Low-Order Model for Prediction of Trailing-Edge Separation in Unsteady Flow

摘要

Computational and experimental results for pitching and plunging airfoils were used to study the time lag associated with boundary-layer convection and to develop a model that can be used to augment inviscid theoretical methods for unsteady airfoil flows to include the effects of trailing-edge separation and unsteady stall. Computations using an unsteady Reynolds-averaged Navier-Stokes code were used to obtain results for airfoils in steady flow and for several pitch and plunge motions. The motions were selected such that stall occurred only due to trailing-edge separation without leading-edge vortex formation. Viscous corrections to inviscid airfoil theory are first calculated in steady flow by implementing a nonlinear decambering flap to model the effect of the separated boundary layer. Aleading-edge suction parameter, from earlier research, is used to connect the aerodynamic state in unsteady motion with a steady-state condition. Computational results showed that the differences in aerodynamic loads between steady and unsteady flows can be attributed to the boundary-layer convection lag, which can be modeled by choosing an appropriate value of a time-lag parameter tau(2). To provide appropriate viscous corrections to inviscid unsteady calculations, the nonlinear decambering flap is applied with a time lag determined by the tau(2) value, which was found to be essentially independent of motion kinematics for a given airfoil and Reynolds number. The predictions of the aerodynamic loads, unsteady stall, hysteresis loops, and flow reattachment from the low-order model agree well with computational fluid dynamics and experimental results, both for individual cases and for trends between motions. The model was also found to perform as well as existing semi-empirical models while using only a single empirically defined parameter.