An analytical model of wake deflection due to shear flow

Abstract

The main motivation behind this work is to create a purely analytical engineering model for wind turbine wake upward deflection due to shear flow, by developing a closed form solution of the velocity field due to an oblique vortex ring. The effectiveness of the model is evaluated by comparing the results with those of a free-wake model. The solution of the velocity field due to an oblique vortex ring is obtained by using the result of an upright ring along with an equivalent point method. The wake model is derived using oblique ring elements with a number of suitable assumptions. Results of wake vertical deflection are compared with a free-wake solution. A linear trend between wake deflection and shear flow exponent is found with both models. The oblique ring model shows some discrepancies from the free-wake result in terms of the dependence of the deflection on the reference tip speed ratio. The oblique ring model needs further refinements and validation with experimental work and is only currently suited for the determination of general wake kinematics. It however provides immediate results for a given input and can be useful in generating databases with wake geometry information.