How does a fan blow more than it sucks?

[aerodave]

@Napier

Here, I hear the original poster asking why the areas are different. The explanation of this requires Reynolds number or at least consideration of the momentum and inertial behavior.

I, personally, would not invoke Reynolds number in an explanation of this fan inlet/exit behavior. That’s not to say the Reynolds number isn’t important (because isn’t it always?), but it’s not driving the effects. Sure, at very low-Re conditions, you could expect the fan to act fairly differently. But none of that is really cruicial to the question at hand.

It’s clear at this point that the reason the air is slow at the inlet of an open fan, and fast in the exit is because the capture area is large upstream of the fan, and the exit area is smaller. Due to mass conservation, the air must move faster through the smaller area, and can move more leisurely through the bigger area. This, however, isn’t a satisfying and complete explanation because it doesn’t answer the question of why the capture area is large and the exit area small. The real answer to that has to do with pressure gradients.

Get far enough upstream of the working fan, and you can say the the velocity of the air is effectively zero. Since it is moving at a given velocity by the time it reaches the fan blades, it must have accelerated. By Bernoulli’s principle, the static pressure of the air is lower at the fan than in the quiescent air upstream. Air likes to go from high to low pressure, so this is considered a favorable pressure gradient.

After going through the fan, the air eventually slows down to zero velocity again. Its static pressure is thus gradually raised back up to where it started. Air doesn’t emjoy moving from low pressure to high pressure (but is forced to by the fan), and so this is called an adverse pressure gradient.

The upshot is that while moving along a favorable pressure gradient, you can make air do most anything you want. Turn around sharp bends, follow walls diverging or converging at various angles…you name it. So ahead of the fan, the air is free to come in from all directions. And it does so gladly, because it’s the most efficient way, space-wise, to get air into the partial vacuum created by the fan.

On the exit, however, the adverse pressure gradient changes the rules. When faced with an “uphill climb” into higher pressure, air gets a lot more irritable, and like a cranky toddler, doesn’t do what it’s told. The most familiar (to aerodynamicists, anyway) consequence of an adverse gradient is that air will not gracefully expand along the walls of a divergent duct. That is, if the walls of a duct get farther apart as you move along, and the angle of this divergence is too wide, the air just won’t stay attached to the walls. Instead, the flow separates from the walls, and makes itself into a “free jet”, expanding at its own pace. So because of the adverse pressure gradient downstream of a fan, you can’t make the fan’s outflow expand faster than it wants to, which isn’t very fast. So if you’re anywhere fairly near the exhaust side of a fan, the air will not have expanded much by that point, and the area of the slipstream will still be small. Small area yields high velocity.

Hope that explanation was clear. It’s tough in text though…if anything needs visual aids, it’s aero.

[CC]

Clear to me. Nicely done. Thank you.

[flight]

@aerodave

I, personally, would not invoke Reynolds number in an explanation of this fan inlet/exit behavior. That’s not to say the Reynolds number isn’t important (because isn’t it always?), but it’s not driving the effects. Sure, at very low-Re conditions, you could expect the fan to act fairly differently. But none of that is really cruicial to the question at hand.

I concur.

It’s clear at this point that the reason the air is slow at the inlet of an open fan, and fast in the exit is because the capture area is large upstream of the fan, and the exit area is smaller. Due to mass conservation, the air must move faster through the smaller area, and can move more leisurely through the bigger area. This, however, isn’t a satisfying and complete explanation because it doesn’t answer the question of why the capture area is large and the exit area small. The real answer to that has to do with pressure gradients.

I think you have reversed the explanation. The pressure gradient is the key to inducing the flow as well as the resulting behavior, but I would be more likely to say that the different areas are a result of the different velocities, rather than vice versa. Of course they are all tied together and are aspects of the same effect.

Get far enough upstream of the working fan, and you can say the the velocity of the air is effectively zero. Since it is moving at a given velocity by the time it reaches the fan blades, it must have accelerated. By Bernoulli’s principle, the static pressure of the air is lower at the fan than in the quiescent air upstream. Air likes to go from high to low pressure, so this is considered a favorable pressure gradient.

Yup.

After going through the fan, the air eventually slows down to zero velocity again. Its static pressure is thus gradually raised back up to where it started. Air doesn’t emjoy moving from low pressure to high pressure (but is forced to by the fan), and so this is called an adverse pressure gradient.

Nope. You missed a part. The fan itself induces a high localized pressure gradient. It is, after all, the reason the air moves at all.

The upshot is that while moving along a favorable pressure gradient, you can make air do most anything you want. Turn around sharp bends, follow walls diverging or converging at various angles…you name it. So ahead of the fan, the air is free to come in from all directions. And it does so gladly, because it’s the most efficient way, space-wise, to get air into the partial vacuum created by the fan.

On the exit, however, the adverse pressure gradient changes the rules. When faced with an “uphill climb” into higher pressure, air gets a lot more irritable, and like a cranky toddler, doesn’t do what it’s told.

Except that the air actually behaves better on the outlet side, following a condensed jet. In fact, the air actually accelerates and the jet narrows well after having left the fan.

The most familiar (to aerodynamicists, anyway) consequence of an adverse gradient is that air will not gracefully expand along the walls of a divergent duct. That is, if the walls of a duct get farther apart as you move along, and the angle of this divergence is too wide, the air just won’t stay attached to the walls. Instead, the flow separates from the walls, and makes itself into a “free jet”, expanding at its own pace.

Though what you describe is a common problem due to an adverse pressure gradient (and what causes flow separation and stall), we are encountering a different phenomenon here. There is no solid surface for the flow to follow or separate from. It is behaving this way on its own.

So because of the adverse pressure gradient downstream of a fan, you can’t make the fan’s outflow expand faster than it wants to, which isn’t very fast. So if you’re anywhere fairly near the exhaust side of a fan, the air will not have expanded much by that point, and the area of the slipstream will still be small. Small area yields high velocity.

Except that the stream does not actually expand at all for a while. In fact, it constricts first (for the first two or three fan diameters past the fan itself if I remember correctly). Take a look at the image I linked to in my earlier post.

[flight]

I am trying to find a good explanation for this on the web with figures and such, but nothing I have seen so far has been acceptable. This (warning pdf) comes closest, but I am having problems getting the figures to show up. The first three pages are all we are concerned with here. If you have an aero book you can look up actuator disk theory (or momentum theory) to get a better explanation.

[aerodave]

Well, I didn’t include my usual aerodynamic disclaimer that I was simplifying things significantly. But nothing I said was wrong. For example, I maintain that the constant-area jet versus expanding jet is the same whether there are walls or not…separated flow in a diverging duct looks just like a free jet.

The only fundamental thing I left out was the constriction of the stream after the fan. And that still doesn’t change the essence of my story. But I have to admit, I don’t know off-hand why that occurs.

[Napier]

>I, personally, would not invoke Reynolds number in an explanation of this fan inlet/exit behavior.

On further thought, I might note the Reynolds number is much bigger than 1, and note that if it weren’t, the flow field would be symmetric front to back, and deduce that inertial effects and time derivatives were essential to the answer. But then I’d not have any further use for the Reynolds number.

>the air blown out the front is directed, so that most of it moves in one direction; the air coming into the back of the fan comes from all directions

This sounds more useful. More specifically, the air coming from the fan has momentum all in the forward direction, while the air approaching the fan has momentum radially directed toward it. Maybe we need more of an explanation why this is true, but it seems like it must be, and like it’s a sufficient condition to create what the OP notices.

>This, however, isn’t a satisfying and complete explanation because it doesn’t answer the question of why the capture area is large and the exit area small. The real answer to that has to do with pressure gradients.

I think the whole system will obey the Navier-Stokes equations and thinking in terms of pressure is equivalent to paying more attention to one field variable than another.

>The only fundamental thing I left out was the constriction of the stream after the fan. And that still doesn’t change the essence of my story. But I have to admit, I don’t know off-hand why that occurs.

Does the stream contract after the fan?

If you push air through an orifice plate, it contracts, because air immediately upstream of the plate and outboard of the hole is moving toward the hole and has a radial momentum. This contraction effect is called the “vena contracta”.

Does it happen with a fan, if the fan reorganizes all the momenta of the air molecules?

Of course, most of the air molecules act only on the basis of their interactions with neighbors. A neglible fraction interact with any of the solid surfaces. If this were not true, we’d be in the Knudsen regime, with fan dimensions on the order of the mean free path length of air, 70 nm or so.

[flight]

@aerodave

Well, I didn’t include my usual aerodynamic disclaimer that I was simplifying things significantly. But nothing I said was wrong. For example, I maintain that the constant-area jet versus expanding jet is the same whether there are walls or not…separated flow in a diverging duct looks just like a free jet.

I would hold that these are very different phenomena. For example, the flow through a diverging duct (or over the top of the narrowing section of an airfoil) is heavily dependent upon the boundary layer. The shear layer between moving and not moving fluid is significantly different. Also, I do not believe you see the same local recirculation effects with a freestream jet as you do with flow past a solid.

I think it is easiest to imagine the jet as having a semi-permeable barrier surrounding it. Though the total pressure of the jet is increased beyond ambient once it passes through the disk, the pressure in the jet is less than the static pressure. This pushes in on the semi-permeable barrier, narrowing and accelerating the flow. It is effectively creating a nozzle out of the ambient air. After a while the boundary (shear layer) of the jet breaks down and the flow diffuses.

This is where Reynold’s Number comes into play. The high Reynold’s Number means that the the effect of momentum is much greater than that of viscosity, thus the shear layer stays thin for much longer than if the Reynold’s Number was low.

[Sofaspud]

I just want to say, I love this place.

Seriously. I ask what seems to me a simple question, albeit one that I don’t really know the answer to, and before I know it I’ve got an answer.

And then I’ve got an even better answer.

And then I’ve got an answer that, I’m sure, is complete, and thorough, and covers everything I could ever possibly want to know about the subject… and I can’t understand a word of it, because I’m dum.

But that’s okay, now I know where to start looking to figure out how to understand the answer. Woohoo!

(What can I say, I’m addicted to learning!)

I’d just like to add, my wife is pissed at me now, and it’s all the Dope’s fault. See, I was trying to visualize the airflow through the fan, but wasn’t quite getting it, so figured, hey, if I put the grill under the window, and the fan in the window, and throw a bunch of wet wood chips on the grill…

Note to self: aim the fan OUTSIDE, next time I get a bright idea. Very cool smoke plume, though!

[flight]

Don’t feel bad about not understanding. I am finishing my doctorate in aerospace specializing in helicopters and this topic still managed to get me and my coworkers in an hour long debate about what causes lift. Aerodynamics is complex.

[engineer_comp_geek]

@Mangetout

It’s also how pop-pop boats manage to propel themselves by just sucking and blowing water in and out of the same tube(s)

Look at what you made me do:
http://home.comcast.net/~sokosfamily/pop.htm

After you described it as “feeble” I wasn’t expecting much, but it scooted across my bathtub pretty well once it got going.