Computational approximation of nonlinear unsteady aerodynamics using an aerodynamic model hierarchy

Modeling nonlinear unsteady aerodynamic effects in the simulation of modern fighter aircraft is still a very challenging task. A framework for approximating nonlinear unsteady aerodynamics with a Radial Basis Function neural network is provided. Training data were generated from a hierarchy of aerodynamic models. At the highest level, solutions of the discretized Reynolds-Averaged Navier–Stokes (RANS) equations provide the quantitative and qualitative solution of flow around aircraft, although the results are expensive in terms of computational resources. The Euler simulations are less expensive and provide qualitative data up to moderate angles of attack. The integration of these data is promising for generating accurate aerodynamic models at moderate computational cost. To illustrate the method, an airfoil undergoing pitching and plunging motion is considered. The primary and secondary aerodynamic model data are computed using RANS and Euler equations, respectively. A description for a mapping between the aerodynamic loads and the motion parameters based on the implicit function theorem is described. The mapping is then augmented by adding the secondary data to the input dataset. The selection of training data is then discussed. Once the network is trained, it can compute the unsteady aerodynamic loads from motion descriptions on the order of a few seconds. The framework is examined for different motions, and in all cases, the ROM predictions closely represent the actual aerodynamic responses. It is also demonstrated that the aerodynamic hierarchy aids in the rapid development of a reduced-order model.