Finding an absolute maximum theoretical power coefficient for ducted wind turbines

Abstract

This study investigates power coefficients for ducted wind turbines to determine an absolute maximum value corresponding to a maximum ideal power output. A maximum power coefficient using the rotor area in the available kinetic energy is still an open question in the research community. Here, the available kinetic energy of a free stream uses the largest device area, diffuser outlet, funnel inlet, and virtual diffuser outlet areas in the power coefficient calculation. The virtual diffuser outlet is defined as the downstream location at which the static pressure of the fluid inside the stream tube recovers to the pressure of the free stream flow. This study performs a one-dimensional analysis based on the continuity, momentum, and energy principles and the Euler Turbomachinery equation. The results show the absolute maximum power coefficient of 0.384 using the virtual diffuser outlet area in the available kinetic energy calculation. Another finding is that both the maximum ideal power output and the cp = 0.384 happen at the same value of the rotor thrust coefficient, CT,R≈ 2/3. The power coefficient based on the rotor area is more convenient for idealized bare turbines; therefore, the power coefficient based on the virtual diffuser outlet area applies only to ducted wind turbines.