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

[256bits]

given the streamline compression

The streamline figures in post 27 can be somewhat deceiving at first glance.

The streamline figure spacing is shown compressed, rather than equally spaced, at near y/D = 0 at location x/D = -2 at the left of the figure, with similar streamline compression with x/D increases. The streamlines are originally compressed likely to show better detail of formation of the 'bubble' at Rcr as the flow velocity increases.
The colored velocity change diagrams are the ones to look at to show the velocity distribution over different edges of the object.

Anyways, the flow is laminar in the study, with low RE, ( inertial << frictional ( viscous ) ) . The curvature of the edge is apparently affecting the velocity flow distribution.

"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.

For a building, depending upon the wind velocity, Re can be anything from to Re 10⁶ for a windy day. Inertial forces dominate at higher Re. At some Re, the wind inertia will cause it to separate from the building surface ( flat roof or sides ) and overshoot upwards as seen in the ASHRAE picture. Re characteristic length would be something involving wetted surface of the H,D, and W of the building, with every building design being different.

I interpret both of these to be saying higher than freestream.
As do I, with a caveat below.
Studies have shown that the amplification can be greater than 1, extreme case up to 1.2, mostly less than that.
Question is "What freestream velocity is, or should be, based upon - the U_T at the undisturbed region, the U_max above the ABL, the U_r at the roof height, or some other U_e, where e is some factor to determine the horizontal, or vertical, distance from the building face based upon building W and H, where the flow velocity has not yet been disturbed by the building as seen in the velocity diagrams in post 27.
U_T nor U_max do not seem to be all that relevant, so we are left with the free stream velocity at building height, or some calculated velocity.

From the original post 1

TL;DR: I want to know whether a flow created by a simple fan will show Edge Effect when hitting a flat and vertical surface.

when an airflow hits the walls of buildings and its velocity will increase. Some market available shroud augmented wind turbine types are claiming that they used this effect to increase the output of their own designed wind turbine

Within the Atmospheric Boundary Layer, the velocity flow distribution will not be so neat as the ASHRAE suggests. There will be a velocity frequency distribution around the mean. We can call a measure of this frequency distribution as the wind's 'gustiness'. And everyone knows that wind gustiness is a bane of most wind turbine designs.
Reason windmills are tall and away from hill, trees, and buildings --> get as high as possible away from ABL effects --> less gustiness and higher wind velocity.[/SUB]

 

[FactChecker]

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

There are other things going on. Please try to understand Bernoulli's equation, which gives the trade-off between pressure and velocity.

 

[russ_watters]

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).

Right. And these are forms of energy: kinetic energy increases, pressure energy decreases. That's the energy that gets traded from one form to another.

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

That isn't in the equation, is it?

 

[T C]

Right. And these are forms of energy: kinetic energy increases, pressure energy decreases. That's the energy that gets traded from one form to another.

At the end of the day, it's enthalpy.

 

[russ_watters]

I interpret both of these to be saying higher than freestream.
As do I, with a caveat below....

Reason windmills are tall and away from hill, trees, and buildings --> get as high as possible away from ABL effects --> less gustiness and higher wind velocity.[/SUB]

Agreed. I think that in certain specific/limited/contrived circumstances it is likely to be possible for a given small wind turbine to perform better on a roof edge than in freestream wind. But there's definitely good reasons why that's not the preferred place to put them.

 

[T C]

There are other things going on. Please try to understand Bernoulli's equation, which gives the trade-off between pressure and velocity.

Other things means factors like humidity etc. In Bernoulli's equation, it has been considered that the there would be no change in volume despite the fall in pressure. But in reality, there should be fall in volume and temperature as gas laws suggest. As for example, we can consider the g to be the same at Marinara trench and the top of Mt. Everest as here the change in distance from the centre of earth is negligible. The condensation of vapour over wings of aircrafts proves that a change in temperature certainly occurs. But that change is negligible and therefore doesn't effect the lift force (as deduced from Bernoulli's Principle) much.

 

[renormalize]

At the end of the day, it's enthalpy.

Enthalpy is just a particular form of energy that is characteristic of certain configurations of matter. And energy in total is conserved. What's your point?

 

[T C]

Enthalpy is just a particular form of energy that is characteristic of certain configurations of matter. And energy in total is conserved. What's your point?

My point is simple, the increased velocity comes at the cost of enthalpy. And for compressible fluids, pressure and internal energy is very closely tied and fall/rise in one means fall/rise in the other too if it's an isenthalpic process i.e. no energy can enter or leave the system.

 

[renormalize]

no energy can enter or leave the system.

OK, good. I think that we are in agreement: we both accept the predictions of standard fluid dynamics (like the Betz limit that bounds the maximum energy that can be extracted by any wind turbine).

 

[T C]

There is no question of denying the Betz limit. Point is whether this acceleration can increase the overall output or not.

 

[renormalize]

There is no question of denying the Betz limit. Point is whether this acceleration can increase the overall output or not.

• "this acceleration"--what "acceleration"? Please define what you're referring to specifically.
• "increase overall output"--"overall output" of what quantity? And "increase" relative to what baseline?

 

[T C]

"this acceleration"--what "acceleration"? Please define what you're referring to specifically.

The acceleration of the flow above its initial velocity while trying to overcome the barrier.

"increase overall output"--"overall output" of what quantity? And "increase" relative to what baseline?

Overall output means increase in output due to this I.e. above the level in comparison to any conventional wind turbine of similar size placed in open air instead of the edge of the building roof.

 

[A.T.]

Overall output means increase in output due to this I.e. above the level in comparison to any conventional wind turbine of similar size placed in open air instead of the edge of the building roof.

If you google "optimal placement wind turbine hill" or similar, you will find more information on exploiting obstacles to improve wind turbine performance.

For example this thesis:
https://www.diva-portal.org/smash/get/diva2:1176088/FULLTEXT01.pdf

The speed-up over the hills acted in favour for the power performance of the wind turbines. An increased maximum power coefficient was observed when introducing hills, without drastically increasing the thrust coefficient of the turbine compared with a flow case over flat terrain.

 

[T C]

If you google "optimal placement wind turbine hill" or similar, you will find more information on exploiting obstacles to improve wind turbine performance.

For example this thesis:
https://www.diva-portal.org/smash/get/diva2:1176088/FULLTEXT01.pdf

If wind can speed up over the hills, it will certainly speed up over tall multi-storeyed buildings or similar kind of structures.

 

[A.T.]

If wind can speed up over the hills, it will certainly speed up over tall multi-storeyed buildings or similar kind of structures.

For any obstacle in a wind, you will have areas with slower and areas with faster than free-stream local flows. The size and shape of the obstacle determines if the faster areas are large and steady enough to exploit them efficiently.

 

[T C]

For any obstacle in a wind, you will have areas with slower and areas with faster than free-stream local flows. The size and shape of the obstacle determines if the faster areas are large and steady enough to exploit them efficiently.

The main point is whether the speeding up can exceed the initial velocity or not. At least, it seems that you and me agreed on one point that in the fastest areas, the velocity exceeds the initial velocity. But many participants here are saying that such things can't happen.

 

[FactChecker]

For any obstacle in a wind, you will have areas with slower and areas with faster than free-stream local flows. The size and shape of the obstacle determines if the faster areas are large and steady enough to exploit them efficiently.

Would that be true in the steady state flow or only in turbulence? Some diagrams here seem to indicate reduced velocity everywhere yet very close-together streamlines at the leading corners. IMO, that would require a lot of compression at those corners. They seem a little contradictory.

 

[256bits]

@A.T. T
Great article, where did you find it.

I think a speedup is implied already for flow over an obstacle, such as a building. Somewhere along the lines of a factor of 1.1, more less than more.
U∞ would have to be addressed for each and every building, and then find Uref, the velocity at the hub; not a one size fits all.


A problem encountered for an urban environment is the ABL, that gustiness, or a velocity frequency imposed upon the power or exponential free stream velocity, affecting wind turbine performance and lifetime. As seen in the article.

Using nothing other than Bernouilli, a derivation of the Betz limit is produced for a wind turbine in this section. Seems a bit more entailed than what I went through in fluid course.

The reduction of U_ref ( the author uses an incoming air velocity of U∞ = 7.5m/s ) with spires and grids to model an ABL more accurately as an exponential ( ie Uo = 0 ) . Uref decreased to 6.25 m/s at the turbine hub.
And also Fig 5.3 - the effect the turbine itself had upon incoming/outgoing wind velocity.

This discussion interested me the most.
This sounds like a gravity wave being set up close to the ground due to the hill.

https://en.wikipedia.org/wiki/Gravity_wave

 

[russ_watters]

The main point is whether the speeding up can exceed the initial velocity or not. At least, it seems that you and me agreed on one point that in the fastest areas, the velocity exceeds the initial velocity. But many participants here are saying that such things can't happen.

I don't think anyone is saying it can't happen.

 

[T C]

Then, as per my described scenario, the flow can accelerate above the initial value or not. If it can exceed the that in case of natural winds, why not for a flow created by a fan!

 

[FactChecker]

One obvious difference is that natural winds are very broad and the airflow from a fan is very narrow. I don't know what that changes, but it might be a lot.