Coupled unsteady actuator disc and linear theory of an oscillating foil propulsor

Linear unsteady aerofoil theory, while successfully used for the prediction of unsteady aerofoil lift for many decades, has yet to be proven adequate for predicting the propulsive performance of oscillating aerofoils. In this paper we test the hypothesis that the central shortcoming of linear small-amplitude models, such as the Garrick function, is the failure to account for the flow acceleration caused by aerofoil thrust. A new analytical model is developed by coupling the Garrick function to a cycle-averaged actuator disc model, in a manner analogous to the blade-element momentum theory for wind turbines and propellers. This amounts to assuming the Garrick function to be locally valid and, in combination with a global control volume analysis, enables the prediction of flow acceleration at the aerofoil. The new model is demonstrated to substantially improve the agreement with large-eddy simulations of an aerofoil in combined heave and pitch motion.