Why Does Air Flow Faster Along S-T-E on a Aerofoil?

[Rishi Gangadhar]

Consider this aerofoil. Let the leftmost point be S and rightmost point be E. Let the topmost point be T and a point on the bottom of the foil be B.
Let the wind blow as shown in the figure above.
Bernoulli's principle says that the air blowing along S-T-E must travel a path longer than than that traveled by air blowing along S-B-E, and for the time taken to reach E must be the same, the wind blowing through the top of the foil must have a higher velocity and hence the pressure on the top of the foil is lesser than that on the bottom part of the foil and hence the plane takes off.
But, why should the air blowing along S-T-E and S-T-B take the same time to reach E?
Let me frame this question in a different way. Consider two particles in air coming towards the foil, one which will take the path S-T-E (for convenience sake let this be particle 1) and the other which will take the path S-B-E (let this be 2). Until they reach the foil, they have the same velocities. But after they reach the foil, either particle 1 speeds up, or particle 2 slows down, or both happen. Thus, at least one of them accelerates. According to Newton's first law, which says that no object accelerates unless an external force is applied, there must be a force acting on this particle. Where does this force arise from and for what reason does it arise?

 

[boneh3ad]

Bernoulli's principle says that the air blowing along S-T-E must travel a path longer than than that traveled by air blowing along S-B-E, and for the time taken to reach E must be thesame

No. Bernoulli's principe does not say this. Nothing in physics says this. It flat out is not correct. In fact, the air moving over the top move much faster than below and leaves the trailing edge quite a bit before a particle reaching the leading edge at the same time but traveling underneath reaches the trailing edge. This is commonly called the equal transit time fallacy.

Also, I am not sure why any of that was relevant to this necrothread.

 

[A.T.]

the time taken to reach E must be the same

Check out the video below at 0:38, to see if the smoke stripes split by the leading edge reach the trailing edge at the same time.

 

[russ_watters]

The others took care of the rest, but:

But after they reach the foil, either particle 1 speeds up, or particle 2 slows down, or both happen. Thus, at least one of them accelerates. According to Newton's first law, which says that no object accelerates unless an external force is applied, there must be a force acting on this particle. Where does this force arise from and for what reason does it arise?

Bernoulli's principle does describe why a packet of air might speed up or slow down (that's basically its entire point): it's the pressure that provides the force to accelerate the packet of air.

 

[boneh3ad]

The others took care of the rest, but:

Bernoulli's principle does describe why a packet of air might speed up or slow down (that's basically its entire point): it's the pressure that provides the force to accelerate the packet of air.

Eh, but it doesn't really, though. It does establish the relationship between pressure and velocity but doesn't provide any means for calculating a flow field in such a situation without knowing one of them a priori or without another equation to describe either the pressure or the velocity field.

 

[russ_watters]

Eh, but it doesn't really, though. It does establish the relationship between pressure and velocity but doesn't provide any means for calculating a flow field in such a situation without knowing one of them a priori or without another equation to describe either the pressure or the velocity field.

I'm not sure what your point is, but it doesn't seem related to the very basic question I was answering.

 

[boneh3ad]

My point is that Bernoulli's equation doesn't really deal with forces at all. It ultimately deals with energy. It's all related, of course, but for someone who clearly doesn't understand what Bernoulli's equation is (Rishi), using it to explain forces is likely misleading.

 

[Rishi Gangadhar]

Bernoulli's principle says that the air blowing along S-T-E must travel a path longer than than that traveled by air blowing along S-B-E, and for the time taken to reach E must be the same
Sorry, I did not notice that I typed the words "Bernoulli's principle" in the beginning
my question is all about why time taken should be the same for air blowing along S-T-E and S-B-E.

 

[Rishi Gangadhar]

The others took care of the rest, but:

Bernoulli's principle does describe why a packet of air might speed up or slow down (that's basically its entire point): it's the pressure that provides the force to accelerate the packet of air.

Your explanation is somewhat cyclic.
You say that the pressure provides the force to accelerate the packet of air, and at the same time, the acceleration of the particle causes the change in pressure (because of acceleration, there is difference in velocities of the packets of air along S-T-E and S-B-E, and hence pressure decreases according to bernoulli's principle)
This says nothing about why the time taken should be the same

 

[A.T.]

my question is all about why time taken should be the same for air blowing along S-T-E and S-B-E.

The time isn't the same. See video in post #3.

 

[rcgldr]

Your explanation is somewhat cyclic.

More like coexistent. Air accelerates from higher pressure zones to lower pressure zones, and absent external forces (so that the total energy remains constant), Bernoulli's equation relates the reduction in pressure and increase in speed (speed^2) as air accelerates from a higher pressure zone towards a lower pressure zone. Bernoulli doesn't explain why pressure differentials exist around a wing, only how the air will react once those pressure differentials exist.

I'm not sure how Bernoulli's equation applies to curved flows, since the centripetal (perpendicular to the flow) component of acceleration is related to a pressure differential, but not to a change in speed, only a change in direction, while at the same time the existence of a pressure differential related to centripetal acceleration is going to have an impact on the speed of the air in the direction of flow.

 

[RandomGuy88]

I'm not sure how Bernoulli's equation applies to curved flows, since the centripetal (perpendicular to the flow) component of acceleration is related to a pressure differential, but not to a change in speed, only a change in direction, while at the same time the existence of a pressure differential related to centripetal acceleration is going to have an impact on the speed of the air in the direction of flow.

Bernoulli's equation applies along a streamline. When the flow is curved, the pressure gradient is perpendicular to the streamlines and is balanced by the centrifugal force resulting from the fact that the fluid has mass.

 

[Rishi Gangadhar]

Bernoulli's equation applies along a streamline. When the flow is curved, the pressure gradient is perpendicular to the streamlines and is balanced by the centrifugal force resulting from the fact that the fluid has mass.

Bernoulli's equation does not apply to this kind of flow because the flow is turbulent.
Bernoulli's equation applies only to those situations where the fluid is incompressible, which is clearly not the case from what the video shows.

 

[RandomGuy88]

Bernoulli's equation applies only to those situations where the fluid is incompressible, which is clearly not the case from what the video shows.

Are you talking about the video of the smoke flow over the airfoil?
What makes you think that flow is not incompressible, because it definitely is.

There is a compressible version of the Bernoulli's equation.

 

[boneh3ad]

Bernoulli's equation does not apply to this kind of flow because the flow is turbulent.
Bernoulli's equation applies only to those situations where the fluid is incompressible, which is clearly not the case from what the video shows.

There has been nothing in this discussion about compressible or turbulent flows, and the curvature of a streamline does not imply turbulence or compressibility, and therefore does not preclude the use of Bernoulli's equation.

 

[Rishi Gangadhar]

The flow is of course turbulent, otherwise the velocities of air packets would not change. Think about it.
I did not say that it is turbulent because of the curvature of a streamline.

 

[RandomGuy88]

Bernoulli's equation applies only to those situations where the fluid is incompressible, which is clearly not the case from what the video shows.

The flow in the video above is incompressible.

The flow is of course turbulent, otherwise the velocities of air packets would not change. Think about it.
I did not say that it is turbulent because of the curvature of a streamline.

No one is saying anything about the flow not being turbulent. There is clearly turbulence in the wake of the airfoil due to trailing edge separation.

 

[Rishi Gangadhar]

HEY, you can see from the video that the lines are closer to each other on the top part of the foil than the ones on the bottom. Thus the pressure should be higher at the top if you do not consider the velocity part. Thus you can not say anything about the net effect (considering both the velocity and this compression effect), because the engines are the actual ones that help the plane to fly.

 

[Rishi Gangadhar]

I just wanted to mention that point about turbulence because I wanted to say that Bernoulli's equation could not be applied

 

[RandomGuy88]

HEY, you can see from the video that the lines are closer to each other on the top part of the foil than the ones on the bottom. Thus the pressure should be higher at the top if you do not consider the velocity part. Thus you can not say anything about the net effect (considering both the velocity and this compression effect), because the engines are the actual ones that help the plane to fly.

I don't think anything in this post makes any sense.

Pressure is lower on the top of the airfoil not higher. The streamlines get closer together as a result of mass conservation. And the streamlines being closer together is not an indication of compressibility.

Thus you can not say anything about the net effect (considering both the velocity and this compression effect), because the engines are the actual ones that help the plane to fly.

What net effect?

What do you mean "the engines are the actual ones that help the plane to fly" ?

 

[boneh3ad]

The flow is of course turbulent, otherwise the velocities of air packets would not change. Think about it.
I did not say that it is turbulent because of the curvature of a streamline.

What is it exactly that you think turbulence means? I'm not sure you are clear on the concept. Further, a turbulent boundary layer doesn't mean you can't apply Bernoulli's equation to an airfoil as long as you apply it along the inviscid streamlines outside the boundary layer. That's done frequently and you can calculate lift very effectively that way from a given flow field.

 

[Rishi Gangadhar]

This is turbulent because there is a change in pressure with space (the pressure does change as the air moves towards the foil).
Turbulence does occur when you have variation of pressure with space and time.

This is What actually happens in the case of an aerofoil (look at the second diagram).

 

[Rishi Gangadhar]

Lines getting closer does indicate compressibility. Can you tell me what else can possibly indicate compressibility.

 

[Rishi Gangadhar]

What do you mean "the engines are the actual ones that help the plane to fly" ?

Without the engines, the plane can't fly.
This is what I meant by that statement.

 

[boneh3ad]

This is turbulent because there is a change in pressure with space (the pressure does change as the air moves towards the foil).
Turbulence does occur when you have variation of pressure with space and time.

This is What actually happens in the case of an aerofoil (look at the second diagram).

So what you have shown here are turbulent separation bubbles. Yes, those bubbles contain turbulent flow, but they are not the definition of turbulent flow. Turbulence itself is a much broader concept. Turbulence is characterized by rapid changes in both time and space of the various flow variables like temperature, pressure, and velocity. If you were to measure one point in a turbulent flow, it would be highly erratic and look essentially like fairly large random fluctuations around the mean quantity of whatever you are measuring. In the scope of the whole turbulent flow, the most notable characteristic is that it contains eddies (or vortices) of many different sized, where the larger eddies contain a lot of energy and gradually dump energy into smaller and smaller eddies until it is small enough that viscosity can dissipate the energy. In other words, in the pictures you posted, the important part that indicates turbulence are the crazy, "chaotic streamlines" drawn in the turbulent regions, not the fact that there is an abrupt change in pressure.

In every single fluid flow that is even remotely interesting, pressure changes with space and time. However, many of those flows are laminar. What is important is how variables like pressure change with space and time. You can certainly have laminar flow over an airfoil or around a sphere, and those certainly involve pressure changes with space and time. In a laminar flow, though, the fluctuations about the mean value are very small and predictable, whereas in a turbulent flow, they are much larger and not practically predictable.

Lines getting closer does indicate compressibility. Can you tell me what else can possibly indicate compressibility.

Lines getting closer does not indicate compressibility. When streamlines change their relative distance, it indicates a change of speed. Given the definition of a streamline, you can view them almost as little walls in the inviscid flow. Since the velocity is always tangent to a streamline, there is always no component of velocity normal to a streamline and no mass flow across them. Therefore, two adjacent streamlines can be treated as what is called a streamtube, and conservation of mass applies in a streamtube. So, in subsonic flow, if streamlines get closer together, the velocity is increasing and vice versa.

Compressibility, on the other hand, is generally indicated by the Mach number. Any flow in which $M \geq 0.3$ is typically considered compressible. Any slower than that and compressibility effects are negligible and the flow may be safely treated as incompressible. Streamlines can get closer together or farther apart in either case. The other indicator (or rather, definition) of compressibility is that $\nabla \cdot \vec{v} \neq 0$ in a flow field.

 

[Nidum]

In true streamline flow the streamlines getting closer together means that the flow is speeding up . Draw the stream lines passing through a 2D venturi and all should become clear .

The 'turbulence' shown in lower diagram is actually a vortex street - horizontal axis vortices rolling off in succession from the trailing edge .

Vortices are always there in embryo but may not fully form at lower angles of incidence and speeds . Vortices form in whole or part because there is a difference in speed of air coming off top and bottom surfaces of aerofoil .

If flow actually becomes chaotic at trailing edge all is lost and you are going into the sea .

Just for interest - in classical flow dynamics the flow over an aerofoil can be characterised by a circular flow going right round the wing section and with a linear flow superimposed .

 

[rcgldr]

Going back to the original post:

Bernoulli's principle says that the air blowing along S-T-E must travel a path longer than than that traveled by air blowing along S-B-E

The longer path can be on the bottom and a wing will still produce lift, but the lift to drag ratio will not be as good as a conventional wing. Example lifting body:

why should the air blowing along S-T-E and S-T-B take the same time to reach E?

As already posted it doesn't take the same time.

According to Newton's first law, which says that no object accelerates unless an external force is applied, there must be a force acting on this particle. Where does this force arise from and for what reason does it arise?

The wing is the source of the force external to the air. Using the wing as a frame of reference, as the air passes backwards across the wing, it is diverted downwards (lift) and slowed down (drag). Using the air as a frame of reference, as the wing passes forwards through a volume of air, it accelerates the air downwards (lift) and a bit forwards (drag) and in this frame, the energy of the air is increased (zero velocity before, non-zero velocity as it's pressure returns to ambient afterwards). In either frame, there are a pair of Newton third law forces, the wing exerts a downwards and somewhat forwards force onto the air, and the air exerts an upwards and somewhat backwards force onto the wing.

The bottom of the wing directly pushes downwards and forwards on the air. Once a bit behind the leading edge of a wing, the upper surface curves / recedes away from the relative flow, drawing the air to fill in what would otherwise be a void if the air didn't accelerate towards the convex / receding upper surface. If the flow is attached, the air approximately follows the upper surface. If the flow separates, then vortices or even mostly one very large vortice fills in what would otherwise be a void, called a stall.

Engines - In the case of a glider, gravity is the power source, and in the special case where an updraft matches the gliders sink rate, a glider can maintain level flight.

 

[Nidum]

Nice to see pictures of one of the lifting body experimental aircraft which came before space shuttle .

I don't honestly know why the Bernoulli explanation of aerofoil lift is still used so much - the quite simple air wedge explanation as outlined by yourself is clearer and more intuitive I've always thought .

I was brought up on compressor and turbine blading more than on aircraft wings but they have a lot in common and study of what happens to airflow over each is fascinating .