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Flight dynamics analysis using computational models is a key stage in the design of aircraft. The models used in industry consist of two main parts. The first is a tabular aerodynamic model which is essentially a large database of aerodynamic data. The tabular aerodynamic model is a highly dimensional database containing aerodynamic loads and moments for different parameter combinations. In order to reduce the size of the tables, a number of assumptions are made. These include having sufficient resolution of the parameter space to capture the variation in the flow dynamics; decoupling certain parameters to reduce the dimensionality; using a single dynamic derivative, assuming independence from the flow conditions; and finally neglecting flow history effects which are dominant during manoeuvres with highly unsteady flow phenomena. Secondly is the use of dynamic derivatives to simulate unsteady motion effects. These are calculated using small--amplitude forced oscillatory motions. In order to accelerate their computation, frequency domain methods are used. The Linear Frequency Domain and Harmonic Balance are two such methods used in this work. As part of the frequency domain calculations, linear solvers are used to provide solution to the frequency domain problem. These solvers use preconditioners to accelerate the time to solution. An alternative method of preconditioning is proposed in this work based on the first and second order spatial discretisation Jacobian matrices. It is shown that there is significant speed up achieved by varying the proportions of the first and second order terms in the preconditioner matrix. In order to assess the performance of the tabular models, an initial assessment is carried out using a hierarchy of manoeuvres of increasing complexity. For each test case, the replay from the tabular model is compared with the fully unsteady time--accurate CFD solution. This is in line with a framework proposed in the literature. It is shown that the tabular model performs well through the linear aerodynamic regime, although breaks down where history effects become significant. The assessment continues with a study of each of the assumptions used to formulate the tables. Again a hierarchy of test cases of increasing complexity is used. Also used are both forced and free--response manoeuvres. It is shown that the resolution and coupling assumptions have little impact on the performance of the tabular model. The use of a single dynamic derivative is not shown to have an impact either, although it is suggested that for more complicated manoeuvres, this could be important. Finally, the most significant error is introduced through neglecting history effects. It is shown that for manoeuvres where history effects dominate, such as those at the extremes of the flight envelope, the tabular model is not sufficient to effectively model the aerodynamics during these manoeuvres. |
