Reduced-order modelling for prediction of aircraft flight dynamics

Abstract

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.