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 Topic: Question how number of blades affects TSR
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DaveP68
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Joined: 25 November 2014
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 Posted: 01 July 2017 at 3:41am | IP Logged
Hope someone on here can give me a more in depth understanding on how the number blades on a wind turbine affects Tip Speed Ratio of those blades?

Found this in an article on "Wind Speed and windmills explained" by Don Brown while doing a search on this site re unrelated subject of disc braking.

Tip Speed Ratio
This is the ratio between the wind speed and the turbine blade tip speed, and is the starting point for designing the turbine itself. The optimum TSR band changes with the "solidity" of the turbine disc (i.e. how many blades it has).

When operating at its design TSR, maximum power can be extracted from the wind. As the actual TSR shifts above or below its design point, the available power decreases substantially. A turbine with a single blade (and a counter weight on the other side) might be designed for a TSR of 10 to 15. As you add blades, the optimum TSR decreases, and a 3 blade turbine will work most effectively with a TSR in a band between 4 to 7. The typical multi-blade farm "windmill" pump operates at a TSR of less than one. For a 3 blade turbine with a 2 metre diameter and a TSR of 4.5 in a 5 metre per second wind, the optimum tip speed would therefore be 5 X 4.5, or 22.5 metres per second. This translates to a turbine shaft speed of 215 rpm. For a 20 metre diameter turbine, the rotational speed would be only 21.5 RPM to maintain the same TSR. These low speeds do not suit most alternators or generators and, in the case of the 20 meter turbine, would certainly require stepping up by a gearbox.
Note also that, if the wind speed doubles, then the turbine speed must double to permit maximum power to be extracted.

How I see it is when you add more blades the TSR drops, thus lowering the shaft operating RPM range. This would make the choice of the PMA different if more blades are added from say 3 to 4 or 5 or even more. If using 3 blades then a PMA that operates from 90 to say 600 RPM would be chosen. With 4 or 5 blades this may require a PMA that will operate from 60 RPM to 400 RPM. Have left out the blade diameter as this is for illustration purposes only for helping with choosing the optimum number of blades for a given setup of wind turbine.

It all revolves around this graph to illustrate what's outlined above.

If blades are giving more power at "X" m/s of wind providing a lower RPM than what a PMA can generate at that RPM, it could go pear shaped! I'm more referring to what happens in the more extreme conditions, where the blades take off and the PMA just can't keep up with whats going on.

A well designed furling system should keep things in check, but would have to be carefully designed to operate at the correct wind speed.

Edited by DaveP68 on 01 July 2017 at 5:22am

oztules
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 Posted: 01 July 2017 at 10:54am | IP Logged
As a rude rule of thumb for a set blade shape.... more blades, means lower tsr due in part to the wake of the proceeding blade... add another blade and the TSR drops.... and on an old pumper we used to pull off half the blades to speed it up... BUT....

But in reality, the number of blades should make no difference to your calculations.
The CP limit is .6... the Betz limit... calculated by Betz on the basis of using an infinite number of blades..... interesting.

Real life Cp of .5 is obtainable if your good.

Windmission of Netherlands used to build 12 blade windflowers of a CP of .47
You can still find some pics on the net of them... very skinny blades, but reasonable TSR up to 4kw some driving induction motors from memory.

In theory, any number of blades can be used for whatever TSR you wish, but building it in the real world may not be so easy.... so an infinite number of blades of infinite thinness will work fine too... ask Betz.... but try to actually build it... or make it so it stands up to the wind... and there is the problem.

The solidity of the 12 blades compared to 3 is the same if the blade chord is decreased proportionally i suspect..... but not if you keep adding the same blade profile. .... thats the difference I think.

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DaveP68
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 Posted: 02 July 2017 at 4:33am | IP Logged
Thanks oztules

The main reason I asked, is you do get more torque in low winds to start up with more blades and make low power from. The draw back is there can be a lack of reasonable RPM to match what the PMA my want to produce some decent power output. Also in high winds can have control problems with blade run away.

In this wind turbine game it all comes down to trade offs.

Cheers

David

SparWeb
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 Posted: 03 July 2017 at 4:14am | IP Logged
Hi Dave,

Quote:
 The optimum TSR band changes with the "solidity" of the turbine disc (i.e. how many blades it has)...

This is really where you're zeroing in on the answer.
Associated with "solidity" is also the "rotation" of the wake.
The more blades you have, the more energy is expended causing the wake to rotate, also called the vortex, which does NOT produce the more useful forces of lift and thrust. Instead, what is created is the turbulent wake.

It's a bit like induced drag in aircraft, as opposed to profile drag - two components that have different causes but both add up to the total drag on a wing. Similarly, the solidity of the blade and it's design TSR combine to an ideal "working" speed but you can't change one without affecting the other.

For more, there is a lot (and golly is there ever a lot) of technical data on the NREL and Sandia labs websites, if you are really aching to do the math...

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DaveP68
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 Posted: 06 July 2017 at 10:35am | IP Logged
SparWeb wrote:
 For more, there is a lot (and golly is there ever a lot) of technical data on the NREL and Sandia labs websites, if you are really aching to do the math...

Thanks for the heads up for those websites, take a bit of work to trawl through them to find what I'm after.

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