Blade Design

Question 1

What are the assumptions of the ideal rotor?

Answer 1

• Homogeneous, incompressible, steady state flow (continuity equation is valid)
• No friction drag
• Infinte number of blades (like a disk)
• Non-roration wake
• Uniform thrust over the disc (or rotor area)
• Static pressure upstream and downstream of the rotor is equal to the undisturbed static pressure

Question 2

What is the CV in the actuator disc model?

Answer 2

• a stream tube
• widening up
• with three planes:
  1)
  freestream bevor the rotor
  2) rotorplane / actuartor disk
  -2) directly before the rotor
  +2) directly behind the rotor
  3) far behind the rotor

Question 3

What is the thrust force?

Answer 3

The Wind force on dirsc or rotor area

• perpendicular to the rotor area
• uniformely distributed over area (resulting force in the middle)
• mass flow times the difference of the velocity far in front and behind the rotor
  or
• rotor area times the difference of the pressure directly behind and before the rotor

Question 4

Froude-Rankine theorem

Answer 4

u2 = (u1+u3)/2

• Bernoulli
  p1 = p3
  u(-2)=u(2)=(+2)

Question 5

Pressure distribution in rotor

Answer 5

increase of pressure before the rotor, pressure drop in rotorplan, increase to zero behind the rotor

Question 6

Axial induction factor a

Answer 6

fractional decrease in wind velocity between A1 and A2

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Question 7

What is the extracted energy?

Answer 7

The difference between the kinetic energy in the wind and the kinetic energy in the wake

Question 8

What is the extracted power?

Answer 8

the derivative of extracted energy in time

• stationary conditions so u1 and u3 are constant
• m is timedependent (mass flow m dot)

Question 9

What is the power coefficent

Answer 9

• the ratio between power extracted by the rotor and the power included in the wind
• dimensionless magnitude giving the portion of power extraced by the rotor from the wind (not output power!)

Question 10

What are the coeffiecents for optimal conditions?

Answer 10

u2 = 2/3*u3
cpmax =  16/27 = ca.0.59
- also called cpBetz 
- axial induction factor of a=1/3
- ct = 8/9

Question 11

How is the thrust force defined?

Answer 11

Thrust coefficient times the resultant dynamic pressure times the rotor area

Question 12

What is Betz theory part 1 about?

Answer 12

Optimal power extraction

Question 13

What is Betz theory part 2 about?

Answer 13

Optimal blade design

Question 14

What is the relative inflow velocity?

Answer 14

The resulant force of rotational velocity urot and wind velocity u2

Question 15

What is the inflow angle phi?

Answer 15

The angle between the rotational component and the relative inflow velocity

Question 16

What is the angle of attack?

Answer 16

The angle between the chord line abd the relative inflow

Question 17

what is the meaning of the torque force?

Answer 17

• needed to generate torque, power and electricity

- thrust force generating mechanical loads

Question 18

What is the design tip speed ratio lambda d?

Answer 18

the ratio between omega times the rotor diameter R and the freestream velocity

Question 19

Why do most rotors have three blades?

Answer 19

• cheaper than more blades
• benefitial for structural dynamics of turbine (smoother than for two blades)
• acceptance (less visual aspect, looks smoother, like a disk)

Question 20

Blade element theory

Answer 20

Discretize the blade in radiant direction into blade elements
- constant chord length

Question 21

What are the assumptions for blade element theory

Answer 21

• ideal rotor (acuator disk)
• uniformly loaded
• independent from each other

Question 22

What characterizes a good arifoil?

Answer 22

cD &laquo_space;cL

- at least one order of magnitude (sometimes two orders)

Question 23

What is the meaning of the twist angle?

Answer 23

Has to be out in in such a way to achieve the angle of attack

• difference between inflow angle and angle of attack

Question 24

Why is there wake rotation?

Answer 24

• Rotor only rotates because of torque
• actio = reactio
• torque is also acting on the flow, so flow is starting to rotate