Blade Design Flashcards
What are the assumptions of the ideal rotor?
- 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
What is the CV in the actuator disc model?
- 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
What is the thrust force?
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
Froude-Rankine theorem
u2 = (u1+u3)/2
- Bernoulli
p1 = p3
u(-2)=u(2)=(+2)
Pressure distribution in rotor
increase of pressure before the rotor, pressure drop in rotorplan, increase to zero behind the rotor
Axial induction factor a
fractional decrease in wind velocity between A1 and A2
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What is the extracted energy?
The difference between the kinetic energy in the wind and the kinetic energy in the wake
What is the extracted power?
the derivative of extracted energy in time
- stationary conditions so u1 and u3 are constant
- m is timedependent (mass flow m dot)
What is the power coefficent
- 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!)
What are the coeffiecents for optimal conditions?
u2 = 2/3*u3 cpmax = 16/27 = ca.0.59 - also called cpBetz - axial induction factor of a=1/3 - ct = 8/9
How is the thrust force defined?
Thrust coefficient times the resultant dynamic pressure times the rotor area
What is Betz theory part 1 about?
Optimal power extraction
What is Betz theory part 2 about?
Optimal blade design
What is the relative inflow velocity?
The resulant force of rotational velocity urot and wind velocity u2
What is the inflow angle phi?
The angle between the rotational component and the relative inflow velocity
What is the angle of attack?
The angle between the chord line abd the relative inflow
what is the meaning of the torque force?
- needed to generate torque, power and electricity
- thrust force generating mechanical loads
What is the design tip speed ratio lambda d?
the ratio between omega times the rotor diameter R and the freestream velocity
Why do most rotors have three blades?
- cheaper than more blades
- benefitial for structural dynamics of turbine (smoother than for two blades)
- acceptance (less visual aspect, looks smoother, like a disk)
Blade element theory
Discretize the blade in radiant direction into blade elements
- constant chord length
What are the assumptions for blade element theory
- ideal rotor (acuator disk)
- uniformly loaded
- independent from each other
What characterizes a good arifoil?
cD «_space;cL
- at least one order of magnitude (sometimes two orders)
What is the meaning of the twist angle?
Has to be out in in such a way to achieve the angle of attack
- difference between inflow angle and angle of attack
Why is there wake rotation?
- Rotor only rotates because of torque
- actio = reactio
- torque is also acting on the flow, so flow is starting to rotate
