Wind Turbine Blade Analysis

Question 1

Which two methods of examining wind turbine operation does the Blade Element Momentum Theory adopt?

Answer 1

1. Momentum balance on a rotating annular stream tube passing through a turbine.
2. Examine forces generated by aerofoil lift and drag coefficients at various sections along blade.

Question 2

What are the equations for the coefficient of thrust?

Answer 2

Ct=T/(0.5ρAv^2)=4a(1-a)

Question 3

What are the equations for the coefficient of power?

Answer 3

Cp=P/(0.5ρAv^3)=4a(1-a)^2

Question 4

How are the maximum values of Ct and Cp determined?

Answer 4

Differentiate eqns and set equal to 0, factorise for value of a and sub into original equation

Question 5

What is the name for the theoretical maximum value of Cp and what is this value?

Answer 5

The Betz Limit, Cp = 0.593

Question 6

What are the two key assumptions made with the Blade Element Momentum Theory?

Answer 6

1. There are no aerodynamic interactions between different blade elements.
2. The forces on the blade elements are solely determined from the lift and drag coefficients.

Question 7

Why must the overall performance characteristics of a turbine blade be determined via numerical integration along the blade span?

Answer 7

Along the span of the blade, slightly different flow is experienced due to differences in the rotational speed (Ωr), chord length (c) and angle of twist (γ).

Question 8

What is the equation for the local tip speed ratio at a specific point along a blade element?

Answer 8

λr=(Ωr/v)

Question 9

What is the equation for local solidarity at a specific point along a blade element?

Answer 9

σ’=Bc/2πr

Question 10

Under what theoretical conditions could the value of Cp be greater than the Betz Limit?

Answer 10

When the tip losses and drag coefficient of the blade are assumed to be zero.