Aerodynamic Influence Coefficient Matrices Research Articles

A two-level strategy for aeroelastic optimization of a 3D wing with constant and variable stiffness skins

In this work, optimization strategies employing a standard heuristic free-derivative algorithm combined with a first-order gradient approach are used to maximize the flutter or divergence airspeed, using the fibre material orientations as design variables. The aeroelastic stability analysis calculations are performed by a classical PK method. The finite element method is used to obtain the structural modes and frequencies and the unsteady aerodynamic influence coefficient matrices are obtained with a doublet-lattice model. Numerical studies are performed with a complex 3D model that includes curved surfaces and internal elements such as spars and ribs. The main goal of the article is to use the heuristic part with a small number of parameters, to reduce the design space and provide an efficient initial guess for the gradient search, so that the optimization complexity is substantially reduced. Results for constant and variable stiffness composite wings are presented for laminates with different numbers of plies. It is shown by several examples that the pres.

Uncertainty quantification in free vibration and aeroelastic response of variable angle tow laminated composite plate

The influence of uncertainty in material properties on free vibration and aeroelastic response of variable angle tow (VAT) laminated plates is presented in this work. Free vibration analysis is conducted by a finite element model based on third-order shear deformation theory. The FE model is further coupled with MSC. Nastran to carry out aeroelastic analysis of VAT laminates in the subsonic regime. MSC. Nastran helps to extract the aerodynamic influence coefficient matrix at discrete values of reduced frequencies using Doublet Lattice Method. The accuracy and adaptability of the highly efficient radial basis neural network (RBFN) based surrogate model developed for uncertainty analysis are checked by comparing the result with that of the Monte Carlo simulation. Stochastic analysis of natural frequencies and flutter characteristics of VAT laminates are conducted through various parametric studies. Variance-based sensitivity analysis is used to calculate the contribution of individual material properties to the free vibration and aeroelastic response of VAT laminates. Further, the influence of the highly sensitive properties on the structural failure probability is estimated. This research can be leveraged to predict the probability of failure of the structure at different levels of material uncertainty present in it.

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.

Geometrically Nonlinear Effects on the Aeroelastic Response of a Transport Aircraft Configuration

This paper investigates geometrically nonlinear aeroelastic effects on an industry-level aircraft configuration. Results are obtained via a new approach that uses geometrical information to compute nonlinear effects and seamlessly integrates with conventional, linear aeroelastic load packages. The starting point is a generic finite-element model and frequency-domain aerodynamic influence coefficient matrices, and the resulting system includes control inputs, longitudinal trim, or gust disturbances in time domain, which can be employed separately or in combination to obtain a nonlinear dynamic model for loads and stability analysis. The aeroelastic response of a long range aircraft is studied, highlighting the difference between linear and nonlinear approaches in the calculations of the aircraft flying equilibrium, dynamic perturbations, and variations to the flutter boundary. Results justify the need for geometrically nonlinear analysis in the production environment of airplanes with ultrahigh-aspect-ratio wings.

Subsonic source and doublet panel methods

This work presents a source and doublet surface panel method for solving unsteady subsonic flows around wing and bodies. The approach is based on Morino’s theory but features three modifications. The impermeability boundary condition is defined as zero mass flux normal to the surface instead of zero normal velocity, a new methodology is introduced to calculate the aerodynamic influence coefficient matrices and the pressure distribution around the surface is evaluated using a nonlinear unsteady Bernoulli equation. The method is demonstrated on three experimental test cases from the literature; it is shown that it can predict more accurately the steady and oscillating pressure distribution around the surface than Morino’s original linear approach. Crucially, the modified approach can represent asymmetries in the pressure distribution due to both asymmetric motion and shape. While higher fidelity alternatives exist for solving such flows, the present method has very low computational cost and would be suitable for optimization procedures during preliminary design, as long as the flow remains subcritical and attached at all times.

A non-intrusive geometrically nonlinear augmentation to generic linear aeroelastic models

A new approach to build geometrically-nonlinear dynamic aeroelastic models is proposed that only uses information typically available in linear aeroelastic analyses, namely a generic (linear) finite-element model and frequency-domain aerodynamic influence coefficient matrices (AICs). Good computational efficiency is achieved through a two-step process: Firstly, a geometric reduction of the structure is carried out through static or dynamic condensation on nodes along the main load paths of the vehicle. Secondly, manipulation of the resulting linear normal modes (LNMs), the condensed stiffness and mass matrices, and the nodal coordinates provides the modal coefficients of the intrinsic beam equations along these load paths. This preserves the LNMs of the original problem and augments them with the geometrically nonlinear terms of beam theory. The structural description is in material coordinates and modal AICs are thus naturally included as follower forces. Numerical examples include cantilever wings built using detailed models, for which effects such as nonlinear aeroelastic equilibrium, nonlinear dynamics and structural-driven limit-cycle oscillations are shown. Results demonstrate the ability of the methodology to seamlessly and efficiently incorporate critical nonlinear effects to (linear) arbitrarily large aeroelastic models of high aspect ratio wings.

Calculation of the Hinge Moments of a Folding Wing Aircraft during the Flight-Folding Process

A folding wing morphing aircraft should complete the folding and unfolding process of its wings while in flight. Calculating the hinge moments during the morphing process is a critical aspect of a folding wing design. Most previous studies on this problem have adopted steady-state or quasi-steady-state methods, which do not simulate the free-flying morphing process. In this study, we construct an aeroelastic flight simulation platform based on the secondary development of ADAMS software to simulate the flight-folding process of a folding wing aircraft. A flexible multibody dynamic model of the folding wing structure is established in ADAMS using modal neutral files, and the doublet lattice method is developed to generate aerodynamic influence coefficient matrices that are suitable for the flight-folding process. The user subroutine is utilized, aerodynamic loading is realized in ADAMS, and an aeroelastic flight simulation platform of a folding wing aircraft is built. On the basis of this platform, the flight-folding process of the aircraft is simulated, the hinge moments of the folding wings are calculated, and the influences of the folding rate and the aircraft’s center of gravity (c.g.) position on the results are investigated. Results show that the steady-state method is applicable to the slow folding process. For the fast folding process, the steady-state simulation errors of the hinge moments are substantially large, and a transient method is required to simulate the flight-folding process. In addition, the c.g. position considerably affects the hinge moments during the folding process. Given that the c.g. position moves aft, the maximum hinge moments of the inner and outer wings constantly increase.

Parametric aeroelastic modeling based on component modal synthesis and stability analysis for horizontally folding wing with hinge joints

To investigate the aeroelastic stability of a folding wing effectively, a parametric aeroelastic analysis approach is proposed. First, the fixed interface component modal synthesis is used to derive the structural dynamic equation for a folding wing, in which the elastic connection is considered. The unsteady aerodynamic model is established by the doublet lattice method (DLM), and the aeroelastic model is achieved from integration of the DLM with the component modal analysis. The generalized aerodynamic influence coefficient matrix is established by modes kept and constraint modes of each component. The aeroelastic stability of a folding wing is investigated based on the Gram matrix in control theory. The effectiveness of the proposed method is verified via comparison with traditional flutter eigenvalue analysis for both extended and folded configurations. The proposed method identifies coupled modes and improves computational efficiency when compared to classical aeroelastic stability analysis methods, such as the p–k method.

The nonlinear aeroelastic characteristics of a folding wing with cubic stiffness

This paper focuses on the nonlinear aeroelastic characteristics of a folding wing in the quasi-steady condition (namely at fixed folding angles) and during the morphing process. The structure model of the folding wing is formulated by the Lagrange equations, and the constraint equation is used to describe the morphing strategy. The aerodynamic influence coefficient matrices at several folding angles are calculated by the Doublet Lattice method, and described as rational functions in the Laplace domain by the rational function approximation, and then the Kriging agent model technique is adopted to interpolate the coefficient matrices of the rational functions, and the aerodynamics model of the folding wing during the morphing process is built. The aeroelastic responses of the folding wing with cubic stiffness are simulated, and the results show that the motion types of aeroelastic responses in the quasi-steady condition and during the morphing process are all sensitive to the initial condition and folding angle. During the morphing process, the transition of the motion types is observed. And apart from the period of transition, the aeroelastic response at some folding angles may exhibit different motion types, which can be found from the results in the quasi-steady condition.

Unsteady Aerodynamic Force Sensing from Strain Data

A simple approach for computing unsteady aerodynamic forces from simulated measured strain data is proposed in this study. First, the deflection and slope of the structure are computed from the unsteady strain. Velocities and accelerations of the structure are computed using the autoregressive moving average model, online parameter estimator, low-pass filter, and a least-squares curve fitting method, together with analytical derivatives with respect to time. Finally, aerodynamic forces over the wing are computed using modal aerodynamic influence coefficient matrices, a rational function approximation, and a time-marching algorithm. A cantilevered rectangular wing is used to validate the simple approach. Unsteady aerodynamic forces as well as wing deflections, velocities, accelerations, and strains are computed using the CFL3D computational fluid dynamics code and the MSC/NASTRAN finite element analysis code; and these CFL3D/NASTRAN-based results are assumed as measured quantities. Computed deflections, velocities, accelerations, and unsteady aerodynamic forces are compared with the CFL3D/NASTRAN-based results. Computed aerodynamic forces based on lifting-surface theory at subsonic speeds are in good agreement with the target aerodynamic forces generated using CFL3D code with the Euler equation. This research demonstrates the feasibility of obtaining induced drag and lift forces through the use of distributed sensor technology with measured strain data.

Aeroelastic study for folding wing during the morphing process

This paper focuses on the aeroelastic characteristics of a folding wing during the morphing process. The folding wing structure is modeled by using the flexible multi-body dynamics approach, and an efficient method is proposed to calculate the aerodynamic force of the folding wing during the morphing process. The aerodynamic influence coefficient (AIC) matrices at different folding angles are obtained by the Doublet Lattice based aerodynamics theory, and then the orders of these AIC matrices are reduced by the spline interpolation technique. Through the minimum state approximation, the reduced AIC matrices are described as rational functions in the Laplace domain. Then the Kriging agent model technique is used to interpolate the coefficient matrices of the rational functions obtained from several different folding angles and to build the aerodynamics model in the time domain. At some different folding angles, the element values of the coefficient matrices before and after the interpolation are compared to verify the accuracy of the aerodynamics model, and then the aeroelastic responses of the folding wing during its morphing processes are simulated. The results demonstrate that the folding and unfolding processes have opposite influences on the dynamic aeroelastic stability of the folding wing, and the influences become much more significant with the increasing of the folding and unfolding rates. When the folding wing is morphing with a very slow rate, the dynamic aeroelastic stability will be similar to that obtained by the quasi-steady aeroelastic analysis.

Correction of aerodynamic influence matrices for transonic flow

The authors present a novel correction approach for the doublet-lattice method in this paper. The doublet-lattice method is a standard tool for calculating unsteady aerodynamic loads in aeroelasticity. It solves the linear potential equations and is thus valid only at subsonic flow conditions. Hence, corrections have to be applied for transonic flow. The proposed correction method, CREAM (CorREction of Aerodynamic Matrices), uses surface pressure distributions obtained using computational fluid dynamics (CFD) simulations for the correction. It is based on a Taylor expansion of the aerodynamic influence coefficient matrix, where the Taylor coefficients are corrected successively. The approach can be applied to quasi-steady as well as to unsteady aerodynamic calculations. The method is demonstrated on the AGARD LANN wing at transonic attached flow conditions and compared to linearized unsteady CFD computations. Two different correction orders are examined: a “zeroth order correction” with a quasi-steady CFD sample as correction input and a “first order correction” with an additional unsteady CFD sample. It is shown that CREAM gives improved results for small reduced frequencies, where the first-order correction is always superior to the zeroth order correction.

Control-point-placement method for the aerodynamic correction of the vortex- and the doublet-lattice methods

The use of correction factors to improve the accuracy of the aerodynamic influence coefficient (AIC) matrices produced by the vortex-lattice and the doublet-lattice methods has been an engineering practice in the field of aeroelasticity. In order to account for either viscous or transonic flow effects not considered in the linearized formulation of such methods, the most frequent correction techniques have been to pre-multiply or to post-multiply the AIC matrices by diagonal matrices comprising semi-empirical weighting factors. This paper proposes a different correction approach: the control-point-placement method (CPPM), based on the idea of displacing the control point of each panel – the point where the boundary condition of flow tangency must be satisfied. Both the vortex- and the doublet-lattice methods have been developed with the singularities placed at the quarter-chord line of the panels and the control points at three quarters of their mean chords. With the calculation of modified control point positions, the CPPM intrinsically changes the mutual aerodynamic influence between the panels and allows the lifting surface methods to predict steady-state pressure distributions that match or approximate with minimum error those derived from wind tunnel measurements or higher-fidelity CFD solutions. Different approaches to extend the aerodynamic correction for application at non-zero reduced frequencies in the doublet-lattice method are then studied. Results are presented that are in acceptable agreement with benchmark wind tunnel data and comparisons are made between the proposed methodology and the traditional diagonal matrix corrections.

Frequency domain analysis for wing transonic flutter

In the time domain aerodynamics calculation, a new approach for flow field boundary controlling is suggested in the present study, in which the wing was forced to oscillate harmonically under small amplitude. The transonic aerodynamic force was computed by solving unsteady Euler equations, and then modal aerodynamic force was calculated using modal matrix. The least square method is used to fit the modal aerodynamic force coefficient time history. From the physical meaning of aerodynamic influence coefficient ( AIC ) matrix, the formulation of AIC matrix are derived according to time domain solution of modal aerodynamic force. Based on the transonic AIC matrix, wing transonic flutter characteristics can be obtained by frequency domain flutter solution. The transonic flutter charac-teristics of AGARD 445.6 wing are studied and the flutter boundary under different Mach numbers was presented. The results obtained by the present method are in good agreement with those obtained by experimental data of literatures.

Static Aeroelastic Response Analysis of Aircrafts Based on CFD Pressure Distribution

An analysis method for static aeroelastic response considering the effect of Computational Fluid Dynamics (CFD) aerodynamic pressure distribution was developed in this paper. The aerodynamic pressure and the steady aerodynamic influence coefficient matrix were computed by the high-order panel method and then were corrected according to CFD pressure distribution on the 3D body-surface panel element. The static aeroelastic response was solved by modal method coupling with the structural model. A high-aspect-ratio wing was taken as an example to evaluate the analysis method, and the aerodynamic pressure obtained by CFD method with Euler equation was used for aerodynamics correction on 3D body-surface panel element in this study case. The method was then evaluated by comparing the results with those from the low-order panel method using external aerodynamic pressure and the high-order panel method. The results indicate that the method could provide correct results. The method could be used in the preliminary stage as well as in the detailed stage of aircraft design to provide design guideline of static aeroelastic response analysis.

Unsteady Aerodynamic Model Tuning for Precise Flutter Prediction

A simple method for an unsteady aerodynamic model tuning is proposed in this study. This method is based on the direct modification of the aerodynamic influence coefficient matrices. The aerostructures test wing 2 flight-test data is used to demonstrate the proposed model tuning method. The flutter speed margin computed using only the test validated structural dynamic model can be improved using the additional unsteady aerodynamic model tuning, and then the flutter speed margin requirement of 15 percent in military specifications can apply towards the test validated aeroelastic model. In this study, unsteady aerodynamic model tunings are performed at two time invariant flight conditions, at Mach numbers of 0.390 and 0.456. When the Mach number for the unsteady aerodynamic model tuning approaches to the measured fluttering Mach number, 0.502, at the flight altitude of 9,837 ft, the estimated flutter speed is approached to the measured flutter speed at this altitude. The minimum flutter speed difference between the estimated and measured flutter speed is -0.14 percent.

Flutter suppression of a high aspect-ratio wing with multiple control surfaces

This paper presents a systematic study on active flutter suppression of a high aspect-ratio wing with multiple control surfaces distributed throughout the span. The dynamic characterization of the wing structure is done by the finite element method. Doublet lattice method is used to model unsteady aerodynamic loads acting on the lifting surface with leading-edge and trailing-edge control surfaces. The open-loop aeroelastic equations with input delays are established by the modal transformation of the structural equations and the minimum state approximation of the aerodynamic influence coefficient matrix. To suppress flutter of the time-delayed system, a dynamic controller is synthesized in H ∞ control theory framework. The delay-dependent stability of the closed-loop system is analyzed by tracing the rightmost eigenvalues of the system. Numerical simulations are made to demonstrate the effectiveness of all the above approaches.

Extension of the g-Method Flutter Solution to Aeroservoelastic Stability Analysis

Extension of the g-Method Flutter Solution to Aeroservoelastic Stability Analysis

Overset Field-Panel Method for Unsteady Transonic Aerodynamic Influence Coefficient Matrix Generation

The overset field-panel method presented solves the integral equation of the time-linearized transonic small disturbance equation by an overset field-panel scheme for rapid transonic aeroelastic applications of complex configurations. A block-tridiagonal approximation technique is developed to greatly improve the computational efficiency to solve the large size volume-cell influence coefficient matrix. Using the high-fidelity computational-fluid-dynamics solution as the steady background flow, the present method shows that simple theories based on the small disturbance approach can yield accurate unsteady transonic flow predictions. The aerodynamic influence coefficient matrix generated by the present method can be repeatedly used in a structural design loop, rendering the present method as an ideal tool for multidisciplinary optimization.

Study on the Aerodynamic Characteristics of Wings Flying Over the Nonplanar Ground Surface

Aerodynamic analysis of NACA wings moving with a constant speed over guideways are performed using an indirect boundary element method (potential-based panel method). An integral equation is obtained by applying Green's theorem on all surfaces of the fluid domain. The surfaces over the wing and the guideways are discretized as rectangular panel elements. Constant strength singularities are distributed over the panel elements. The viscous shear layer behind the wing is represented by constant strength dipoles. The unknown strengths of potentials are determined by inverting the aerodynamic influence coefficient matrices constructed by using the no penetration conditions on the surfaces and the Kutta condition at the trailing edge of the wing. The aerodynamic characteristics for the wings flying over nonplanar ground surfaces are investigated for several ground heights.