerostructural deflections of aircraft structures. This study aims to develop and validate a high-fidelity static aeroelastic analysis environment that is efficient and that can be used in an industrial setting. The aerodynamics is represented by numerical solutions of the Reynolds-averaged Navier-Stokes equations with appropriate turbulence closures. The load transfer process uses finite element shape functions in order to distribute the aerodynamic loads into the structural discretization. The structural analysis employs a modal basis approach, and a wingtip deflection convergence study is performed to find an adequate modal basis size. Radial basis functions are used for the fluid mesh displacement, and the influence of the support radius is evaluated to determine the optimal values relative to the wing mean aerodynamic chord. The capability is tested using the static aeroelastic benchmarks of the High Reynolds Aerostructural Dynamics Project (HIRENASD) and NASA's Common Research Model (CRM). The static aeroelastic results demonstrate robustness and consistency for the aerodynamic coefficients, pressure distributions, and structural deflection predictions at different normalized dynamic pressure values and grid refinement levels.

Investigation of Static Aeroelastic Analysis and Flutter Characterization of a Slender Straight Wing

Investigation of Static Aeroelastic Analysis and Flutter Characterization of a Slender Straight Wing

Aeroelastic tailoring of stiffened cantilever plate using composites and structural layouts: A parametric study

AbstractThis paper studies the aeroelasticity of a stiffened cantilever plate using composite material and novel structural layouts. A comprehensive parametric study is conducted to determine the influence of different design parameters on the aeroelastic boundaries. Design parameters include plate sweep angle, ply orientation, stringer cross-section and stringer sweep angle. Nastran is used to run the aeroelastic analysis, and the process is automated using ${\rm{Matla}}{{\rm{b}}^{}}$ . The structure of the plate is modelled using laminate elements whereas the stringers are modelled using the Euler-Bernoulli beam elements. The unsteady aerodynamic loads are modelled using doublet-lattice method (DLM) and the structural and aerodynamic meshes are connected using an infinite plate surface (IPS) spline. A mesh sensitivity analysis is conducted to ensure fine meshes for the aerodynamics and structure. The study’s findings demonstrate the benefits of employing forward swept (Fw) stringers since it increases flutter speed by almost 38% compared to the unswept stringers case and prevents divergence. Moreover, the static aeroelastic analysis illustrates that the utilisation of Fw swept stringers can reduce the average tip displacement and tip twist effectively. T-shaped stringers are recommended to stiffen the plate due to their lower impact on the total mass of the plate. In some configurations, the structural layout has a much higher effect on the aeroelastic instabilities when compared to the material effect (ply orientation). However, results suggest combining both for some cases to get balanced washin and washout effects.

Aeroelastic reduced-order modeling for efficient static aeroelastic analysis considering geometric nonlinearity

The computational fluid dynamic/computational structural dynamic (CFD/CSD) coupling method plays an important role in static aeroelastic problems accounting for structural geometric nonlinearity. However, a huge computational burden comes from the CFD simulation, which also dominates the computational cost of the CFD/CSD coupling method. Therefore, this paper presents a reduced-order framework for steady aerodynamics to replace the CFD simulation, which is then coupled with the CSD solver for efficient static aeroelastic analysis considering geometric nonlinearity. Results first show that the proposed approach is capable of accurately predicting the surface pressure distribution of a high-aspect-ratio wing in its rigid undeformed shape at different Mach numbers and angles of attack, with at most a 2.5% relative error compared to CFD simulation. In addition, the geometrically nonlinear structure, a seminal benchmark without a tip slender body, is simulated by a three-dimensional open-source finite element solver coupled with either the CFD solver or the proposed reduced-order models (ROMs). The results demonstrate that the proposed ROM/CSD coupling approach can reflect the deformation and surface pressure distribution at static aeroelastic equilibrium with high accuracy and efficiency, thereby reducing the total computational cost at least five times while maintaining reasonable accuracy.

Static aeroelastic analysis of very flexible wings coupled with distributed propellers

Distributed propellers are widely used as propulsion for high-aspect-ratio long-endurance UAVs, and their load and slipstream will change the structural and aerodynamic characteristics of the wing, making geometric nonlinear effects more prominent. To address the aeroelastic interference of distributed propellers on the large flexible wing, firstly, on the basis of the vortex theory, a slipstream tube model is used to rapidly calculate the induced velocity of the slipstream, realizing the coupled aerodynamic modeling of the propeller and wing. Secondly, the coupled modelling of propellers and the nonlinear structure is achieved through the derivation and transformation of the coordinate system in the co-rotation method. Finally, combined with the space beam spline, a nonlinear static aeroelastic analysis framework for the large flexible wing considering the effects of distributed propellers is established. The simulation example of flexible wing with distributed propellers shows that the propeller pull will cause negative twisting of the wing due to large deformations, resulting in approximately 10% loss of lift and 20%-40% decrease in static stability margin; the propeller slipstream will change the local flow velocity and the angle of attack, bringing about 2.5% lift gain and 2%-8% increase in static stability margin; propellers increase lift when it is close to the wing root, but decrease when close to the wing tip, and the closer to the wing tip, the more significant the effect is. The analysis method established in this paper can provide guidance for the coupling design of distributed propellers and large flexible wings.

Static aeroelasticity analysis of a rotor blade using a Gauss-Seidel fluid-structure interaction method

The present study introduces a Gauss-Seidel fluid-structure interaction (FSI) method including the flow solver, structural statics solver and a fast data transfer technique, for the research of structural deformation and flow field variation of rotor blades under the combined influence of steady aerodynamic and centrifugal forces. The FSI method is illustrated and validated by the static aeroelasticity analysis of a transonic compressor rotor blade, NASA Rotor 37. An improved local interpolation with data reduction (LIWDR) algorithm is introduced for fast data transfer on the fluid-solid interface of blade. The results of FSI calculation of NASA Rotor 37 show that when compared with the radial basis function (RBF) based interpolation algorithm, LIWDR meets the interpolation accuracy requirements, while the calculation cost can be greatly improved. The data transmission time is only about 1% of that of RBF. Moreover, the iteration step of steady flow computation within one single FSI has little impact on the converged aerodynamic and structural results. The aerodynamic load-caused deformation accounts for nearly 50% of the total. The effects of blade deformation on the variations of aerodynamic performance are given, demonstrating that when static aeroelasticity is taken into account, the choke mass flow rate increases and the peak adiabatic efficiency slightly decreases. The impact mechanisms on performance variations are presented in detail.

High-fidelity aeroelastic transonic analysis using higher-order structural models

A novel computational approach for static aeroelastic analysis of metal and composite wings in transonic flows is proposed. Static aeroelastic analysis is often performed coupling beam/plate structural formulations with low-fidelity inviscid and irrotational aerodynamics. When high subsonic, transonic or supersonic regimes are met, low-fidelity aerodynamics is unable to accurately describe flow separation, viscous phenomena, and/or shock waves, unless suitable corrections are considered. This work combines the use of a variable-order kinematics structural model with Computational Fluid Dynamics (CFD), with the aim of developing a flexible computational aeroelastic framework. In particular, the structural model is based on the Carrera Unified Formulation and Equivalent Plate Modelling, whose governing equations are then solved through the Finite Element Method. The CFD analysis is performed using the high-fidelity open-source software SU2. The fluid–structure interaction is captured resorting to an energetic approach based on the Moving Least Squares patch technique. The generality and flexibility of the developed tool is demonstrated considering: the structural analysis of a wing exhibiting taper ratio, sweep angle, spars and ribs; the aeroelastic static analysis of a transonic AGARD 445.6 wing; and a prototype aeroelastic tailoring study on a composite wing. Comparison with available literature results confirms the robustness of the approach.

The influence and application of nonlinear aerodynamics on static derivatives in transonic regime

This paper details two static aeroelastic analysis methods applied to a passenger aircraft model with high aspect ratio wing. The influence of nonlinear aerodynamic force on static aeroelastic derivatives in the transonic regime is analysed. The traditional aerodynamic influence coefficient (AIC) matrix method can produce fast and reliable aerodynamic force and is widely used in aeroelastic analysis. However, the AIC matrix computed by linear aerodynamics will lead to some errors in transonic regime because of the nonlinear effect of aerodynamics. By generating the correction matrices, the AIC matrix is modified, and the accuracy of transonic static aeroelastic correction of aerodynamic data can be improved. The static derivatives are compared to the results of the computational fluid dynamics (CFD) / computational structural (CSD) interaction method.

Flare folding wing tips for static and gust loads alleviation

The Passive gust load alleviation device can effectively simplify the control system by relying on the adaptive deformation of the structure. This research examines the influence of using folding wingtips during flight as a means of reducing static loads and gusty loads. Effects of hinge direction, wing-tip weight, stiffness and wing-tip centre of gravity on static and gust alleviation performance has been examined. The results show that the flare folding wing-tip can significantly reduce the static load and gust load of the aircraft. In a static aeroelastic trim analysis, a folding wingtip can increase span by 25% without increasing the wing root bending moment and decrease the trim angle of attack by 0.14°. In the gust response analysis, the maximum bending moment of wing root can be decrease by nearly 50% compared with the fixed wing-tip, only 17% higher than the baseline model without a wing-tip.

Influence of Single External Store on Geometrical Nonlinear Flutter of High-aspect-ratio Wings

High-altitude and long-endurance UAVs, distributed electric propulsion aircraft and large passenger aircraft often use high-aspect-ratio wings, which have obvious geometric nonlinear large deformation effect, and are usually arranged with a certain number of external stores, which have an impact on their geometric nonlinear aeroelastic characteristics. Based on the “quasi-linear” hypothesis, the updated Lagrange incremental finite element method and doublet-lattice method are used to perform the geometrically nonlinear static aeroelastic analysis, and the mass, stiffness and aerodynamic matrices of large deformation are updated, and the geometrically nonlinear flutter characteristics of high-aspect-ratio wings are calculated. The influence of the position and mass of the external store on geometrical nonlinear flutter characteristics of high-aspect-ratio wing structure is investigated. Results show that the change of the position and mass of the external store causes the relative position between the elastic axis and the center of gravity of the wing, and the wing’s large deformation equilibrium state to change, resulting in differences in the stiffness characteristics of the wing and the natural vibration frequency of the equilibrium state, thus affecting the wing flutter characteristics. When a single external store is installed near the wing root, changing the mass and direction of the store has no significant effect on the geometric nonlinear flutter characteristics of the wing. The improvement of wing flutter speed is most obvious when the hanging point is moved to the leading edge of the wing near 0.65 times the wingspan.

Nolinear Static Aeroelastic Analysis and Optimization for High-Altitude Solar-Powered UAV With Large Aspect Ratio

According to the static aeroelastic characteristics of Solar-Powered UAV (SP-UAV) with large aspect ratio, this paper develops a nolinear aeroelastic analysis method which takes into account both the calculation accuracy and efficiency. Firstly, we establish the finite element model of the geometric nonlinear structure, which is verified by the static test of the whole UAV to reduce the calculation error caused by the simplified method of structure model. Then, the aerodynamic model of SP-UAV is established by using Curved Vortex Lattice (CVL), and the structure-aerodynamic coupling interpolation is realized by the Thin Plate Spline-interpolation (TPS) method, so as to complete the full static aeroelastic analysis. The analysis indicate that the calculated results of the longitudinal trim are well match the first flight condition. In particular, considering the elevator efficiency loss occurred in longitudinal trim analysis of the UAV, we design an optimization scheme to improve the efficiency of the elevator by about 15%. The simulation results show that the loss of elevator efficiency of flexible solar UAV with high aspect ratio is non-negligible, with the maximum value higher than 40% under high dynamic pressure. In actual flight, the speed of UAV must be reduced as much as possible to minimize the loss of rudder efficiency, while the elastic control method should be considered in flight control.

A computational aeroelastic framework based on high-order structural models and high-fidelity aerodynamics

A computational framework for high-fidelity static aeroelastic analysis is presented. Aeroelastic analysis traditionally employs a beam stick representation for the structure and potential, inviscid and irrotational flow assumptions for the aerodynamics. The unique contribution of this work is the introduction of a high-order structural formulation coupled with a high-fidelity method for the aerodynamics. In more details, the Carrera Unified Formulation coupled with the Finite Element Method is implemented to model geometrically complex composite, laminated structures as equivalent bi-dimensional plates. The open-source software SU2 is then used for the solution of the aerodynamic fields. The in-house fluid-structure coupling algorithm is based on the Moving Least Square technique. The paper contains a thorough validation of each disciplinary solver of the aeroelastic framework, and provides a few application test cases. For an unswept, untapered and isotropic wing, it was found that the method provides results in agreement with predictions from models based on potential flow theory for moderate freestream velocities. Departures were reported for very low speed and in the high-subsonic regime, alerting the need of adopting high-fidelity flow solutions at these flow conditions. The computational framework was then applied to the static aeroelastic tailoring of a composite wing. The paper concludes providing an overview of future implementation steps towards a tool for the seamless analysis of composite structures subject to different flow conditions, from low to high speed.

Static aeroelastic instability analysis of an inverted plate in ground effect and comparison with a wind-tunnel test

This paper visits the static instability of an inverted cantilevered plate in axial flow with the ground effect. This plate model is clamped at the trailing edge, and its leading-edge is allowed to move freely. A theoretical analysis strategy and corresponding convergent numerical solutions are reported and compared with a wind-tunnel experiment. In theory, we try a new way to study such an instability problem. We derive the instability equation by operator theory in state-space formulation and model such an instability problem as a mathematical function approximation problem. Glauert’s expansion and the least square method are applied for the numerical solutions of vorticity in ground effect using the mirror image method. The unknown function of the plate slope is expanded as a series of essential polynomial functions based on the Weierstrass theorem, and the least square method is applied for its numerical solutions. The experimental study develops a multi-point contact method using a control rod to preload the tested plate with a slight static deformation close to its natural modal shape. The contact state change between the initially deformed tested plate and the control rod is reflected by the evolution of the voltage output of a designed circuit. A criterion for determining the critical condition of plate instability is established based on such voltage change, and it has a better anti-interference ability to the flow. Results show that the present theoretical analysis agrees well with the experiment and other archived theories. The critical plate slopes (i.e., the plate instability modes) are not dependent on the ground confinement. This conclusion allows us to establish an analytical approximation between the critical dynamic pressure and the ground confinement. The present study and results can successfully predict the plate instability in the ground effect.

Modeling and analysis of a geometrically nonlinear joined wing under thrust force

The joined-wing aircraft is an alternative configuration compared to general cantilevered configuration because of its superiority. In the present work, an efficient modeling method for flexible joined wing is proposed. The fully intrinsic formulation is applied for the geometrically nonlinear effect and the static indeterminacy of joined wing is addressed based on the force method. To avoid mathematically over-determined problem, an orientation compatibility condition with profound physical meaning is established and subsequently a strict mathematical proof is given for the existence and uniqueness of rotation. By adopting Peters finite inflow theory, the unsteady aerodynamic model for joined wing is built up. The joined-wing aeroelastic model is eventually represented by a set of differential-algebraic equations. Following validation studies show that although the displacements and rotations are excluded, contributing to higher computing speed than the mixed formulation, the numerical accuracy of present method is close to mixed formulation and superior to the incremental method. Finally, the static aeroelastic analysis for a planar joined wing under a thrust force at wingtip is implemented within flutter boundary. Results show that the thrust force can lead to an axial compressive load in front wing and the co-existing solutions are revealed because of the buckling of front wing when the thrust force exceeds a threshold value. Further studies indicate that although either solution path is possible theoretically, the “upward-bending solution” is a more likely practical solution for the planar joined wing.

Three-Dimensional Uncoupled Fluid Structure Analysis of Small Unmanned Aerial Vehicle Wing

Analyzing the interaction between a fluid and an exposed structure is vital in the design of numerous applications, including the optimization of aerodynamic bodies such as the flexible wings of small unmanned aerial vehicles. Various techniques currently exist to study such fluid/structure interactions, including experimental approaches and numerical techniques that couple fluid and structural analysis tools. In this study, a novel uncoupled static aeroelastic analysis method is demonstrated for determination of the aeroelastic response of three-dimensional wings for the first time. The results indicate that this uncoupled static aeroelastic analysis method is capable of accurately predicting the pressure and displacement fields of a flexible wing, exhibiting at most a 2% error relative to traditional coupled aeroelastic analysis results and a 2.3% error relative to experimental results. Additionally, because the fluid and structural solvers are uncoupled, it is herein demonstrated that the uncoupled static aeroelastic analysis method is capable of reusing a single computationally expensive fluid data set to evaluate multiple internal wing structural configurations across a range of angles of attack while maintaining similar levels of accuracy, thereby reducing the total computational expense by as much as 70%. Furthermore, it is also demonstrated that the uncoupled static aeroelastic analysis method is suitable for preliminary design optimization of the internal structure of wings, which may experience either simple (bending only) or complex (bending and twisting) deformation.

Geometric Nonlinear Static Aeroelastic Characteristics Analysis of High-Aspect-Ratio Wing with Large Deformation

Geometric Nonlinear Static Aeroelastic Characteristics Analysis of High-Aspect-Ratio Wing with Large Deformation

Nonlinear Aeroelastic Analysis of High-Aspect-Ratio Wings with a Low-Order Propeller Model

A nonlinear aeroelastic analysis framework for high-aspect-ratio wings that includes the aerodynamic effects of propellers is described. The high computational cost required for modeling aerodynamic interaction between the wing and propeller wake is reduced by taking advantage of the relatively slow dynamics of the wing. Consequently, the propeller wake is modeled as a straight vortex cylinder that does not require a computationally expensive wake updating process. By leveraging the smallness of the propeller, an averaged vortex cylinder method is proposed that calculates the induced velocities of the propeller vortex cylinder efficiently without suffering from a numerical singularity and loss of accuracy. The induced velocities are considered in the wing aerodynamic force calculation using an unsteady vortex lattice method. An efficient propeller cylinder coordinate generation method modeling the propeller-attached wing by absolute nodal coordinate formulation with a multibody dynamic theory is also proposed. The developed framework is validated by comparison with other formulations. A static aeroelastic analysis on a low-speed high-aspect-ratio wing demonstrates that the propeller-induced axial velocity causes the deflection change of 5.4%. A nonlinear dynamic result shows that the propeller decreases the vibration amplitude by 6.7% because the propeller-induced axial velocity enhances the aerodynamic damping.

Numerical and Experimental Study of a Flexible Trailing Edge Driving by Pneumatic Muscle Actuators

A static aeroelastic analysis of the flexible trailing edge is conducted to calculate the deformed shape, aerodynamic coefficients and corresponding driving pressure. A physical flexible trailing edge model is manufactured using a honeycomb structure, which is measured based on binocular vision. The quadratic response surface method is adopted to establish the pneumatic artificial muscle actuator model. The wire-pulley transmission model is built to identify the existence of equivalent forces and produce the equivalent forces as the substitute of actuation force. A finite element model of the flexible trailing edge is established, which is validated by the test data. A nonlinear relationship is found between the driving pressure and deflection angle. The pressure needed to bear the structural stiffness is found to be much larger than that of the aerodynamic load. With the increase in pressure, the magnitude of the lift coefficient increases less. However, the magnitude of the drag coefficient increases more with the increase in pressure under 0.2 MPa. When the driving pressure exceeds 0.2 MPa, the relationship between them is nearly linear.

Uncoupled method for static aeroelastic analysis

Fluid–structure interaction (FSI) analysis is often highly computationally expensive, making it infeasible to conduct iterative aeroelastic design studies or rigorous optimizations. This work develops a new method for aeroelastic analysis that can be more efficient in the determination of final structure/fluid equilibrium configurations, especially during design studies where attributes of a structure may be altered but those of the flow are unchanged. In this new scheme, referred to as the uncoupled static aeroelastic analysis method, the usual approach of performing fluid and structure analysis that increments in time in a coupled manner is replaced by many fully decoupled, and thus highly parallelizable, structural and fluid analyses. Surrogate modeling of results enables analytical determination of interpolation intersections between physical solution fields, such intersections being proposed as the solution to coupled FSI analysis. Since the fluid and structure result sets are calculated and stored separately, fluid results can be re-used without additional analysis when the structure considered is modified (e.g., as during a design study), enabling new solutions to be quickly obtained while avoiding the more expensive fluid evaluations. This new method is demonstrated herein on three examples: (1) a rigid baffle, (2) a cantilevered deformable baffle, and (3) an aeroelastic wing. For each, the solution found via the uncoupled method is shown to closely approximate the FSI solution. Parallelization of the evaluations required to generate data for the uncoupled method enables solutions to be obtained in significantly less time as compared to the coupled scheme.