TSR for wind turbine

[kcchow]

Hi,

I'm a newbie in wind turbine, may I know how the TSR can affect wind turbine's performance? What is the range of TSR for the wind turbine? How to improve it? Is it the same for Horizontal Axis Wind Turbine (HAWT) and Vertical Axis Wind Turbine (VAWT)?

Beside that, seems like the HAWT are more commonly use (correct me if I'm wrong), may I know what is the main reason of this?

Thanks!

[ChrisOlson]

The Tip Speed Ratio is a function of the airfoil used on the rotor blades.  It can't be "improved", as such.  High TSR rotors typically spin at high speed and have no torque to speak of.  Low TSR rotors don't spin as fast and have more torque.  Low TSR rotors are better for low winds, high TSR rotors perform best in high winds. The generator can be designed for either type.

Vertical axis turbines usually run at very low TSR (2 or less), the typical range for horizontal axis machines is 4-8.
--
Chris

[wpowokal]

Have a read of this article..............http://www.thebackshed.com/windmill/articles/DonBrown1.asp

allan

[wpowokal]

This is also a rather in depth paper.

allan

[Ungrounded Lightning Rod]

Horizontal wind turbines (of the "propeller" type) tend to be designed with an operating TSR of 6 or thereabouts.

Basic idea is that higher is somewhat better.  Running the RPM/torque tradeoff toward lower torque means you leave less energy in the "twisting" of the exhaust air -  which is a minor portion of your losses but why have it greater than the amount you can't avoid?  And higher RPM means you need less magnets and copper for a given amount of power.

But you don't want the blades to spin too fast in a storm.  The faster the spin, the higher the strength you need to hold it together.  And you especially don't want the airflow over part of the blades to go supersonic and start things shaking.  It's a good way to make the blades come apart catastrophically and fly around your yard at several hundred MPH.  6 to maybe 7 is about as high as you want to go.

VAWTs are a different animal.  Things like the Savonius inherently run best about TSR 0.8.  Things like the Darrieus run in the same range as HAWTs and have somewhat higher efficiency than a good Savonius - but that applies enormous alternating and fatiguing forces to inherently weak structures, making the engineering and materials issues difficult - even for trained engineers with big budgets.

Not sure what TSR the Lenz VAWT design runs at.  Ed?

[SparWeb]

I find it very useful to compare TSR in a wind turbine with the angle of attack of an aircraft wing.  Mathematically one is the inverse of the other, in fact.

A high angle of attack, in a wing, has both high lift coefficient and high drag coefficient, and usually relates to low speed flight.  The same state in a wind turbine is a low TSR, because the rotor blades turn at a slower speed for a given speed of wind.  At low TSR, the wind turbine blades also have a high angle of attack, so the analogy is universal.

The opposite is true, too:

A low angle of attack in a wing has both low lift coefficient and low drag coefficient, and usually relates to high speed flight.  The same state in a wind turbine is a high TSR, because the rotor blades turn at a higher speed for a given speed of wind.  At high TSR, the wind turbine blades also have a low angle of attack.

[Kwazai]

Any idea how to estimate TSR on something like this?


Mike

[DamonHD]

Zero?   B^>

Rgds

Damon

[Kwazai]

Zero?   B^>

Rgds

Damon

THANKS

[kcchow]

Hi All,

Thanks for all the explanation, since the wind turbine efficiency is proportional to TSR, does it means that HAWT has higher efficiency than VAWT? but I heard from few VAWT supplier, VAWT can produce more than HAWT is that true? Beside that, how do we calculate the efficiency of wind turbine?

Thanks in advance.

[Ungrounded Lightning Rod]

I find it very useful to compare TSR in a wind turbine with the angle of attack of an aircraft wing.  Mathematically one is the inverse of the other, in fact.

However that's inaccurate.

The angle-of-attack is only the inverse of the TSR if the turbine is not spinning.  The blades "fly in the APPARENT wind", which is the vector sum of the actual wind with the headwind from their motion.  They have their own angle-of-attack (dependent mainly on how heavily loaded the mill is) and mills with the same airfoil profile but different TSRs will have the same angle of attack at their max power point.  (The twist of the typical blade exists so the sections along the length of the blade all have the same angle-of-attack when the mill is in normal operation.)

The main TSR-related losses occur because the blades don't just slow the air down but also deflect it sideways.  (A mill could avoid them by having two, counter-rotating, sets of blades on the same axis.  But that requires a lot of structure - more blades, a gearbox - to scavenge a small percentage of the power.  So it's better dollars-per-watt to let it go, and use that money to make the mill bigger or build a second one.)  A low-TSR blade needs more torque to provide a given horsepower so it deflects more air sideways than a higher-TSR blade and wastes more power as a result.  This loss mechanism ramps down with increasing TSR more than drag ramps up, so higher TSR wins the efficiency contest.

[SparWeb]

Kcchow,

...since the wind turbine efficiency is proportional to TSR, does it means that HAWT has higher efficiency than VAWT?

Probably a large over-simplification.  As long as you get the point that VAWT's are junk and HAWT's are the way to go, maybe discussing the reason for this is just academic! 

ULR,

Here's a good example of writing with one thing in my mind, but others who read it will picture something else.  I think of one condition and you think of another.  Oops.  I endeavour to be clear and consice but don't always succeed.  The only "innaccuracy" that disagrees with my books is the "2-pi" to convert radians to degrees, and actually you're supposed to take an arctan().  Drop the math stuff and the concept works well enough.

Do a search on "advance ratio" or "advance coefficient" for aircraft propellors, and you'll find "J=V/nD"  ...sound familiar?

[Ungrounded Lightning Rod]

Hi All,

Thanks for all the explanation, since the wind turbine efficiency is proportional to TSR, does it means that HAWT has higher efficiency than VAWT?

The "Higher TSR is more efficient" business is about a geometry issue mainly characteristic of the typical HAWT - which is a wing flying in a circle at right angles to the incoming wind, extracting its torque by diverting the air sideways.  It doesn't necessarily map to other geometries.

VAWT designs have their own peculiar issue - having to fight their way upwind for part of the rotation.  That tends to make them less efficient than HAWTs - though by how much depends on their geometry (especially how they handle the upwind part of the trip).  But though they tend to be less efficient (wind-to-horsepower) than HAWTs, there are some designs where the efficiency is still very good.

VAWTs have other advantages that may make them attractive in some cases - especially for turbulent sites.

but I heard from few VAWT supplier, VAWT can produce more than HAWT is that true? Beside that, how do we calculate the efficiency of wind turbine?

Sounds like somebody selling them, all right.  B-)  Not sure what he's talking about.  For a given cross-section presented to the wind, a HAWT will normally collect more power than a VAWT.  But a HAWT typically presents a circle to the wind while a VAWT typically presents a rectangle, intercepting more area.  (I once did a back-of-the-envelope calculation which suggests that a Savonius using the patented optimized profile, the same diameter as a really good HAWT, would only have to be about 12% taller than the diameter to collect the same power.)  Perhaps he's talking about the possibility of making a VAWT that is as wide as a HAWT and the height of the tower.  B-)

One of the downsides of a VAWT's typically lower efficiency is that it requires more horizontal support for a given amount of power collection.

Most of the people here build HAWTs because they are easier, especially if you want to mount them on top of a tower, than a VAWT of equivalent power.  Putting something up in the air a few tens of feet gives it access to faster, less turbulent, wind.  Available power goes up with the CUBE of the wind speed so wind a bit faster is a LOT better.

[Ungrounded Lightning Rod]

ULR,

Here's a good example of writing with one thing in my mind, but others who read it will picture something else.  I think of one condition and you think of another.  Oops.  I endeavour to be clear and consice but don't always succeed.  The only "innaccuracy" that disagrees with my books is the "2-pi" to convert radians to degrees, and actually you're supposed to take an arctan().  Drop the math stuff and the concept works well enough.

Do a search on "advance ratio" or "advance coefficient" for aircraft propellors, and you'll find "J=V/nD"  ...sound familiar?

Sounds more like it. B-)

I just wanted to correct the use of the wrong term, to head off confusing a new guy.  This stuff can be confusing enough as is without getting a wrong idea about angle-of-attack.

[scoraigwind]

The Tip Speed Ratio is a function of the airfoil used on the rotor blades.  It can't be "improved", as such.  High TSR rotors typically spin at high speed and have no torque to speak of.  Low TSR rotors don't spin as fast and have more torque.  Low TSR rotors are better for low winds, high TSR rotors perform best in high winds. The generator can be designed for either type.

Vertical axis turbines usually run at very low TSR (2 or less), the typical range for horizontal axis machines is 4-8.
--
Chris

I would not entirely agree with the above statements. 

Tip speed ratio is the speed of the tip of the blade in relation to the wind speed.  High tip speed ratio blades need to be more slender since they don't need much meat in them to catch all of the power that there is to catch, and they do need a good lift to drag ratio since drag is the main loss, in high speed blades.  So yes a good airfoil helps but that's only a small part of it.  they also need to be slender and correctly pitched.

I can't really understand why people think that low TSR blades are a better idea in low winds.  They do have more starting torque but if you use an axial flux alternators with easy starting then this is a non issue.  There is no virtue in starting up in a wind that can produce no power, and when the wind is strong enough to produce power then a high TSR blade will work at least as well as a low one.  The generator can be designed for either type, but the low speed ones are about 5 times as heavy and costly.

Savonius VAWTs run at TSR around one, and are reliable but very inefficient.  Darrieus rotors need to run much faster (if you can get them to start) but have no better efficiency than HAWTs.  They also have various fatigue issues and no obvious method of control.

my 2 cents

[poco dinero]

[quote my 2 cent
 [/quote]

Hugh,

Your comments are always worth much more than 2 cents.  Unlike some others.

Ungrounded LR:  How in the world do you get it to say who the quote was from???

poco

[SparWeb]

poco,
you missed a square-brace.

I find I have to type the code in manually, and copy-paste the text I want to quote.

While replying, like I am now, I can hit the link in the text of your last message.  This happens:

Code: [Select]

[quote my 2 cent
 [/quote]Hugh,

Your comments are always worth much more than 2 cents.  Unlike some others.

Ungrounded LR:  How in the world do you get it to say who the quote was from???

poco

...but even so, I had to jimmy the automatically-created quote field because you have the square braces of your own in it.  The page editor gets confused by that.

[ndurrani]

Hi,
Can anyone please help me with the following query?

Cp = Performance Coefficient = ratio of the power output from turbine and the input from the oncoming wind.
TSR = Tip speed ratio = radius of turbine*rotational_velocity_omega/freestream_velocity
Question: Generally we describe the performance of a wind turbine in terms of performance coefficient with respect to the TSR figure. I am not clear that how a vertical axis wind turbine (VAWT) can have more than one TSR. Ideally, for a given wind speed the vawt should have one TSR (as the ‘radius' and  ‘freestream velocity' are constants). Then why do we show the VAWT for different TSR values? Even for experimental data we get different TSR values plotted against Cp and typically they are 'hump' sort of curves.
If I imagine building one vawt and running it for a given wind speed, it will have one fixed TSR and corresponding Cp. Then why even the manufacturers show different TSR values and corresponding Cp for the same vawt? Please guide!!!!

[DanB]

I guess I'll add my two cents.

Seems like so far tests have indicated that the 'most efficient' wind turbines (HAWT) run at TSR around 6.

going faster (some machines run up around 12 or so) allows for a smaller / less expensive alternator and a less expensive machine overall - at the cost perhaps of slightly reduced efficiency (less power per given unit of swept area), and probably blade noise, and probably a machine that wears out sooner.

Like Hugh said, it's a bit of function of the airfoil and likely more to do with the width of the blade and getting the angle of attack about right.  Machines that are clamped down to battery voltage will have to run over a range of TSR - they cannot track the 'ideal' TSR in all wind speeds.  How they behave will depend on how they're loaded which has a lot to do with the nature of the alternator.



The image above shows the approximate efficiency of different types of machines running at different TSR's.

[ndurrani]

Thanks indeed DanB.
Perhaps your last line contains some hint to my query.
Like Hugh said, it's a bit of function of the airfoil and likely more to do with the width of the blade and getting the angle of attack about right.  Machines that are clamped down to battery voltage will have to run over a range of TSR - they cannot track the 'ideal' TSR in all wind speeds.  How they behave will depend on how they're loaded which has a lot to do with the nature of the alternator.
Q1. If I build a 2m diameter vertical axis wind turbine (VAWT) and put it in an oncoming wind of 12 m/sec. Now due to this wind if it is rotates with an rpm of 12 rad/sec. Its TSR comes out to be r*w/v = 1*12/12=1. One possibility to get different TSR is to vary the RPM of my designed vawt. For instance, if I could rotate it with a speed of 24 rad/sec at the same wind speed, I get a TSR of 2. Any manufacturer will give a whole range of theTSR for its vawt. Can we use the alternator in someway to control (increase/reduce) the rotational speed of the vawt? Can you/Hugh please elaborate the role of alternator w.r.t. TSR?
Q2. Do the experimental Cp Vs TSR charts as shown in picture above have TSR variation corresponding to same wind speed (by changing rotational speed) or actually are generated for different combinations of wind speed and corresponding rotational speed?
Thanks for your time and patience in bearing me 

[Ungrounded Lightning Rod]

Ungrounded LR:  How in the world do you get it to say who the quote was from???

Just noticed this question when the thread got reawakened.

I hit the "quote" button at the top-right of the article I'm quoting.
The system presents me with a "Post reply" box with the quote
control already filled in correctly to quote the entire previous
posting (including embedding any second-or-higher-level quotes.)

Once I have that, I can easily add my comments, edit down the quote,
and otherwise play with the reply.

If I want to do interstitial stuff I put a open-square slash quote close-square
at the the point where I want to inject my comment, type it in there,
then insert open-square quote close-square (without the rest of the
junk) to go back to the quoted stuff.

[Ungrounded Lightning Rod]

I am not clear that how a vertical axis wind turbine (VAWT) can have more than one TSR. Ideally, for a given wind speed the vawt should have one TSR (as the ‘radius' and  ‘freestream velocity' are constants). Then why do we show the VAWT for different TSR values? Even for experimental data we get different TSR values plotted against Cp and typically they are 'hump' sort of curves.

In a given wind speed the more you load it the slower it will spin.  Since the wind is constant and the RPM is variable due to load, the TSR is also variable due to load.

Unloaded it will run near the right end of the "hump" in the TSR vs. CP graph, extracting just enough power to make up for bearing losses and air friction.  Load it down and the TSR drops, moving you leftward up the hump "to get the power you're pulling out" - changing the angle-of-attack between the blades and the "apparent wind" to give you more torque.  Load it too much and it spins still slower, giving you less power than if your load was less and it spun faster.  (With some rotors your torque will still be high or even rising but you lose horsepower due to falling RPM.  With others you also lose torque due to airstream detachment - "stalling" in the aerodynamic sense - typically with more torque loss as the TSR drops more, as the area of attached airflow gradually shrinks.)

When freewheeling the blades slide through the air and leave it moving in about the same direction and speed it was going before it encountered the blades.  When under load and turning slower the blades have a different angle-of-attack due to a different apparent wind due to the different vector sum of the wind and the blades' motion.  They deflect the air, slowing the wind through the swept area and extracting power from it.

So the TSR is not a constant but is load-dependent and the CP vs TSR graph is roughly a power vs. speed-due-to-load curve.

The "design TSR" is the TSR at which you intend to run the mill.  Typically it's the high point on the curve.  But the mill will only spin at the design TSR if the load is right.

Make more sense now?

[ndurrani]

Yes, I have developed much better understanding now. Thanks a lot guys...you made my day.
One more question....as I have never practically operated or used any VAWT, so just want to clarify this aspect.
How we change the load of a rotating wind turbine? I understand from your explanation that if there is no load we are on the right end of the "hump" in the TSR Vs Cp graph with little power. In order to increase the power output, we need to apply load which results in slowing the rotational speed of the wind turbine (and we find the optimum combination of the power extracted with respect to the applied load). I am particularly interested in vertical axis wind turbine (H-type with 3 vertical blades connected with central shaft).
Q1. But how in practice we increase the applied load to extract more power?
Q2. In real wind turbines, do we have some controller that tries to achieve the best performace (to remain at the top of "hump" in the TSR Vs Cp graph)?
Cheers

[Ungrounded Lightning Rod]

One more question....as I have never practically operated or used any VAWT, so just want to clarify this aspect.
How we change the load of a rotating wind turbine?
...
Q1. But how in practice we increase the applied load to extract more power?
Q2. In real wind turbines, do we have some controller that tries to achieve the best performace (to remain at the top of "hump" in the TSR Vs Cp graph)?
Cheers

Using a permanent-magnet alternator the voltage goes up with the RPM.  To "ride the hump" you'd want an electrical load where the current went up with the square of the voltage.  Think "the right half of a parabola".

A battery-charging application presents a load which is approximately the sum of a near-constant (the battery voltage - which varies about 10% with state-of-charge - plus two diode drops - which are close to constant) with the series resistance of the coils and wiring.  The series resistance causes the current to go up linearly with voltage (i.e. making a straight line on the graph with a slope inversely proportional to the resistance) while the battery+diode "cut-in" voltage offsets that line to the right from passing through the origin.  By picking your coil windings and magnet strength (and fine-tuning the latter by adjusting the rotor spacint) you can get the line to cross the "ideal" parabola twice in the range corresponding to a bit lower than the middle of your typical useful wind speeds, which puts it reasonably close to that optimum for much of your operating conditions.  (You bias it a tad toward the lower end so you can be efficient when winds are low and power is precious.)  For high winds you have more power than you need and don't want to fry the stator, so falling off the optimum as you approach furling speed is actually helpful.

For better efficiency you can use a peak power tracker.  This is essentially a switching-regulator power supply, that can trade away excess voltage from the genny to produce more current into the battery, with an automatically adjusted setpoint that makes it vary the load on the mill to track the optimum.

A downside of "being optimum" is that the current goes up with the square of the wind speed.  Since the resistive heating goes up with the square of the current it ends up going up with the FOURTH POWER of the windspeed.  This makes the furling adjustment critical to avoid burnout, if the peak power tracker isn't set up to also limit mill current (in which case it also interferes with furling.)

But IMHO it makes more sense to keep it simple.  You can make up for the less-than-optimum loading by just making the mill a little bigger.  (The power collected goes up with the square of the radius.  B-) )

[kcchow]

Hi DanB,

Thanks a lot for the useful graph showing the Cp versus TSR, however, do you have any similar graph to show Cp versus wind speed?

Thanks in advance!

[DanB]

Hi DanB,

Thanks a lot for the useful graph showing the Cp versus TSR, however, do you have any similar graph to show Cp versus wind speed?

Thanks in advance!

Cp vs windspeed will depend on the turbine.  Simple machines (like most of us build) that cut in at 7mph or so and are clamped to a fixed battery voltage will could have pretty decent Cp in low winds, but it will be bound to drop off a lot in higher winds as I^2 * R losses increase in the alternator and the rest of the system.

With any sort of MPPT scheme - (which is included with most direct grid tie inverters) the Cp could stay quite good across the board.

So the graph I posted just shows what you might expect from 'different designs'  - and the best you'll likely do is build a HAWT that runs at a TSR of about 6.  That sort of machine, properly loaded could easily run with a Cp between .3 and .4.  Seems like the most efficient small wind turbines out there today are running at about .35.

[JW]

TSR