New generation combat aircraft are expected to operate over extended flight envelopes, including flight at high flow angles and rapid maneuvers. Conditions beyond traditional limits are giving rise to nonlinear phenomena, such as flow separation, large scale energetic vortices, fluctuations etc. These phenomena have significant impact on aircraft performance and if not resolved accurately design uncertainties are increased risking lack of performance or even costly redesigns. Thus, accurate modelling of unsteady nonlinear aerodynamics is essential for modern and future combat aircraft.

Unfortunately, conventional modelling tools either lack the required fidelity or they are too expensive. Traditional, highly-efficient approaches are not suitable for modelling nonlinear flow phenomena. Concurrently, high fidelity Computational Fluid Dynamics (CFD) simulations are computationally demanding and therefore impractical in many cases. To enhance aircraft design, it is desirable to obtain models joining the best of these two worlds. A common approach is to distill high fidelity methods into Reduced-Order Models (ROMs) that can accurately approximate unsteady aerodynamics at orders of magnitudes lower costs than CFD. Relevant literature offers many different ROM techniques for varying purposes. Nonetheless, constructing such models is still challenging and currently there is no generally agreed method.

In the current thesis a ROM technique that may be applicable to wider ranges of problems and simpler to construct is sought. The objective is to obtain a model that can promote aircraft control design, performance assessment and structural analysis throughout dynamic maneuvers over complete flight envelopes. The thesis proposes a novel approach utilizing modern, deep convolutional neural networks (CNNs). The devised model consists of three main components. First it incorporates a geometry description constituted by coordinates of an aircraft CFD surface grid. Second, a primary encoding-decoding CNN predicts pressure distribution at the grid points of the geometry. The final and third part of the model is an auxiliary encoding CNN deriving integral aerodynamic loads corresponding to the pressure field predictions of the primary network. The model evaluates and produces instantaneous values. Given a maneuver, it proceeds in timesteps. The predictions of the separate instances are computed directly without the need of subiterations (as it would be the case for CFD simulations).

As a proof of concept, the model is applied to symmetric motions in the vertical plane at fixed Mach number and altitude. The subject of the investigations is the MULDICON configuration of the 251 th Science and Technology Organization work-group of NATO. To fully exploit the advantages of reduced-order modelling, flow characteristics are inferred from a single excitation following an efficient system identification technique using Schroeder sweeps as input signals. The performance of the model is assessed by numerous test cases performed in CFD. First, steady conditions of varying incidence angles are investigated. Second, harmonic pitch and plunge oscillations around different angles of attack at different amplitudes and frequencies are considered. Third, additional test cases of a linear pitch up-down -- and a climbing maneuver are studied.

Considering computational efficiency, the results show robust model performance. GPU-accelerated CNN calculations are conducted roughly 5000 times faster than CFD simulations. The primary network can accurately resolve the pressure distributions over large portions of the geometry. Lower surface predictions are very accurate. However, among certain conditions discrepancies are observable on the upper surface towards the wingtips. Still, the secondary network can predict corresponding aerodynamic forces accurately. In contrast, its moment predictions are sensitive to errors in pressure distributions. Consequently, moment predictions can largely deviate from reference data, especially when nonlinear phenomena are prominent. However, in many cases errors are attributed to insufficient regressor space coverage, i.e.\ certain input combinations are explored poorly by the Schroeder sweeps. Reconsidering system identification practices might mitigate those issues. Nevertheless, the thesis proves the applicability of deep CNNs to the problems at hand. Additionally, the results encourage further investigations.

During aircraft design,multiple tools are utilised to inspect the performance of the configuration. As the design matures, higher fidelity analyses are conducted to predict the flight dynamics of the aircraft. These analyses are conducted by using semi-empirical relations, numerically analysing flow behaviour, conducting wind-tunnel tests and performing scaled test flights. However, Semi-empirical relations might not hold for next generation aircraft and wind tunnel testing and scaled test flights are extensive and are also prone to accuracy issues. A best of both worlds can be found in numerical analysis. However, an increase in flow fidelity modelling comes with an increase in computational cost. Besides, complete analysis of all possible manoeuvres of a design increases the number of computations significantly. Current methods cope with this issue by using flight dynamics models based on so called stability derivatives, instantaneous values which couple flight state parameters to aerodynamic loads to predict aircraft flight dynamics. However, these models do not take into account time dependency. Therefore, these methods do not accurately predict the flight dynamics of agile aircraft, such as unmanned combat aerial vehicles, undergoing rapid manoeuvres where unsteadiness dominates flow behaviour. This conventional reduced-order modelling method, in which samples of the full-order model are taken in the form of stability derivatives, causes design iterations to be analysed inaccurately. The objective of this report is to investigate reduced-order modelling for flight dynamics prediction, thereby comparing conventional techniques to a method which does take into account unsteadiness in flow behaviour.
The method investigated is based on indicial step response functions, which are samples in the form of unsteady aerodynamic flow behaviour functions of the full-order model. The idea is that once these samples are known, any flight manoeuvre can be analysed within minutes. Research found in literature has assessed some of the capabilities and limitations of this method, but not yet applied this to flight dynamics prediction. The research described within this report will address this gap by using two test cases. The first testcase is used to assess the assumptions made in literature, on aerodynamics loads modelling, by applying the method on a two-dimensional airfoil in subsonic flow conditions. It was found that the indicial step response functions are indeed representing the full-order model, thereby taking into account unsteady flow behaviour in aerodynamic loads prediction. In longitudinal motions, the angle of attack and pitch rate effect need to be taken into account to predict lift, drag and pitching moments. Multiple frequencies of the same manoeuvre can be analysed within minutes once the samples are calculated. Results show that the accuracy of the predictions becomes a trade-off issue between samples calculated and accuracy required. The second testcase is used to apply the indicial response functions to flight dynamics prediction of an agile
unmanned bomber aircraft undergoing fast manoeuvres. A longitudinal-directional climbing manoeuvre was calculated by developing a flight dynamics model based on stability derivatives. The flow behaviour encountered during this manoeuvre was analysed to include highly unsteady and non-linear phenomena (e.g. vortices and flow separation) at higher angles of attack. By comparing the results of themethod under investigation to the full-order solutions, it was shown that aerodynamic flight dynamics predictions were accurate in capturing unsteady behaviour and weak non-linear flow behaviour. However, the samples proved to be inaccurate in representing behaviour in highly non-linear regions. Concluding, this means that indicial step response functions provide more accurate flight dynamics predictions than conventional stability derivatives in representing unsteady flow behaviour. The accuracy of the predictions are highly dependent on the samples chosen. Several samples suffice to predict the unsteady behaviour for linear and weak non-linear flow regions of the flightmanoeuvre. If surrogate modelling is applied, the method can become more computational efficient than conducting multiple full-order time-marching numerical calculations. It is recommended that more research is performed on indicial step response functions
in capturing highly non-linear flow behaviour, as the research showed that the size of the samples affects the flow behaviour representation.