Computational approximation of nonlinear unsteady aerodynamics using an aerodynamic model hierarchy

Abstract

, "Computational approximation of nonlinear unsteady aerodynamics using an aerodynamic model hierarchy" (2013 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.

Experimental Study and Neural Network Modeling of Aerodynamic Characteristics of Canard Aircraft at High Angles of Attack

“…Growth in computing capacity and the development of numerical techniques has recently led to significant progress in finding solutions for Navier-Stokes equations coupled with the dynamics equations governing the aircraft motion, facilitating flight dynamics studies [3,[5][6][7][8][9][10]. However, at present the problems of fluid mechanics and flight dynamics cannot be solved simultaneously in certain flight mechanical applications-for example, in semi-realistic simulation of the aircraft flight using ground-based flight simulators or control system design [3,11].…”

“…Surrogate modeling approaches, which use mathematical approximations of the true responses of the system, are a cost-effective tool for unsteady aerodynamics. The most popular surrogate modeling techniques are artificial neural networks [23][24][25][26][27], Radial Basis Function (RBF) interpolation [9,10], and kriging [28]. Neural Networks (NN) have been recently shown to be a formal and effective tool for modeling nonlinear unsteady aerodynamics regardless of the aircraft configurations.…”

Transonic Aerodynamic Loads Modeling of X-31 Aircraft

“…Glaz et al 50 developed a mapping between aerodynamic loads and time histories of both motion parameters and loads and then tried to learn this mapping using a surrogate model with the aid of Design of Experiments. Ghoreyshi et al 51 extended this mapping to include both RANS and Euler calculations and used RBF neural networks trained from some special training maneuvers. Da Ronch et al 47 also tried to establish this mapping using a SBRF model for a pitching airfoil at transonic speed.…”

Transonic Aerodynamic Load Modeling of X-31 Aircraft Pitching Motions

“…The network is then trained to minimize the error between the target (desired) values and the network predicted values. The performance and data-preparation process of RBFNN are detailed in [53].…”

“…They showed that SBRF can predict the strongly nonlinear effects of moving shocks on the unsteady pitching moments. Ghoreyshi et al [53] extended this mapping to include both RANS and Euler calculations and used RBF neural networks (RBFNNs) trained from some special training maneuvers. Da Ronch et al [49] also tried to establish this mapping using a SBRF model for a pitching airfoil at transonic speed.…”