Physics-Based Low-Order Model for Transonic Flutter Prediction

Abstract

This paper presents a physical low-order model for two-dimensional unsteady transonic airfoil flow, based on small unsteady disturbances about a known steady flow solution. This is in contrast to traditional small-disturbance theory, which assumes small disturbances about the freestream. The states of the low-order model are the flowfield’s lowest moments of vorticity and volume-source density perturbations, and their evolution equation coefficients are calibrated using off-line unsteady computational fluid dynamics simulations through dynamic mode decomposition. The resulting low-order unsteady flow model is coupled to a typical-section structural model, thus enabling prediction of transonic flutter onset for wings with moderate to high aspect ratios. The method is fast enough to permit incorporation of transonic flutter constraints in conceptual aircraft design calculations. The accuracy of this low-order model is demonstrated for forced pitching and heaving simulations of an airfoil in compressible flow. Finally, the model is used to describe the influence of compressibility on the flutter boundary, and its accuracy is demonstrated for the Isogai Case A classical flutter test case.