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Old Sep 17, 2006, 05:53 PM
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Help!
Designing a bifurcated tail pipe

I’m looking for the best design solution for a long bifurcated tail pipe. With "the best design" I mean the solution where I loose as less as possible thrust.

The given facts:

Fan output diameter (DS-94 or TurboFan 4000) : 120mm
Nozzle output diameter: 2 x 72mm (for 85% FSA)
Distance between the centers of the two nozzles : 98mm
Length of pipe: 690mm

Now, there are many ways to design the tail pipe:

1. two side-by-side tubes, each wrapping half the circumference of the fan shroud (with vertical divider wall at the fan center) and smooth changing the shape to a circle at the pipe ends

2. a long section with the diameter of the fan, bifurcating in the end section to the two nozzles.

3. the reversal of 2. Bifurcating behind the fan to two pipes with circle shapes with 77mm (100% FSA) with a cone at the end of the pipe to reduce the circle to 72mm

4. somthing between solution 2 and 3

I’ve tried to draw the 4 design concept for better understanding.

Are there experiences, which kind of tail pipe is the best?

Thanks for your help
Norbert
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Old Sep 17, 2006, 06:10 PM
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I played around a bit with my 750 pipe for my EF2000 and mine was like #1, nice and smooth with a sharp splitter starting early then slowly openeing up. And as for forming it, it wasnt too hard. I wired foam from fan diameter to exit diameter, not total exit diameter though, just straight to one exit diamter.(i.e 120mm=4 3/4" to twin 2 3/8" exits, I instead went from 4 3/4" to a single 2 3/8 circle. Then I ct it up the middle of that circle splitting it into pants, 4 3/4 on one side, 2 half circles fromt he 2 3/8 on the other end. Then I wired a seperate pice of foam from a 4 3/4 tall to a half circle of 2 3/8 and inserted those in the inner sides. The fan end on the inserts are not fan diamter but more they were wired from 1/16th ply strip that was 4 3/4 tall, that way it was like a thin slice that fit right into the wedge area. hope that made sense. Those sizes are not exact, there just there for example sake. You can then plastic bag this and glass over it, or just glass and do lost foam method.

Barry
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Old Sep 18, 2006, 08:30 AM
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Quote:
Originally Posted by ePower
I'm looking for the best design solution for a long bifurcated tail pipe. With "the best design" I mean the solution where I loose as less as possible thrust.
The given facts:
Fan output diameter (DS-94 or TurboFan 4000) : 120mm
Nozzle output diameter: 2 x 72mm (for 85% FSA)
Distance between the centers of the two nozzles : 98mm
Length of pipe: 690mm

Thanks for your help Norbert
Hi Norbert

at least you think logical.

The conditions for least loss in ducting for EDF are easily defined:
1. minimise friction drag
2. avoid flow separation
3. no “double conversions”

Point 1 divides again into three constituents:
1. minimum “whetted” area
2. least possible flow velocity
3. small friction coefficient

and point 2. can be achieved by:
1. no abrupt area changes
2. no sharp corners

point 3. “double conversion” refers to the change of velocity of the air flow in the duct when there is a duct contraction followed by an expansion or visa versa.

For minimum whetted area one should lead the exhaust in a straight single duct as far as possible to the nozzle(s) up to the point where the split is. This requires a conical duct piece which brings down the fan diameter to the equivalent pipe diameter after the motor housing. The length of this duct piece can be as short as ¾ of the fan diameter. A cone inside this duct which smoothes the flow after the motor helps to reduce the length but has hardly any influence on the loss itself.
One can often see that the pipe which follows the actual fan housing is of the same diameter as the fan and that inside of it is a cone which is supposed to reduce the “drag” of the motor housing. This actually has several drawbacks: firstly it causes the air flow to retard towards the cone end, which secondly causes the flow to separate from the cone (unless it is very long) and it also increases the whetted area. Worst of all is however that the arrangement acts like a diffuser and requires an additional flow velocity increase afterwards, which constitutes a “double conversion”
The least possible flow velocity for minimum drag after the fan is always the same as the axial velocity through the fan itself. Any attempt to reduce it further will only cause more secondary drag. The situation in front of the fan can easily be quite different, but that is another problem.
A small friction coefficient for the duct after the fan will require a smooth duct surface, but otherwise there is not much one can do, since the air flow after the fan will certainly be turbulent. So it is best to carry on with a straight pipe with the correct diameter. Perhaps one should bear in mind that the circumference of two circular ducts compared with a single duct with the same cross section is always larger by the factor of 1.41 (square root of 2), to see, that a singular duct has less resistance than two ducts for the same air flow.
The bifurcated section of the duct should start with a straight division which results in two half round ducts. Transition from half round to round at the nozzles should be smooth and with the same cross section areas. It is particularly important that the two duct pieces are symmetrical and accurate to cause the same resistance. If the two pieces are not symmetrical and have different resistances, the flow will not divide equally at the partition and cause flow separation with the inevitable losses.

I made a little sketch which shows how I would tackle the duct geometry.
As in all engineering tasks there are other solutions as well.

Have fun with fans

Klaus
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Old Sep 18, 2006, 02:25 PM
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Hi Claus

Thank you very much for the perfect explanations. I try to summarize:

Conditions for least loss:
1. minimise friction drag
1.1. minimum “whetted” area
1.2. least possible flow velocity
1.3. small friction coefficient

2. avoid flow separation
2.1. no abrupt area changes
2.2. no sharp corners

3. no “double conversions”

All my duct concepts could be designed to solve more or less all this points. The disadvantage of #1,#3,#4 is, that this solutions will have more surface and this means more friction. Are you agree with me?

Do you have an idea about the loss of a bifurcated duct compared to a straight one?

Today I had drew a more detailed concept. What do you think about it compared to your design, if I calculate all circles to get the same cross section areas at all points?

@Barry:
I will build positive forms to laminate the duct. So I get a very smooth duct surface. I will append a pic from the Alca duct I've built.

Best regards - Norbert
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Old Sep 19, 2006, 01:40 PM
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Quote:
Originally Posted by ePower
Hi Klaus
All my duct concepts could be designed to solve more or less all this points. The disadvantage of #1,#3,#4 is, that this solutions will have more surface and this means more friction. Are you agree with me?
Could? One can always find the solution with the least “whetted” surface, building it is a different matter

Quote:
Originally Posted by ePower
Do you have an idea about the loss of a bifurcated duct compared to a straight one?
Sure, but beforehand I should explain something else which has not come out in the prev. reply: the actual contraction of the duct down to the final nozzle diameter only happens in the last 40mm of the two duct pieces as shown in the sketch (but without dimensions for the diameters). The equivalent ½ Ae calculates to 78mm diameter. Up to there the duct has no contraction at all = constant cross section area. The nozzle can be made very short, in this case 40mm, and it necks down to 72mm to give you that magical 85% of the fan annulus (FSA). This arrangement also has the advantage that you can change it easily if that becomes desirable.

Losses in ducts are generally given as pressure drops measured in psi or in the civilised world in N/m^2. The latter is just so much more convenient when one has got used to it There is a general formula for this: [delta]P = velocity pressure times pipe length / pipe diameter times a [certain] coefficient. The coefficient is dependent mainly on the Re value but also on the quality of the whetted surface and can be found in various text books, it usually carries the designation [lambda]from the Greek alphabet. Another very similar formula is used for bends and other individual components like a branch or division. In those cases the coefficient is called [zeta].
The pressure loss for the bifurcated part of the duct compared to a straight piece is as follows:
straight single duct: [delta]P = q * L/D * [lambda], with q=4210N/m^2, L/D=2.03 and [lambda]=0.02 [delta]P = 171N/m^2
two small ducts: [delta]P = 2 * as above, with L/D = 2.75 and [lambda]=0.028 = 648N/m^2
Additional loss due to flow separation: [delta]P = q * [zeta] with [zeta] = 0.016, loss = 67N/m^2
The calculations were based on the assumption that the fan produces 40N static thrust without any exit ducting or nozzle contraction.
For the whole duct a loss of either 710n/m^2 (for a single nozzle) or 1254n/m^2 can be calculated. You can see that bifurcated ducts are really not a good idea compared to a single one. Fortunately when these pressure losses are converted into thrust losses the picture is not quite as bleak


Quote:
Originally Posted by ePower
Today I had drew a more detailed concept. What do you think about it compared to your design, if I calculate all circles to get the same cross section areas at all points?
I have not checked on the individual cross sections but in my view you have not achieved the least possible whetted surface by a long stretch. An oval or a figure of eight combined from two circles certainly has a larger circumference than a circle of the same area. You also introduced a ridge, which runs axially, but nevertheless could produce some additional drag if the air flow still has some whirl left (which it always has).

For your consolation however, I found with some calculations that other solutions for this duct exist, which are equally well suited and may even give slightly better results. One could run the duct up to the bifurcation as a single straight piece, which would constitute a slight diffusion in the first part of it, but that is so slight that the loss is easily offset by the lower mean velocity in the duct. Only a rigorous examination of all the factors will offer the best solution in the end. One could also avoid the sharp edge at the partition, which may give rise to some losses due to the rest whirl in the duct.
These are things one can only determine when someone actually makes the different duct forms and measures them in a rig.

Have fun with fans

Klaus
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Old Sep 20, 2006, 05:52 PM
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Hi Klaus

Thanks again for the detailed explanation. I tried to understood the calculation but I have troubles in two points.

1. You say L/D = pipe length / pipe diameter and your quotient is 2.03 for the single and 2.75 for the two small ducts. But 690mm / 120mm = 5.75? Should it be length / circumference ?

2. In the conclusion you get a pressure loss of 710N/m^2 for the single nozzle or 1254n/m^2 for the two small pipes solution. I don't see the correlation to the calculations before?

Could you please help me again?

Best regards - Norbert
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Old Sep 22, 2006, 09:07 AM
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Quote:
Originally Posted by ePower
Hi Klaus
Thanks again for the detailed explanation. I tried to understood the calculation but I have troubles in two points.
1. You say L/D = pipe length / pipe diameter and your quotient is 2.03 for the single and 2.75 for the two small ducts. But 690mm / 120mm = 5.75? Should it be length / circumference ?
2. In the conclusion you get a pressure loss of 710N/m^2 for the single nozzle or 1254n/m^2 for the two small pipes solution. I don't see the correlation to the calculations before?Could you please help me again?
Best regards - Norbert

Hi Norbert

It’s hardly possible to give you a detailed picture here of the complete power and loss calculation. That has to wait until you can read it in my article or book (when it gets published).

But first you have to refer to the original sketch I made.
If you compare the difference of the losses of different arrangements you should only compare the parts which are different – in case here the bifurcated part with an equivalent single duct of the same length. The bifurcated section is 206mm long and then there are still the nozzles (which on my original hand sketch were only 14mm long). So I took the length as 220mm. The equivalent diameter of the bifurcated ducts is 80mm, so L/D = 220/80 = 2.75. For the single duct section the diameter is 108, not 120, so the L/D is 220/108 = 2.03. But that is only the rear part of the duct so you have to add the long duct, which is also 108mm diameter and creates a loss of 539N/m^2, which is applicable for both arrangements.

There are several paths to tackle such a loss calculation. As already said, one of the major aspects is to reduce the whetted surface to a minimum.

Whether one then calculates the friction losses as a pure surface friction problem or a pipe friction problem is rather academic, the results are very similar. I found that the two methods render results which are within plus/minus 3 to 5 %, well within usual engineering calculation of this type accuracy and not far from reality.
I prefer to treat it as a pipe problem, mainly because it is easier and there is a whealth of empirical data available. If using pipe loss calculation methods one must however bear in mind that many assumptions for pipe flow are not applicable, since our ducts are just not long enough for a true fully developed pipe flow. It is also important to use the right set of friction coefficients and Re-numbers, otherwise the results are nonsense. Re numbers in pipes are derived with the characteristic length being the diameter, whilst on the flat plate it’s the length of the plate. So it can easily happen that for the same situation you get very different Re numbers.
The only occasion when I use flat or bent plate "rules" is when I want to investigate BL (Boundary Layer) development and when I want to compare with the pipe calculations.
I have attached a graph which shows the friction coefficient for pipes of the most common diameters in respect of the Re number. It is one of the many graphs which I use in my articles.

To contradict myself (my prerogative) I have also made a sketch in which I have not followed the constant area rules, an arrangement I normally would not advocate. I'm still not finished with the mathematics (for which I'm developing an Excel spread sheet program) but first calculations did surprise me.

How does the front end of your installation look like?

Have fun with fans

Klaus
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Old Sep 22, 2006, 12:28 PM
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Thanks again Claus

I think I will now understand the most of your explanations.

The thrust tube is for a 1:9 Eurofighter. The two parted rectangular inlets will also not have the optimal shape But this part will be built by an other person. My job is to build the thrust tube (as good as possible) and I will do thrust measures on a test rig with the whole equipment.

I plan to build a single pipe thrust tube with the same (690mm) length for reference only and one or more versions of bifurcated thust tubes (if the first bifurcated tube will give more thrust compared to the straight one, I don't design a second one )

Now I'm unsure about the diameter for the thrust tube!? Would you recommend to use also a tube of 120mm with a nozzle down to 100mm or should I use the well-tried Ae rule, resulting in a tube with 109mm diameter and the nozzle reducing to 100mm?

Thanks for your really competent help.

Norbert
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Old Sep 22, 2006, 05:07 PM
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this wasw the inlet i ended up with, i made about 5 different ones till i got it right. turned out with a inlet this shape a 3/8ths inlet lip worked out the best. And the swoop worked out well cause it allowed the fairing for the nose leg, but the wheel missed the duct completely.


Barry
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Old Sep 24, 2006, 09:12 AM
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I've started to build the first form of the bifurcated tail pipe for the Eurofighter. Following the first suggestion from Claus, the bifurcation section including nozzle is now 200mm to 250mm long. So the straight section will be 440mm to 490mm. Should I use a straight section between bifurcation and nozzle and if yes how long?

Some more information about the Eurofighter project you will find at

http://members.aon.at/projektef2000/

If I see the work for the finish of the EF surface, I'm very happy about my part of work for this project

Regards - Norbert
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Old Sep 28, 2006, 05:51 AM
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Quote:
Originally Posted by ePower
I've started to build the first form of the bifurcated tail pipe for the Eurofighter. Following the first suggestion from Claus, the bifurcation section including nozzle is now 200mm to 250mm long. So the straight section will be 440mm to 490mm. Should I use a straight section between bifurcation and nozzle and if yes how long?
Some more information about the Eurofighter project you will find at
http://members.aon.at/projektef2000/
If I see the work for the finish of the EF surface, I'm very happy about my part of work for this project
Regards - Norbert
Hi Norbert

quite an impressive project you got there!
Make the "trouser" piece as short as possible, no straight piece necessary before the nozzle (unless there are installation reasons).

Have fun with fans

Klaus
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Old Sep 30, 2006, 10:11 AM
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I have changed again the concept for the first version of the bifurcated thrust tube. Daniel Schubeler has recommended also to build the long straight section with the output diameter of the fan (120mm). So I've cut a new version of the Y-part. The whole reduction to 86% of the FSA is now done in the last 50mm with the nozzle. Appended some pictures of the foam parts before laminating.

Good news for me also for the thrust measurement equipment . I got the force transducer and a measuring amplifier for a symbolic price. Many thanks to http://www.rezhla.ch Other sponsors for the Eurofighter project are warm welcome

Regards - Norbert
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Old Oct 01, 2006, 09:16 PM
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Hi Norbert

Here is a little pic where I have overlaid your photo with the drawing outline. See the red highlighted lines, which indicate that you may have to check those areas. I think there could be another deviation from the constant cross sections?

Here is also, as promised, the calculation for the straight pipe. It's not any better than the first, to the contrary. But the difference is not very great. It only confirms my contention that double conversions should be avoided.

Have fun with fans

Klaus
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Old Oct 02, 2006, 12:36 PM
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Hi Klaus

Thanks a lot for this professional reflection of my work. I've calculated the area for each 20mm segment. So the deviations from the 120mm diameter area should be marginal. Now I'm building the forms and if I end with a loss of 14% of thrust I'm very happy.

I have also drew a second version with another (yours :-) ) bifurcation shape (changing from semicircle to circle). Should I end with more then 15% loss of thrust with V1 I will start with V2

Best regards - Norbert
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Old Oct 12, 2006, 04:29 PM
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Some news about the progress. Just now I've finished the work for the form. I've built it in three parts. One for the straight pipe section and two for the Y-pipe. This weekend I will laminate the first tail pipe.

Are there any suggestion about the glas I should use? I have no experience building this X-Large type of pipes Are two layers with 80g/m2 (2.8 ounze/m2) enough?

Appended some pictures from the finished Y-pipe forms. The paint of the straight pipe is still wet.

I also work for a new test stand. All my "old" equipment is to weak for this project. With the new test stand, I will be able to measure thrust up to 200N (45 pound-force) 50V battery voltage and 140A current. Should be enough for the next year

Unfortunately I have do do a break for about 3 weeks, because a business trip to Australia. But within this time I hope that all the missing equipment will be delivered. The critical part could be the PowerJAZZ?

Regads - Norbert
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