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

[Tklfserve]

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???

 

[Tklfserve]

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.

I now get 69.2m/second or 158 Mph efflux velocity. – Your Comments Please-

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/...lade_Alloy_EDF_2200kv_Motor_1900watt_6s_.html

So Next thing what about this???
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

 

[rb1957]

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