Can a flow created by a fan show an Edge effect when hitting a wall?

[T C]

I am curious to see the velocity and pressure distribution part of this scenario. And, by the way, what's the source of this photo/drawing?

 

[renormalize]

And, by the way, what's the source of this photo/drawing?

Here's the link to the published paper containing the second drawing as part of Fig. 5a:
Two-dimensional steady flow over a semi-circular cylinder: drag coefficient and Nusselt number
If you search this title on Google Scholar you can find a PDF version of the paper.

 

[T C]

Can't see it as I don't have an account. Whatsoever, I am curious about the velocity distribution and pressure distribution diagram of the second photo.

 

[renormalize]

Can't see it as I don't have an account. Whatsoever, I am curious about the velocity distribution and pressure distribution diagram of the second photo.

Did you search the title in Google Scholar for a free PDF as I suggested? What did you find?

 

[256bits]

Ok, I see it, and see that you capitalized "Edge" but not "effect" because that's how it is shown in the video subtitles. Near as I can tell, it's typically called "corner effect" and is about what happens whe a fluid flows around a sharp corner (it accelerates):

Is this your understanding if flow around a house, building, mostly low rise?
The reference given in the post 17 shows that flow around buildings, especially high rise downtown areas, can have complicated air movement patterns.
The upwind velocity U profile need not be that as shown in the figure below, especially if other buildings, or obstacles are in the vicinity. The U shown for the free stream is modelled as either an exponential or as a power function. At ground level, the U velocity is zero, producing the swirl under the stagnation zone. The dead zone is evident on the lee side of the building. ( Note the similarity to an idling car and carbon monoxide poisoning, where the noxious gas can enter the passenger compartment even if the exhaust is exiting at the rear ). ( And snowbank overhang extensions ).

Since the streamlines compress over the building ( and sides as well ), a velocity increase does occur.
It would seem the greatest velocity amplification occurs not at the actual edge but is a function of height and distance from the edge, surpassing U_{roof_height}, and possibly surpassing U_z under particular conditions.

https://www.aivc.org/resource/air-flow-around-buildings
Chapter 14 of Fundamentals 1981 ASHRAE , a copy of which these nice people have provided.
( Can't find my copy of Fundamentals, same year, ( dagnabit )
https://www.aivc.org/resource/air-flow-around-buildings

 

[T C]

Since the streamlines compress over the building ( and sides as well ), a velocity increase does occur.
It would seem the greatest velocity amplification occurs not at the actual edge but is a function of height and distance from the edge, surpassing Uroof_height, and possibly surpassing Uz under particular conditions.

If that's true, then from where the extra energy can come?

 

[256bits]

If that's true, then from where the extra energy can come?

Bernoulli

 

[T C]

That means the fall in temperature following the fall the pressure and the energy released in this way is being converted into kinetic energy, right?

 

[256bits]

That means the fall in temperature following the fall the pressure and the energy released in this way is being converted into kinetic energy, right?

No.
Bernoulli says nothing about a change in temperature.
https://efficientengineer.com/bernoulli/

 

[FactChecker]

It does seem clear from the diagrams @renormalize put in post #27, that the leading corners squeeze the streamlines together. That indicates an increased velocity.

 

[T C]

Bernoulli says nothing about a change in temperature.

Condensation above aircraft wings are a very common phenomenon for a long time i.e. from subsonic to supersonic. Condensation occurs means there is fall in temperature otherwise it's simply not possible.​

 

[FactChecker]

View attachment 369036​

Condensation above aircraft wings are a very common phenomenon for a long time i.e. from subsonic to supersonic. Condensation occurs means there is fall in temperature otherwise it's simply not possible.​

That is a consequence in certain situations of Bernoulli's equation. It is not Bernoulli's equation.

 

[T C]

That is a consequence in certain situations of Bernoulli's equation. It is not Bernoulli's equation.

Whatsoever, it's a proof that temperature fall occurs due to the increase in velocity. I am just curious to know that happened to the energy that has been released due to this phenomenon.

 

[russ_watters]

If that's true, then from where the extra energy can come?

Bernoulli

This answer may be too short/flippant for @T C to have grasped. To expand: Bernoulli's principal/equation is a conservation of energy statement: there is no extra energy. To put a finer point on it, any obstruction will result in a net loss of energy in the flow.

The question here is whether a localized velocity increase can be exploited to provide greater power from a given wind turbine vs the same turbine in freestream. The answer is probably but it is complicated and very situation-specific.

 

[russ_watters]

Whatsoever, it's a proof that temperature fall occurs due to the increase in velocity. I am just curious to know that happened to the energy that has been released due to this phenomenon.

Please look at the standard form of Bernoulli's equation @FactChecker provided and tell us what you see the answer is. You've been looking at related issues to this for years and this question is answered in the first hour of a lecture or chapter on Bernoulli's Principle. It's inexcusable for you to not grasp this by now.

 

[renormalize]

Whatsoever, it's a proof that temperature fall occurs due to the increase in velocity. I am just curious to know that happened to the energy that has been released due to this phenomenon.

The energy "released" by the temperature-fall is exactly balanced by the energy required to increase the flow-velocity. Bernoulli's equation for a compressible fluid (like air) can be written $v^2/2+C_pT=\text{constant}$, where $C_p$ is the specific heat of the fluid. So simple conservation of energy for compressible flow implies higher-velocity $v$ = lower-temperature $T$.

 

[256bits]

Whatsoever, it's a proof that temperature fall occurs due to the increase in velocity. I am just curious to know that happened to the energy that has been released due to this phenomenon.

The Bernouilli equation that one mostly sees, and the one that is presented as an introduction to fluid flow, is of the form in post 42 by @FactChecker. Below about Mach 3, this form can solve the velocities and pressures from one point to another along a streamline quite adequately for a great deal of phenomena.
This form has several assumptions that need explaining
- flow is streamlined
- steady flow in time
- no change in density along a streamline
- viscous effects neglected, ie fluid is considered inviscid, and thus no internal friction
- volume work is considered to be zero, so no work done on or by the fluid
- no change in temperature, so no change in internal energy of the fluid

A general energy equation of the form from the first law of thermodynamics.
Q + W = ΔU + ΔPE + ΔKE + ΔPV

Since Q = 0, W = 0, ΔU = 0, we are left a constant energy from point 1 to 2 along a streamline in terms of the changes in only KE, PE, and PV of the fluid.

 

[FactChecker]

The question here is whether a localized velocity increase can be exploited to provide greater power from a given wind turbine vs the same turbine in freestream. The answer is probably but it is complicated and very situation-specific.

Good point. I think that is the unexpressed question of the OP. The diagrams that @renormalize included in post #27 seems to indicate that the velocity can be higher than the freestream velocity. The streamlines appear closer together at the leading corners of the obstruction than they were in the freestream.

 

[renormalize]

The diagrams that @renormalize included in post #27 seems to indicate that the velocity can be higher than the freestream velocity. The streamlines appear closer together at the leading corners of the obstruction than they were in the freestream.

I don't think that's the right interpretation. The flow-speed plots in fig. 6 of my post #26 show lower speeds (blue) everywhere around the building compared to the higher incoming freestream speed (yellow/green). But what you can say is this: if you have a turbine of finite aperture-width $w$, placing it at the corners is better because it will capture a higher average flow speed (since the streamlines are more closely spaced there), compared to putting it nearer the stagnation point on the front wall. But in neither location will those average speeds be as high as the freestream speed. Obstacles always diminish nearby flow speeds to below that of the unperturbed freestream.

 

[FactChecker]

I don't think that's the right interpretation. The flow-speed plots in fig. 6 of my post #26 show lower speeds (blue) everywhere around the building compared to the higher incoming freestream speed (yellow/green).

Sorry. I stand corrected. I was thinking about incompressible fluid flow. Thanks.

 

[T C]

The energy "released" by the temperature-fall is exactly balanced by the energy required to increase the flow-velocity. Bernoulli's equation for a compressible fluid (like air) can be written $v^2/2+C_pT=\text{constant}$, where $C_p$ is the specific heat of the fluid. So simple conservation of energy for compressible flow implies higher-velocity $v$ = lower-temperature $T$.

In short, a part of enthalpy has been converted into this extra velocity. There is no other explanation.

 

[russ_watters]

I don't think that's the right interpretation. The flow-speed plots in fig. 6 of my post #26 show lower speeds (blue) everywhere around the building compared to the higher incoming freestream speed (yellow/green).

Those colors don't make any sense to me, given the streamline compression. & @256bits here's what AHRAE Fundamentals says (I'm trying to access the digital version or I'll scan my book):

"Flow accelerates as the streamlines compress over the roof and decelerates as they spread downward over the wake on the downwind side of the building."

"For an isolated high-rise building...high wind speed at pedestrian level can be caused by.... the corner streams."

I interpret both of these to be saying higher than freestream.

Note, Post #27 is showing flow around the sides of a long cylinder, not over the top of a building low to the ground (more like the second scenario than the first in the ASHRAE quotes. Note also, as you make your "cylinder" more aerodynamic it will start looking like a wing, where you certainly do get flow speeds above freestream.

The wikipedia article, for what it's worth, has images of flow around a cylinder showing velocity vectors with magnitude based on arrow size:

 

[renormalize]

There is no other explanation.

I am unsure of your point. Have there been "other explanations" proposed to explain velocity increase?

 

[russ_watters]

The energy "released" by the temperature-fall is exactly balanced by the energy required to increase the flow-velocity. Bernoulli's equation for a compressible fluid (like air) can be written $v^2/2+C_pT=\text{constant}$, where $C_p$ is the specific heat of the fluid. So simple conservation of energy for compressible flow implies higher-velocity $v$ = lower-temperature $T$.

I don't think this is very useful for low flow velocity situations, where the temperature and density changes are negligible and therefore ignored (incompressible), and that form of the equation doesn't describe the interplay between velocity(pressure) and static pressure. I think it's a Prego thing; "It's in there", but doesn't show it.

Plugging in a reasonable wind change of 10 m/s yields a temperature change from standard of 0.05 K.

 

[russ_watters]

In short, a part of enthalpy has been converted into this extra velocity. There is no other explanation.

I am unsure of your point. Have there been "other explanations" proposed to explain velocity increase?

I'd like for @T C to answer the question based on the incompressible flow form of Bernoulli's equation provided in Post #42.

 

[T C]

I'd like for @T C to answer the question based on the incompressible flow form of Bernoulli's equation provided in Post #42.

Plain and simple explanation, the compression-expansion and related fall in temperature is small in comparison to the overall temperature and therefore it can be neglected and we can consider it to be "practically" incompressible. The condensation over aircraft wings is a reality and can't be overlooked.

 

[russ_watters]

Plain and simple explanation, the compression-expansion and related fall in temperature is small in comparison to the overall temperature and therefore it can be neglected and we can consider it to be "practically" incompressible.

So then what does the equation say is going on?

The condensation over aircraft wings is a reality and can't be overlooked.

It can be overlooked if it's irrelevant to the topic we were discussing.

 

[T C]

So then what does the equation say is going on?

The equation simply says that as the velocity increases, the pressure decreases. And the decrease in pressure is proportional to the square of the increase in velocity (the gz part can be neglected).

 

[FactChecker]

The equation simply says that as the velocity increases, the pressure decreases. And the decrease in pressure is proportional to the square of the increase in velocity (the gz part can be neglected).

Yes. So that is where the velocity can come from -- decreased pressure. This just means that the random directional movement of atoms causing pressure can be somewhat redirected to the forward direction of motion, causing an increase of airflow velocity and a decrease in pressure.

 

[T C]

Yes. So that is where the velocity can come from -- decreased pressure. This just means that the random directional movement of atoms causing pressure can be somewhat redirected to the forward direction of motion, causing an increase of airflow velocity and a decrease in pressure.

Decreased pressure means fall in temperature and that means energy is released. That energy is being converted into the kinetic energy.