A GENERALISED MODEL FOR AIRFOIL UNSTEADY AERODYNAMIC BEHAVIOUR AND DYNAMIC STALL USING THE INDICIAL METHOD.

Within the context of rotor airloads prediction, the requirements for the computation of unsteady 2-D airfoil lift, pitching moment and drag are shown to be fulfilled by an aerodynamic model using the indicial response formulation. It is shown how the total linearised unsteady aerodynamic response can be idealised into components of circulatory and impulsive loading, which may be computed independently via indicial aerodynamic transfer functions. A hypothesis for the approximate decay of the impulsive pressure loading has been postulated, and used to compute the impulsive lift and pitching moment indicial response. Using the superposition of a series of indicial responses, validation of the total loading idealisation has been conducted with theoretical and experimental data. The non-linear lift characteristic of trailing edge separation was evaluated via Kirchhoff flow. Furthermore, it is shown, how the Kirchhoff model may be used to evaluate the non-linear effects on chordwise force and pressure drag response. The centre of pressure variation with separation was however represented empirically, based on the airfoil static behaviour. Using timewise lags representing the additional airfoil temporal pressure modification and the unsteady boundary layer response, the dynamic variation of the trailing edge separation point was computed and used as a primary degree-of-freedom in the modelling. The onset of vortex shedding during dynamic stall was denoted using a generalised criterion for the onset of leading edge or shock induced separation, the consequences of which also modified the trailing edge separation calculation. During dynamic stall, a timewise increment in vortex lift strength was evaluated, but simultaneously the accumulated strength was allowed to decay exponentially with time thereby allowing a progressive transition between the static and dynamic stall characteristic. The associated increment in pitching moment was obtained by allowing the centre of pressure of the vortex lift to move during dynamic stall. It is shown how the modelling of the above features may be incorporated in a general numerical algorithm for airfoil unsteady aerodynamic behaviour and dynamic stall, formulated for arbitary forcing and in a computationally efficient format suitable for inclusion within rotor airloads analyses. Validation of the modelling has been conducted with experimental 2-D unsteady test data for the NACA 0012 airfoil in the ramp and oscillatory pitch modes.