Introduction
A wind turbine is a device that uses the kinetic energy derived from wind to create mechanical energy. This simply means the wind’s force pushes the blade into motion. Different wind turbines have different ways of extracting wind energy like most machines. Aerodynamics, on the other hand, simply refers to the flow of air about a body. This makes aerodynamics to be a critical aspect of wind turbines as this flow of air about the turbines is what determines its power output. This paper focuses on the aerodynamic behavior of wind turbines (Hansen 21).
Calculation of forces acting on a body needs understanding of motions of air around a body. The fundamental forces affecting body in flight are lift, drag, thrust and weight. Of these, lift and drag are aerodynamic forces, which mean forces due to airflow over a solid body. Lift and drag are the two main aerodynamic forces at work in wind turbine rotors. Lift acts perpendicularly to the direction of flow of wind. Drag on the other hand acts parallels to the direction of flow of wind. Turbine blades like airplane wings also use an airfoil design. An airfoil design means one surface of the blade is rounded, and the other surface is flat.
Lift force
Air will move faster along the upper surface of the blade than on the lower surface.
This means that the pressure will be lower on the upper surface than the lower surface. This creates the lift effect. The force, which pushes the blade upwards or enables a plane to rise up in the air, is perpendicular to the direction of the wind.
The lift force is described by the lift coefficient CL:
CL= (L/AL)
_____
½ Pv2
Where:
P is the air density (kg/m3)
V is the wind speed (m/sec)
Al is the cross-sectional area of the airfoil (m3)
L is the lift (Newtons)
Drag force
Drag is the force that resists objects that move rapidly through air. The direction of the drag force is parallel to the wind direction. Engineers who build aircraft wings and wind-turbine rotor blades are mainly concerned with aerodynamic drag. This is because it reduces the efficiency of both machines. It is similar to friction. Drag increases proportionally to the cross-sectional area of an object facing the winds. Drag also depends on the shape of the object and the square of the wind. The size of the drag for a given shape is usually measured by the drag coefficient, CD. Drag coefficient is defined as the drag force per square meter frontal area of the object. CD is affected by roughness of the object’s surface. Therefore, it is important to have smoother surfaces to minimize drag. Drag also increases with the square of the wind.
Equation for CD:
CD= (D/AD)
_____
½ PV2
Thrust force
The lift and drag forces acting together on a rotor blade creates a resultant force called thrust force, which rotates the blade of the wind turbine (Hansen 45).
Stall
This a situation where the angle of attack of the blade is increased relative to the direction the wind or airflow resulting into an air flow separation on the upper surface as air flow stops to stick on the surface. These results in air are rotating around the blade causing a turbulent vortex. Finally, the lift effect due to low pressure on the lower surface disappears and the rotor blade stops rotating. Therefore, the angle of attack is important so as not to cause a stall. A stall can also be caused if there is a dent or if the blade is not smooth as this can change the shape and angle of attack. Icing of the rotor blades during winter can also cause stall. Wind turbine blade engineers also use stall conditions in their favor as generating stall prevents the wind turbine from rotating at high speeds in weather conditions i.e., during a storm that can lead to its failure (Rahgeb 9).
The governing equation for power extraction on a wind turbine is as follows:
P= F.V
Where P is the power, F is the force vector and v is the velocity of the moving wind turbine blade. The force F is generated by the wind interacting with the blade.
Turbine blades are twisted at an angle that takes advantage of the ideal lift-to-drag force ratio, as this is important in creating an efficient turbine blade. Therefore, it is essential to use rotor blades with a very high lift force and as low drag force as possible( high lift to drag ratio) In order to obtain high efficiency. All turbines can be generally grouped to be either lift based or drag based.
Actuator Disk Model
The actuator disc theory is important in analyzing efficiencies of turbines, but it cannot be used to design the turbine blades to get the desired performance. In this theory, the turbine is replaced by a circular disk through which the airstream flows with a certain velocity and there is a pressure drop across. This theory (Actuator disc model) is based on the following assumptions: an infinite number of blades, no frictional drag, incompressible, steady state fluid and flow homogenous (Wilson 35).
Novel methods such as blade element momentum (BEM) theory, momentum theory and blade element theory can also be used. BEM theory is used to determine the optimum blade shape and also to predict the performance parameters of the rotor for ideal, steady operating conditions. Blade element momentum theory combines two methods to analyze the aerodynamic performance of a wind turbine: momentum theory and blade element theory. These two methods are used to outline the governing equations for the aerodynamic design and power prediction of an HAWT rotor. Momentum theory analyses the momentum balance on a rotating annular stream tube passing through a turbine and blade element theory examines the forces generated by the aerofoil lift and drag coefficients at various sections along the blade. BEM combines equations of both momentum theory and blade-element theory theories creating one equation used to analyse the blades aerodynamic performance.
Conclusion
All the energy contained in a blowing wind cannot be extracted. This is because conservation of mass requires that the amount of mass that enter the turbines to be same as the mass leaving the turbines. Some of the kinetic energy is used to move the air stream itself after interacting with the blade. According to Betz's law, the maximum extraction of wind power by a wind turbine is 59% of the total kinetic energy of the air flowing through the turbine. Wind-turbine blade drag and friction, gearbox losses, generator and converter losses, reduce the power delivered by a wind turbine. On the other hand, a high lift-to-drag ratio increases power output.
Works Cited
Kulunk, Emrah. Aerodynamics of Wind Turbines, Fundamental and Advanced Topics in Wind
Power.2008. [retrieved online from] http://www.intechopen.com/books/fundamental-and-advanced-topics-in-wind-power/aerodynamics-of-windturbines [on 3 December 2014]
Hansen, Martin. Aerodynamics of wind turbines: rotors load and structure. London: Earthscan,
2000. Print.
Wilson, Robert. Applied Aerodynamics of Wind Power Machines. New York: Indiana University Press,
1974. Print.
