www.pulse-jets.com

PyroJoe wrote: Is there a reasoning why the Logan and various side ports configurations are linear instead of "Partial Reflex".

First of all, there is nothing even remotely special about the "Logan". The designer merely wanted a pulsejet
that could be mounted at the end of helicopter rotor with its fuel and air charges delivered very conveniently
down the rotor. Thus the side port configuration. While I understand the term "linear" reads as "in a line", it
may help you to visualise the various intake-combustor layouts with an "electric eye", ie., diagrammatically.

Simply put, "linear" combustors offer more than one path in and out of the combustor, and in particular, the
fresh air charges are delivered via paths that do not directly intersect any exhaust trunk(s) (any tailpipe(s)).

A "reflex" combustor more closely resembles a human lung: there is only one trunk leading to the combustor,
but many branches are possible (typically multiple induction pipes (intake ducts)). It makes a BIG difference.

It is certainly possible to imagine a combustor with multiple trunks, each with multiple branches; however,
the cross communications (ie., branches in one trunk 'signaling' branches in another) would complicate both
analysis and classification. The bigger questions would be: "Why do it?" and "What advantages does it offer?"

I hope I answered you question?!

Cheers,
M.

.
Hello Graham --

Graham C. Williams wrote: Thank you for all the time and effort you have put into this analysis. It's much appreciated.

No worries! It did delay the release of the sch-8.9e specification (Fredrik's entry in the 1.5 liter challenge).

Graham C. Williams wrote: The sections of audio track I tested, near the end of the run (at full power) gave me peaks at the following...
354 Hz is not a long way from your results.

As I was very tired (and getting "foggy" ), when I checked the video I only scrutinised the earliest tics.
This certainly could account for a 3 Hz delta. I will go back to check the entire length, section by section.

The quality is good enough for basic analysis, but don't let that stop you from making a better recording!

Graham C. Williams wrote: 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.

Sure! Just not in this post; it's dinner time here. I will leave you with the teaser that the sigma scores
mathematically bind pulsejets to the other main jet engine types: (sc)ramjets, turbojets (and turbofans).

Graham C. Williams wrote: Total length of Motor: 560mm.

After sleeping on it, I realised what is needed is for you to audit this engine: measure each segment and
then report back any variances from the drawing you provided. The acoustic model is too precise to miss
by 6-7 Hz. Historically, these "misses" have always resulted in the audited engine not matching the plans!

I have worked with many builders, some of them are quite talented; but there are always build variances!

Edit: When I suggest that you audit this motor to determine its actual ("as built") dimensions, I mean all
dimensions: lengths and diameters, especially the lengths and diameters of the induction pipes, couplers
and (most especially) the inlet flares. Despite Larry's opinions to the contrary, the resonant frequency of
this duct is determined by the intake lock up ratio, which is a function of induction pipe acoustic lengths.

Edit: It does appear the subjective frequency is the synthetic value (ie., a weighted average of the open
and closed pipe modes). This is an interesting result, if true; it makes the whole process worth my while!

Graham C. Williams wrote: 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?

Any statements containing the term heat release will not map onto my methodology. This concept does
not have any bearing on what I do. It is not needed to determine or fix acoustic properties, thrust, fuel
consumption, anything. I make many thermokinetic calculations, but they do not (can not?) disrupt duct
acoustics. Much more the other way around: the combustion events are locked to the Helmholtz mode(s).

We can discuss this subject later, if you wish.

Graham C. Williams wrote: A great read. Thanks.

You're welcome!

Graham C. Williams wrote: Expect many more questions.

Did I mention my upcoming vacation?! (joke!)

Cheers,
M.

Dear Graham, for your amusement:

Graham C. Williams wrote: The sections of audio track I tested ... gave me peaks at the following frequencies: 354, 708, 1062, 1415 Hz.

I checked snippets from one end of the audio track to the other for the first four peaks (F1-F4).
The lowest fundamental observed was 352 Hz; the highest 358 Hz. So this is our working range.

Let's assume, for "edutainment purposes": that this is the synthetic frequency (ie., a weighted
average of the open and closed pipe modes); that the lock up ratio is 6:1 with dominant closed
pipe properties as reported yesterday. This places the open pipe in the 330's and closed pipe in
the 360's; a high fidelity recording could display peaks corresponding to each mode's harmonics.

Next...

Graham C. Williams wrote: Total length of Motor: 560mm.

I drop back into the model with the corrected length (ie., assume a 27 mm combustor cap) and
to make things more interesting, assume that the exit diameter is 66.9 mm (spec is 66.5 mm)
and that the inlet flares are each 29.5 mm across (spec is 31.0 mm; a most incredible amount).

These changes simulate realistic build errors and will illustrate the acoustic leverage they have.

We find...

First of all, the 1 mm longer end cap and small change in exit diameter are nonetheless enough
to lift the limit thrust from 2.22 kg to 2.25 kg (4.95 lbf). Total volume increases, from 1009 cc
to 1015 cc; volume thrust density rises to 21.7 N/liter. Wrt. thrust, we are "deep in the noise"!

A change in exit diameter has effects that simultaneously raise and lower the Helmholtz modes.
The net effect is to 'accelerate' the duct to slightly higher acoustic temperatures and resonance.
In contrast, small changes in inlet flare diameter produce large effects on the Helmholtz modes.

Solving for the stipulated changes raises the acoustic temperature to 388 K (was 371 K), with a
similar rise in the equilibrium flame temperature to 1821 K (was 1768 K). The Helmholtz modes
also also elevated, with the lower Helmholtz mode reaching 369.3 Hz (was 361.7 Hz, up 7.6 Hz).
(all but ~1 Hz of the rise in the lower Helmholtz frequency is from the change in flare diameter)

The new open and closed pipe frequencies are 340.3 and 368.7 Hz (was 333.7 and 364.0 Hz), a
12:13 ratio; the arithmetic average of these two frequencies is 354.5 Hz, a near perfect match.

But...

I am not suggesting the above is physical reality; I am only making my point. Without an audit,
we may never have an exact solution. I do want to settle this question of synthetic frequencies.
(if this duct has this property, then I may pursue a reflex combustor that "straddles the fence")

As Mike would say: "Faaaaassscinating!"

Cheers,
M.

PS: I owe you an explanation wrt. sigma metrics and step ratios; I will post it on my next visit!

Dear Larry, M. and Mark.
I owe you all a lot of thought and a many words.
Life has got in the way for a few days. Please excuse me.

Graham.

Dear M.
Many thanks again I deeply appreciate the efforts you have made. I need to reread your papers and collect my comments but 'In general' the comments suggest, " Reasonably good but could do better". Ha

One point that strikes me. Some of the concepts and ideas bound into this motor owe a lot to the work of Mike Evermann I'd like to acknowledge that here.

On the issue of combustor length. I'm now in 2 minds. Initially happy to accept your idea of it being about 100mm in effective length I did some modelling over the weekend. The results of this make me ask a lot of questions but first I must ask - What do you mean when you say the CC is effectively about 100 long? Are you referring to: Combustion boundaries, Mixing boundaries or what? What are the criteria bound into this statement?
I'm not interested in whether your value is 100mm or 120mm. My question stems from the fact that I see combustion conditions exist over a large fraction of the pipe. The potential for partial CV combustion, defined by: the induction and exhaust Hot/Cold or Cold/Hot interfaces and Velocity Zero crossing points (with the correct gradient) indicate that useful work can be done over almost all the pipe. It's only the timing issue that dictates if this work will act to damp the pipe or otherwise.

This paper has been very useful; it's made me ask many questions (that's good in my books). I now have some issues about the definitions of induction length and coupler/transition (or whatever the name is) length with reference to his motor. I'll need to ‘prep’ some diagrams first.

Graham.

Dear Mike.
Looking at my technique for unpacking this motor.
My approach gives me very good correspondence between the models predictions and the physical motor but perhaps more importantly suggests how this motor may be satisfying both your criteria at once. I think it is inherent in the unpacking method and the simple way I've defined the induction pipe lengths and Coupling/Transition lengths.
So, for my model only. The induction pipe length is simply that distance down the middle of the induction pipe (inc bends etc.) from the open end to the point where it joins the CC if the hole were not there.
The Transition length (for this twin opposing pipe layout) is simply the distance from the rapid transition (induction pipe to CC wall) to the Theoretical or noted location of the centre of early combustion. (Please note that this will not necessarily be half the dia. of the CC at the point where the induction pipes join the CC wall. In this model there is an angle involved.)
These components are simply added to the front of the unchanged CC and tailpipe.
It is a lot simpler than the number of words it takes.

Turning to ‘Thrust’ for a moment.
Thrust has 3 components: Induction pipe Thrust (2 components in itself), Exhaust Thrust (2 components again) and that Thrust due to the internal momentum.
When a motor is bent into a U form or 'packed' from its 'Linear' form a number of things happen. Again, thinking simply:
The induction pipe Thrust term changes sign.
Part of the internal momentum will change sign and partly cancel components from other parts of the motor and finally,
The location of the induction pipe entry will change with reference to the exhaust pipe location.

Using this simple model to calculate the Thrust of my packed motor (I get very accurate results); first from the point of the internal momentum cancellation I define the apex of the bend (or packing) as being that place that results in the open end of the induction pipe being in the correct location on the motor. Second, change the sign of the induction pipe contribution. ( Note that other locations for the apex can predict more power, in the model, but I believe that they do not meet the criteria for the correct loaction of induction pipe entry to the CC. This last is I'll defined in my mind and will probably change)

I hope you see how this may result in the motor satisfying both your criteria?

Regards
Graham.

larry cottrill wrote: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

Dear Larry.
NUDiS doesn't work quite like that. Using NUDiS you can start the motor (if it's going to start that is!) with any half reasonable gas temps over its length. I tend to start with 1400K across the motor. Within about 4 cycles of running these temps will self-adjust. You can see how they change over the cycles then stabilise into a rhythmic pattern. Typical upper and lower values are:
Induction pipe - 300 to 400K to 1400K
Combustion region - 1000K to 2000K but mostly in the 1500K to 2000K regions.
Middle Exhaust pipe - 1400K to 1600K some times a bit higher
End of the Exhaust pipe - similar to the induction pipe.

In early versions of the combustion programme I had applied a restriction, limiting the upper combustion temp to 2000K. For later versions (probably not yet released) I've removed that restriction and just let it go where it will. I was surprised with the results - very little change, maybe a momentary maximum to 2300K but not a lot more.

I realise you and Joe are making copies or something similar to this motor for your tests. Is there any more information you need from me?

Regards
Graham.

Graham C. Williams wrote:Typical upper and lower values are:
Induction pipe - 300 to 400K to 1400K
Combustion region - 1000K to 2000K but mostly in the 1500K to 2000K regions.
Middle Exhaust pipe - 1400K to 1600K some times a bit higher
End of the Exhaust pipe - similar to the induction pipe.

Yes, I realize it's a different story, since you can simulate the heat injection from the combustion event. Fascinating, just the same.

I realise you and Joe are making copies or something similar to this motor for your tests. Is there any more information you need from me?

Ha. I don't have time to make much of anything. It's all up to Joe at the moment.

Of course, the basic dimensions you've given us were the main thing. I guess my most important remaining question would be: Do you feel you've achieved experimentally a "best" or "final" location for fuel spouting that gives you best possible running? If so, how does this seem to fit with pressure wave action and flow velocities in the intake pipe as revealed by nudis? What I'm really after is how good a prediction we can make about the correct fueling point. (I realize that there's a lot more to this than meets the eye, because of turbulence effects, mixing path length, etc., etc. of course, but I'm most interested in what we can predict with one-dimensional analysis alone, momentarily disregarding these real-world factors.)

L Cottrill

larry cottrill wrote: What I'm really after is how good a prediction we can make about the correct fueling point. (I realize that there's a lot more to this than meets the eye, because of turbulence effects, mixing path length, etc., etc. of course, but I'm most interested in what we can predict with one-dimensional analysis alone, momentarily disregarding these real-world factors.)

L Cottrill

Dear Larry.
My model is not sophisticated enough to answer these questions; all fuelling locations for the physical motor are empirically derived. Think about ‘Mixing path lengths’ because I don't see how the correct injector location for Propane can also be the correct location for Gasoline - well, at least not for small motors?

Regards
Graham.

Graham C. Williams wrote:Dear Larry.
My model is not sophisticated enough to answer these questions; all fuelling locations for the physical motor are empirically derived.

Graham, I'm sure I wasn't clear with my question. What I'm asking is really this: After you get a fueling point that gives you "best running" in the real motor, can you then go back to nudis and see an indication as to why this turned out to be a "sweet spot"? That's why I was talking about looking at it with those real-world considerations temporarily removed from the picture. What I'm really after is whether you would agree with me that there is a "theoretical" starting point for carbureted fueling experimentation.

My concern is that all we (or at least, some of us) seem to know about fueling is a handful of "rules of thumb" gathered more-or-less empirically: If you're too far out, you lose a lot of fuel in external combustion; if you're too far in, you don't have enough path for good mixing; and so on.

Everyone who's thought about this realizes that the most basic problem is the alternating flow in the intake. Carburetion assumes that air flow (in either direction) can create a serious drop in static pressure, driving fuel flow. As Joe's experiments have shown, the overall intake action is just as effective for fuel delivery as the "constant" suction of a piston engine carburetor. However, UFLOW analysis shows that the problem is more complex, because the juxtaposition of flow and the transit of high and low pressure waves is not simple. HOWEVER, it also shows that there IS what I would call an "ideal" zone in the intake for carburetion. It is where the low pressure wave transit is superimposed on a high INflow velocity and yet the high pressure wave transit takes place at an instant of high OUTflow velocity. In other words, the pressure wave pulls fuel on inflow but helps to "valve off" fuel flow on outflow !!! This, in effect, actually gives us perfectly "timed fuel injection". It seems to me that this is the main reason why, even with a vapor fuel like propane, spouting location does make such a big difference in running (perhaps much less so if there is a high inward fuel velocity, as with the Rosscojector and the like). Another way to say this is that low velocity vapor injection is actually a "carbureted" fueling mode, to a very large extent.

Joe's experimentation with the liquid fueling wand shows that there is a LOT of suction available throughout almost the whole length of the intake. However, this is not enough information, because it doesn't reveal how much of the fuel delivery would have been wasted in the outflow part of the cycle. The example Mark sent me of liquid carburetion in the center of the straight pipe (on a running Chinese engine) probably illustrates the need for compromise between a point of ideal "timed injection" and adequate mixing path length. (Or, it might be the point of "best suction" for that particular engine design!) Fortunately, the zone where reasonably good pressure/velocity juxtaposition takes place is actually fairly large (about the innermost third of the straight pipe, on the current FWE intake layout).

Think about ‘Mixing path lengths’ because I don't see how the correct injector location for Propane can also be the correct location for Gasoline - well, at least not for small motors?

Yes, I am absolutely sure you're right about this. For liquids, it will even depend a lot on how small you can get the droplet size of the fuel spray achieved. This in turn depends to a large part on air velocity, which in our case obviously varies all over the place during the engine cycle. Just another reason why experimental evidence is the only definitive guide. But, that doesn't mean we can't theoretically determine a "best place to start from" and work (probably, outward) from there.

Go back to your nudis runs and have a look at the pressure vs flow at particular points in the intake, and let me know whether you agree.

L Cottrill

Good morning.
This video clip was shot at 600FPS and looks at the tailpipe of the motor when running at full power. No sound. Enjoy!!!

Graham.

The Induction pipes. 600FPS. No Sound.

Graham.

Zoom into the induction. Again, 600fps. No Sound.

Graham.

Graham -

Well, that is pretty cool. I wish you could do it with a little Schlieren system set up around it. "They always want more." Ha.

But, very interesting -- worth studying a few times, for sure. What kind of camera do you use to give you 20x normal speed?

L Cottrill

.
Hello Graham -- I just found your posts...so many!

Graham C. Williams wrote: Dear M.
Many thanks again I deeply appreciate the efforts you have made.

You are most welcome. I still owe you the definitions (and more!) but at the moment I am rather preoccupied
or overwhelmed by pulsejet-related events on my side of the hemisphere. I promise to reply here, post haste.

To spice up my return, I have just completed a high-fidelity analysis of the "classic" Chinese (drawn by Laird).

As the FWE-VIII rev. 8 owes so much to this type, I felt it would be useful to refine my observations and then
bring them back here to share with you. This may? help answer some of your questions, eg., effective length
of the combustion zone. In any event, these latest results were interesting, to say the least.

Be back soon!

Cheers,
M.

PS: Thanks for the video: I am looking forward to watching them all!