Ducted fan theory and practice

[Stefan Hafner]

Posted by Richard Sharman on 20/10/2011 20:49:34:

For example, no one has commented yet on the relationship between static thrust and dynamic thrust -- what is it? Because it's not obvious.

Static thrust is when the fan is fixed, fairly self explanatory for this part I think Dynamic thrust is the trust that is being generated when the aircraft is moving through the air, and will be less than static because the relative angle of attack of the airflow over the blades is reduced due to the velocity of the aircraft.

This is a lecture slide from at uni, where it can clearly be seen that when going faster that the effective angle of attack is lower, and as the prop can be treated as a wing at lower angle of attack the trust (lift) will be less. this example is for a propeller but the same princlple will apply to a fan.

 

Posted by Keith Simmons on 21/10/2011 09:05:10:

Also on SR71 Blackbird, there is more thrust generated in front of the engine cone at M3 so is that due to a vacuum effect due to pressure shock wave generated in front of the aircraft.

I wasn't aware of any engine generating more thrust in front of it, but the SR71 is a tricky example because of the science involved. At low speed the engines worked in a conventional low bypass engine, but at about M2.3 I believe the engines started to operate on RAMJET principles as the forces were too high for a conventional engine. As for shock waves, the cones on the front were variable geometry (they moved back and forth) to create the shock waves, the reason being that the engine would not work with supersonic flow in the combustion chamber, and the shockwaves reduce the flow speed, and increased the pressure, but i've never heard of the lower pressure at the intake.

[Erfolg]

I have also read that the Blackbird operated as a ram jet at speed.

 

From what I read the cone was driven in to optimise the requirements of a ram jet, that was the tricky bit going from one configuration to the other. It must have been more difficult than I thought, as I assumed it was essentially an after burner.

 

From what has been written, to aerodynamics were tricky, as were the materials of construction. I would be surprised if any true secrets have been given, just the obvious to those who would know. Even some misleading info possibly will have been provided.

 

I think the optima, fanjet and the ducted engines seen on blimps, have more in common in what interests us modellers than the exotic, however much they excite us (well at least me).

[Tony K]

Posted by Stefan Hafner on 21/10/2011 12:27:45:

 

This is a lecture slide from at uni, where it can clearly be seen that when going faster that the effective angle of attack is lower, and as the prop can be treated as a wing at lower angle of attack the trust (lift) will be less. this example is for a propeller but the same princlple will apply to a fan.

 

 

Hence constant speed props on upmarket light aircraft. For fixed pitch props/fans surely the RPM will increase until the resistance matches the available motor torque?

 

 

Posted by Erfolg on 21/10/2011 13:09:10:

 

I think the optima, fanjet and the ducted engines seen on blimps, have more in common in what interests us modellers than the exotic, however much they excite us (well at least me).

 

Agreed. Better to leave supersonic aircraft out of this discussion.

 

 

[Dizz]

"For example, no one has commented yet on the relationship between static thrust and dynamic thrust -- what is it? Because it's not obvious."

 

2 of my models have definitely generated more thurust once moving than when stationary (Modified Phase3 EF-16 and P1091): static thrust measured nose down on the scales indicated a T:W approx 0.9-0.95, but once in the air and "on the step" they will maintain a 90 degree climb without slowing. Both are(were) fast (120mph+ stright and level), have(had) bends in the intakes and sealed ducts (no openings for ESC cooling): I have a feeling that there is a gain from a dynamic pressure increase in the duct ahead of the fan - but lots of facors/variables involved and I have no way of finding out what is actually happening in flight..............especially the EF-16 because it exceeded Vne and is no-more

[Stefan Hafner]

Posted by Dizz on 21/10/2011 13:58:50:

2 of my models have definitely generated more thurust once moving than when stationary

I would think this lies in the design of the fan, if the setting angle of the blades is a very high then when static it may be that the blade is effectively stalled, and therefor will have a very high drag figure and be putting a large load on the motor. When it starts to move the relative angle of attack (effetive anlge of attack) of the fan blades will reduce, as in the diagram in my previous post, and the angle of attack of the blades will then be lower than the stall angle, meaning that the power that was being used overcoming drag prviously is now available for going faster :D

 

Agreed. Better to leave supersonic aircraft out of this discussion.

 

Aww, no-one want to try and go supersonic

[Tony K]

After a quick google I have found quoted figures for the Memotec mini fan powered by a Mega 16-15-2F of 10N thrust drawing 55A from a 3s lipo.

 

Using 3,5 V/cell the power consumption is 577,5 W. That means 57 Watts per Newton thrust.

 

Now I don't know how these figures were obtained, static/dynamic, with/without ducting, etc. or whether they are even accurate.

 

Richard's Hawk is using 350 W to provide 3,9 N, that is 89 Watts per Newton - a considerable difference.

 

 

 

 

[Erfolg]

I thought that the paper of Scharnhorst was all about the differnce in performance with respect a DF fan, when static and flying.

 

Tony K points to the difference in pitch requirements relative to static and operational at a conceptual level. What he has at presented ommitted is the relationship between power and propeller equations. I am sure that they are in his notes. I know that some will say but it is a propeller, yet you need to start somewhere. It could be as simple as omitting the terms for tip losses, to obtain an adequate fan expression. I should have notes on propeller performance from my own studies. In my case they are in the loft, in one of a number of boxes, probably about 40 years old, but at least ISO metric units.

 

At the end of the day DF units could be tested by mounting on a piece of wood, and attached to a roof rack or hung out of a car window, with a suitable logging system.

 

[Keith Simmons]

That's an excellent idea to mount an EDF outside a car and map out a graph for dynamic thrust at different speeds up to 70mph and ideally try out different ducting arangements and see how well they work. (or you could time the model flying pass and work it out with onboard logging system)

Static thrust only give one side of the story, perhaps suitable for the EDF model taking off from grass and/or tarmac.

[Richard Sharman]

Posted by Dizz on 21/10/2011 13:58:50:

.....2 of my models have definitely generated more thurust once moving than when stationary........

I find this slightly hard to believe - what could cause this ? Can you say what the entry area, fan swept area, and exit area values were? We could then use the theory to compare the static and dynamic cases.

[Keith Simmons]

I think the moving EDF has less work to suck the air in the intake so the fan was able to spin a bit faster and so a more thrust as a result.

[Richard Sharman]

Consider the following experiment concerning static vs dynamic thrust:

The KS theory gives a way of calculating, for a given model, the dynamic thrust at a specific flight velocity. If we use the theory to calculate these values for a set of velocities from zero to some large value we would obtain a table of values vi:T which could be used to draw a graph. The shape of the graph should show some interesting properties. Call this the vi:Td graph.

 

FURTHERMORE, the theory gives a way of calculating the static thrust which corresponds to the dynamic thrust which is calculated for the plane which cruises at a particular velocity. It is not the static thrust AT that velocity (because that is obviously nonsense), but it is the static thrust that corresponds to the plotted dynamic thrust, and so with that caveat, should be interesting. Call this the vi:Ts graph.

 

Another caveat: the actual Hawk flies straight and level at its ideal velocity of around 40m/sec. It probably doesn't actually fly straight and level at many other speeds as it seems to have quite a small flight envelope (guess how I know!).  But, imagine for a moment that it could.

 

Here is the graph, using the Hawk parameters given before (each plane type would have its own graph, not necessarily the same as this):

This shows two interesting properties:

A. the faster you want to go the more thrust you need (obvious, and it's non-linear)

B.The corresponding static thrust is always greater than the dynamic thrust. So the thrust you measure on the bench is never likely to be achieved in the air -- interesting ?

Remember, these are calculated values, not observations.

R

 

Edited By Richard Sharman on 21/10/2011 21:58:51

[Richard Sharman]

Posted by Keith Simmons on 21/10/2011 21:26:20:

I think the moving EDF has less work to suck the air in the intake so the fan was able to spin a bit faster and so a more thrust as a result.

I have heard this "explanation" before, but admit to being a bit skeptical about it. Some people even say they can hear the motor note increasing (because it is running faster) in the air. But when challenged to tell the difference between that and the Doppler effect of an approaching model they usually can't. I can't hear anything that could be interpreted this way. And I've never seen the phenomenon of "on the step" which I suspect is a myth. Certainly my planes speed up as they get airborne and climb to cruising height, but so does my biplane, and my pattern ships. What we need is some observations of rpm, current draw and velocity in flight, which I want to do some day.

[Dizz]

Posted by Richard Sharman on 21/10/2011 21:14:12:

Can you say what the entry area, fan swept area, and exit area values were? We could then use the theory to compare the static and dynamic cases.

 

P1091

Wemo mini fan HET 2W-20 on 2650mAh 4S 40C pack.

FSA=29.4cm^2 Exhaust =25.5cm^2 (87% FSA) Total Intake area 29.8cm^2

 

30s WOT figures:

 

Installed Static thrust = 1064g (10.43N); 800W on the Wattmeter; efflux velocity measured with the How Fast = 135mph

Static thrust on the test stand=1140g ( 11.2N); 765W; efflux 146mph (no ducting)

 

I do have a Doppler speed for the P1091, but only one slightly into wind pass so I can't really declare an airspeed.

Haven't got any fan figures for the dead EF-16, but I have several Doppler 'grams - max speed straight and level I have recorded is 122.8mph +/-1.8mph

 

Edited By Dizz on 21/10/2011 23:29:34

[Dizz]

Posted by Richard Sharman on 21/10/2011 21:51:28:

Posted by Keith Simmons on 21/10/2011 21:26:20:

I think the moving EDF has less work to suck the air in the intake so the fan was able to spin a bit faster and so a more thrust as a result.

I have heard this "explanation" before, but admit to being a bit skeptical about it. Some people even say they can hear the motor note increasing (because it is running faster) in the air. But when challenged to tell the difference between that and the Doppler effect of an approaching model they usually can't. I can't hear anything that could be interpreted this way. And I've never seen the phenomenon of "on the step" which I suspect is a myth. Certainly my planes speed up as they get airborne and climb to cruising height, but so does my biplane, and my pattern ships. What we need is some observations of rpm, current draw and velocity in flight, which I want to do some day.

Can't say I have heard any change in rpm - the Doppler analysis doesn't show it either.

Stu Maxwell of Stumax EDFs fame is a member of the "the higher pressure in the duct ahead of the fan improves efficiency" school..........having followed his recommend to keep the intake duct sealed and seen positive results (in my opinion) I am too.

Would an increase in pressure not mean that the fan is shifting a greater mass for the same rpm?  It is a fact that EDFs do not work so well at altitude (just read the US forum threats).

Am asking Santa for a DX8 for Christmas - the telemetry options should be useful for in-flight EDF.

Edited By Dizz on 21/10/2011 23:55:39

[Tony K]

I still have a problem with the assumption vi=0. As Dizz stated earlier,

 

"6. In the static case intake air has to be moving into the duct: the mass of air being expelled has to be the same as the air entering the duct ..."

I think in the static case we need to look outside of the system (the system being that which is between the inlet and outlet apertures). In order to draw surrounding air into the inlet there must be work done to the surrounding air, it is given some energy. That energy comes from power consuption of the fan.

 

Dynamically the free stream velocity is very close to inlet velocity so does not need any work done to it.

 

So for the static inlet flow to equal dynamic we need more power. If more power is not available the static inlet flow will be less than dynamic.

 

I think this is Keith Simmons' point.

 

 

[Richard Sharman]

On the assumption that vi=~0.......????

 

Well, I think we all realise that this can't be exactly true,as the air to be expelled has to come from somewhere. That is so self-evident I didn't bother to mention it. Tbe fair to KS, he doesn't actually say vi=0 in so many words, but does say w=0, where w is flying speed, and elsewhere equates w=~vi. So I may have overstated the case in my summary.

Here is his figure 1 which shows what might be happening in the two cases (it's 2 diagrams shoe-horned into one picture, unfortunately):

 

One point he is making is that the size of the inlet and the velocity of travel define the volume of air moving in unit time for the dynamic case, but in the static case it is less clear what the inlet size is because air is being drawn from a much wider area, inevitably at lower speed.

 

On page 10 (talking about the static case) there is the comment:

"...dv is now equal to the exit velocity ve of the air stream at the nozzle since the airstream has been accelerated from 0 to ve...."

 

Your can see what he is trying to say, I think, and so I have interpreted this as being to effectively set vi=~0, and we know from measurement that vi is very low. But since vi itself doesn't enter in the subsequent calculation perhaps it's best to ignore it and concentrate instead on whether dv=ve is true, because dv is needed in the derivation.

 

In the absence of a much more sophisticated treatment of the whole subject, I'm prepared to accept this approximation as a working hypothesis.

 

[Richard Sharman]

Posted by Tony K on 21/10/2011 10:08:58:

Richard, do you have any static figures for your Hawk?

 

Yes, here they are. Response was a little delayed as I was flying during a short spell of good weather, then had to check figures. Figures are recorded on the bench via wattmeter and telemetry at full throttle for 20seconds..

 

Test 1 Complete airframe as shown, battery is 3S 2600mAh 60C

watts=368 static thrust Ts=6.17N exit velocity ves=47m/sec with watts/N = 59.7

I don't have a real airspeed for test 1 so I can't test the theory for that case.

Test 2 Complete airframe as shown, battery is 4S 2200mAh 60C

watts=791 thrust=10.5N exit velocity ves=58m/sec with watts/N = 75.3

I have a measured airspeed for the plane flying as setup for test 2: vi=42m/sec.

In this case the theory predicts static thrust should have been Ts= 7.9N and ves=51.2m/sec

 

The speed would have to be vi=48m/sec for Ts=10.3 and ves=58.5 according to calculation. If the airspeed indicator was under-reading that could be an explanation.

 

For test 1the speed would have to be vi=37 for Ts=6.13 and ves=45.1 to give agreement, but while this is plausible, I have no way of knowing if it was so. I am reluctant to try flying this combination again because the flying characteristics were a bit marginal.

More testing required I think.

[Richard Sharman]

Posted by Dizz on 21/10/2011 23:01:26:

Posted by Richard Sharman on 21/10/2011 21:14:12:

Can you say what the entry area, fan swept area, and exit area values were? We could then use the theory to compare the static and dynamic cases.

 

P1091

Wemo mini fan HET 2W-20 on 2650mAh 4S 40C pack.

FSA=29.4cm^2 Exhaust =25.5cm^2 (87% FSA) Total Intake area 29.8cm^2

 

30s WOT figures:

 

Installed Static thrust = 1064g (10.43N); 800W on the Wattmeter; efflux velocity measured with the How Fast = 135mph

I do have a Doppler speed for the P1091, but only one slightly into wind pass so I can't really declare an airspeed.

Thanks for providing this information, Pete.

 

P1091

It's a little difficult to process this as we don't have a flying speed, so can't do the calculation in the normal way which is to work out the dynamic case and then infer the probable static conditions which would lead to this.

 

However, doing the calculation in reverse from the efflux velocity ves=135mph=63m/sec would suggest that if the plane flew at 51m/sec = 111mph then Td=5.7N and the static setup that should have been observed would be Ts = 11.6N with an efflux ves=62.2m/sec.

 

So, there if you think that 111mph was plausible we would have a reasonable measure of agreement between theory and practice, but we'd need to get a real observation to check this, it's just a hypothesis at present.

 

EF16

If you have the duct size for the EF16 we could do the corresponding calculation as you have a measured airspeed -- is it possible to get figures somewhere ?

 

[Dizz]

But Richard it is you who makes the assumption vi=0 (in your 18/10/2011 18:57 post calculations). I agree with the other guys and think the static intake velocity is actually quite high. I am going to bed in a WM400 fan on the test stand tomorrow so will measure the intake velocity. It will not provide an accurate figure though because the static probe will not be facing into the flow, however it will give an indication..

 

Not sure about your mph to m/s conversions. I make 135mph=60.35m/s and that will obviously affect your calculated results. I'll still hold back on the P1091 Doppler speed I have and see what is predicted.

 

I could get the EF-16 intkae area from the replacement that I'm slowly progressing, but I don't have the exhaust area or efflux velocity so there is no point.

Pete

 

PS

Planning on an EDF session next Sunday, so (weather permitting) I should be able to get decent airspeeds for my  P1091, M52 and Typhoon - may be a few others too - to feed the verification process.

Edited By Dizz on 22/10/2011 20:56:08

[Dizz]

WM400 with ARC 28-58-1, CC120HV ICE and Zippy 3000 40C 6S.

FSA= 30.4cm^2 Exhaust area = 23.7cm^2 (78% FSA)

 

30 seconds into run: 1709W, 53,728rpm, Ve=189.5mph 84.7m/s (from How Fast system).

 

Then I stopped the fan, reset the How Fast and ran it up to full power again, but this time I held the pitot tube against the side of the shroud with the opening about 3mm ahead of the edge (I didn't use a rounded intake lip).

 

vi=109.4mph 48.9 m/s......................not exactly "very low"

 

[Tony K]

I must admit I am struggling with this.

 

Quote, "...but in the static case it is less clear what the inlet size is because air is being drawn from a much wider area, inevitably at lower speed".

 

I take this to mean that at some point upstream of the system boundary V=0. By the same argument, at some point downstream of the system boundary Ve reverts to zero.

 

Shouldn't we also set Ve to zero and ignore it?

 

Also, quote, "...dv is now equal to the exit velocity ve of the air stream at the nozzle since the airstream has been accelerated from 0 to ve...."

A system which has an exit velocity and no inlet velocity is a rocket.

 

Looking at the thrust curves it appears that the pink curve ( I hope you don't mind if I do not refer to it as the static curve ) has a Y value about twice that of the dynamic curve (I also have some doubts about this). Is this because half the equation is missing?

 

 

Beause of the questions above and Dizz's observationsI can not accept Scharnhorst's theory as realistic.

[Tony K]

To expand on my doubts about the dynamic calculation and thinking about Richard's question on page 1, "where are all the watts going?"

 

The dynamic thrust calculation is based on one fundamental assumption, that Vi = flying speed but is that assumption correct?

 

Richard's Hawk uses 350W from the battery to push it through the air at 42 m/s but the calculations suggest that the power output is considerably less than 350W. Perhaps, then, the calculated thrust figure is simply too low.

 

Let's say that Vi is 48m/s so the intake is drawing air faster than the 42m/s free stream. One could visualise this as a partially static condition.

 

Running this Vi figure through the calculations gives a thrust of 4,9N and a power output of 296W. Adjust this for 15% losses and you have 350W. W/N = 71.

 

Richard, your static "Test 2" figures show a thrust of 10,5N for an input of 791W, 75W/N. It would be interesting to see what thrust you get with 350W input. I suspect it would be close to 4,9.

 

 

[Richard Sharman]

Pete,

Apologies for the m/sec to mph conversion. I am doing all my calculations in m/sec and converting mph at the last moment, and have been using 1m = 3.28084feet as the conversion factor, but sadly had typed some of the digits in the wrong way round! Thanks for the correction.

 

P1091 update, the theory predicted figures are now:

if static ve, ves=135mph=60m/sec then at vi=118mph=53m/sec we would have dynamic thrust Td=5.0N and the corresponding static thrust Ts=10.7N. I think you said Installed Static thrust = 1064g (10.43N) so we are close. I was worried before, but this seems to be useful confirmation.

 

Thanks for your offer of more test results - it's only by comparing theory and practice that we are going to get a feel for whether this could be a useful tool.

[Richard Sharman]

More on the subject of vi=0....!!

 

I'm a little surprised at the controversy that seems this seems to stirred up, and take full responsibility for muddying the waters. However, let me try once more to suggest what might be happening.

 

As far as the static case is concerned, Scharnhorst says that the system (fan and ducts) speed up the airflow to some value which we call ve(static) or ves. Since the free airflow speed is 0 (we are doing the test in a room) the air has been speeded up by deltav, dv, which is the difference between 0 and ves. Then dv is used to calculate static thrust, Ts, once we know what ves is, which we do by the strange looking equation. In the real world we can of course also measure this.

 

So, as a simplification, I suggested that since we normally define dv = ve - vi in the dynamic case, that effectively amounts to saying that vi=0 (and I did say originally that this was an approximation). Mathematically, it's AS IF the inlet velocity was zero. Physically, obviously it isn't, and we'll come to that in a minute. Since vi never features in the static calculations it doesn't actually matter. What matters is that something has speeded up the airflow to ves, and that something is the system. When I measured vi in the static case (with a specially shaped pitot tube) I got a low result, and looking at Scharnhorst's diagram I could see that strange things were happening around the lip anyway, so I wasn't too worried by the approximation. We discussed testing and strange things that might or might not be relevant.

 

But, let's say vi>>0, what does this mean ? It means that the system is gaining energy from outside (just like it does in the dynamic case where the Impulse gain is calculated from the mass of air being ingested at intake speed. Where is the energy coming from to create this impulse gain ? - only from the ducted fan system, since that is the only energy source around. So the system has an energy loss exactly equal to this unknown inlet energy gain, and the two cancel out. There is not one missing term in the equation, but two. Since they cancel out, we can ignore them. Whatever vi is in the static case, it doesn't matter.

 

I hope this clears the air a bit?

[Richard Sharman]

Posted by Tony K on 24/10/2011 12:07:50:

The dynamic thrust calculation is based on one fundamental assumption, that Vi = flying speed but is that assumption correct?

 

.......Let's say that Vi is 48m/s so the intake is drawing air faster than the 42m/s free stream. One could visualise this as a partially static condition.....

 

Well, it's an interesting idea. My only concern is to know where this air speed up, from the free air velocity of w=42 to the intake velocity of vi=48m/sec, could come from ? Something must be doing work to achieve this energy gain, and the something would have to be the EDF system. I don't think you can say that a 6m/sec speed up is a static property of this example, since it would have to be caused by something. But what is it, and how do we estimate it? Consequently, I think this approach leads to some difficulties.

 

I prefer to follow the line of reasoning that says the calculation of motor power required depended on a figure of 85% efficiency. The power which the system needs to drive the plane at the observed speed has to be divided by 0.85 to get the motor power required figure, which we know does not agree with actual tests. So, since this was an empirical value (probably relevant to some other, unknown, model) it is not right here. To get a value in the right range the efficiency figure would have to be in the 30% -> 40% range. Could this be right ? well, it's certainly plausible: the ducts are bifurcated, narrow, bent in an S-shape, probably have rough edges, etc. There is definitely a heat loss.

 

To understand this better we need to turn the discussion to the question of the INTERNALS of the EDF system, and consider what is happening at the various stages of entry duct, fan and exit duct. Fortunately, there is help here in the shape of Scharnhorst's second paper, on duct design.

What I would like to turn to shortly is a discussion of the