Part 1: Meteorology, measurements, resource assessment

Question 1

Name two devices for measuring wind

Answer 1

Sodar and Anenometer

Question 2

What are the advantages and disadvantages of a SODAR?

Answer 2

Expensive but can be placed at ground level but still measure at high altitudes.

Question 3

What are the advantages and disadvantages of an Anenometer?

Answer 3

Cheap and good accuracy but sensitive to ice.

Question 4

Give two factors that effect the wind close to the surface and explain.

Answer 4

Surface roughness: Is provided by the surface and has a direct negative affect on the wind speed close to the ground. This effect decreases with height.

Topography: Different topography can give rise to turbulence for instance.

Question 5

State 6 motives why real production is lower than Betz?

Answer 5

1. Infinite number of blades are assumed
2. No wake losses assumed
3. No drag forces assumed
4. Homogeneous wind assumed
5. No losses due to tip speed is assumed
6. No mechanical losses in gear

Question 6

All available power in the wind cannot be harvested. The theoretical upper limit was described by Betz. State this expression and explain why not 100 percent of the energy in the wind can be harvested.

Answer 6

It is defined as the maximum fraction of the power which can be extracted from the wind to the wind turbine. C_pmax=16/27 C_p=P_out/P_wind
Mathematically it can be proven why this is the case.
P_out=P_wind* 4a(1-a)^2. a is the axial induction factor. Sätt till noll lös ut a.

Question 7

What is the axial induction factor?

Answer 7

It is the fractional decrease in wind velocity

between the free stream and the rotor plane.

Question 8

What does C_p stand for?

Answer 8

Power coefficient

Question 9

Explain why not 100 percent of the energy in the wind can be harvested.

Answer 9

In order for a wind turbine to harvest any kinetic energy there must be a flow of air going across. It can’t as velocity of the wind downstream would be very low and by knowledge of Bernoulli’s law the pressure would become very high if velocity suddenly stepped down to 0

Question 10

What is the F(v) function called?

Answer 10

distribution function

Question 11

Derive the formula for the power in the wind.

Answer 11

E_k=(mv^2)/2 Kinetic energy in the wind
P=dE/dt=(dm/dtv^2)/2 Power in the wind
dm/dt=\rhodV/dt \rho density of wind, dV/dt=change of volume. dV/dt=vA A=swept area
P=(\rhoA*v^3)/2