Viscous Extension of Theodorsen's Lift Frequency Response

Many studies invoked an alternative auxiliary condition to the Kutta condition for the analysis of unsteady flows around wings with sharp edges. Some of these reports, because of the observed discrepancies at zero lift conditions, suggested a fundamental revision to the classical theory of unsteady aerodynamics. That is, since the vorticity generation and lift development are essentially viscous processes, a purely inviscid theory of unsteady aerodynamics might be fundamentally flawed. In this work, an unsteady boundary layer approach (triple deck theory) is adopted to develop a viscous correction to the unsteady lift frequency response; i.e., a Reynolds-number-dependent extension of Theodorsen function. The developed model is compact and efficient so that it may be used in flight dynamics, control, and aeroelastic analyses. It is found that the viscous correction induces a significant phase shift to the circulatory lift component, particularly at low Reynolds numbers and high-frequencies, that matches previous experimental results and current computational simulations. This enhancement in the predicted phase of the unsteady loads is envisaged to boost the current predictability of aeroelastic flutter boundaries.