Transonic Aerodynamic Loads Modeling of X-31 Aircraft

Abstract

The generation of reduced order models for computing the unsteady and nonlinear aerodynamic loads on the X-31 aircraft from pitching motions in the transonic speed range is described. The models considered are based on Duhamel’s superposition integral using indicial (step) response functions, Volterra theory using nonlinear kernels, Radial Basis functions, and a surrogate-based recurrence framework, both using time-history simulations of a training maneuver(s). One of the biggest challenges in creating these reduced order modeling techniques is accurate identification of unknowns. A large number of step function calculation is required for any combination of angle of attack and free-stream Mach number. A method to efficiently reduce the number of step function calculations is proposed. This method uses a time-dependent surrogate model to fit the relationship between flight conditions (Mach number and angle of attack) and step functions calculated from a limited number of simulations (samples). Each sample itself is directly calculated from unsteady Reynolds-Averaged Navier-Stokes simulations starting from an initial steady-state condition with a prescribed grid motion. An indirect method is proposed to estimate the nonlinear Volterra kernels from time-accurate computational fluid dynamic simulations of different training maneuvers. These maneuvering simulations were also used to estimate the unknown parameters in a model based on Radial Basis functions. A Design of Experiment method was used to generate several pitching motions at different amplitudes and free-stream Mach numbers. The model based on a surrogate-based recurrence framework then approximates the aerodynamic responses induced by pitching motions at new flight conditions. Results are reported for the X-31 configuration with a sharp leading-edge geometry, including canard/wing vortices. The validity of models studied was assessed by comparison of the model outputs with time-accurate computational fluid dynamic simulations of new maneuvers. Overall, the reduced order models were found to produce accurate results, although a nonlinear model based on indicial functions yielded the best accuracy among all models. This model, along with a developed time-dependent surrogate approach, helped to produce accurate predictions for a wide range of motions in the transonic speed range within a few seconds.