Gust Loads Analysis Research Articles

On the Aeroelasticity of the Active Span and Passive Pitching Polymorphing Wing: A Parametric Study

This paper presents an aeroelastic analysis of a polymorphing wing capable of active span extension and passive pitch variation. The wing is split into two segments: an inboard segment responsible for span extension/retraction and an outboard segment capable of pitch variation. The two segments are connected through an overlapping spar and a torsional spring. A finite element aeroelastic model is developed where the wing structure is discretized into Euler–Bernoulli beam elements and the aerodynamic loads are calculated using Theodorsen’s unsteady model. A comprehensive parametric analysis is carried out with and without span extension to analyze the effect of varying critical design parameters, such as elastic axis position of outboard section and torsional spring rigidity, and conditions for aeroelastic phenomena of flutter and divergence are studied. A gust load analysis is carried out to quantify the capability of the outboard wing passive twist mechanism to alleviate loads. Finally, a nonlinear analysis is carried out by replacing the linear torsional spring with a nonlinear cubic spring to study the effects of cubic hardening and softening on the aeroelasticity of the polymorphing wing.

Gust Load Alleviation of Flexible Composite Wing

Gust load due to atmospheric turbulence is mandatory to be considered in aircraft analysis as part of airworthiness requirement. This safety related issue becomes more relevant recently in relation to the global warming that induces more frequent and extreme atmospheric disturbances encountered during air transportation. A direct application of gust load on the wing structural analysis, however, is not recommended since it will result in a significant weight increase due to the overdesign of the wing structure. At this point, the gust load alleviation plays an important role to effectively utilize the wing structural flexibility without ignoring the safety issue. In the present work, a method to alleviate the wing gust load is proposed by considering different configurations of the wing planform, wing sweep angle, wing dihedral angle and composite material layers. The objective of the study is to minimize the wing root bending moment due to the gust. The gust load analysis of the Kim-Hwang’s wing model will be used and the results are compared to the literature for the validation purpose. A finite element approach is used to simulate the wing structure in combination with the doublet lattice method to model the wing aerodynamics. It is found that the wing dihedral angle plays insignificant changes to the wing root bending moment due to the gust load. The wing sweep angle, however, gives significant changes to the wing root bending moment. For the present configuration, the optimum swept back configuration with a 45° sweep angle and optimum composite lay-up showed an average decrease of the bending moment by 12% for frequency range of 0 to 100 Hz.

Nonlinear Unsteady Reduced-Order Modeling for Gust-Load Predictions

A tremendous number of gust-load cases need to be computed during the aircraft design and certification process. From an aerodynamic point of view, gust-load predictions in industry rely on linear potential flow methods, which are inappropriate at transonic flight conditions. Prediction accuracy can be enhanced by accounting for aerodynamic loads computed with computational fluid dynamics, eventually resulting in lighter, more efficient designs. However, full-order, unsteady time-marching simulations are still prohibitively expensive in an industrial environment. Therefore, different reduced-order modeling techniques have been proposed to decrease the computational cost. This paper focuses on an unsteady nonlinear reduced-order model based on least-squares residual minimization and a comparison to the linearized frequency-domain method. Although the latter is in line with current industrial practice of sampling aerodynamic forces in the frequency domain, it neglects dynamic nonlinearities, which are included in the former approach. Results are presented for an airfoil and the NASA Common Research Model at transonic flow conditions exhibiting shock-induced separation during the airframe–gust interaction. Essential quantities for the gust-load analysis, such as global coefficients, sectional forces, and distributed quantities, are evaluated and compared to highlight the strengths and weaknesses of both model reduction techniques.

Flexible aircraft gust encounter simulation using subspace projection model reduction

Reduced-order modelling of multidisciplinary computational fluid dynamics can enable routine industrial gust load analysis. Key to the herein presented model reduction approach is that it modularly builds upon the widely accepted modal structural reduced-order model, where high-fidelity aerodynamics are simply projected onto the structural degrees-of-freedom, while opening a novel route to account for dominant modal aerodynamics in multidisciplinary edge-of-the-envelope flight physics. The influence of the flexible structure is captured by aeroelastic eigenmodes which originate in the structural equations. Such global aeroelastic modes for a large aircraft case with nearly 50 million degrees-of-freedom are computed for the first time using exact aerodynamics from computational fluid dynamics via the Schur complement method. The influence of atmospheric gusts is captured by modes from proper orthogonal decomposition applied to sinusoidal gust responses at discrete frequencies. Afterwards, the two sets of modes are combined and the linearised operator of the Reynolds-averaged Navier–Stokes equations coupled with a modal structural model is projected onto the resulting subspace. The constructed low-dimensional model can be solved rapidly for practical gust analysis giving accurate agreement with the full-order reference results throughout. Feasibility of aeroelastic model reduction, using the industry-grade computational fluid dynamics package DLR–TAU, for a relevant use case in transonic flight gust encounter is demonstrated.

Model reduction for flight dynamics simulations using computational fluid dynamics

Multidisciplinary simulation involving flight dynamics and computational fluid dynamics is required for high-fidelity gust loads analysis in transonic flow. However, the main limitation to a more routine use is prohibitive computational cost involved. A promising trade-off between accuracy and low-cost is model reduction of high-fidelity methods. Thus investigation of such reduction of coupled models is presented. The reduction technique relies on an expansion of the full order non-linear residual function in a truncated Taylor series and subsequent projection onto a small modal basis. Two procedures are discussed to obtain modes for the projection. First, an operator-based identification is exploited to calculate eigenpairs of the coupled Jacobian matrix related to the flight dynamics degrees-of-freedom. Secondly, proper orthogonal decomposition is used as a data-based method to obtain modes representing the system subject to external disturbance such as gusts. Benefits and limitations of the various methods are investigated by analysing results for initial disturbance and gust encounter simulations. Overall, reduced order models based on the presented approaches are able to retain the accuracy of the high-fidelity tools to predict accurately flight dynamics responses and loads while reducing the computational cost up to two orders of magnitude.

Evaluation of Quasi-Static Gust Loads Certification Methods for High-Altitude Long-Endurance Aircraft

Aeroelastic gust loads analysis can be approached using quasi-static, transient, or continuous methodologies. Pratt method is a quasi-static approach that forms the basis for Federal Aviation Regulation Part 23 gust loads certification requirements. This work evaluates the usefulness of Pratt method for unconventional high-altitude long-endurance aircraft. The derivation of Pratt method is reviewed, and all assumptions are identified. Error of a key curve fit equation is quantified directly. A state-of-the-art nonlinear aeroelastic code was upgraded and used to facilitate quantification of application-dependent errors by comparing quasi-static results to results from nonlinear transient analysis. Application-dependent errors are presented in the context of a SensorCraft-inspired joined-wing model and a Helios-aircraft-inspired flying-wing model. Recommendations are made on the usability of Pratt method for aircraft similar to the two high-altitude long-endurance models. It is concluded that Pratt method is useful for preliminary design of the joined-wing model but inadequate for the analysis of the flying-wing model. Further recommendations are made regarding the subtleties in the implementation of Pratt method for unconventional configurations.

Aeroelastic Loads and Sensitivity Analysis for Structural Loads Optimization

An aeroelastic integrated loads subsystem (AILS) is being developed and verified for the calculation of aeroelastic loads for analysis and design. AILS will fit within the aeroelastic design optimization program. The purpose of AILS is to integrate the maneuver and gust loads calculation process with structural analysis and optimization. AILS' active control capabilities and analytical sensitivity analysis will allow a simultaneous optimization of loads, structures, and active load alleviation system with flutter and other aeroelastic constraints. This first version of AILS includes a linear analysis for steady maneuver and unsteady aeroserv oelastic gust loads and their sensitivities to structural design variables and control parameters. AILS static aeroelastic analysis offers 1) full aircraft aeroelastic trim using aircraft angles of attack and sideslip, control-surface deflections, and/or motion rates and accelerations; 2) balanced distributed aeroelastic loads; 3) stress-based critical loads selection; 4) wing jig shape calculations for a specified nominal cruise wing shape and loading; 5) static aeroelastic stability and control derivatives and control effectiveness; and 6) static aeroelastic load sensitivities to structural design variables with constrained or variable nominal cruise shape to be used in optimization. The aeroservoelastic gust load capabilities in AILS include 1) random frequency response analysis for displacement, velocity, acceleration, element force, and stress; 2) flight control and active load alleviation system; 3) calculation of rms and zero-crossing frequency; and 4) analytical derivative of random gust response to control gains. These analyses are compared with MSC/NASTRAN and a proprietary dynamic analysis program (C4EZ). The results of comparisons for the static aeroelastic and gust response analyses of AILS are shown for two commercial transport aircraft: one is a wide-body subsonic transport and the other is a high-speed civil transport configuration at subsonic conditions. The static loads and stability derivatives for two models are compared with MSC/NASTRAN for both aircraft, and gust loads are compared with a production gust-load analysis for the subsonic transport case. In all cases excellent agreement is obtained. Validation of AILS' load sensitivity calculations was done through comparison with the finite difference approach. Excellent agreement was obtained between analytical and numerical derivatives.

Matched Filter Concept and Maximum Gust Loads

In the course of NASA evaluations of the statistical discrete gust method for determining worstcase gust loads on aircraft, it was found that the concept of the matched Ž lter from signal processing theory could be applied to the analysis of time-correlated, worst-case gust loads for mathematically linear aircraft models. Much of the work on the matched Ž lter approach to gust loads analysis that followed had been geared toward a fundamental understanding of the implications of the matched Ž lter theory interpretation of the gust loads analysis problem, as well as various attempts at extending the techniques to nonlinear aircraft models. A rigorous development of the matched Ž lter interpretation of gust loads within the context of the theory of random processes is presented and includes discussion of its relationship to existing statistically based methods for the calculation of design gust loads for linear aircraft. It is shown, using the matched Ž lter theory formalism, that the load peak-to-rms ratio can be related to the energy of the matched excitation waveform. Also, it is shown that a candidate design value of the peak-to-rms ratio that has been reported in the literature to be around 3 may have its basis in the discretization process that accompanies both data reduction and stochastic simulation on digital computers.

Statistical discrete gust-power spectral density methods overlap - Holistic proof and beyond

The statistical discrete gust (SDG)-power spectral density overlap of y = 10.4A claimed by J. G. Jones, and verified by B. Perry III, A. S. Pototzky, and J. A. Woods, does exist. The analytical results consist of numerical substantiation of specific aircraft models. The claim is valid up to approximately ±10% about the 10.4 factor. This article presents a mathematically rigorous proof from basic principles without specific aircraft models and very restricted gust shapes. By invoking Chebyshev's inequality, the extension to ymax = 25-150A for true design gust loads becomes a reality to complete the holistic proof. This article also introduces the allencompassing fractal geometry representation of turbulence that uses their respective Hausdorff (fractal) dimensions to derive all known spectral shapes. A sample case explains the obvious impacts from these different shapes on gust load exceedance. A two-tier approach proposes concrete changes in FAR 25 requirements. Realistic assessment of SDG method's role in gust load analysis points out some of its shortcomings and virtues.