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# Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?3

## Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

(OP)
This is My Really Hard Question:

I have a 70mm EDF [Electric Ducted Fan] it generates 2.45 kg force at maximum thrust. I then calculate its exhaust efflux velocity to be something like 526 m/s based on an Air density of 1.21kg/m³ to get the same volumetric flow.
Mass=Volume*Density
2.45kgs thrust = 2.45kgs exhausted
2.45kgs=Pi*.07²/4 *Length*1.21 [density of air]

So then it follows: The length=526 meters
or that the flow is 526m/s

For my project: I need to know how far back from its exhaust. Is a distance where I can see an exhaust air velocity 1/10 or 10% of this jet efflux. {As I wish to Scale/Calculate the EDF Size up and down and play with varying the exit velocities in a number of different configuration's and vary distances [limited scope] to a attached cube of 10cmx10cmx10cm and Cd of 1.05 and see what force it has on it negatively.

How do I come up with a 'simple' formula to work this out mathematically???

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

I don't think there is a 'simple' solution.

If you were looking at the inlet side, I'd say you could model the isobars as hemispheres.

On the exit side, things are different. A jet exiting from a plane will have generally paraboloidal isobars, but the edges of the jet shear against initially quiescent fluid and entrain it, causing it to also move, so the jet diverges. At the same time, a radial inflow is induced along the exit plane. If the jet is issuing into a finite chamber, it induces a generally toroidal flow within the chamber.

The math is a mess, and the math does not govern what happens.
Better to mock up the geometry of the application, and measure the flow field, rather than trying to predict it.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

(OP)

'Maths a mess'!-Hmmm I was hoping you weren't going to say that
no simple approximations then?- any?
And Best way to measure a flow field down at this small RC model scale?

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

Probably with a 'hot wire anemometer', which could be just a small power resistor, if you don't need millisecond response.

Mike Halloran
Pembroke Pines, FL, USA

(OP)

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

That looks like a decent price for a commercial sensor. You can do it for less cash if you're into homebrew electronics and don't mind expending a lot of time building and calibrating.

The flow field looks about like I'd _imagine_ it to be.
The anemometer will let you map what's actually going on.
... it will probably be different from what either of us might expect.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

(OP)
Thanks Mike
A small part of a big problem, for a possible US patent in the works...
Let you know in 2014 how I turns out!

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

Your initial assumptions appear to be suspect. 526 m/s is substantially faster than the speed of sound at ~20ºC, which is the temperature for which your air density is valid.

Using your 2.45 kgf thrust, I only get about 100 m/s velocity through the fan area of 70mm diameter:

TTFN
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### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

(OP)
IRStuff

Correct. Mach 1 is 340.29 m/s, Or 1125 km/hr, or 761 MPH. So 526/340 m/s =Mach 1.68!

Wow.... I better stick it on Ebay and sell it for \$1000's of dollars that would be one Mean unit!...

100.5 m/s = 361km/hr is also very fast exhaust or efflux! over twice what my car can do flat out... but about sounds right when you think a typical EDF plane hits 160km/hr without too much trouble
I'm kicking myself, for not picking it up. And I can see where some of the issue lies -check the original spec sheet from manufacturer attached to first post it says 2.45 kg, not 2.45 kgf big difference! I have then misinterpreted 2.45kg along the lines of a simple weight calculation.
not the Sqrt (F/(0.5*p*a) you are suppose to.

So thanks for pointing it out. I would have sail straight on past it and then ended up with some of the other results could have been hilarious:)
A lesson for all of us: do a mental check to see if the numbers match real world expectations.... even if your feeling tired.

So... what to do... about rough estimating the force? on a 10cm x10cm say 1 meter away from the tail.........till an Anemometer comes?

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

You don't say what the aspect ratio of your duct to fan diameter is, which I would presume to have some influence on the results. Something like this: http://parkrcmodels.com/product_info.php?products_... has a relatively low aspect ratio, so spherical isobars would seem to be plausible worst-case scenarios. I would then propagate the aspect ratio out to 1 m and use the ratio of areas. I would also deprecate the lateral velocity of the exhaust, and make some assumptions about how much is still perpendicular at 1 m.

TTFN
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### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

(OP)
IRstuff
Yesterday was full of activity so wasn’t able to post a reply as soon I want to.
So things to discuss:

Aspect ratio:
69.9mm diameter x 52.5 mm long so 1:0.75 ratio
So for this ‘unusual’ application, high rate dispersal would be a good thing and having high torque is more important than high power
So have no intention at this stage of adding Trust tubes or Inlet Extensions [ and not ruling it out either inlet extensions might be good]. Will consider it later if things change
Although it’s an interesting feature here’s a look and a link on basic designs: http://www.rcpowers.com/community/threads/an-edf-t...

Again to repeat: My need is to understand the relationship between exhaust velocity and how far it travels backwards I’m prepared to do calibration when all the bits and pieces finally arrive. And what I’m looking for is basic level of understanding if say, I took the concept and where to then scale it between say a 50mm diameter EDF fan to say a 250mm EDF fan. What happens? Could I predict a possible force outcome That would probably cover it.
The Air drag on the block looks simple enough. http://en.wikipedia.org/wiki/Drag_equation
I do a reasonable amount of liquid metal flow and Reynolds numbers and some CFD on our critical jobs at work to be conversant enough with this aspect of it.
Sphere Volume i= 4/3Pir³ and the Areas = 4Pir²
And my understanding if correct, the velocity is dropping by some factor of V=Distance x 1/X² [V= velocity X = distance] with the coefficient unknown at this stage.

So if you are up to it? Could you scan a quick working out sheet on paper and I’ll return the favor putting it into an excel sheet and a post for any who want to follow the thread at a later date.
All under the understanding its “rough approximations only” - all care no responsibility.

If not, don’t worry I’ll get some ‘real data in a few weeks’ time when all bits and pieces arrive.
I have some EDF books on back order from Amazon, somehow though, I don’t think they are going to cover this topic.
Regards

J Mayer
Vic, Australia

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

One data point: A helicopter turbine of ~400mm dia under test can knock down a flimsy wooden fence at a distance of ~50m. The flimsiness of the fence is an issue being debated by the owner of the turbine and the owner of the fence.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

"to understand the relationship between exhaust velocity and how far it travels backwards"

IR's estimate of exhaust velocity seems ok but I think the CL of the fan blade should be in there somewhere.

research propeller design. I'm sure (?) that thrust = Ct*q*A ... IR has assumed Ct = 1, I suspect that that is pretty low.

in any case you're interested in how the airspeed of the slipstream changes after it's been exhausted ... Y?

research propeller slipstream. it is a complicated thing, due to mixing with air outside of the slipstream.

Quando Omni Flunkus Moritati

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

(OP)
Mike that's funny!!
It didn't happen to be 'your' turbine by any chance!
that would make must see on Utube for most of us eng. types

Rb1957- thanks for pointing it out - will start and see what I can find on goggle. "propeller slip stream"

J Mayer
Vic, Australia

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

(OP)
V=Distance x 1/X² [V= velocity X = distance]
V= C x 1/X² [V= velocity X = distance C= coefficient]
my apologies

J Mayer
Vic, Australia

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

(OP)
"to understand the relationship between exhaust velocity and how far it travels backwards"
puts it very succinctly...

J Mayer
Vic, Australia

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

I'm not sure that we have enough info to get a good answer. IR's 100m/s still sounds awfully fast ... this fan, about 10sq.in is generating only 5 lbs of thrust.

one thing I think we need is propeller rpm ... research propeller design.

another thing to remember is momentum ... if the slip stream velocity decays as an inverse square law (maybe, maybe not) then the cross-section area of the slip stream is increases (proportional to distance^2). ie at the exhaust you've got a 70mm diameter flow of Vj surrounded by a large volume, call it Dmm diameter, of free stream flow (what is the free stream flow ? is the fan moving ??) then at a distance downstream you've got a larger diameter of slipstream going slower and a smaller diameter of freestream ... yes?

it sounds like you've bought this fan and are trying to do some numbers ahead of time to get ready. I suggest reading up on propeller design and this'll get you to slipstreams.

I just did IR's calc again ... I think you mixed mm and m ... I get v = 32m/s ... sqrt(2*2.4/(1.21*0.004)) = v

Quando Omni Flunkus Moritati

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

I suggest that you re-look at the 2.4; it's not 2.4 kg, but 2.4 kg-force, so I think it's missing a 9.8 m/s^2 in the numerator. That is precisely why I use Mathcad, since it does the math accordingly. A dimensional analysis would show that the aforementioned calculation is missing an acceleration. If you refer to my cited link, the engine described therein is stipulated to have "Static Thrust: as much as 1.70kg at 4S and 2.45 at 6S or more," which is consistent with http://www.ductedfans.com/Storm_EDF_fan_Unit_70mm_... which has a "4.21 lb" thrust" which translates to 1.91 kgf.

TTFN
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### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

(OP)
O.K.
-Lots to discuss now:-
The suggestion to look up "research propeller slipstream" was fruitful and helpful thanks- rb1957
Sometimes it’s all about getting the right ‘key words’ to search on – and away you go, find all sorts of wonderful and weird things,
It also leads to find out how complicated this question can really be if you go for fine details:
I never heard of “Blade Element Momentum Theory” B.E.M.T. -till today!
It also leads to finding a book called “Ducted Fan Design Volume-1” this was a good find with some good simplified formula in it
I have include a few snippets here, [see here]

So I’m prepared to be embarrassed; and I have done a working out sheet based on using Mass/FSA/Air Density
As the temperature is relatively stable the velocity from fan pick up is close to exit speed this can be used provided Areas remain the same
As it’s likely the “device” is operating in a low speed range maybe 7.5mtrs/ second I’m choosing to ignore that for now.

This is a link to what I think was the original spec [unit had original markings removed]. So previous links should be equivalent enough in previous posts
http://www.hobbyking.com/hobbyking/store/__35002__...

In the process of measuring up the internal diameters I notice this 2.4mm “SQUARE” Shoulder just after GRP fan.
1. Am I correct in assuming this is a BAD feature? It doesn’t it make more sense to have a nice radius blend here. Or even a small chamfer to get better transitions- I just don’t get why it would be put there. Is this good Aerodynamic practice? – Please tell…

2. Are the fine grooving in it for fan cooling of vortex control?

I found this image in searching: and added this as it might help in visualizing the ‘device’ and reason for question “what efflux velocity at what distance”. Not ‘entirely graphically correct’ but good enough for explaining.

Mike Halloran --I’m still smiling, about that fence that was blown down….
And thanks to others for putting your thought in.

J Mayer
Vic, Australia

### RE: Ducted Fan Efflux - How to calculate distance travelled to its approximate velocity?

I accept IR's comment on "g" ... you need thrust in N for the units to be consistent ... I think it's 2.4kgf*9.81 = 24N.

looking at your sketch, if you're after the exit velocity, well that'll be higher 'cause of the blockage (you've lost a 1/4 of the area of fan, yes?). if you're interested in the slipstream velocity some distance downstream, well this area should work itself out of things, but I think you still might need to consider that best estimate of exhaust velocity as being through the annulus.

looking at your calc ... why should mdot be 2.45 ? ... it looks like you've said (as in your original post) that thrust is equivalent to a mass of air

the grooves look like some sort of flow control.

the 2.4mm step ... not a good design feature, and if they took the trouble to groove the duct, then maybe they looked into it at said it wasn't worth "fixing".

remember too it's max thrust ... there'll be an optimum forward speed which combined with the blade rotation velocity will have the blades producing max lift (which is why the blades twist), so maybe the static thrust is less than this.

you started asking about the exhaust velocity a distance downstream ... why do you need to know this ? is this really what you want to know ? (it seems a little "odd"?

Quando Omni Flunkus Moritati

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