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# Energy Vol. 8: Wind Energy, 808 Progress in Magnus Type Wind Turbine Theories

**ABSTRACT**

A large number of researches have been conducted on increasing lift to drag ratio of aerofoils used in the commercial type horizontal axis wind turbines. For the most efficient aerofoils in practical situations, the maximum lift to drag ratio is less than 200. One of the attracting concepts to produce high lift is by using the Magnus type devices. Traditionally, the Magnus effect is

misinterpreted as generation of high lift force from spinning cylinders, spheres, or disks. However, the Magnus lift can be produced from circulating any aerodynamic shape. With progressing innovative Magnus type wind turbine generators, it is essential to analysis such devices as correctly as possible. First, the importance of research carried out on the flow around rotating circular cylinders is highlighted and reviewed here. Then, the theoretical methods used in modelling aerodynamics of the commercial

aerofoil type wind turbines are extended and applied on the Magnus types. The potential flow analysis is developed around the Magnus type blades and the blade element momentum (BEM) theory formulation is extended for the Magnus type wind turbines. From the BEM analysis, a cubic function based on the angular induction factor is obtained which its coefficients are dependent

on the axial induction factor, the local speed ratio, and the drag to lift ratio. The resulted power coefficient of the Magnus type wind turbine seems strongly dependent on the drag to lift ratio. Next by examining drag to lift ratio of spinning cylinders as reported by a number of computational or experimental works, it is realized that the generation of high lift to drag ratio from spinning cylinders is a very difficult job because the drag force is simultaneously increases by increasing lift. Second, the generation of high lift to drag ratio

is sought by studying circulating aerofoil surfaces rather than spinning cylinders. To see that the Magnus effect can also be produced by the circulating aerofoil surfaces, the symmetrical NACA0015 aerofoil with treadmill like motion of its surface is computationally investigated. The governing RANS equations of compressible fluid flow motion are solved using a class of implicit,

time marching, high-resolution, second order accurate, symmetric and upwind TVD schemes around the aerofoil section in a C-type structured algebraic-hyperbolic mesh. The zero-equation Baldwin-Lomax turbulence model was employed at this stage. At zero angle of attack, non-zero values of the lift force reveals that the Magnus force can also be produced by circulating aerofoils. Examining this at different incidence angles and treadmill speeds, it is approved that a favourable increase in lift coefficient simultaneously with decrease in drag coefficient is achieved. Interestingly, an approximately near to zero drag value can be achieved at around the incident angle of 5 degrees with a dimensionless treadmill speed of 3 which produces a lift to drag ratio of 684; although, the accuracy of the present computational results should be improved using more advanced turbulence models. This is still very promising compared with the most efficient aerofoils used in conventional wind turbines. The emerging treadmill concept may be further investigated experimentally to fully discover all its features and merits for application in Magnus type wind turbines and industrial manufacturing processes.

**Key words:**Wind power, Magnus effect, Horizontal axis wind turbine, Potential flow, CFD, Treadmill motion, Circulating aerofoils,

Blade element momentum theory.

Books Chapter

Month/Season:

May

Year:

2014