Nonlinear Aerodynamic and Aeroelastic Model Reduction Using a Discrete Empirical Interpolation Method

Abstract

A novel surrogate model is proposed in lieu of computational-fluid-dynamics solvers, for fast nonlinear aerodynamic and aeroelastic modeling. A nonlinear function is identified on selected interpolation points by a discrete empirical interpolation method. The flowfield is then reconstructed using a least-square approximation of the flow modes extracted by proper orthogonal decomposition. The aeroelastic reduced-order model is completed by introducing a nonlinear mapping function between displacements and the discrete empirical interpolation method points. The proposed model is investigated to predict the aerodynamic forces due to forced motions using a NACA 0012 airfoil undergoing a prescribed pitching oscillation. To investigate aeroelastic problems at transonic conditions, a pitch/plunge airfoil and a cropped delta wing aeroelastic models are built using linear structural models. The presence of shock waves triggers the appearance of limit-cycle oscillations, which the model is able to predict. For all cases tested, the new reduced-order model shows the ability to replicate the nonlinear aerodynamic forces and structural displacements and reconstruct the complete flowfield with sufficient accuracy at a fraction of the cost of full-order computational-fluid-dynamics model.