Simao Marques

Transonic Aeroelastic Stability Analysis Using a Kriging-Based Schur Complement Formulation

A method is described to allow searches for transonic aeroelastic instability of realistically sized aircraft models in multidimensional parameter spaces when computational fluid dynamics are used to model the aerodynamics. Aeroelastic instability is predicted from a small nonlinear eigenvalue problem. The approximation of the computationally expensive interaction term modeling the fluid response is formulated to allow the automated and blind search for aeroelastic instability. The approximation uses a kriging interpolation of exact numerical samples covering the parameter space. The approach, demonstrated for the Goland wing and the multidisciplinary optimization transport wing, results in stability analyses over whole flight envelopes at an equivalent cost of several steady-state simulations.

Transonic Aeroelastic Stability Predictions Under the Influence of Structural Variability

DOI: 10.2514/1.46971 Flutter prediction as currently practiced is almost always deterministic in nature, based on a single structural model that is assumed to represent a fleet of aircraft. However, it is also recognized that there can be significant structural variability, even for different flights of the same aircraft. The safety factor used for flutter clearance is in part meant to account for this variability. Simulation tools can, however, represent the consequences of structural variability in the flutter predictions, providing extra information that could be useful in planning physical tests and assessing risk. The main problem arising for this type of calculation when using high-fidelity tools based on computational fluid dynamics is the computational cost. The current paper uses an eigenvalue-based stability method together with Euler-level aerodynamics and different methods for propagating structural variability to stability predictions.The propagation methodsare Monte Carlo,perturbation, andinterval analysis. Thefeasibility of this type of analysis is demonstrated. Results are presented for the Goland wing and a generic fighter configuration.

Framework for Establishing Limits of Tabular Aerodynamic Models for Flight Dynamics Analysis

This paper describes the use of Computational Fluid Dynamics for the generation and testing of tabular aerodynamic models for flight dynamics analysis. Manoeuvres for the AGARD Standard Dynamics Model wind tunnel geometry for a generic fighter are considered as a test case. Wind tunnel data is first used to validate the prediction of static and dynamic coefficients at both low and high angles, featuring complex vortical flow, with good agreement obtained at low and moderate angles of attack. Then the generation of aerodynamic tables is described based on an efficient data fusion approach. An optimisation is used to define time optimal manoeuvres based on these tables, including level flight trim, pull-ups at constant and varying incidence, and level and 90 degree turns. The manoeuvre description includes a definition of the aircraft states and also the control deflections to achieve the motion. The main point of the paper is then to assess the validity of the aerodynamic tables which were used to define the manoeuvres. This is done by replaying them, including the control surface motions, through the time accurate CFD code. The resulting forces and moments can be compared with the tabular values to assess the presence of inadequately modelled dynamic or unsteady effects. The agreement between the tables and the replay is demonstrated for slow manoeuvres. A study for the pull-up at increasing rates shows discrepancies which are ascribed to vortical flow hysteresis at elevated motion rates.

Framework for Establishing the Limits of Tabular Aerodynamic Models for Flight Dynamics Analysis

This paper describes the use of Computational Fluid Dynamics for the generation and testing of tabular aerodynamic models for flight dynamics analysis. Manoeuvres for the AGARD Standard Dynamics Model wind tunnel geometry for a generic fighter are considered as a test case. Wind tunnel data is first used to validate the prediction of static and dynamic coefficients at both low and high angles, featuring complex vortical flow, with good agreement obtained at low and moderate angles of attack. Then the generation of aerodynamic tables is described based on an efficient data fusion approach. An optimisation is used to define time optimal manoeuvres based on these tables, including level flight trim, pull-ups at constant and varying incidence, and level and 90 degree turns. The manoeuvre description includes a definition of the aircraft states and also the control deflections to achieve the motion. The main point of the paper is then to assess the validity of the aerodynamic tables which were used to define the manoeuvres. This is done by replaying them, including the control surface motions, through the time accurate CFD code. The resulting forces and moments can be compared with the tabular values to assess the presence of inadequately modelled dynamic or unsteady effects. The agreement between the tables and the replay is demonstrated for slow manoeuvres. A study for the pull-up at increasing rates shows discrepancies which are ascribed to vortical flow hysteresis at elevated motion rates.

Prediction of Transonic Limit-Cycle Oscillations Using an Aeroelastic Harmonic Balance Method

This work proposes a novel approach to compute transonic limit-cycle oscillations using high-fidelity analysis. Computational-Fluid-Dynamics based harmonic balance methods have proven to be efficient tools to predict periodic phenomena. This paper’s contribution is to present a new methodology to determine the unknown frequency of oscillations, enabling harmonic balance methods to accurately capture limit-cycle oscillations; this is achieved by defining a frequency-updating procedure based on a coupled computational-fluid-dynamics/computational-structural-dynamics harmonic balance formulation to find the limit-cycle oscillation condition. A pitch/plunge airfoil and delta wing aerodynamic and respective linear structural models are used to validate the new method against conventional time-domain simulations. Results show consistent agreement between the proposed and time-marching methods for both limit-cycle oscillation amplitude and frequency while producing at least a one-order-of-magnitude reduction in ...

Calculating the Influence of Structural Uncertainty on Aeroelastic Limit Cycle Response

Previous work by the authors has considered the impact on aeroelastic stability of uncertainty in structural parameters. Particular consideration has been given to how large dimensional systems like those arising from computational fluid dynamics can be made tractable for the stability analysis. There is considerable practical interest in evaluating the impact of structural parameter variability on limit cycle responses. This is a demanding task since nonlinearity must be involved in some form (which tends to render model reduction through methods like proper orthogonal decomposition less effective than for linear problems). The best current approach seems to be that described in reference, which contains a good review of the current state of the art. The current paper has the objective of reconsidering the (nonlinear) model reduction presented in references 6 for application to parametric variability studies. The approach is to calculate the critical eigenspace of the linearised system and use this as a basis for model reduction. The full order system is manipulated using a Taylor expansion which is then projected onto the critical eigenspace basis. The extra step here is to add the influence of an uncertain parameter to the Taylor Series. This allows the reduced model (two degrees-of-freedom) to be precomputed, and then exploited for the variability analysis. The feasibility of this approach was demonstrated in a recent paper, where the application was made to a two degree of freedom system with a structural nonlinearity, and a linear model for the aerodynamics. Results showed that the nonlinear reduced model was effective for computing the LCO probability density function when a distribution for one of the structural parameters was assumed. In the current paper this work is extended to a three dimensional case with a nonlinearity introduced into the structural model of a wing/tip store test case.

How Structural Model Variability Influences Transonic Aeroelastic Stability

This paper considers the ways in which structural model parameter variability can influence aeroelastic stability. Previous work on formulating the stability calculation (with the Euler equations providing the aerodynamic predictions) is exploited to use Monte Carlo, interval, and perturbation calculations to allow this question to be investigated. Three routes are identified. The first involves variable normal-mode frequencies only. The second involves normal-mode frequencies and shapes. Finally, the third, in addition to normal-mode frequencies and shapes, also includes their influence on the static equilibrium. Previous work has suggested only considering the first route, which allows significant gains in computational efficiency if reduced-order models can be built for the aerodynamics. However, results in the current paper show that neglecting the mode-shape variation can give misleading results for the flutter-onset prediction, complicating the development of reduced aerodynamicmodels for variability analysis.

CFD based aeroelastic stability predictions under the influence of structural variability.

Flutter prediction as currently practised is almost always deterministic in nature, based on a single structural model that is assumed to represent a fleet of aircraft. However, it is also recognised that there can be significant variability, even for different flights of the same aircraft. The safety factor used during flutter clearance is in part meant to account for this variability. Simulation tools can however represent the consequences of structural variability in the flutter predictions, providing extra information which could be useful in planning physical tests and assessing risk. The main problem arising for this type of calculation when using high fidelity tools based on Computational Fluid Dynamics (CFD) is the computational cost. The current paper uses an eigenvalue based stability method together with CFD level aerodynamics and different methods for propagating structural variability to stability predictions. The propagation methods are Monte Carlo, perturbation and interval analysis. The feasibility of this type of analysis is demonstrated. Results are presented for the Goland wing and for a generic fighter configuration.

Parametric design velocity computation for CAD-based design optimization using adjoint methods

This paper presents an efficient optimization process, where the parameters defining the features in a feature-based CAD model are used as design variables. The process exploits adjoint methods for the computation of gradients, and as such the computational cost is essentially independent of the number of design variables, making it ideal for optimization in large design spaces. The novelty of this paper lies in linking the adjoint surface sensitivity information with geometric sensitivity values, referred to as design velocities, computed for CAD models created in commercial CAD systems (e.g. CATIA V5 or Siemens NX). This process computes gradients based on the CAD feature parameters, which are used by the optimization algorithm, which in turn updates the values of the same parameters in the CAD model. In this paper, the design velocity and resulting gradient calculations are validated against analytical and finite-difference results. The proposed approach is demonstrated to be compatible with different commercial CAD packages and computational fluid dynamics solvers.

Nonlinear Aerodynamic and Aeroelastic Model Reduction using a Discrete Empirical Interpolation Method

A novel surrogate model is proposed in lieu of computational-fluid-dynamics solvers, for fast nonlinear aerodynamic and aeroelastic modeling. A nonlinear function is identified on selected interpol...