Ducted fan theory and practice

[Tony K]

OK Richard, let's do some sums.

Using your first figures-

vi=46, ve=68.5, dv=22.5, mdot=0.21 (I prefer to use "mdot" for mass flow), gives a thrust T=dv x mdot = 4,725 N.

 

KS equation Pf = (1/2)*M*(ve^2 - vi^2) = (1/2)*0,21*(68,5^2 - 46^2) = 270,5 W.

 

My equation Pf = T x Vav = 4,725 x 57,25 = 270,5 W.

 

Therefore Ploss - Pgain = T x Vav.

 

 

[Stefan Hafner]

Myron, I know the actual principles of the engines are worlds apart, i'm intrigued to see if the same ducting principles can be used, ie: use a diverging duct to increase the pressure and reduce the velocity at the fan to create a higher enegy gain in the flow.

 

Richard, I would think the longer the pitot tube is the better, as the calculation done for airspeed relies on the difference in static and dynamic pressure, and at the nose of the plane i would expect boundary layer effects and flow stagnation will occur for a reasonable distace in front of the nose and affect the pressure.

[Richard Sharman]

Tony K,

fair enough, the calculations give the same results, but be aware of considerations:

1. the actual numbers calculated can vary according to the precision of the data used as input. I have used higher precision in the calculations that in the summary numbers presented, so rounding is present.

2. The formulation using average velocity is algebraically equivalent, but in my opinion, less insightful than the gain/loss formulation. This is useful in further developments of the theory.

[Tony K]

Richard, I see now that Scharnhorst is using the kinetic energy equation, 1/2 (mv^2), but by using mass flow instead of mass he has introduced the time factor which gives a result in Joules/sec and Watts = J/s.

 

The other equation gives a result in (Nm)/s = J/s, so as you say they are algebraically equvalent.

 

I would be interested in seeing your analysis of the static condition although I think it is the free stream velocity which should be zero not vi. If vi = 0 there is no flow at all through the system.

 

Stefan, this thread was created after "Rickenbangler's" question about inlet duct size and Richard has set himself the task of analysisng the theory with the hope of applying it to practice. I am sure that various ducting principles will come up at some stage of the discussion. Be careful about using the term pressure, air is considered to be incompressible at our velocities.

 

TK

[Erfolg]

Just found the link Richard.

 

I am almost certain I have never read this paper before, though, I feel I have read something very similar.

 

The difference with the article I have read is in that other relationships were brought in, linking Reynolds numbers and friction factor, and one of the standard energy loss relationships commonly used in fluid flow assessemnts for pipework. Without going into the loft, and finding my old, study notes and text books, for the life of me I cannot remember either. In the real world I am not sure that it would be useful anyway. Although I do suspect (pretty certain) that the longer the duct, or more complex, the more relevant the friction losses, would become.

 

There is one comment made by a lecturer which seems highly relevant, to DF. The comment went along the lines, fluid flow is very difficult to adequately describe mathematically, other than within a narrow range of conditions. It was also apparent that very small irregularities in the system conditions, be it a bump in a pipe (glass in the case under consideration) made a fool of the experiment. Which leads me to a general conclusion that a poorly made joint in the model duct, a trivial irregularity will result in unexpected poor performance.

 

The paper you have highlighted, after a very quick glance, does seem to highlight the importance of duct entry, and its effect on system performance.

 

I do suspect the bifurcation is a major source of problems. Again I suspect that splitters and other structures within this type of duct system, in aircraft, are an attempt to mitigate possible major changes to flow conditions, due to uneven pressures due to turning etc and the effect on blanking or apparent flow.

 

[Erfolg]

I have, had a read of the paper now.

 

I had a few gripes about the expressions, requiring the rearrangement of terms to be accurate. But grumbling is what old ......... do.

 

In essence the paper agrees with information, to be found in many text books. The big difference is that the values and arrangements were tailored to model aircraft.

 

His argument that the inlet area and shape, is one that needs to be repeated. As many modellers are very tempted to reduce the inlet areas relative to the fan area, to achieve a closer scale appearance. The second aspect is that some modellers are very tempted to have sharp inlet nose profiles, as many supersonic aircraft exhibit this arrangement or that at model sizes, any scale radius, essentially becomes a sharp edge.

 

The outlet area is easier for most modellers to live with, as full size outlets are often a significant feature of the aircraft, being large.

 

It is unfortunate that the effects of internal ducting are glossed over, as I feel, there is tremendous scope in making losses far worse by poor geometry or workmanship.

 

Yet models I would be hesitant to build apparently work well. I am specifically thinking of the WW Hunter and Hawk.

 

It is noticeable that some long duct models I have seen, only fly well, once at flying speed, i.e. Mig 15. Needing cheater holes and bungee launch.

 

One of the best low cost/power models I have seen is the GWS Thunderbolt 2. Essentially shrouded ducts/pods.

[Richard Sharman]

Tony K - thanks for your clarification on the correspondence of Nm/sec and J/sec. Scharnhorst does mention this in the paper. My summary of the argument was exactly that - a summary, as I assumed those interested would read the paper.

 

Erfolg, yes the style of the paper does leave a bit to be desired, which is why I thought a summary would be useful. I believe this was one of 16 papers, some of which cover ducting, but I have been unable to locate them on the web - perhaps more diligent searchers than me will find them ?

[Richard Sharman]

Moving on....The STATIC case

 

When the plane with its embedded ducts and fans is strapped to the bench and run up it produces a strong airflow from the rear. It is common to test this by making the plane press up against a digital weigh scales, the resulting figure (in ounces or grams) being called the "static thrust" of the system. It is usual to observe the watts consumed by the motor at the point of maximum "static thrust".

 

Obviously a strong thrust is better than a weak thrust, but how do these observations correspond to what happens in the air? Is the thrust more, or less, than the thrust in the air? Is the watts consumed figure similar to what will happen in the air? Can the figures be used to help estimate flight performance criteria like "duration of flight" ?

 

Here is summary of what KS says about this case (again, I abbreviate for the sake of the forum, but you are recommended to read the original. I'm not saying I agree with all of this, I'm just trying to capture the main ideas):

 

1. On the bench the model is not moving, so flying speed, w=0, as opposed to the dynamic case when flying speed w =~= vi (is approximately the air intake speed). If, conceptually, at speed the system is taking in air from straight ahead, then at rest is drawing air from all around the intake, the rounded entry lip probably helping to guide the air without too much flow detachment. Consequently vi is very low, let us assume as an approximation that vi=0, (see my note 1, below) and Pgain=0, therefore Pfan = Ploss.

 

2. In that case, dv = ve-vi = ve. So, using the equations developed in the dynamic case, the static thrust, T0 = M * ve (where these variables ought really to have a 0 suffix to distinguish them from the dynamic case - I omit here for simplicity).

 

3. [Recall rho = density of air (~1.2 kg/m^3)]. We know that Ploss = (1/2) * M * ve^2 and also that M = Qe * rho = Ae * ve * rho, so substituting for M, we have

Ploss = (1/2) * Ae * ve * rho * ve^2, or re-arranging:

 

ve = ((2 * Ploss) / (Ae * rho))^(1/3) .............KS 1

 

that is, the cube root of the expression (2*Ploss)/(Ae * rho). This is the celebrated equation which KS first published in 1982. It is important because it gives us a way of calculating the exit velocity of the air when the system is at rest, and there is also a way of calculating the static thrust at rest.

 

KS now uses a "legitimate trick" to allow the equation KS1 to be evaluated. He suggests that Ploss(static) =~= Ploss(dynamic) and we have already calculated that in the dynamic case. Breath-taking, but useful ! (For the full argument, see the paper).

 

The implications of the theory so far:

A. given a specific duct-fan geometry (Ai and Ae) we can work out the values for Newtons of Thrust,T, and of watts need for the fan,Pfan, and so on, for a particular model speed vi (of course, initially we don't know what vi will be).

B. Making legitimate assumptions we can work out what the static Thrust, T0, and the static exit velocity, ve0, ought to be.

 

C. We can measure T0 and ve0 on the bench, and test the theory. If they correspond correctly, we then have a theory that would enable us to measure ve0 on the bench and (with some work) to predict flying speed and thrust, which would be very useful. (see note 2 below)

 

Note 1. Using my airspeed indicator system I have tested the duct entry velocity on the bench and found it is very low, indeed approximately zero.

 

Note 2. I have measured exit velocity on the bench, and found good agreement with figure obtained using the actual airspeed observed in flight as reported earlier in the forum.

 

I'm pretty impressed with KS' reasoning, and if valid would represent a very valuable tool, although I admit I have some doubts. What do others think?

PS. I apologise in advance for any errors I have made in summarising the first 11 pages of KS' paper - I hope I have captured the main points.

[Dizz]

I have been following this thread since it started and as you have asked what others think here goes: I don't think many of the assumptions are valid when considering modern brushless EDF power trains and this will impair your estimation process:

1. Air pressure does change through the ducting as indicated by collapsing intake ducts and exhaust ducts that press outwards.

2. In a 69mm fan at 30k rpm the blade tips have a velocity of approximately 220 mph - at 50k rpm (a fairly common figure these days with 6S EDFs) the tips are doing 368mph (M=~0.5). Drag (hence power required to over come it) is proportional to the velocity squared, so the prediction equations need to incorporate a rpm factor.

3. No allowance in the losses for how many blades, wetted area or pitch - all absorb power apparent as a "loss".

4. It is generally accepted that compressibility effects start to be noticed around 350mph - see (2).

5. Prediction results seem to be independent of airframe characteristics (drag) and intake duct geometry/length - in reality this is obviously not so.

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 otherwise air propelled from ahead of the fan and out of the exhaust wouldn’t be replaced resulting in a vacuum ahead of the impeller…………….or given your measured low (tending to zero) intake velocity and high efflux velocity, the efflux flow has to be at a lower pressure than the intake (pV=constant or p1V1=p2V2– Boyle’s Law).

7. Finally………I would put money on the fact that the pressure inside your Hawk isn’t true static atmospheric pressure (probably lower) purely because of the shape of the fuselage and its relationship to the openings in it – static vents on full size aircraft are very carefully placed and carefully calibrated. Because velocities are squared, the effect of any measurement errors will be increased and lead to even greater inaccuracy.

Regards

Pete

Edited By Dizz on 19/10/2011 01:54:14

Edited By Dizz on 19/10/2011 01:55:39

[Erfolg]

Was thinking about Scharnhorst and the difficulties with his paper.

 

Much of the difficulty for us Brits is that he uses s for g etc. It should not take much to change schwerkraft for gravity etc.

 

I was a little surprised "fly Navy", with respect to air pressure and its effects. I did not think anyone suggested that the pressure was constant. I would expect in accelerating of the air through the duct would cause a reduction in pressure as predicted by Bernoulli. Any expansion and contraction of the duct will vary the pressure, relative to atmospheric acting on the duct walls.

 

As for the comments with respect to the fan, I do not know, yet suspect the fan is important. What is important I do not know and would be interested in a better understanding at a theoretical level, so as to be able to relate to what can be engineered at a practical level.

[Richard Sharman]

Dizz (Pete), thanks for your comments - that what this thread is all about !

 

Just a few quick responses before a full scale discussion gets going:

 

1. On the Hawk the ducts are deliberately stiff, and don't collapse or expand, although I have had that phenomenon on another plane.

 

2,3,4 The analysis we are currently looking at is from the viewpoint of the system as whole, as if it were a black box that just does something. How it does it inside is another way of looking at the problem. It's important not to confuse the two approaches.

 

5 airframe characteristics ARE taken into effect since we are considering the plane flying straight and level at cruising speed, w =~= vi. In this steady state thrust = drag of course.

 

6 the concept of vi =~= 0 in the static case seems to be causing some raised eyebrows. But, measurements of airflow just ahead of the Entry duct show very low readings. However, measurements in the throat and down the inlet duct show quite high velocities, but these are INTERNAL observations and thus not relevant to this particular EXTERNAL analysis.

 

7 is your money safe ? the instruments inside the Hawk are in an enclosed compartment with no open vents (as recommended by EagleTree in their Installation and setup manual) and not connected to the ducts in any way. Fuselage shape shouldn't have any effect? The EagleTree system has been used widely on many model planes. So I think any error in my measurement will be small ?

 

Richard.

PS I have found another KS paper on INTERNAL duct design and analysis, in which he presents his second equation major equation, this time for duct design. I'll post this to make it more conveniently available, and summarise it here soon.

[Erfolg]

Richard

 

I will be looking forward to the internal duct paper.

 

It was just a fortnight ago i spotted an old text on duct design by "Woods of Colchester", I should have picked it up, when I go back I will try and remember to pick it up. Although for industrial duct systems, the principles will be similar. Especially the air curtain sections, as the velocities are high, which are (broadly) similar to our systems.

[Tony K]

Erfolg, it was I who suggested that pressure is constant. By that I mean air pressure, which is 1 atm (about 101 kPa). This is not the same as pressure head (units of length) which can change according to Bernoulli.

 

As regards the collapsing ducts, take the duct downstream of the fan. Air leaves the exit faster than it passes through the fan and part of the net trust or force is gained from this acceleration. Now imagine a cross section anywhere in the duct. Its job is to receive air from the previous cross section and squeeze it (exert a force on it) so that it fits into the next cross section. This squeezing does not increase the air density (or air pressure) because it is able to escape downwind if it moves a bit faster but the sqeezed slice of air is also exerting an equal and opposite force on the duct wall. If this force overcomes the strength of the wall, plus the atmospheric pressure outside, the wall will fail.

 

 

 

 

[Erfolg]

Tony

 

I have no trouble with atmospheric being as far as we modellers are concerned at approx. sea level experiencing 1 atmosphere be it 101 pascals or 15 psi in old units.

 

I have no trouble with ducts experiencing values above and below atmospheric pressure as it passes through the duct. It is what i expect.

 

As for it collapsing etc. Well that is just an engineering issue.

[Myron Beaumont]

Probably irrelevant ,but having been instrumental in producing EPR (engine pressure ratio )charts for engines a few years back ,I do remember that the figures were to three decimal places to set the engine (Speys) for TO and max cruising (between one and two ).Such a small differencial between "what goes in & what comes out" so to speak .As I say -Probably very difficult to measure for modellers & EDF power outputs & probably irrelevant .

I'll get mi coat!

Never could get my head round "suck & blow " regardless of the laws of physics & I bet I'm not the only one .An EDF just speeds up airflow & that is it -is it not?

Edited By Myron Beaumont on 19/10/2011 15:52:08

[Richard Sharman]

Posted by Myron Beaumont on 19/10/2011 15:48:58:

..........An EDF just speeds up airflow & that is it -is it not?............

Err..., well.....,no, actually! Because when designing a plane we need to work out what the exact geometry of duct is to build it, and when flying a plane we need to select the right battery for the desired duration/performance. So how would you do that? trial and error ? or theory and practice ? As our friends across the water would say, it's a no-brainer !

[Richard Sharman]

On the subject of AIRSPEED INDICATOR...

 

A couple of people have expressed concerns in this thread that the airspeed measurements I reported as observed on my Hawk may not be accurate because of potential problems with pitot placement, pitot size, static pressure location, etc.

 

The Hawk has now flown with GPS logging, and I can confirm that the GPS speed correlates very closely with the Indicated airspeed reading. Where the plane is flying into wind the GPS speed is a little less than airspeed, and when flying downwind the GPS speed is a little more, by about the ambient wind speed. Where the plane is flying across wind the two agree almost exactly.

 

Consequently, I claim the value given above for average flying speed is reliable, at least to the level of accuracy we are working here.

 

[Andy Gates]

How can you have "almost exactly"?

[Dizz]

Posted by Erfolg on 19/10/2011 11:39:30:

I was a little surprised "fly Navy", with respect to air pressure and its effects. I did not think anyone suggested that the pressure was constant. I would expect in accelerating of the air through the duct would cause a reduction in pressure as predicted by Bernoulli. Any expansion and contraction of the duct will vary the pressure, relative to atmospheric acting on the duct walls.

 

As for the comments with respect to the fan, I do not know, yet suspect the fan is important. What is important I do not know and would be interested in a better understanding at a theoretical level, so as to be able to relate to what can be engineered at a practical level.

 

I was using the example of the collapsing duct to illustrate that there is obviously a difference in pressures in the duct from that outside. For a unit mass of gas at constant temperature, if the pressure changes then so does the volume (hence density too).

 

I have test stand power and efflux velocity figures for several different EDF and motor combinations which show that fan design definitely does have a bearing on the power consumed(lost) and efflux velocity.

 

IMHO, without a wind tunnel and some pretty sophisticated instrumentation we are not going to be able to improve on what we can already achieve using basic static testing and fairly well known rules of thumb.

Pete

[Dizz]

Richard

I appreciate you are looking at it as a system, but where are the system boundaries? I was taking the plane of the intake and exhaust faces. If you extend the boundary "a long way" from there both velocities will tend towards zero. However you were questioning where the missing Watts in your example calculation were going - I'm saying that without considering what is happening inside the system you wont be able to improve the Ploss figure.

 

wrt airframe characteristics: consider 2 aircraft with the same ducted fan units/motors/intakes/exhaust such that static thrust is the same - one a very large and draggy (but lightly loaded aircraft) that can only achieve an airspeed of x m/s where thrust=drag, then a second highly streamlined dart where thrust = drag at 5x m/s.

How do the equations handle that?

 

Yep, reckon my money is pretty safe. If the static vent for the unit is inside a enclosed compartment with no openings it will relate to the pressure inside the enclosure when it was closed, not the current static atmospheric. The air inside the fuselage will tend towards the air pressure at the openings to the fuselage eg the gap around the canopy hatch. Where the local airflow accelerates (like over that lovely aerofoil shaped cockpit) it will be less than static, where it slows down it will be greater than static. Of course everything may balance out for a certain set of conditions, but that will change the next day.

What is the % error between the "almost exactly" in agreement airspeed and averaged GPS ground speed? I have the How Fast pitot static system from BRC and that is claimed to have an accuracy (instrument error) of 2%, but as I said, small errors are magnified when a square appears in the equation.

Regards

Pete

[Dizz]

Err..., well.....,no, actually! Because when designing a plane we need to work out what the exact geometry of duct is to build it, and when flying a plane we need to select the right battery for the desired duration/performance. So how would you do that? trial and error ? or theory and practice ? As our friends across the water would say, it's a no-brainer !

Third way...............experience ("rule of thumb").

 

Fourth way................use/adapt a proven design (use the experience gained by another).

 

[Erfolg]

I am not sure that Boyles Law or the Universal Gas Law, would produce any measurable increase in temperature or volume, as a consequence of the pressure changes in a DF system, at a practical level.

 

With respect to fan performance. I believe you. The question I am asking, is why, what is important?

 

I guess that Richard is pulling together all the theoretical information that is available. Again I am guessing that he is attempting to isolate all the elements and the factors which affect them. By treating each element as a "Black Box", the functions each box represents can be strung together into a model. Many maths type people call this approach "the sausage machine", you crank the handle and out pops the answer. Engineers call the approach a FBD (free body diagram) as each element is isolated and evaluated in detail, which can be represented within a larger, but stripped down FBD. The approach has an advantage that Richard will be able if he wishes to change the variables within the functions in addition to the inputs, to evaluate a system, or one aspect, under varying conditions within something like a spreadsheet or even a relational data base. That is my guess.

[Richard Sharman]

Posted by Erfolg on 19/10/2011 22:27:31:

............I guess that Richard is pulling together all the theoretical information that is available...........

 

well, some of the information, yes.

 

When studying problems like this I think it's important not to get bogged down in too many details all at once. The scientific method is to abstract, generalise, hypothesise, experiment, and so on. Trying to combine everything all at once usually leads to insoluble complexity.

 

So what I've been suggesting (or rather KS is suggesting) is that the first thing to do is look at the overall function of ducted power systems in terms of inputs and outputs. This applies whether it's EDF, ic-ducted fan, or turbine. What the analysis shows is that there is a certain amount of power required to push the plane along at a given speed**, and we have a good idea of what value that is. Now, when we compare that value against the measurement of what the motor is actually consuming we find a discrepancy. The answer to the question "where are the watts going ?" is that they are being lost (as heat, etc) because whatever is converting watts of electricity into useful work (forward movement) is not very good at it. And we know by how much. This is a useful step forward, and is the basis for deciding how to design and build better systems. So, no rules of thumb, no guesswork, just a more rational thought process.

 

The second thing to do (and which we haven't done on this thread yet) is to look at the specific method of achieving the end result (forward motion) by the expenditure of stored energy (In our case that is mAh in a battery, so we diverge here from what we would have to do for i.c. for example). This involves motor efficiency, fan efficiency, duct losses and so on. We should discuss this, but not before we've wrestled the first step down, which we haven't yet. For example, no one has commented yet on the relationship between static thrust and dynamic thrust -- what is it? Because it's not obvious.

 

** this is the key to Pete Dizz's puzzle: the equations solve his problem correctly: he has two planes with the same EDF set-up, and therefore the same static thrust, but one is large and draggy, and the other is small and sleek. Therefore they fly at different speeds, using different values of dynamic thrust and requiring different amounts of energy. And most probably working at different levels of efficiency. Their solutions to the equations are different, and in neither case is the dynamic thrust directly related to the static thrust.

 

R. (I'll reply to the other points later).

[Keith Simmons]

I am no good at theory, but I have got this month's Jets Monthly (November 2011) and on pages 12/13 about Hawker's first jets and at the start of the project with the Nene with 4500 lb thrust on the Hawker jet, the engine was installed amidships with the long exhaust exiting at the fuselage rear, It was soon realised that the long exhaust arrangement would cause significant loss of thrust, so the design developed into a P1040 with a split jet exhaust exiting on each side of the fuselage aft of the wing.

That's why Jet engines are now mounted towards the end with minimal exhaust ducting and does that effect EDF in the same way?

 

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 know we would never be able to build models to go fast enough to create that effect !

Edited By Keith Simmons on 21/10/2011 09:05:49

[Tony K]

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