Ducted fan theory and practice

[Richard Sharman]

This is a new thread which is aimed at discussing the theory and practice of electric ducted fans (EDF). There is considerable practical experience of ducted fans, and the models they have been used in (see the threads going back here as far as 2008), but it is still a mystery to some (probably me as well) how to make best use of the information to do things like:

 

* choose the best EDF unit for a given model

* design a new model around a particular EDF unit

* check the performance of the model and EDF unit is as it should be

* improve the performance of a given model set up,

 

...and of course, many other questions. In short, what we need is a common understanding on how fans work, the physics of the process, and therefore a method of agreeing on how to solve problems, make adjustments and so on.

Having set the scope of this thread, I will now post an offering on the topic...

 

Richard

 

[Richard Sharman]

As you make all know, there was an important paper published by Klaus Scharnhorst in 2005 which is available  by google-ing "scharnhorst ducted fan". This paper is well worth a read, despite containing a number of equations, some physics, and a little germanic english.

 

The paper is a rewrite of some articles which appeared in various model mags earlier, going back to an MFI article of 1984 (!) in which he derived a famous equation for the velocity of air exiting from a coming out of a static fan (i.e. one strapped to the bench). This is important because it is a value which can be measured, and therefore theory can be checked against observation. This can then be related to the values the theory predicts for the performance of the fan in the moving model (which is harder to measure).

 

The net of it is that given the geometry of the model (ducts, fans, etc) which doesn't change, and a few other bits of information (such as the speed of the model - hard to know) we can work out how much power is needed, and therefore what motor, battery is required -- surely a useful aim!

I've used this method to verify the performance of my West Wing Bae Hawk, and can confirm that the theory does correspond to the measurements with a fair degree of accuracy. I'll post a summary of the experiment shortly.

 

Richard

 

Edited By Tim Mackey on 12/10/2011 19:10:53

[Stefan Hafner]

Sounds like this could be an interetsing thread, and will be interesing for me, as I had to do a whole class on Turbine design at uni, so might be able to bring something usefull to it too

 

Also, will be handy as i'm designing an A-10 at the moment that I'm hoping to sell later on as a kit

[Richard Sharman]

For those interested, here is a brief summary of the Scharnhorst paper (you'll have to read the whole thing to get the full reasoning, but I'll precis it here for reference and refer to it as KS ).

 

Firstly, assume there is an entry duct leading to the fan unit which exhausts through an exit duct The whole thing is one system, looked at from the outside it has an entry and an exit, and we don't need to consider the internals in too much detail at the moment. Then:

 

1. The inlet area is Ai and air enters this with velocity vi (the speed of the model), The volume of air passing through this in unit time is Qi = Ai * vi. Note: area is measured in sq metres, or m^2, and velocity in m/sec.

2. the air entering must exit. Since there is no combustion, or temperature change, involved we can assume that air in incompressible, so the volume of air exiting in unit time is Qe = Ae * ve where Ae is the exit area and ve is the exit velocity. So, Qe = Qi by our assumption. Volume is measured in m^3.

 

3. The mass of air being moved is M = Qi * rho where rho is the density of air (about 1.2Kg/m^3). Mass flow is measured in kg/sec.

 

4. The speed up of the air produced by the fan is dv = ve - vi. The thrust produced is T = M * dv. Thrust is measured in Newtons. The power needed for flight at this speed is Pflight = T * vi measured in watts.

 

5. (this bit may be unfamiliar to a number of modellers, please hold onto your seat). The impulse gain by the system because of the input of flowing air is Pgain = (1/2) * M * vi^2 measured in watts. The impulse loss to the system by ejecting flowing air is Ploss = (1/2)* M * ve^2 also in watts. So the power produced by the system (due to the fan working away inside) is Pfan = Pgain - Ploss measured in watts.

 

6. The "efficiency" of the fan is the nearness to which the energy required is matched by the energy provided, or Efficiency = Pflight / Pfan. As a percentage this is usually around 80%. The Power required from the motor, Pmot, also depends on the losses in the system due to friction in the duct, restrictions in the geometry of the duct and so on. KS assumes (from an analysis of pipe flow theory, etc) that Pmot = Pfan/0.85 is a reasonable approximation. This needs more exploration IMHO.

 

So (sorry if this is lot to digest) we have a theory which requires ONLY the size of the entry and exits, AND the speed of the model in level flight, to determine the likely power consumption of the motor -- quite an achievement, I think you'll agree ?

 

In a moment I'll post the figures I've got for my Hawk.

Richard

 

 

[Chris Channon]

Why just EDF ? what about us Glow engined D/Fan flyers?

Regards

Chris.

[Richard Sharman]

Observed vs calculated figures for my West WIngs Bae Hawk.

 

The area of the inlet is 3667 mm^2 and the outlet is 2463 mm^2.

 

But what is the speed ? It is much faster than my scale Tucano (which flies around 60mph) , but not as fast as a pylon racer at around 180mph. This is a difficulty (which I plan to fix by fitting an Eagle Tree logger measuring airspeed in the next flight). For the moment let's assume it could be 46m/sec.

 

So, ve = 58.8m/sec (a bout 127mph)

Then, Q = 0.17 m^3 and M = 0.21 kg/sec.

Thrust T = 4.6 Newtons and Pmot = 313 watts.

Actual consumption as measured by battery depletion is 350 watts, the difference going in making the ESC hot, the motor hot, the battery hot, etc, So, some measure of agreement there ?

 

Note that these are NOT the figures for static thrust and consumption as obtained on the bench. The whole problem of understanding the STATIC thrust is also analysed by KS, and I could precis that too, if there is interest ?

 

The important point is that we can EASILY measure static thrust, but we cannot easily measure dynamic thrust. Yet dynamic thrust is what we want to know, since that determines model performance. What we need is to calculate dynamic thrust from static thrust, and this KS does.

 

.....more later, Richard

[Richard Sharman]

Stefan,

great. I think the comparison of turbines and ducted fans should raise some interesting discussion.

 

Chris,

ok, i.c. ducted fans should have their day in court too. I just get the feeling that most people in that community have moved either to EDF or to turbines -- is this right? Understanding EDF would be a good start.

 

Richard

[Richard Sharman]

Just for interest, and to lighten the mood a bit, here are some pictures of my Hawk which flew again today in 14mph wind. We collected some airspeed, ve , data as I'll show in minute.

 

First, here is a general view of the plane as built from the kit - flies really well on a 4S 2600Mah 60C lipo. I uses a Wemotec mini fan with a Mega16EDF motor, Spectrum 8 radio, and E-FLite electric retracts. Notice the relatively small inlet ducts, but they are 107% of fan-swept-area.

 

Now the view from the rear. Note the apparently large exit duct is actually only 84% of FSA.:

[Richard Sharman]

To find out how fast the Hawk flies I fitted an EagleTree logger, programmed to record airspeed as sensed by a pitot tube. First job was to fit the equipment as shown in the picture. Fortunately there is masses of room in the from as the battery is located further back, quite near the CG.

 

The logger is sitting in the payload bay, on top of the noseleg retract unit, as it happens. The tube connects through to the aluminium tube seen projecting out of the front of the nose on the left to give a dynamic air pressure sensor in clean air. The static air pressure port is inside the logger, but care must be taken to ensure that the fuselage is enclosed, as draft inside the body could affect the pressure reading. Too bad about cooling for the battery/ESC, but that doesn't seem to be a problem at present.

The measured airspeed varies quite a lot depending on the behaviour of the model, and as one naturally flies in large horizontal figure-of-8 patterns the speed (and altitude) does vary quite a bit.

 

The summary is that with wheels down the model cruises in level flight at around 37m/sec (80 mph) and with wheels up at about 42m/sec(90mph). So the corresponding calculations of the theory are a bit lower that previously guessed:

air flow Q = 0.15 m^3 and M = 0.19 kg/sec.

Thrust T = 3.9 Newtons and Pmot = 238 watts.

So, how do we account the discrepancy? Or, in common language, "where are all the watts going?"

[Myron Beaumont]

Hang on chaps

I will attempt to do what I always do when confronted with a problem to make the solution maybe easier to come by .(never mind the maths etc for a moment even though it's relevant ). OK Lets start with a EDF unit on its own .Bags of thrust just like a normal prop on an engine .Now then ,Add an inlet duct and an exhaust tube outlet .The thrust diminishes a lot (friction /air turbulence /boundary layer effects throughout the mechanism) .So you might ask ,what do you do ? You can't seperate the inlet flow from the outlet to keep the velocities /pressures seperate apart from a brick wall.of infinite size between the two.It's nothing like a gas turbine engine where the thrust is produced by a multi internal expansion of gases syndrome . In other words "What goes in comes out".It's only air in our case!

I have an Eze Fan Nigel Hawes design --No inlet nor outlet tubes whatever . It has virtually no inlet nor outlet bits in the way of the airflow .The thrust is obviously less than perfect but I can't feel any discernible difference from my fan whether in or out of the model.

Myron (Ex RR aero engine Derby engineer -Performance dept /service dept)

[Erfolg]

Richard

 

The link to the Scharnhorst article does not work for me!

[Tim Mackey]

Duff link...Ive removed it.

[James40]

Richard, it's hard to tell from the picture as it's taken from the rear but, is the pitot tube far enough away from the nose of the aircraft? You will have a substantial pressure wave building up in front of the the nose that could affect the readings.

[Richard Sharman]

James,

how far into the airflow do you think the pitot should project ? How far would the pressure wave extend? suppose this would have the effect of registering a low value ?

 

In the past I have usually mounted pitots on the leading edge of the wing, but that proved too difficult in this application. I recall the Eagle Tree documentation saying it should project about 1/2 inch which it is.

[Richard Sharman]

Posted by Erfolg on 12/10/2011 19:04:01:

The link to the Scharnhorst article does not work for me!

Erfolg,

apologies, the link was the one given by Google, but it is for a PDF download and obviously has not copied correctly.

 

I have posted the paper on our own web site, where it is under "designing". Perhaps you can try this url I know it works because I've just tested it.

Richard

[Richard Sharman]

Posted by Myron Beaumont on 12/10/2011 17:38:07:

....never mind the maths...........EDF....Bags of thrust...........Add an inlet duct... "What goes in comes out".It's only air.....I can't feel any discernible difference from my fan whether in or out of the model.

 

Myron, well, quite a few points here ! I think most people know that EDF works by making a draught at the back of the plane and hoping it pushes something forward, so I didn't mention it. The real question is how many watts does it take to create a decent draught? what motor do I need to put in to achieve that? what battery will satisfy the cravings of a thirsty motor? If I enlarge the openings will it help or hurt ? and so on. For this we need some science.

 

On the question of the Ezefan (I've built and flown two) there is no duct front or rear as you just have the fan unit mounted on a vertical plate forming the fuselage (a clever idea) - so it's hardly surprising if the fan unit on its own, or the fan unit in the plane have the same effect? Actually I think a small exit duct would do wonders to improve the thrust of the raw fan unit. A yoghurt pot turned into a tapering tube should do it!

 

There is another, deeper, question. Since an EDF unit is just a cylinder (with a motor and propellor inside it) why does it work at all?

[andy watson]

Since I am currently venturing into EDF for the first time, with a very simple 4 fan scale Vulcan, and as a science teacher, this thread should be right up my street.

 

But I must be honest- ignorance is bliss!! (beyond working out my intake/outlet values).

[Richard Sharman]

Posted by andy watson on 13/10/2011 18:00:16:

Since I am currently venturing into EDF for the first time, with a very simple 4 fan scale Vulcan, and as a science teacher, this thread should be right up my street.

 

But I must be honest- ignorance is bliss!! (beyond working out my intake/outlet values).

 

Andy, your FIRST project is a 4 FAN VULCAN ...? I can only gasp! Courageous, or what? Why not play around with an EZEfan just to get going ? Just a thought !

 

I started this thread to give some exposure to the basic physics of EDF, as it's been known about for about 20 years now, but apparently not widely disseminated, at least in the UK. If there are topics you think are relevant I hope you'll raise them.

 

I plan to cover the following topics shortly:

 

** the analysis of the static operation of EDF, i.e. when vi=0. The calculation of ve when vi=0 led to the famous equation first published in 1982. It's important because it is one of the few parameters that can actually be measured on the bench.

 

** The effect of ducts, and how to design them. Generally speaking, ducts only make things worse, but we can aim for the least worst outcome.

 

** the relationship between thrust and power. The modellers ruin : "just apply more power -- in the end only more power helps", but that means bigger motors, heavier batteries, and so on.

 

 

[James40]

Richard, without knowing the scale of the hawk you are using it would be hard to say but I would go for a scale size probe, I'm not sure 1/2" would be scale on your model, it may be too short?

[andy watson]

I only build what I want to see flying Richard.

 

If that means I spend most of my time out of my depth (and it does) well that just adds to the fun! I wanted to build a vulcan- there are plenty of pusher prop versions- but I know that's not right.

[Erfolg]

Andy

 

To be right, a Vulcan needs jet engines.

 

[andy watson]

Of course, but as with all building, compromises have to be made. A compromise to EDF (which can be argued produce the same effect as jets- accelerated air out from the rear pushes the airframe forwards via an internal thrust tube) is acceptable in my eyes since the alternative (turbine power) means the plane doesn't get built at all.

 

Better get back on topic before we get shouted at!

[Tony K]

Richard, thank you for your comments on the other thread, I will be following this one with interest.

 

Paragraph 5 in your Scharnhorst summary is confusing. Shouldn't Pgain be that which you get out of the system and Ploss be what you have to put in.? The way it is written will result in a negative Pfan value.

 

Anyway is this impulse calculation necessary? As the thrust is produced by the whole system, from intake to exit, wouldn't the average velocity (1/2 Ve - Vi) be the factor in the equation. ie. P=T x Vaverage.

 

Using your airspeed figure of 46 m/s as Vi, the Ve is 68,5 m/s. So Vav is 57,25 m/s and dV is 22,5 m/s.

The Qi value gives a mass flow (mdot) of 0,2 kg/s so net thrust = mdot x dV = 4,5N.

 

P = thrust x velocity = 4,5 x 57,25 = 257 Watts.

 

Using a fan efficiency of 85% we are now up to 321 Watts for the motor.

 

By the same process an airspeed of 42 m/s gives a motor power of 253 Watts so about 28% of your 350 W is missing.

 

This all assumes that Vi = airspeed. Is that assuption correct? Could there be some acceleration of the air in front of the intake?

 

 

 

 

[Richard Sharman]

Tony,

apologies, I mispoke. Following the notation used in the original paper (which I'm sticking to for the sake of simplicity) the sentence should read:

 

So the power produced by the system (due to the fan working away inside) is Pfan = Ploss - Pgain measured in watts.

This results in a positive value for Pfan. (thanks for pointing this out. glad someone is paying attention !) [for others, remember Pgain is what the system gains at the entry, and Ploss is what the system loses at exit).

 

I don't think it's right to talk about "average velocity" because then

Pfan = (1/2)*M*( (ve - vi)/2 )^2 = (1/8)*M*(ve - vi)^2

which is not the same as the required value

Pfan = (1/2)*M*ve^2 - (1/2)*M*vi^2 = (1/2)*M*(ve^2 - vi^2)

except possibly at some singularity. Also, you would have to justify why an "average" would be a physically satisfactory assumption to make? In the absence of a suitable argument for that I favour the more rigorous treatment that KS gives.

 

Back to the example of the Hawk, my current figures are (for comparison):

vi=46, ve=68.5, dv=22.5, M=0.21, T=4.6, Pflight=213.8, Pfan=266, Pmot=313

vi=42, ve=62.5, dv =20.5, M=0.19, T=3.9, Pflight=162.7, Pfan=202, Pmot =238

Currently, where I think the discrepancy is creeping is due to two factors:

(1) the expected consumption figure is based on an indirect calculation, rather than a real observation, so it may be out. I'll explain calculation shortly.

(2) The "fudge factor" of 0.85 (given by KS in the original paper) may not be right. This is an average figure based on his assumptions about duct losses, motor inefficiencies and so on. Perhaps it was right for the cases he studied, but it would be remarkable if it were true for all models.

 

Final point: is vi = true airspeed ?

It is true that the "lip" on the entry duct is smooth and rounded, so there is some narrowing of the duct exactly at that point, and therefore some slight speed up (due to Bernoulli). However, the lip is small, its main effect being to slightly enlarge the duct size. KS assumes that the airflow is approaching the duct entry in a direct line, and before the air reaches the model the velocity truly is the velocity of the model, or vi. What happens next as the air enters the duct is part of the discussion about what happens internally, and this type of mass flow analysis doesn't need to consider that. Where the rounded lip really comes into play is the static case (vi=0) but we haven't discussed that yet !

It was exactly this kind of clarification that I hoped the forum discussion would throw up, so I'm delighted we are back "on topic" !

 

 

[Richard Sharman]

Posted by James40 on 13/10/2011 19:45:46:
Richard, without knowing the scale of the hawk you are using it would be hard to say but I would go for a scale size probe, I'm not sure 1/2" would be scale on your model, it may be too short?

 

James,

the model Hawk is 1 / 112. scale (don't ask why -- that's just the way the WW kit is! Perhaps it was really aimed at being 1/12 and didn't quite make it?). The Pitot on a fullsize Hawk is quite long (2 ft ? I haven't been able to find out exactly - does anyone know?) and this would make the scale size be about an inch and three quarters. On the model it is actually half an inch. I am not keen on making it longer for practical reasons : it would be fragile, perhaps a danger, maybe not rigid enough, etc.

 

However, the fullsize Hawk travels at up to Mach 1.15 which the model certainly doesn't. And scaling down may not be accurate, because you can't scale the viscosity of air, so allowance would have to made for that. I'm making the assumption that at the low speeds our models fly (relative to fullsize) any effect of frontal pressure wave is small.

 

On the other hand, in the EagleTree guidance notes it does not say exactly what should be used, although practical considerations on the equipment provided suggest that half an inch is about right. I have therefore used this over a number of years on several models and always got what I believe to be realistic results.