A. Da Ronch

Evaluation of Dynamic Derivatives Using Computational Fluid Dynamics

This paper focuses on the evaluation of the dynamic stability derivative formulation. The derivatives are calculated using the Euler and Reynolds-averaged Navier–Stokes equations, and a time-domain solver was used for the computation of aerodynamic loads for forced periodic motions. To validate the predictions, two test cases are used. For the standard dynamic model geometry, a database of dynamic simulations illustrates the effects of the systematic variation of motion and fluid parameters involved. A satisfactory agreement was observed with available experimental data, and the dependency of dynamic derivatives on a number of parameters, such as Mach number, mean angle of attack, frequency, and amplitude, was assessed. For the transonic cruiser wind-tunnel geometry, static and unsteady aerodynamic characteristics were validated against experimental measurements. The ability of models based on the dynamic derivatives to predict large-amplitude motion forces and moments was assessed. It was demonstrated that the dynamic derivative model does not represent all of the important effects due to aerodynamics.

Linear frequency domain and harmonic balance predictions of dynamic derivatives

Dynamic derivatives are used to represent the influence of the aircraft motion rates on the aerodynamic forces and moments needed for studies of flight dynamics. The use of computational fluid dynamics has potential to supplement costly wind-tunnel testing. The paper considers the problem of the fast computation of forced periodic motions using the Euler equations. Three methods are evaluated. The first is computation in the time domain, which provides the benchmark solution in the sense that the time-accurate solution is obtained. Two acceleration techniques in the frequency domain are compared. The first uses a harmonic solution of the linearized problem, referred to as the linear frequency-domain approach. The second uses the harmonic balance method, which approximates the nonlinear problem using a number of Fourier modes. These approaches are compared for the ability to predict dynamic derivatives and for computational cost. The NACA 0012 aerofoil and the DLR-F12 passenger jet wind-tunnel model are the test cases. Compared to time-domain simulations, an order of magnitude reduction in computational costs is achieved and satisfactory predictions are obtained for cases with a narrow frequency spectrum and moderate amplitudes using the frequency-domain methods.

Nonlinear model reduction for flexible aircraft control design

The paper describes a systematic approach to the model reduction of large dimension fluid-structure-flight models, and the subsequent flight control design of very flexible aircraft. System nonlinearities may be due to the large wing deformations, the coupling between flexible and rigid body dynamics and/or flow separation at large angles of incidence. A nonlinear reduced order model is used to reduce the computational cost and dimension of the large-order nonlinear system for a practical control law design. The approach uses information on the eigenspectrum of the coupled system Jacobian matrix and projects the system through a series expansion onto a small basis of eigenvectors representative of the full-order dynamics. For a pitch-plunge aerofoil with structural nonlinearities, a controller based on reduced models was designed to alleviate gust loads. The approach to model reduction was also demonstrated for a two-dimensional problem with aerodynamics modelled using the computational fluid dynamics equations, and a flexible wing modelled using the geometrically-exact nonlinear beam equations. In all cases, the model reduction was found adequate to predict the large order system dynamics at a neglegible cost compared to that incurred by solving the nonlinear full-order system.

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.

Validation of Vortical Flow Predictions for a UCAV Wind Tunnel Model

A study of the aerodynamic behaviour of the Stability And Control Configuration wind tunnel model is presented. Both the sharp and round leading edge versions of the model are analysed in terms of the flow characteristics. A validation of the Reynolds Averaged NavierStokes predictions obtained using two block structured codes is made. Both static and dynamic cases are compared with wind tunnel measurements. The vortical flow features are described in detail for the range of conditions analysed. The predictions are in good agreement with the experiments at low angles of attack, whereas for higher incidences, α > 15◦, discrepancies are seen. A dual vortex structure is present in this region for both leading edge configurations resulting in a highly nonlinear aerodynamic behaviour.

Simulation of Aircraft Manoeuvres based on Computational Fluid Dynamics

The use of computational fluid dynamics to generate and test aerodynamic data tables for flight dynamics analysis is described in this paper. The test case used is the Ranger 2000 fighter trainer for which flight test data is available. The generation of the tables is done using sampling and reconstruction to allow a large number of table entries to be generated at low computational cost. The testing of the tables is done by replaying, through a time accurate CFD calculation which features the moving control surfaces, manoeuvres and comparing the forces and moments against the tabular values. The manoeuvres are generated using a time optimal prediction code with the feasible solutions based on the tabular aerodynamics. The generated maneouvres are evaluated against flight data to show that they are qualitatively representative. Then the time accurate and tabular aerodynamics are compared, and as expected are in close agreement.

Vortical flow prediction validation for an unmanned combat air vehicle model

As part of the NATO Applied Vehicle Technology 161 technical group, a study of the aerodynamic behavior of the stability and control configuration wind-tunnel model is presented. Sharp and round leading-edge versions of the model are computed. A validation of Reynolds-averaged Navier–Stokes predictions obtained using two block structured codes are made. Static cases are analyzed and compared with wind-tunnel measurements. The vortical flow features are described in detail for a range of angles of attack. The predictions are in good agreement with the experiments at low angles of attack, whereas for higher angles of incidence (alpha > 15), some discrepancies are seen. A dual vortex structure is present in this region for both leading-edge configurations, resulting in highly nonlinear aerodynamic behavior.

Model reduction for linear and nonlinear gust loads analysis

Time domain gust response analysis based on large-order nonlinear aeroelastic models is computationally expensive. An approach to the reduction of nonlinear models for gust loads prediction is presented in this paper. The method uses information on the eigenspectrum of the coupled system Jacobian matrix and projects the full order model through a series expansion onto a small basis of eigenvectors which is capable of representing the full order model dynamics. Linear and nonlinear reduced models derived from computational fluid dynamics and linear/nonlinear structural models are generated in this way. The novelty in the paper concerns the representation of the gust term in the reduced model in a manner consistent with standard synthetic gust definitions, allowing a systematic investigation of the influence of a large number of gusts without regenerating the reduced model. The methodology is illustrated by results for an aerofoil, with a combination of linear and nonlinear structural and aerodynamic models used, and a wing model with modal structural model.

A nonlinear controller for flutter suppression: from simulation to wind tunnel testing

Active control for flutter suppression and limit cycle oscillation of a wind tunnel wing section is presented. Unsteady aerodynamics is modelled with strip theory and the incompressible two-dimensional classical theory of Theodorsen. A good correlation of the stability behaviour between simulation and experimental data is achieved. The paper focuses on the introduction of a nonlinearity in the plunge degree of freedom of an experimental wind tunnel test rig and the design of a nonlinear controller based on partial feedback linearization. To demonstrate the advantages of the nonlinear synthesis on linear conventional methods, a linear controller is implemented for the nonlinear system that exhibits limit cycle oscillations above the linear flutter speed. The controller based on partial feedback linearization outperforms the linear control strategy based on pole placement. Whereas feedback linearization allows to suppress fully the limit cycle oscillations, the pole placement fails to achieve any significant reduction in amplitudes