How the flow angle along the blade would change along the length

[t0mm02]

Homework Statement

Using a windspeed of 15m/s, a blade length of 10m, and a rotational speed of one revolution per second, show how the flow angle along the blade would change along the length.

Relevant Equations

I don't know what formula to use

I am not sure how to do this at all or what exactly he is asking me.

[Mentor Note -- Two threads on the same problem have been merged into one]

 

[berkeman]

Do you have diagrams of similar problems or setups? If the wing section of the wind turbine blade did not change, how would it cut through the air?

 

[t0mm02]

Do you have diagrams of similar problems or setups? If the wing section of the wind turbine blade did not change, how would it cut through the air?

I have no diagrams at all. This tutor is a bit special in the way he designs his questions. That is literally the only information he gives me.

 

[berkeman]

I did the following Google Images search, and got some helpful diagrams. Try a similar search to see what kinds of airflow diagrams you can find...

 

[t0mm02]

I did the following Google Images search, and got some helpful diagrams. Try a similar search to see what kinds of airflow diagrams you can find...

View attachment 275278

Oh sorry, I was thinking you were asking me if the specific question showed me a diagram. I can see that but I have no idea how to calculate it, hence why I am asking.

 

[berkeman]

Well, as a first cut, the airflow over the turbine blade will be faster near the tip, right? If the airflow over the blade were just the addition of the wind speed and the angular velocity of the blade, what would that look like? Something like 15m/s near the base of the blade, and something higher near the tip...?

 

[t0mm02]

Well, as a first cut, the airflow over the turbine blade will be faster near the tip, right? If the airflow over the blade were just the addition of the wind speed and the angular velocity of the blade, what would that look like? Something like 15m/s near the base of the blade, and something higher near the tip...?

I agree and understand your information but when I think about how to calculate the change of flow from that first cut to the tip of the blade, I do strugle.

 

[berkeman]

Homework Statement:: Using a windspeed of 15m/s, a blade length of 10m, and a rotational speed of one revolution per second, show how the flow angle along the blade would change along the length.

Well, maybe they are asking a simpler question -- what is the air flow vector field that the turbine blade is rotating in? That is just the linear airspeed past the blade plus the "sideways wind" from the rotation of the blade.

It's probably simplest to use cylindrical coordinates with the z-axis parallel to the center of rotation of the turbine (so parallel to the ground). The "sideways wind" is in the plane of the rotating turbine blades, and the speed increases from zero at the central axis out to a maximum at the blade tip. What is that maximum sideways component? And what is the vector sum of the linear wind through the turbine blades plus the sideways component as you go from the central axis out to the tips? Again, it's probably simplest to use cylindrical coordinates for that sum, but they may want the answer in rectangular coordinates.

 

[t0mm02]

Well, maybe they are asking a simpler question -- what is the air flow vector field that the turbine blade is rotating in? That is just the linear airspeed past the blade plus the "sideways wind" from the rotation of the blade.

It's probably simplest to use cylindrical coordinates with the z-axis parallel to the center of rotation of the turbine (so parallel to the ground). The "sideways wind" is in the plane of the rotating turbine blades, and the speed increases from zero at the central axis out to a maximum at the blade tip. What is that maximum sideways component? And what is the vector sum of the linear wind through the turbine blades plus the sideways component as you go from the central axis out to the tips? Again, it's probably simplest to use cylindrical coordinates for that sum, but they may want the answer in rectangular coordinates.

So basically what I understand is that the teacher is asking me for The Tip Speed ?

 

[berkeman]

So basically what I understand is that the teacher is asking me for The Tip Speed ?

Not exactly, I don't think. The question refers explicitly to the "flow angle", which for the undisturbed wind would vary from zero at the central axis (zero being parallel to the z-axis I mentioned above) to some angle at the tip determined by the 15m/s horizontal wind speed and the ___m/s apparent sideways wind speed from the circular movement of the blade tip.

What do you get for the horizontal tip speed in m/s? You use the length of the blade and the angular speed to calculate it.

 

[t0mm02]

Not exactly, I don't think. The question refers explicitly to the "flow angle", which for the undisturbed wind would vary from zero at the central axis (zero being parallel to the z-axis I mentioned above) to some angle at the tip determined by the 15m/s horizontal wind speed and the ___m/s apparent sideways wind speed from the circular movement of the blade tip.

What do you get for the horizontal tip speed in m/s? You use the length of the blade and the angular speed to calculate it.

Let's leave it because I really don't understand it. Thank you for trying to help me though

 

[haruspex]

Let's leave it because I really don't understand it. Thank you for trying to help me though

It's two steps: conversion of angular speed to linear speed and addition of vectors.

Imagine you are attached to the blade at a distance r from the axle, facing the wind.
If the blade is rotating at 2π rad/sec, how fast are you moving sideways? That makes it feel as though the wind is blowing at that speed across you.

At the same time, the wind has a velocity 15m/s into your face. Draw a diagram showing these two perpendicular components of the wind's apparent velocity. Completing the rectangle, the diagonal represents the resultant velocity. At what angle is the resultant?

 

[t0mm02]

It's two steps: conversion of angular speed to linear speed and addition of vectors.

Imagine you are attached to the blade at a distance r from the axle, facing the wind.
If the blade is rotating at 2π rad/sec, how fast are you moving sideways? That makes it feel as though the wind is blowing at that speed across you.

At the same time, the wind has a velocity 15m/s into your face. Draw a diagram showing these two perpendicular components of the wind's apparent velocity. Completing the rectangle, the diagonal represents the resultant velocity. At what angle is the resultant?

Right, what I don't understand is what exactly he is asking me with that question. Is he asking me for the angle of attack, for aerodinamic twist distribution? or what exactly he is asking me for.

 

[haruspex]

Right, what I don't understand is what exactly he is asking me with that question. Is he asking me for the angle of attack, for aerodinamic twist distribution? or what exactly he is asking me for.

Aerodynamic twist is a feature of the blade itself.
Angle of attack is the relationship between the apparent direction of wind and the angle of the wing or blade, but you are not given the shape of the blade, so it's not that.
The question is simply about the way the apparent direction of wind changes along the length because of the blade's rotation. For this purpose, the blade might as well be a thin rod.

 

[t0mm02]

I am wondering what is the flow angle and whether the flow angle and pitch angle or angle of attack are related are related.

 

[BvU]

[Edit] This was post #2 in a thread that started with #15. That thread was merged into an ongoing thread, as stated in #1. When I wonder about things, I first do some googling myself ...

 

[t0mm02]

When I wonder about things, I first do some googling myself ...

View attachment 275670

So you are telling me the flow angle is the same as the angle of attack?

 

[Lnewqban]

How do you define flow angle?

 

[haruspex]

How do you define flow angle?

View attachment 275686

I hope your diagram helps, because I already explained this, pretty clearly I thought, in thread https://www.physicsforums.com/threa...-change-along-the-length.997846/#post-6437906.

 

[haruspex]

So you are telling me the flow angle is the same as the angle of attack?

No, as I already explained in your earlier thread.

 

[t0mm02]

I hope your diagram helps, because I already explained this, pretty clearly I thought, in thread https://www.physicsforums.com/threa...-change-along-the-length.997846/#post-6437906.

It doesn't help because unfortunately, we are not all experts in engineering and some of us struggle quite a lot. I do not understand what the relation or the difference is between inflow angle and angle of attack

 

[haruspex]

It doesn't help because unfortunately, we are not all experts in engineering and some of us struggle quite a lot. I do not understand what the relation or the difference is between inflow angle and angle of attack

Imagine you are standing still and a wind is blowing. The direction you feel the wind is going is the inflow angle.
Say it's coming from the North at 3m/s. Now you run East at 3m/s. You now feel the wind as though it is coming from the Northeast at 3√2 m/s. As far as you are concerned, this is now the flow angle (i.e. towards the SW).
What about a turbine blade rotating to the East? Near the hub it is only moving slowly, so the flow angle is pretty much from the North. Further out, the wind will seem to be more and more from the East.
Note that this has nothing to do with the shape of the blade.

Back to you, standing still. You now hold out a flat plate, vertically, pointing North. This is parallel to the wind. The angle of attack of the wind on the plate is zero. Turning the plate to the NE, the angle of attack on the plate is 45 degrees. Still holding the plate at that angle, you run E at 3m/s again. The apparent direction of the wind is from the Northeast, as before, so is again parallel to the plate, and the angle of attack is back to zero.

A turbine blade has a twist, so even when it is not rotating the angle of attack of the wind changes along its length. When it is rotating, the angle of attack at a given radius depends partly on this twist and partly on the way the flow angle changes.

 

[t0mm02]

I have to calculate the pitch angle from the angle of attack and lift coefficient but I have no idea what formula to use.

 

[anuttarasammyak]

I observe some information is missing:
Cl, Alpha in the attached graph, what they are, which axes they are on and what units they have ?
What is the relation between angle of attack and them?

 

[Lnewqban]

What is the meaning of pitch angle?
As angle of attack increases, CL increases, up to the point of stall; then most lift effect is lost.

 

[t0mm02]

Based on this picture, I understand what the angle of attack is. However, I understand that the pitch angle is formed by the twisted angle and the global pitch angle. I do understand what the twisted angle is but I do not know the definition of global pitch angle or what it does to the wind turbine blade. Could someone help me please?

 

[haruspex]

Based on this picture, I understand what the angle of attack is. However, I understand that the pitch angle is formed by the twisted angle and the global pitch angle. I do understand what the twisted angle is but I do not know the definition of global pitch angle or what it does to the wind turbine blade.

It looks to me that the global pitch angle is the angle between the plane of blade rotation and the chord line.
But I could interpret the diagram as saying it is the angle between the section twist angle and the chord line. That would be a problem for me because I cannot figure out from it what the section twist angle means.
You say you know what the "twisted angle" means. Is that the same as "section twist angle"? If so, please define it.
Similarly, you mention a "pitch angle", as distinct from "global pitch angle", but that is not mentioned in the diagram.

Please try to use exactly the same terminology as in the diagram, and for any terms not covered by the diagram please provide your definition.

 

[t0mm02]

It looks to me that the global pitch angle is the angle between the plane of blade rotation and the chord line.
But I could interpret the diagram as saying it is the angle between the section twist angle and the chord line. That would be a problem for me because I cannot figure out from it what the section twist angle means.
You say you know what the "twisted angle" means. Is that the same as "section twist angle"? If so, please define it.
Similarly, you mention a "pitch angle", as distinct from "global pitch angle", but that is not mentioned in the diagram.

Please try to use exactly the same terminology as in the diagram, and for any terms not covered by the diagram please provide your definition.

So, I would tell you the definitions I have for everything because it seems like it is a very tricky subject.
ANGLE OF ATTACK
The angle of attack calculates how effectively lift force is produced from the angle formed by the chord length of the airfoil with respect to the incoming wind
PITCH ANGLE
The pitch angle is composed of two parts: the twist angle and the global pitch angle.
Twisting of the angle refers to the angle formed between the blade tip’s chord line and the chord of the blade root
But yeh I am missing the definition of global pitch angle and can not see to figure it out

 

[haruspex]

So, I would tell you the definitions I have for everything because it seems like it is a very tricky subject.
ANGLE OF ATTACK
The angle of attack calculates how effectively lift force is produced from the angle formed by the chord length of the airfoil with respect to the incoming wind
PITCH ANGLE
The pitch angle is composed of two parts: the twist angle and the global pitch angle.
Twisting of the angle refers to the angle formed between the blade tip’s chord line and the chord of the blade root
But yeh I am missing the definition of global pitch angle and can not see to figure it out

I found your diagram at https://www.sciencedirect.com/science/article/pii/S221509861500155X.
There it explains that
"With respect to plane of rotation, the chord line of the cross section is given a twist called the section twist angle β."
What's confusing is that there should be two diagrams. In the base diagram φ would be zero and the chord line would be at the section twist angle. The local pitch angle would be the same as the section twist angle.
Typically (?), there is a swivel at the base of the blade, where it attaches to the hub. Rotating this swivel adds the same twist all along the blade. The extra twist this provides is the global pitch angle.
So, at any section along the blade, the local pitch angle equals the global pitch angle plus the (local) twist angle. This is the situation in the given
diagram.

I strongly disagree with the pitch angle definition in post #28. It should not specify "tip". There is a twist angle and pitch angle at each point (section) along the blade,

 

[Lnewqban]

So, I would tell you the definitions I have for everything because it seems like it is a very tricky subject.
...
But yeh I am missing the definition of global pitch angle and can not see to figure it out

Do you get it now?