Vawt Math

[commanda]

Hi all,

I'm really new here, but I've been searching for ages & can't seem to find what I'm looking for; so it's time to start asking dumb questions.

For a HAWT, TSR is a function of the blade profile (yes?).

How do you calculate TSR for an airfoil for a VAWT ?

Amanda

[edy252]

hi....

try this free blade calculator; it will help u a bit

http://warlock.com.au/bladecalc.htm

[LEXX]

Hey that's pretty cool, how do you decide blade efficiency??

Lexx

[commanda]

that's a great calculator for designing horizontal axis wind turbines. How does it help me design a vertical axis machine? I'm sure the answer to this question will make everything else fall into place.

So far I've figured out the potential energy in a given cross-sectional area

watts = 0.625 * Area(sq metres) * velocity(m/sec) ^ 3.

I can assume an efficiency of 0.35 to 0.4 (from other published results) so I can work out the shaft power(watts).

I can assume a tip speed ratio of 3, though I've no idea how to actually work it out.

So my blade velocity is the wind velocity * TSR.

For a given diameter and blade velocity, I can work out the RPM.

For a given diameter & rpm, I can calculate the g-force on the blades (this is scary).

So, for a height of 3 metres, diameter of 2 metres, wind velocity of 6 m/s

rpm = 171.89    watts =    324    g-force = 8.27

and at 10 m/s

rpm = 286.48    watts = 1500    g-force = 22.96

Can somebody tell me if these numbers seem reasonable?

Amanda

[edy252]

blade efficiency is mostly between 0.25 and 0.35 (somebody correct me plz if im wrong)

[windstuffnow]

  Is this a Darrieus or Savinous type VAWT?  

Windstuff Ed

[commanda]

Darrieus. More correctly cycloturbine or giromill since I believe the Darrieus, by definition, has blades which are fixed to the spar & not articulated.

I've seen your site by the way Ed, nice stuff.

Using the Fisher & Paykel smart drive motor. However, I'm looking at running it at High Voltage to decrease transmission losses, and using 3 toroidal transformers at the battery box to put the voltage down to 12 volts.

Picture of toroidal.....

http://www.oatleyelectronics.com/images2/tor1.htm

Blurb....

(NEW) 250VA TOROIDAL TRANSFORMER:  2 x 120V primary, 2 x 9V secondary. No mounting hardware available. The unit weighs 4Kg:

These people are in the next street from where I work. Very handy.

Also, with 2 primaries & 2 secondaries, I'm bound to find a series/parallel combination to optimise the characteristics. Even relay switch the connections for different wind speeds.

Amanda commanda

[windstuffnow]

  I believe the Darrieus patent covers the cycloturbine type.  In the patent he shows a cam/tail assembly to articulate the wings.

  Typically, the darrieus is the most efficient at a TSR of over 4 and 6 seem to stick in my mind as the best.  

   Be careful with it, spend alot of time on your structural math.  These things can go balistic very quickly.

Have Fun

Windstuff Ed

[commanda]

Where I work is indeed fortunate. We make beltweighers for conveyor belts, so we have several mechanical engineers, plus toolmakers & welders, etc. But I've had no luck finding any worked examples for design methodology.

Is there a way of designing to get a TSR of 6, or do you just assume that unloaded it will accelerate forever, and match the load to peak at whatever RPM equals a tsr of 6, and then dynamically brake it past that.

I was also thinking that the tail could be designed assymetrical, so it would de-tune the angle of attack at higher wind speeds. Thinking on the run here; what about using one tail fin per blade, mounted above the piviot axis of each blade. Nah, the rotational force would defeat it.

OK, I just updated my spreadsheet with a tsr of 6, and got these numbers.

Height(m)    3                       

Diameter(m)    3                       

TSR guesstimate    6                       

N guesstimate    0.3

m/sec    Rpm    revs/sec  Shaft Power(W)  G-force

1.     38.2    6             1.69        0.61
   
2.     76.39    12            13.5        2.45
   
3.     114.59    18            45.56       5.51
   
4.     152.79    24            108         9.8
   
5.     190.99    30            210.94     15.31
   
6.     229.18    36            364.5      22.04
   
7.     267.38    42            578.81     30
   
8.     305.58    48            864        39.18
   
9.     343.77    54           1230.19     49.59
   
10.     381.97    60           1687.5      61.22
    
11.     420.17    66           2246.06     74.08
    
12.     458.37    72           2916        88.16
    
13.     496.56    78           3707.44    103.47
    
14.     534.76    84           4630.5     120
    
15.     572.96    90           5695.31    137.76