Lady Anne variation.

[Graham C. Williams]

Hi Mike.
Yes please. The unpacked model I'm using is about 2 years if not more years old . I'd like to run one of your unpackings and see what NUDiS makes of it.
Come to think of it I may have your technique here somewhere.
Did you get the numbers I posted above for you?

Regards
Graham.

[Mike Everman]

Yes, I literally just hit the last "equals" sign! I converted my estimate of the combustion locus, converted to your longer intake unpack and it is at 30-33% Ha! Locus percentages residing in the upper middle of your data table; I assume somewhat "into" the run?

Cool!

[Nick]

Hi guys,

well it looks like you have all been very busy, sorry ive been away so long but work work work

brilliant stuff as usual guys and having read up on this thread im going to put my head in a bucket of iced water for a while to stop my ears bleeding.
looking forward to th bandages coming off and reading more

Nick

[milisavljevic]

...im going to put my head in a bucket of iced water for a while to stop my ears bleeding.

Does that really help?!

Just 7 or 8 hours back Mike and I were discussing glass jam-jars and pulsejets...were your ears burning?

Welcome back!
M.

[Graham C. Williams]

Good morning Nick.
With the price of household energy going up I think we should get that pot of yours running again!!
Keep well. I hope to see you soon. Let's make some waves on the Welsh boarders?

Best Regards
Graham.

[larry cottrill]

Using UFLOW1D, my usual temperature range and my traditional unpacking technique with the new dimensions (and using a 28mm ID intake stack to approximate James' twin stacks) I show her perfectly in tune (pressure antinode spot on the chamber shoulder), with slightly reduced end velocities but much improved mass flows vs the Rev 07 motor. The frequency is significantly higher, of course, due to the reduced impedance at both ends -- I come up with 400 hz almost exactly. The "buzzing" of the intake is much less pronounced than on the Rev 07 -- I don't know what that means, just something that jumped out at me. It's so good I ought to do an animation of this one, but of course I don't really have time right now to mess with it.

Very nice machine, gentlemen! Got to build one ... of course, I don't have time for that, either.

Graham, I'll have to try some runs with constant temps throughout the pipe and see if I can get an equivalent run, then get back to you with the temp that works and see how it compares with what you're using. A single temp in the pipe would certainly simplify the initial setup.

L Cottrill

[larry cottrill]

With UFLOW1D, looks like I get precisely equivalent results with the unpacked pipe (including the transition zone) at initial internal temps of 1800 degrees throughout and the intake stack at just 350 degrees throughout. Same frequency, same antinodal point, virtually identical curves overall. Interesting.

Graham, does this come close to how you're setting it up?

L Cottrill

[milisavljevic]

.
Dear Graham,

Sorry for the long delay in getting this report to you. As another enthusiast has said, there are
times when "Life gets in the way". Most of what follows the text section is simply data, and it
is for expedience that I have avoided definitions. In any event, your approach to modeling the
pulsejet is fundamentally different to mine; thus my definitions may not be meaningful to you.

Please post any questions you may have here or by Private Message; I will answer as best I can.

Finally, please note that I am NOT attempting to belittle the efforts you and James have made,
should I point out any significant deficiency with this duct. In my own thinking, you and James
have made great strides in making a "silk purse from a sow's ear" (albeit a stainless steel ear).

Best regards,
M.


Pulsejets are generally based upon one of two (2) combustor schemes: "Linear", and "Reflex".

Linear combustors feature one (or more) intake ports in opposition to one (or more) exhaust
ports, eg., the IAME Escopeta or the Lockwood-Hiller type. Side-ported ducts, eg., the Logan,
are also classified as linear combustor pulsejets. Reflex combustors feature one transition at
one end of the combustor, from which the intake and exhaust ports extend, eg., the Chinese.

Combustor shape is not a determinant, but rather the path intake charges take in reaching it.
From this perspective, the Thermojet type is a reflex combustor pulsejet. Combustor scheme
limits aspiration (intake charge induction) and ultimately, thermal and propulsive efficiencies.

Reflex combustor designs trade thermal efficiency for the 'convenience' of thrust rectification.


Name; Type: FWE-VIII Revision 8; Hybrid (multi-meme, multi-port reflex combustor)
Designer(s): Larry Cottrill, Graham Williams, James Docwra
Builder(s): James Docwra

Dimensioned drawing provided by Graham Williams (non published)

Basis of simulation: self-sustaining operation at 100% static thrust
Ambient conditions: ICAO Standard Day, sea level at 15 C (288 K)


Basic dimensions (mm); acoustic stations (%)

• intake (2x) ....... ID 20.5 x 20.5 x LN 70.0 (on centerline)
• coupler (2x) ...... ID 20.5 x 20.5 x LN 42.0 (on centerline)

note: intakes flared to 31.0 mm

• combustor cap ... ID 64.0 x 00.0 x LN 26.0 ... 04.5%
• combustor ........ ID 64.0 x 49.0 x LN 73.7 ... 17.2%
• transition ......... ID 49.0 x 29.0 x LN 98.3 ... 34.2%

note: intake couplers intersect transition at -3.7 mm

• fore cone ......... ID 29.0 x 42.0 x LN 82.0 .... 48.4%
• rear cone ......... ID 42.0 x 32.0 x LN 38.0 .... 54.9%
• exit cone ......... ID 32.0 x 66.5 x LN 241.0 ... 96.6%

Length as modeled: 559.0 mm (physical); 579.0 mm (acoustic)
Volume as modeled: 1009 cc (overall); 214 cc (combustor only)

Tailpipe aspect ratio: 8.8 (wrt. volume); 9.4 (wrt. acoustic length)

While I understand that in the eyes of some (if not all) of the designer(s), the combustor that
is fitted to this duct is a 172 mm long truncated cone (and a 25-28 mm long end cap), what is
missing from such perspective is the fact that the intrusion of the intake coupler (transitions)
into this cone effectively terminates the active combustion zone. As demonstrated below, my
methodology yields an almost exact match wrt. calculated and measured values of limit thrust.

A topic for future discussions, no doubt...


Induction efficacy (%)

• intakes, couplers: 148% (ideal: 100%)
• intakes only: 92% (reflex; ideal: 80%)

The induction system delivers 100% of the oxygen required for combustion; however, the total
charge delivered per cycle must be balanced against the combustor volume and thrust required.

Over-aspirated ducts may exhibit significant difficulties in start up and limited throttle ranges.
A self-sustaining pulsejet 'self-regulates' the average air-fuel ratio cycle to cycle, as a function
of thermal power (thrust); over-aspirated ducts tend to 'lean out' too rapidly when throttled off
high power settings and consequently flame out. This phenomena is strongly affected by shape,
with greatest throttle instability associated with high aspect ratio (L/D) cylindrical combustors.

• Combustor aspect ratio: 1.5 (relatively short)
• Intake only aspect ratio: 3.4 (relatively short)

Step ratios (combustor confinement, %)

• s0 = n/a (n/a)
• s1 = 3.22 (53.7%)
• s1' = 3.16 (52.7%)
• s2 = 2.06 (84.1%)

Edit: The step ratios were misnumbered; that has been corrected here.

Thrust production (kg, lbf)

• limit thrust = 2.22 (4.90); see my note
• intake thrust = 0.62 (1.37); 28% of total
• exhaust thrust = 1.60 (3.53); 72% of total

Volume specific thrust density: 21.6 N/liter ("Laird" = 17.0; "sc-8.1a" = 21.5)

Actual motor was reported as developing 2.25 kg (4.95 lbf), a 1.0% difference from this model.

Discounting measurement error, no correction has been made for test site altitude or ambient
conditions. The design allows for 3 mm of freedom in the length of the combustor cap (overall
lengths from 558-561 mm); selection of a longer cap for the modeled duct would have resulted
in a higher limit thrust. The modeled length was selected from convenience: 559 mm = 22.0 in.

Sigma scores (propulsive efficacy, %)

• sigma ∞ = 4.8 (39.6%)
• sigma n = 1.4 (36.7%)
• sigma x = 3.2 (44.2%)

For comparison, consider these sigma scores from other reflex combustor pulsejets:

• Classic Chinese "Laird" ... 6.5, 2.1, 1.0
• James Irvines' "Raptor" ... 7.1, 2.1, 0.8
• M.'s "Superchine 8.1a" .... 7.5, 2.3, 1.0

Cronje scores (propulsive efficacy, %)

• Cj combustor = 2.22 kg / 3.24 kg (68.5%)
• Cj 2x intakes = 2.22 kg / 3.19 kg (69.6%)
• Cj 3x section = 2.22 kg / 3.21 kg (69.2%)

For comparison, consider these Cronje scores from other reflex combustor pulsejets:

• Classic Chinese "Laird" ... Cj combustor = 2.04 kg / 2.42 kg (84.3%)
• James Irvines' "Raptor" ... Cj combustor = 2.40 kg / 2.42 kg (99.2%)
• M.'s "Superchine 8.1a" .... Cj combustor = 3.75 kg / 3.81 kg (98.4%)

The "Cronje" metrics compare the developed thrust to the theoretical maximum (constraining)
thrust that may be achieved as a function of: (1) combustor diameter (CCID); (2) intake cross
section(s); and (3) total cross section of all ports facing onto the combustor. It is not possible
for a self-sustaining pulsejet operating under static conditions, and in the absence of any fuel
injection system that imparts significant momentum to the air and fuel charges (ie., as found
in pressure jets) to exceed the constraining thrust (smallest of the three values given). These
metrics were named after Cronje (a graduate student of JAC Kentfield) in honour of the graph
he provided in his thesis work, relating thrust to combustor diameter. While I believe Snecma
was aware of all three thrust constraints, it seems obvious that Kentfield and Cronje were not.

What I found very intriguing about FWE-VIII is that all three quantities are in close agreement.
This may be a by-product of your modeling methodology as the algorithms are unknown to you.


Fuel efficiency: no data available at this time

I did not use a model that determines thrust specific fuel consumption (TSFC); at present this
model has difficulty with FWE style combustors. When time permits, I may add that capability.
The model I used for this analysis does not calculate TSFC, but it treats FWE style combustors.

Edit: Fuel efficiency section was misordered; that has been corrected here.


Acoustic performance (dominant mode: closed pipe)

• intake resonance lock up: 6:1 (exact)
• closed-to-open pipe ratio: 12:11 (exact)
• effective acoustic temperature (EAT): 371.4 K
• equilibrium flame temperature (EFT): 1768.0 K

• Helmholtz resonance (H-): 361.7 Hz (delta = 2.3 Hz)
• closed pipe fundamental: 364.0
• open pipe fundamental: 333.7
• VFT virtual frequency: 348.8*

Expected fundamental frequency: 364 Hz

If this were a linear combustor pulsejet, especially one with a head plate, then I would expect
that the synthetic frequency (VFT) is prominent (349 Hz). It is normal in the reflex combustor
pulsejet for the open and closed pipe modes to be synchronised; this is the first example that
defies this expectation. I believe this stems from the 'FWE meme' that this motor still carries.

Not speaking to the quality of the sound recording taken of the running duct, which I have yet
to examine, it should be possible to display (via FFT) the individual peaks for open and closed
pipe modes; the Helmholtz resonance is not audible: it excites the acoustic modes of the duct.

Expected spectra (via FFT, Hz)

• F1 = 364; peaks at 334, 349*, 364
• F2 = 728; peaks at 667, 698*, 728
• F3 = 1092; peaks at 1001, 1047*, 1092
• F4 = 1456; peaks at 1335, 1456
• F5 = 1820; peaks at 1668, 1820

* simple average provided; if this frequency exists, it is likely shifted somewhat higher

This duct also has a possibility of a higher energy mode, which I include here for completeness.

Acoustic performance (dominant mode: open pipe)

• intake resonance lock up: 5.5:1 (exact solution)
• closed-to-open pipe ratio: 8:9 (exact solution)
• effective acoustic temperature (EAT): 626.0 K
• equilibrium flame temperature (EFT): 1978.0 K

• Helmholtz resonance (H-): 430.5 Hz (delta = 2.7 Hz)
• closed pipe fundamental: 385.0
• open pipe fundamental: 433.2
• VFT virtual frequency: 409.1*

Expected spectra (via FFT, Hz)

• F1 = 433; peaks at 385, 409*, 433
• F2 = 866; peaks at 770, 818*, 866
• F3 = 1300; peaks at 1185, 1227*, 1300

* simple average provided; if this frequency exists, it is likely shifted somewhat lower

End of report

Postscript: I just noticed Larry's posting, where he reports a frequency of 400 Hz from UFlow1D.
If this holds up (ie., if the running motor matches his report), then this would indicate that the
dominant acoustic mode for this motor is its open pipe mode: 5.5:1 lockup at 626 K and 1978 K.

This is the second (a higher energy mode) discussed at the end of the acoustic analysis section.

Furthermore, this would also imply that a synthetic frequency below 409 Hz is the fundamental.
While I believe this result unlikely, I will never argue with facts; time for me to check the video!

Cheers!
M.

[milisavljevic]

Acoustic performance (dominant mode: closed pipe)
...

• Helmholtz resonance (H-): 361.7 Hz (delta = 2.3 Hz)
• closed pipe fundamental: 364.0
• open pipe fundamental: 333.7
• VFT virtual frequency: 348.8*

Expected fundamental frequency: 364 Hz
...
Expected spectra (via FFT, Hz)

• F1 = 364; peaks at 334, 349*, 364
• F2 = 728; peaks at 667, 698*, 728
• F3 = 1092; peaks at 1001, 1047*, 1092
• F4 = 1456; peaks at 1335, 1456
• F5 = 1820; peaks at 1668, 1820

* simple average provided; if this frequency exists, it is likely shifted somewhat higher

Okay! I have (quickly) checked out the video clip that Graham and James provided, and have determined
the fundamental to be 357-358 Hz. This is within 6-7 Hz (< 2%) of the expected value. Keep in mind that
no corrections were made in the model to account for the altitude or ambient conditions of the test site;
the corrected frequency result may be closer to the recorded value. In any case, less than 2% is not bad!

A second case to consider is that 357-358 Hz is the synthetic frequency, which I reported to be somewhat
higher than the simple average of 349 Hz. Synthetic frequencies are normal in ducts with stronger closed
pipe contributions, eg., valved pulsjets and valveless ducts with headplates. If it is in fact normal for all
ducts has yet to be shown conclusively; this result may be such an example. There is never enough data.

All from me for now... (tired)

Cheers!
M.

[milisavljevic]

Edit: This post has been superceded by a newer post, so don't bother reading it. Thanks! M.

Okay! I have (quickly) checked out the video clip that Graham and James provided, and have determined
the fundamental to be 357-358 Hz. This is within 6-7 Hz (< 2%) of the expected value. ...

Um... I forgot to mention one thing: the modeled duct is 559 mm long; the actual duct is ??? mm long.
A longer duct will run slightly slower than what I modeled; a shorter duct will run slightly faster, natch!

Graham: Can you please provide us the actual length of the duct, as tested? The altitude and weather
conditions for the test site would also be a nice thing to have. I would like to refine the results here!

Cheers!
M.

[Mike Everman]

Thanks, M.! Man, that's a lot to chew on. Quite a tour de force, er, tour de thrust... My silly models pale. While some aspects work, I do not think they are working the way I think they are working! ha

[Nick]

...im going to put my head in a bucket of iced water for a while to stop my ears bleeding.

Does that really help?!

Just 7 or 8 hours back Mike and I were discussing glass jam-jars and pulsejets...were your ears burning?

Welcome back!
M.

Have a heart guys, my ears are already bleeding, now they are burning too!

[Nick]

Good morning Nick.
With the price of household energy going up I think we should get that pot of yours running again!!
Keep well. I hope to see you soon. Let's make some waves on the Welsh boarders?

Best Regards
Graham.

Hi Graham,

You're right mate, I'll get some more meths, then you're on!

Nick

[Graham C. Williams]

Dear M.
Thank you for all the time and effort you have put into this analysis. It's much appreciated.
I realise the audio track is clipping. Sometime in the next month I'll attempt to make a high quality recording. The sections of audio track I tested, near the end of the run (at full power) gave me peaks at the following frequencies:
354, 708, 1062, 1415 Hz. 354Hz is not a long way from your results. Very Good

To aid my understanding of your report would you please give me a little background in the interpretation of the Sigma scores and how they relate to the real world?
Same again for the Step ratios, Please.

Total length of Motor: 560mm.

Your interpretation of the CC length (100mm) does not surprise me.
My model shows late heat release in the motor suppressing the operating frequency. I don’t know if this is an artefact of the system but how does this sit with the idea of limited combustion length? Do you have any ideas?

The higher energy mode. Interesting, I think I've seen some of this but not really focused in on it.

A great read. Thanks.
Expect many more questions.
Graham.

[PyroJoe]

M.
Good comprehensive work. Is there a reasoning why the Logan and various side ports configurations are linear instead of "Partial Reflex". I understand if the path was taken to simplify. Just curious. Thanks for posting.

Joe