A VORTEX RING THEORY FOR HORIZONTAL-AXIS WIND TURBINES AND EXPERIMENTAL INVESTIGATION OF THE PERFORMANCE CHARACTERISTICS OF A NOVEL VERTICAL-AXIS WIND TURBINE

Abstract

In conjunction with the continuity equation, the Cauchy equation forms the basis in formulating existing wind turbine (WT) aerodynamics theories such as the actuator disk (ADT), rotating annular stream-tube (RAST) and blade element momentum (BEMT) theories. An alternative vortex ring theory (VRT) is proposed in this work. In a nutshell, the VRT predicates on the continuity and Cauchy equations, Kelvin’s circulation, and Helmholtz vortex theorems. These theories predicate on the premise that the flow past a WT is baroclinic or incompressible, inviscid, irrotational, solenoidal and is a potential flow. Baroclinicity reduces the continuity equation to an expression in which the divergence of the flow velocity is null, which establishes the irrotationality and helicity of the flow. The resulting expression is subsequently reduced to the Laplace equation for potential flows. Further expansion of the Cauchy equation from the indicial to the vector form yields the Navier-Stokes (N-S) equation. Neglecting the viscosity term in the N-S equation yields the Euler equation, which when integrated yields the unsteady Bernoulli equation-a thing that forms the basis for all the four theories. A comparison of the VRT to the ADT, the RAST and the BEMT shows piece-wise agreement between the VRT and the existing theories, with the VRT appearing to better capture the flow physics of the WT than the existing theories. A new parameter: "the degree of swirl”, which is a measure of the amount of swirl from an upstream WT that is conveyed to a second row WT is proposed. A nomograph useful in wind farm layout, based on a plot of the number of rotor diameters versus the degree of swirl is proposed. A site characterization of the Maryland Offshore Wind Farm (MOWF) is made based on 24-year historical data compiled and saved as error bars by the National Oceanic and Atmospheric Administration. An experimental investigation of the performance of a novel vertical-axis wind turbine, the Anderson vertical-axis wind turbine (AVAWT), was carried out under conditions different from the conditions that exist in the MOWF, using a purpose-made wind tunnel, equipped with strategically positioned hotwire and digital anemometers for measuring the speed of the airstream upstream and downstream the AVAWT prototype respectively. Experimental data were collected, and graphs were plotted. Experimental results show that at all free-stream speeds and tip-speed ratios, the aerodynamic power coefficient of the AVAWT is higher than its actual power coefficient. Consequently, the power generated by the AVAWT prototype is lower than the aerodynamic power captured, given the same inflow wind conditions. A study of the wind energy economics of the MOWF is made based on two annual energy produced (AEP) scenarios. Both AEP scenarios reveal that the MOWF is profitable.