Static Aeroelasticity Research Articles

Mesh Regeneration Method for Jig-Shape Optimization Design of the High-Aspect-Ratio Wing

A mesh regeneration method was put forward, and its application on the jig-shape optimization design of a high-aspect-ratio wing was carried out in the present study. In the mesh regeneration method, some control lines were selected based on configuration characters of the wing structure firstly. And then a new aerodynamic model was built according to the new control lines distribution which always keeps the same outline. Finally, mesh generation and quality optimization were carried out. Three different jig-shape optimizations based on mesh regeneration method were carried out on a high-aspect-ratio wing. All of them can obtain the designed jig-shapes which have excellent agreement with the expectant one under the impact of static aeroelasticity. Lift coefficients of all the three jig-shape optimization were larger than that of the original flat wing. The results of integrated jig-shape optimization which considered both flexure and torsion were not as well as those in their own independent optimization. An appropriate jig-shape optimization method needs to be selected according to the practical high-aspect-ratio wing design.

Control reversal and torsional divergence analysis for a high-aspect-ratio wing

Modern aircraft tends to adopt more flexible wing structures, such as high-aspect-ratio wings. They also feature advancements in performance, such as increased flight speeds. Thus, their aeroelastic characteristics and related safety factors became more important. By analyzing the static aeroelasticity of aircraft accurately, such as the control reversal and torsional divergence speed, it is expected that safe flights can be guaranteed within a prescribed flight envelope. In this paper, the control surface effectiveness and torsional divergence were analyzed using the following engineering tools: nonlinear multi-body dynamic analysis, DYMORE, cross-sectional analysis, two-cell analysis or VABS, and two-dimensional aerodynamic coefficient analysis for the subsonic isolated airfoil XFOIL. The results were verified through comparisons with those based on a typical section model with thin strip theory. Aluminum and composite single-cell box beam wings were analyzed in this paper. It is found that the control reversal and torsional divergence flight speeds as measured here were in good agreement with those predicted by a typical section model.

Theoretic analysis and experiment on aeroelasticity of very flexible wing

A high-altitude long-endurance aircraft with high-aspect-ratio wing usually generates large deformation, which brings the geometric nonlinear aeroelastic problems. In recent decades, it has become a key focus of the international researchers of aeroelasticity. But some critical technologies are not developed systematically, such as aerodynamic calculation methods of the curved wing with deformation, moreover, there are few experimental validations of these technologies. In this paper, we established the steady aerodynamic calculating method of the curved wing with quite large deformation based on the extended lifting line method, and calculated the unsteady aerodynamics using the strip theory considering curved surface effects. Combining the structure geometrical nonlinear finite element method, we constructed a systematic analytic approach for the static aeroelasticity and flutter of very flexible wing, and further designed the ground vibration and wind tunnel test to verify this approach. Through the test and the theoretic results comparison, we concluded that the extended lifting line method has adaptable precision for the static aeroealsticity and the strip theory considering curved surface effects for flutter analysis can give exact critical speed and flutter mode when the dynamic stall does not happen. The work in this paper shows that the geometric nonlinear aeroelastic analytic approach for very flexible wing has very high efficiency and adaptable precision. It can be used in the engineering applications, especially the iterated design in preliminary stage.

Mass estimation of transport aircraft wingbox structures with a CAD/CAE-based multidisciplinary process

This publication describes a CAD/CAE-based multidisciplinary process for the mass estimation of transport aircraft wingbox structures. The underlying method is physics-based and emulates the structural design process that takes place during the preliminary design phase. A structural sizing algorithm featuring a novel FEM-based buckling criteria is used for the dimensioning of the wingbox structure. Effects of static aeroelasticity are simulated with an iterative fluid–structure coupling method. Following a recent trend in aircraft pre-design, the multidisciplinary process relies on the integrated CAD/CAE software CATIA V5 for the generation of the parametric-associative geometrical and structural models. Besides multi-model generation capabilities, the CAD/CAE software features custom interfaces for the generation and application of wing loads such as aerodynamic or fuel loads. Special emphasis was put on the implementation of local load introduction methods. Fuel loads, for instance, are represented by surface-distributed hydrostatic pressure loads determined by the actual fuel distribution and the acceleration vector acting on the aircraft. The finished process was used to perform a mass estimation of the wingbox of a generic long range aircraft derived from the DLR-F11 configuration.

Nonlinear aeroelastic behavior of compliant airfoils

Since the beginning of aviation and up to the present time, airfoils have always been builtas rigid structures. They are designed to fly under their divergence speed in order to avoidstatic aeroelastic instabilities and the resulting large deformations, which are notcompatible with the typically low compliance of such airfoils. In recent years, research onairfoil morphing has generated interest in innovative ideas like the use of compliantsystems, i.e. systems built to allow for large deformations without failure, in airfoilconstruction. Such systems can operate in the neighborhood of divergence and takeadvantage of large aeroelastic servo-effects. This, in turn, allows compact, advancedactuators to control the airfoil’s deformation and loads, and hence complement oreven replace conventional flaps. In order to analyze and design such compliant,active aeroelastic structures a nonlinear approach to static aeroelasticity is needed,which takes into account the effect of large deformations on aerodynamics andstructure. Such an analytical approach is presented in this paper and applied to acompliant passive airfoil as the preliminary step in the realization of a piezoelectricallydriven, active aeroelastic airfoil. Wind tunnel test results are also presented andcompared with the analytic prediction. The good agreement and the observedbehavior in the wind tunnel give confidence in the potential of this innovative idea.

Accelerated loosely-coupled CFD/CSD method for nonlinear static aeroelasticity analysis

The flexible high-aspect-ratio wings of high-altitude long-endurance unmanned aerial vehicles experience large geometrical deformations. The nonlinear aeroelastic analysis for such a wing is carried out by using a loosely-coupled CFD/CSD method, which treats the fluid and structure as two separate modules and updates the CFD and CSD variables separately with a transfer of variables at the fluid–structure interface. In the loosely-coupled method employed here, an unsteady Euler solver and a nonlinear CSD solver are joined together by a fully three-dimensional integral constant volume tetrahedron (CVT) interfacing technique. The computation process is very time-consuming when the computed incremental displacements of every aerodynamic node on the wing surface are fully added to the previously computed deformed wing configuration. For a maximum deflection of approximately 8.7 mm (0.54% of semi-span length), the coupled computation scheme takes 20 coupling iteration steps with about 72 hours to converge on an HP XW6400 workstation with a 3 GHz Xeon5160 CPU. To reduce the computational expense of this loosely-coupled method, the golden section technique with an empirical parameter is introduced to speed up convergence. The deflections relaxed by using this technique are assimilated, and the wing bends up monotonically to its static equilibrium position with a maximum deflection 44.9 mm. The convergence history shows that, this accelerated algorithm takes just 6 coupling iteration steps with about 24 hours to monotonically converge to its static equilibrium position, although the maximum deflection 44.9 mm is 5 times larger than the maximum deflection 8.7 mm of the above test case with aeroelastic deflections fully assimilated. So, it is employed in the following nonlinear fluid–structure interaction (FSI) computations. After this nonlinear aeroelastic system has reached its static equilibrium position, the aerodynamic loads on wing surface are extracted and then applied onto the linear wing structure to calculate its deformation. In present paper, if the geometric nonlinear effects are taken into account for wing deflection calculation, the wing structure model is named as “nonlinear wing structure”; otherwise, the wing structure model is named as “linear wing structure”. The role of geometric nonlinearity on aeroelastic deformation is analyzed by comparing the deformations of linear and nonlinear wing structures. It is shown that, geometric nonlinearity plays an important role for large static aeroelastic deformation and should be accounted for in aeroelastic analyses for such high-aspect-ratio flexible wings.

Structural optimization of lifting surfaces with regard to static aeroelasticity

A technique for choosing a rational load-carrying scheme and weight analysis at the early stages of designing lifting surfaces with the use of a special model of the finite element method is proposed. The distribution of structure loads is determined with regard for its deformation. The numerical example is presented.

Fluid-Structure Coupled Analyses of Composite Wind Turbine Blades

The composite rotor blades have been widely used as an important part of the wind power generation systems because the strength, stiffness, durability and vibration of composite materials are all excellent. In composite laminated blades, the static and dynamic aeroelasticity tailoring can be performed by controlling laminate angle or stacking sequence. In this paper, the fluid-structure coupled analyses of 10kW wind turbine blades has been performed by means of the full coupling between CFD and CSD based finite element methods. Fiber enforced composites fabricated with three types of stacking sequences were also studied. First the centrifugal force was considered for the nonlinear static analyses of the wind turbine so as to predict the deformation of tip point in the length direction and maximum stress in the root of a wind turbine. And then, the aeroelastic static deformation was taken into account with fluid-structure interaction analysis of the wind turbine. The Arbitrary Lagrangian Eulerian Coordinate was used to compute fluid structure interaction analysis of the wind turbine by using ADINA program. The displacement and stress increased apparently with the increment of aerodynamic force, but under the condition of maximum rotation speed 140RPM of the wind turbine, the displacement and stress were in the range of safety.

On a shear-deformable theory of anisotropic thin-walled beams: further contribution and validations

Within the framework of an existing anisotropic thin-walled beam model, a number of non-classical effects are further incorporated and the model thereby developed is validated. Three types of lay-ups, namely, the cross-ply, circumferentially uniform stiffness, and circumferentially asymmetric stiffness are investigated. The solution methodology is based on the Extended Galerkin's Method and the non-classical effects on the static responses and natural frequencies are investigated. Comparisons of the predictions by the present model with experimental data and other analytical as well as numerical results are conducted and pertinent conclusions are drawn. This work is the first attempt to validate a class of refined thin-walled beam model that has been extensively used towards the study, among others, of dynamic response, static aeroelasticity and structural/aeroelastic feedback control.

Aerodynamic Influence Coefficient Computations Using Euler/Navier-Stokes Equations on Parallel Computers

An efficient procedure to compute aerodynamic influence coefficients (AIC) using high fidelity flow equations such as Euler/Navier- Stokes equations is presented. The AIC's are computed by perturbing structures using mode shapes. The procedure is developed on a multiple-instruction, multiple-data (MIMD) parallel computer. In addition to discipline parallelization and coarse-grain parallelization of the flow domain, embarrassingly parallel implementation of ENS AERO code demonstrates linear speedup for a large number of processors. Demonstration of the AIC computation for static aeroelasticity analysis is made on an arrow wing-body configuration. The computations show that some of the AIC's do not converge at the lower perturbation range since the perturbation is too small to prevail over the initial aerodynamic loads. The effect of initial aerodynamic loads disappears with increasing perturbation amplitude. The demonstrated linear scalability for multiple concurrent analyses shows that the threelevel parallelism in the code is well suited for the computation of the AIC's.

Preliminary Static Aeroelastic Analysis of Reusable Launch Vehicle Stability and Control Derivatives

During the development and design of the X-33 reusable launch vehicle, loads and control analyses had been done using propulsive and aerodynamic loads derived from such sources as computational e uid dynamics and wind-tunnel models of a rigid vehicle. Required control forces and moments were determined using rigid vehicle trajectory analyses, and the detailed control load distributions were determined for achieving the required control forces and moments, again using rigid vehicle analyses. However, static aeroelastic effects on load distributions were not being considered. The objective of the work reported here was the development of models and solutions for including static aeroelasticity in the calculation of X-33 loads and in the determination of stability and control derivatives. The theory underlying the NASTRAN solutions is presented, and some of the results for the stability and control derivatives are discussed.

Integrated Solution for Computational Static Aeroelasticity of Rockets

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

Use of Analytical Flow Sensitivities in Static Aeroelasticity

Modern computational fluid dynamics tools can be used to predict sensitivities for flows encountered by aircraft and missiles throughout the flight regime. In this study, we describe one important multidisciplinary application of aerodynamic sensitivity analysis, namely, the coupling of the aerodynamic sensitivities with a structural dynamics analysis and optimization code

Use of analytical flow sensitivities in static aeroelasticity

Use of analytical flow sensitivities in static aeroelasticity

Static and dynamic aeroelasticity of advanced aircraft wings carrying external stores

Static and dynamic aeroelasticity of advanced aircraft wings carrying external stores

Modal-Based Structural Optimization with Static Aeroelastic and Stress Constraints

The modal-based aeroelastic optimization approach is reformulated and extended such that it can deal with more structural analysis and optimization features. The disciplines treated in this paper are statics under e xed loads and static aeroelasticity of free ‐ free aircraft. The new formulation includes the application of stress constraints under e xed and varied external loads, and the effects of inertial changes on aeroelastic trim. It also facilitates the integration of the modal-based option in common e nite element structural optimization schemes. The new scheme is applied to realistic design cases using the multidisciplinary automated structural optimization system ASTROS code. Application cases of 3761 and 26,259 degrees of freedom exhibit CPU time reduction factors of 4 ‐ 122 in comparison with the conventional discrete approach.

Subsonic wing planform design using multidisciplinary optimization

This article presents basic results from wing planform optimization for minimum drag with constraints on structural weight and maximum lift. Analyses in each of these disciplines are developed and integrated to yield successful optimization of wing planform shape. Results demonstrate the importance of weight constraints, compressibility drag, maximum lift, and static aeroelasticity on wing shape, and the necessity of modeling these effects to achieve realistic optimized planforms.

Application of Alternative Multidisciplinary Optimization Formulations to a Model Problem for Static Aeroelasticity

A new model problem for static aeroelasticity is introduced and used to illustrate several alternative approaches for formulating multidisciplinary design optimization problems. The alternatives are distinguished by the kind of analysis problem feasibility that is maintained at each optimization iteration. In the familiar "multidisciplinary feasible" approach, the full multidisciplinary analysis problem is solved at each iteration of the optimizer. At the other end of the spectrum is the "all-at-once" approach where none of the individual analysis discipline equations is guaranteed to be satisfied until optimization convergence. In between lie other possibilities that amount to enforcing feasibility of the individual analysis disciplines at each optimization iteration, but allowing the coupling between the disciplines to be incorrect until optimization convergence. Results are given for these three approaches applied to the new model. In general, delaying feasibility until optimality reduces the total amount of computing work.

Direct solution of two-dimensional Navier-Stokes equations for static aeroelasticity problems

A new method has been developed to calculate the steady flow and structural deformations for fluid/structure interaction problems. The discretized fluid dynamic and structural equations are regarded as a single set of coupled, nonlinear, algebraic equations. The equilibrium solution is directly obtained using Newton's method. The governing equations used for the fluid flow are the two-dimensional Navier-Stokes equations, and a finite element model is used to represent the structure. This paper describes the analytical method and presents sample calculations demonstrating the technique. The results show rapid convergence and good agreement with experimental data. Nomenclature BW = half bandwidth of tangent matrix D = set of structural displacement variables E - set of governing equations for the aeroelastic system F = flux vector in x direction G = flux vector in y direction h = distance from nozzle throat to centerline / = number of fluid dynamic control volumes in streamwise direction J = number of fluid dynamic control volumes in cross-stream direction L = reference length, total length of nozzle N = total number of variables in system p = pressure pe = exit static pressure pt - total pressure R = system residual R = magnitude of residual r - radius at nozzle throat T = tangent matrix (system Jacobian) t = wall thickness U = set of fluid dynamic variables X = set of variables for the aeroelastic system AX = change in system variables during a Newton iteration x = streamwise coordinate y = cross-stream coordinate

Design load predictions on a fighter-like aircraft wing

Numerical solutions for a transonic design condition have been obtained for a fighter-like aircraft wing geometry using Euler and Navier-Stokes equations. Both rigid and flexible wings are considered. Effects of viscosity and static aeroelasticity on the component loads such as shear, bending moment, and torsion, as well as hinge moments on the flaps and ailerons, are predicted. The flexible wing solutions are obtained by coupling the flow solvers with a simple NASTRAN model. Effects of fuselage and horizontal tail have also been obtained for the rigid wing case using Euler equations. The computed results are compared to available flight test data. It is found that the static aeroelasticity has only a minor role, whereas the effect of viscosity is very pronounced. Comparison with the flight test data is found to be best when viscous effects are included.