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.

Evaluation of linear, inviscid, viscous, and reduced-order modelling aeroelastic solutions of the AGARD 445.6 wing using root locus analysis

“…Development of ROMs based on the Volterra theory is one of several ROM methods that has received attention over the last few years Silva 1999Silva , 1997Silva , 1993Raveh, Levy, and Karpel 2000;Balajewicz, Nitzche, and Feszty 2009;Omran and Newman 2009;Milanese and Marzocca 2009). Although the primary focus of this paper is the development and application of unsteady aerodynamic ROMs for subsequent use in aeroelastic analyses, the development of ROMs for the rapid computation of nonlinear stability and control derivatives using CFD codes (Jirasek and Cummings 2009;Ghoreyshi et al 2012) is an active area of research as well. Silva and Bartels (2004) introduced the development of linearized, unsteady aerodynamic state-space models for prediction of flutter and aeroelastic response using the parallelized, aeroelastic capability of the CFL3Dv6 code.…”

Grid Quality and Resolution Effects on the Aerodynamic Modeling of Parachute Canopies

“…15,16,17,18 These grids have structured cells near solid surfaces and unstructured cells elsewhere. Specifically, an inviscid tetrahedral mesh is generated using the ICEM-CFD code.…”