Showing papers on "Aeroelasticity published in 2005"

AeroDyn Theory Manual

Abstract: AeroDyn is a set of routines used in conjunction with an aeroelastic simulation code to predict the aerodynamics of horizontal axis wind turbines. These subroutines provide several different models whose theoretical bases are described in this manual. AeroDyn contains two models for calculating the effect of wind turbine wakes: the blade element momentum theory and the generalized dynamic-wake theory. Blade element momentum theory is the classical standard used by many wind turbine designers and generalized dynamic wake theory is a more recent model useful for modeling skewed and unsteady wake dynamics. When using the blade element momentum theory, various corrections are available for the user, such as incorporating the aerodynamic effects of tip losses, hub losses, and skewed wakes. With the generalized dynamic wake, all of these effects are automatically included. Both of these methods are used to calculate the axial induced velocities from the wake in the rotor plane. The user also has the option of calculating the rotational induced velocity. In addition, AeroDyn contains an important model for dynamic stall based on the semi-empirical Beddoes-Leishman model. This model is particularly important for yawed wind turbines. Another aerodynamic model in AeroDyn is a tower shadow model based on potentialmore » flow around a cylinder and an expanding wake. Finally, AeroDyn has the ability to read several different formats of wind input, including single-point hub-height wind files or multiple-point turbulent winds.« less

Nonlinear Flight Dynamics of Very Flexible Aircraft

Abstract: This paper focuses on the characterization of the response of a very ∞exible aircraft in ∞ight. The 6-DOF equations of motion of a reference point on the aircraft are coupled with the aeroelastic equations that govern the geometrically nonlinear structural response of the vehicle. A low-order strain-based nonlinear structural analysis coupled with unsteady flnite-state potential ∞ow aerodynamics form the basis for the aeroelastic model. The nonlinear beam structural model assumes constant strain over an element in extension, twist, and in/out of plane bending. The geometrically nonlinear structural formulation, the flnite state aerodynamic model, and the nonlinear rigid body equations together provide a low-order complete nonlinear aircraft analysis tool. The equations of motion are integrated using an implicit modifled generalized-alpha method. The method incorporates both flrst and second order nonlinear equations without the necessity of transforming the equations to flrst order and incorporates a Newton-Raphson sub-iteration scheme at each time step. Using the developed tool, analyses and simulations can be conducted which encompass nonlinear rigid body, nonlinear rigid body coupled with linearized structural solutions, and full nonlinear rigid body and structural solutions. Simulations are presented which highlight the importance of nonlinear structural modeling as compared to rigid body and linearized structural analyses in a representative High Altitude Long Endurance (HALE) vehicle. Results show signiflcant difierences in the three reference point axes (pitch, roll, and yaw) not previously captured by linearized or rigid body approaches. The simulations using both full and empty fuel states include level gliding descent, low-pass flltered square aileron input rolling/gliding descent, and low-pass square elevator input gliding descent. Results are compared for rigid body, linearized structural, and nonlinear structural response.

A Non-Linear Model for the Longitudinal Dynamics of a Hypersonic Air-breathing Vehicle

Abstract: : A non-linear, physics-based model of the longitudinal dynamics for an air-breathing hypersonic vehicle is developed. The model is derived from first principles and captures the complex interactions between the propulsion system, aerodynamics, and structural dynamics. Unlike conventional aircraft, hypersonic vehicles require that the propulsion system be highly integrated into the airframe. Furthermore, hypersonic aircraft tend to have very lightweight, flexible structures that have low natural frequencies. Therefore, the first bending mode of the fuselage is important as its deflection affects the amount of airflow entering the engine, thus influencing the performance of the propulsion system. The equations of motion for the flexible aircraft are derived using Lagrange's Equations. The equations-of-motion capture inertial coupling effects between the pitch and normal accelerations of the aircraft and the structural dynamics. The linearized aircraft dynamics are shown to be unstable, and in most cases, exhibit non-minimum, phase behavior. The linearized model also indicates that there is an aeroelastic mode that has a natural frequency more than twice the frequency of the fuselage bending mode. Furthermore, the short-period mode is very strongly coupled with the bending mode of the fuselage.

Identification of Nonlinear Aeroelastic Systems Based on the Volterra Theory: Progress and Opportunities

Abstract: The identification of nonlinear aeroelastic systems based on the Volterra theory of nonlinear systems is presented. Recent applications of the theory to problems in computational and experimental aeroelasticity are reviewed. Computational results include the development of computationally efficient reduced-order models (ROMs) using an Euler/Navier–Stokes flow solver and the analytical derivation of Volterra kernels for a nonlinear aeroelastic system. Experimental results include the identification of aerodynamic impulse responses, the application of higher-order spectra (HOS) to wind-tunnel flutter data, and the identification of nonlinear aeroelastic phenomena from flight flutter test data of the active aeroelastic wing (AAW) aircraft.

Thin-Walled Composite Beams: Theory and Application

Abstract: Kinematics of Thin Walled Beams.- The Equations of Motion of Open/Closed Cross-Section Beams.- Additional Equations of the Linear Beam Theory.- Several Theorems in Linear Thin-Walled Beam Theory.- Free Vibration.- Dynamic Response to Time-Dependent External Excitation.- Thin-Walled Beams Carrying Stores.- Rotating Thin-Walled Anisotropic Beams.- Spinning Thin-Walled Anisotropic Beams.- Thermally Induced Vibration and Control of Spacecraft Booms.- Aeroelasticity of Thin-Walled Aircraft Wings.- Open-Section Beams.

Harmonic Balance Approach for an Airfoil with a Freeplay Control Surface

Abstract: The nonlinear aeroelastic response of a two-dimensional airfoil, including a control surface with freeplay placed in an incompressible flow, is studied. The model equations are formulated as a set of first-order ordinary differential equations. First, the dynamic response is investigated by a time integration method, and the time integration results are used for the verification of the harmonic balance results. The interesting hysteresis phenomenon and the effect of initial conditions of the subcritical bifurcation are presented. A higher-order harmonic balance method is then derived to investigate the high harmonics of the airfoil motions. The harmonic balance prediction is verified by comparison to the results from a numerical time marching integration and also by comparison to results from a previous experiment. Nomenclature a = nondimensional distance of the elastic axis from the midchord, with respect to the semichord B = damping submatrix b = semichord Ch = stiffness (per unit span) of wing in deflection C(k) = generalized Theodorsen function Cα, Cβ = torsional stiffness (per unit span) of wing around a and of aileron around c c = nondimensional distance of the control surface (aileron) hinge line from the midchord, with respect to the semichord

Nonlinear Aeroelastic Modeling and Analysis of Fully Flexible Aircraft

Abstract: *† This paper introduces an approach to effectively model the nonlinear aeroelastic behavior of fully flexible aircraft. The study is conducted based on a nonlinear strainedbased finite element framework in which the developed low-order formulation captures the nonlinear (large) deflection behavior of the wings, and the unsteady subsonic aerodynamic forces acting on them. Instead of merely considering the nonlinearity of the wings, the paper will allow all members of the vehicle to be flexible. Due to their characteristics of being long and slender structures, the wings, tail, and fuselage of highly flexible aircraft can be modeled as beams undergoing three dimensional displacements and rotations. The cross-sectional stiffness and inertia properties of the beams are calculated along the span, and then incorporated into the 1-D nonlinear beam model. Finite-state unsteady subsonic aerodynamic loads are incorporated to be coupled with all lifting surfaces, so as to complete the state space aeroelastic model. Different Sensorcraft concepts are modeled and studied, including conventional single-wing and joined-wing aircraft configurations with flexible fuselage and tail. Based on the proposed models, roll responses and stabilities are studied and compared with linearized and rigidized models. At last, effects of the flexibility of the fuselage and tail on the roll maneuver and stability of the aircraft are presented.

Dynamic Response of Aeroservoelastic Systems to Gust Excitation

Abstract: Frequency-domain and time-domain approaches to dynamic response analysis of aeroservoelastic systems to atmospheric gust excitations are presented. The discrete and continuous gust inputs are defined in either time-domain or stochastic terms. The various options are formulated in a way that accommodates linear control systems of the most general form. The frequency-domain approach is based on the interpolation of generalized aerodynamic force coefficient matrices and the application of Fourier transforms for time-domain solutions. The time-domain approach uses state-space formulation that requires the frequency-dependent aerodynamic coefficients to be approximated by rational functions of the Laplace variable. Once constructed, the state-space equations of motion are more suitable for time simulations and for the interaction with control design algorithms. However, there is some accuracy loss because of the rational approximation. The spiral nature in the complex plane of the gust-related aerodynamic terms is discussed, and means are provided for dealing with the associated numerical difficulties. A hybrid formulation that does not require the rational approximation of the gust coefficients is also presented for optional use in discrete gust response analysis. The various methods were utilized in the ZAERO software and applied to a generic transport aircraft model.

Joined-Wing Aeroelastic Design with Geometric Nonlinearity

Abstract: An integrated process is presented that advances the design of an aeroelastic joined-wing concept by incorporating physics-based results at the system level. For instance, this process replaces empirical mass estimation with high-fidelity analytical mass estimations. Elements of nonlinear structures, aerodynamics, and aeroelastic analyses were incorporated with vehicle configuration design. This process represents a significantly complex application of aeroelastic structural optimization. Specific fuel consumption for a fixed lift-to-drag ratio was considered in the process for estimating fuel to size the structure to meet range and loiter requirements. This design process was implemented on a single configuration for which two crucial nonlinear phenomena contribute to structural failure: large deformation aerodynamics and geometrically nonlinear structures. A correct model of the nonlinear aeroelastic physics offers the possibility of a successful design. Unconventional features of a joined-wing concept are presented with the aid of this unique design model. Hopefully, insight derived from the nonlinear aeroelastic design might be leveraged to the benefit of future joined-wing designs.

Advances in the linear/nonlinear control of aeroelastic structural systems

Abstract: Active aeroelastic control is a recently emerging technology aimed at providing solutions to a large class of problems involving the aeronautical/aerospace flight vehicle structures that are prone to instability and catastrophic failures, and to oscillations that can yield structural failure by fatigue. In order to prevent such damaging phenomena to occur, the linear/nonlinear aeroelastic control technology should be applied. Its goals are among others: (i) to alleviate and even suppress the vibrations appearing in the subcritical flight speed range, (ii) to enlarge the flight envelope by increasing the flutter speed, and (iii) to enhance the post-flutter behavior by converting the unstable limit cycle oscillation to a stable one. A short review of the available control techniques and capabilities is presented first. Attention is focused on the open/closed-loop of 2D and 3D lifting surfaces as well as on panels exposed to supersonic flowfields. A number of concepts involving various control methodologies, such as proportional, velocity, linear quadratic regulator, modified bang-bang, sliding mode observer, time-delay control, fuzzy, etc., as well as results obtained with such controls are presented. Emphasis is placed on theoretical and numerical results obtained with the various control strategies that are considered in a comparative way. Finally, conclusions and directions for further work are presented.

Body Freedom Flutter of High Aspect Ratio Flying Wings

Abstract: The paper presents results of aeroelastic analysis on a swept flying wing aircraft developed under contract for the Air Force Research Laboratory (AFRL) SensorCraft program. This configuration is characterized by a high aspect ratio, very flexible wing with 30 sweep. This configuration, like other examples of flexible flying wings, is prone to body freedom flutter (BFF) that results from coupling of the rigid body short period mode with wing bending. A NASTRAN finite element model (FEM) is used for an initial aeroelastic flutter analysis. Stiffness and mass properties are derived from the FEM to construct an approximate beam model of the wing for ASWING aero-structural analysis. Flutter analysis for the open loop aircraft explores trades in wing stiffness, altitude and center-ofgravity (CG) location to determine whether passive means can increase flutter speed to acceptable levels. A similar flutter analysis is performed with the addition of a closed loop pitch axis autopilot to stabilize the aircraft over a wider range of static margin. Initial results indicate that BFF is an issue over lower altitude portions of the flight envelope and that active flutter suppression systems should be explored for future work.

Aeroelastic Model Reduction for Affordable Computational Fluid Dynamics-Based Flutter Analysis

Abstract: A new approach is presented to generate computational fluid dynamics (CFD)-based reduced-order aerodynamic and aeroelastic models for rapid flutter analysis at an affordable cost. The technique is based on the single-composite-input/eigensystem realization algorithm (SCI/ERA) that has been newly developed at Boeing. Given a large-scaled, discrete-time CFD model whose moving surface boundary is described by multiple structural mode shapes, the SCI/ERA takes time samples of the unsteady response due to a simultaneous excitation of the inputs and identifies the aerodynamic system in terms of low-order matrices. Because the CFD response is sampled almost exclusively for the single representative input this technique can significantly reduce the model construction time. The reduced-order aerodynamic model is coupled with a discrete-time structural model to generate a reduced-order aeroelastic model. For a demonstration of the method, a representative Boeing wind-tunnel airplane modeled by a finite element method and the CFL3D CFD code is studied. It is shown that for the case of 10 structural modes the proposed scheme can reduce the model construction time by a factor of 4-6, yet its unsteady aerodynamic and flutter results are as accurate as those created by other reduction methods.

Aeroelastic Studies on a Folding Wing Configuration

Abstract: Morphing aircraft can change shape and size substantially in-flight to enable a single vehicle to perform multiple mission roles. The majority of shape change occurs in the wing, resulting in a wide variety of changes in aerodynamic and structural features. In addition, as the wing moves during flight, the stiffness is reduced. One strong candidate for morphing wing design is a folding wing configuration. Several parametric studies were performed to identify aeroelastic features and potential peculiarities of a generic folding wing configuration. Study parameters include inboard and outboard wing folding angles, hinge line flexibility, and sweep angle of the outboard wing. Both the inboard and outboard hinge moments were also computed throughout the wing folding procedure while maintaining 1-g trim flight condition. This information was used to compute the energy requirement for folding the wing as a function of Mach number and aircraft center of gravity (c.g.) position. As a preprocessor, MATLAB is used to generate high fidelity structure and aerodynamic models. MATLAB generates input files for both ZAERO and MSC/NASTRAN to perform aeroelastic analysis. These studies show that as inboard wing folding angle increases the flutter dynamic pressure also increases. For the extended wing configuration, the flutter dynamic pressure is much more sensitive to changes in inboard hinge stiffness than outboard hinge stiffness. For the fully folded wing configuration, however, the outboard hinge stiffness affects flutter results more than that the inboard one. Results of the trim study show that minimum hinge actuation energy for the wing folding can be achieved at lower Mach number and most forward c.g. position.

POD-based Aeroelastic Analysis of a Complete F-16 Configuration: ROM Adaptation and Demonstration

Abstract: T he proper orthogonal decomposition method (POD) is applied to the computational fluid dynamics (CFD)-based reduced-order aeroelastic modeling of a complete F-16 fighter configuration, in order to assess its potential for the solution of realistic aeroelastic problems. The limitation of such a computational approach to a fixed free-stream Mach number is addressed by a Mach-adaptation strategy that interpolates the angle between two POD subspaces rather than the POD basis vectors directly. The predicted aeroelastic frequencies and damping ratio coefficients are compared with counterparts obtained from full-order nonlinear simulations and from flight test data. The results of these comparisons, including in the transonic regime, reveal a good potential of POD-based reduced-order modeling for the near real-time prediction of aircraft flutter using CFD technology.

Nonlinear aeroelastic/aeroservoelastic modeling by block-oriented identification

Abstract: The investigation of aeroelastic/aeroservoelastic stability through flight testing is an essential part of aircraft certification. The stability boundary prediction is especially difficult when the instability is associated with nonlinearities in the dynamics. An approach is presented for the characterization of the nonlinear dynamics by noniterative identification algorithms. Two different block-oriented nonlinear models are considered to augment existing linear models with nonlinear operators derived by analyzing experimental data. Specifically, focuse is placed on the identification of Hammerstein or Wiener block-oriented models from a N-point data record {¯k, ¯ yk} N = 1 of observed input‐output measurements from an aeroelastic/aeroservoelastic system. Central in the identification of block-oriented models is the use of an a priori set of orthonormal bases tuned with the dynamics of the aeroelastic/aeroservoelastic system. In both cases, a method is proposed to generate the orthonormal bases that is based on the cascade of input-normal balanced state-space realizations of all-pass filters. Case studies with a simulated structurally nonlinear prototypical two-dimensional wing section and actual F/A-18 active aeroelastic wing ground vibration test data are presented.

Aeroelastic Stability Enhancement and Vibration Suppression in a Composite Helicopter Rotor

Abstract: An optimization procedure to 1) reduce the 4/revolution oscillatory hub loads and 2) increase the lag mode damping of a four-bladed soft-in-plane hingeless helicopter rotor is developed using a two-level approach. At the upper level, response surface approximations to the objective function and constraints are used to find the optimal blade mass and stiffness properties for vibration minimization and stability enhancement. An aeroelastic analysis based on finite elements in space and time is used. The numerical sampling needed to obtain the response surfaces is done using the central composite design of the theory of design of experiments. The approximate optimization problem expressed in terms of quadratic response surfaces is solved using a gradient-based method. Optimization results for the vibration problem in forward flight with unsteady aerodynamic modeling show a vibration reduction of about 15%. The dominant loads are the vertical hub shear and the rolling and pitching moments, which are reduced by 22-26%. The results of stability enhancement problem show an increase of 6-125% in the lag mode damping. At the lower level, a composite box beam is designed to match the upper-level beam blade stiffness and mass using a genetic algorithm which permits the use of discrete ply angle design variables such as 0, +or-45, and 90 deg, which are easier to manufacture. Three different composite materials are used for designing the composite box beam, thus, showing the robustness of the genetic algorithm approach. Boron/epoxy composite gives the most compact box beam, whereas graphite/epoxy gives the lightest box beam

Static Nonlinear Aeroelasticity of Flexible Slender Wings in Compressible Flow

Abstract: *† A high-fidelity numerical formulation is presented for the high-speed aeroelastic behavior of slender composite wings. The compressible flow is modeled using the 3-D Euler equations on a deformable mesh, and an asymptotic approximation of the 3-D kinematically-nonlinear equations of elasticity models the anisotropic slender structure. The transfer of the distributed loads and displacements at the fluid-structure interface is based on detailed 3-D representations of the deformed aerodynamic and structural domains. Finally, a time-domain solution is implemented for the closely-coupled fluid-structure interaction problem. This procedure handles the large deflections appearing in very slender wings under aerodynamic loads using a description of the deformation that includes all geometrically-nonlinear effects in the aeroelastic analysis. Using this approach, the static nonlinear aeroelastic response of a 16:1 half-aspect ratio wing is investigated for steady flight conditions. The impact of the detailed 3-D representation of the fluid-structure interface on the aeroelastic response is investigated. For that purpose, numerical results are compared to the representation of the structure using a geometricallynonlinear 1-D beam model.

Further Invesitgation of Modeling Limit Cycle Oscillation Behavior of the F-16 Fighter Using a Harmonic Balance Approach

Abstract: A computational investigation of limit cycle oscillation behavior of the F-16 fighter configuration using a nonlinear frequency-domain harmonic-balance approach is presented. The research discussed in this latest paper is a follow-on to our work presented at the 2004 SDM conference. Our latest eorts have been directed toward assessing the eects of mean angle-of-attack, wingtip geometry, wing twist, and static aeroelastic deformation on flutter onset and LCO response.

Experimental evaluation of aerodynamic damping of square super high-rise buildings

Abstract: Aerodynamic damping often plays an important role in estimations of wind induced dynamic responses of super high-rise buildings. Across- and along-wind aerodynamic damping ratios of a square super high-rise building with a height of 300 m are identified with the Random Decrement technique (RDT) from random vibration responses of the SDOF aeroelastic model in simulated wind fields. Parametric studies on effects of reduced wind velocity, terrain type and structural damping ratio on the aerodynamic damping ratios are further performed. Finally formulas of across- and along-wind aerodynamic damping ratios of the square super high-rise building are derived with curve fitting technique and accuracy of the formulas is verified.

High-Fidelity Multidisciplinary Design Optimization of Aerostructural Wing Shape for Regional Jet

Abstract: A large-scale, real-world application of Evolutionary Multi-Objective Optimization is reported. The Multidisciplinary Design Optimization among aerodynamics, structures, and aeroelasticity of the wing of a transonic regional jet aircraft was performed using highfidelity evaluation models. Euler and Navier-Stokes solvers were employed for aerodynamic evaluation. The commercial software NASTRAN was coupled with a Computational Fluid Dynamics solver for the structural and aeroelastic evaluations. Adaptive Range MultiObjective Genetic Algorithm was employed as an optimizer. The objective functions were minimizations of block fuel and maximum takeoff weight in addition to drag divergence between transonic and subsonic flight conditions. As a result, nine non-dominated solutions were generated and used for tradeoff analysis among three objectives. Moreover, all solutions evaluated during the evolution were analyzed using a Self-Organizing Map as a Data Mining technique to extract key features of the design space. One of the key features found by Data Mining was the non-gull wing geometry, although the present MDO results showed the reverse-gull wings as non-dominated solutions. When this knowledge was applied to one optimum solution, the resulting design was found to have better performance and to achieve 3.6 percent improvement in the block fuel compared to the original geometry designed in the conventional manner.

Application of genetic algorithm for aeroelastic tailoring of a cranked-arrow wing

Abstract: A computer code for aeroelastic tailoring of a cranked-arrow wing for a supersonic transport is developed. The code includes static strength, local buckling, and aeroelastic analyses. The original finite element code is used for the static strength and local buckling analyses, and the original code is used for the vibration analysis of the aeroelastic analysis. In the optimization process of this code, a genetic algorithm is employed to find the optimum laminate construction of the wing box for which the structural weight is minimum under the static strength, local buckling, and aeroelastic constraints. These codes are applied to the preliminary design of a cranked-arrow wing. The optimum design satisfying only the static strength and local buckling constraints does not satisfy the aeroelastic constraint. Therefore, the flutter characteristics are optimized, and the optimum laminate construction that satisfies the static strength, local buckling, and aeroelastic constraints is obtained.

Aeroelastic calculations for the hawk aircraft using the euler equations

Abstract: This paper demonstrates coupled time-domain computational-fluid-dynamics (CFD) and computationalstructural-dynamics simulations for flutter analysis of a real aircraft in the transonic regime. It is shown that a major consideration for a certain class of structural models is the transformation method, which is used to pass information between the fluid and structural grids. The aircraft used for the calculations is the BAE Systems Hawk. A structural model, which has been developed by BAE Systems for simplified linear flutter calculations, only has a requirement for O(10) degrees of freedom. There is a significant mismatch between this and the surface grid on which loads and deflections are defined in the CFD calculation. This paper extends the constant volume tetrahedron tranformation, previously demonstrated for wing-only aeroelastic calculations, to multicomponent, or full aircraft, cases and demonstrates this for the Hawk. A comparison is made with the predictions of a linear flutter code.