pulse jet theory V o.1

[paul fellows]

Please heap your disapproval of this attempt at a partial pulse jet theory, upon the theory and not on the author.

To those of you that have built three or more good jets without really knowing how they work, there will be little for you to gain from this effort. But there is plenty that you could contribute. for example if I say something that goes against your experience , then the theory is wrong in that respect. When the theory disagrees with reality, then it is the theory the need to be chained. If you have only built one jet then the rules of thumb that you used to design it are less certain, the jet may have worked despite them, not because of then.

In order to come up with this acoustic theory I have had a number of simplifications.
I have ignored subtleties such as end correction, just to keep the maths simple.
I have straightened the jets.
I have ignored the combustion chambers, assuming in stead that they are of one stranded diameter along there length.
I have assumed that the combustion takes place in a flat sheet across the jet, this this unrealistic but it gives a point for taking measurements from.
Finally and most importantly this is a purely acoustic theory.( and there for incompleat), It dose not include Kadenacy witch is very very very important to pulse jets. (if you have stick a wet rag in one of the intakes to get it to work, then you could probably do with some one working out a good simple theory of pulse jets. Please help. )

I am going to take the position that the reason no one as come up with a really good theory of how a pulse jet works, is because there needs to be three!
Valved pulse jets are quatre wave oscillators, the theory of how they work is well established.
The first type of valveless pulse jet that I will look at are the forced anti node pulse jets, that is the; Escopette, Ecrevisse, Kentfield and Lockwood-Hiller. These can all be viewed as long tubes open at both ends.
The second type of valveless pulse jet are the forced node pulse jets, these include the; Thermojet, the Chinese, and the Logan. These can be viewed collectively as quarter wave oscillators with a tube stuck in there side.

Any way that is me set up for a fall!
The gauntlet has been throne down!
So may the contest be friendly and may the best side win?

[paul fellows]

Could I beg the help of a Lockwood builder, if I wanted to build a Lockwood with a one meter exhaust pipe, to be of the same pitch as a one meter valved pulse jet. How long dose the in let need to be 33.3 cm or 25 cm?

I am going to invoke Popeye's law to help explain the theory of how a Lockwood valveless pulse jet works.

“I am what I am and that's all that I am.” said Popeye the sailor man.
Or in this context. It is what it is and that is all that it is.

So imagine a four foot Lockwood in operation, what is it?

It is a four foot long tube that is open at both ends. If you look in any text on acoustics, a tube that is open at both ends is a half wave resonator. It is not in any sense a quarter wave resonator.
In operation there is a combustion chamber about a quarter of the way along its length that provides pulses of high pressure, forcing it resonate at the pipes second harmonic.

[larry cottrill]

So imagine a four foot Lockwood in operation, what is it?

According to Cottrill's hypothesis, it is a low-Q quarter-wave resonator one foot long and a high-Q quarter-wave resonator three feet long operating symbiotically in perfect synchronization. The absence of a reflecting wall at the pressure antinode does not keep them from behaving as quarter-wave pipes. Seeing them in this way does not invalidate also seeing the whole thing as a half-wave resonator IF you take into account that the antinode is NOT at the halfway point in the overall length (as it would be in some types of organ pipes, for example). This "asymmetry" can be clearly shown with programs like UFLOW1D and NuDis.

The basic difference in the two resonators is as follows: In each cycle, the neck of the short resonator is completely filled with outdoor air (cool, dense, thick) and fuel, the mixture reaching all the way into the chamber. After the explosion, the unused cool air is completely purged out through the neck and the exhaust gas is partially expelled. Behind the expelled gas, negative pressure is developed to re-initiate the cycle (this is the Kadenacy action). On the other hand, in the long resonator, in each cycle the long neck (cone in a Lockwood) is only fractionally filled with cool outdoor air. The explosion drives it all out, but the hot gas which pushes it out did not come from this explosion but rather from a few cycles in the past. In this case Kadenacy action draws the explosion gas back into the chamber; at the far end, fresh air is drawn in but it never gets anywhere near the chamber. This slug of air becomes the new "tail piston" for the next cycle.

Purists will quibble that the foregoing is an oversimplification. I say, let them.

It is possible to have a pulsejet that is a simple quarter wave resonator, but its efficiency will be poor. The most typical example is the famous "jam jar" combustor. However, I once built a tin quarter-wave "jar" about two feet long that ran briefly in true "jam jar" fashion with a little alcohol. It ran so well that it obviously could have been vapor fueled for constant operation. This would not have made it efficient, however -- it still would have had to breathe through its tailpipe.

You cannot simply divorce "Kadenacy" from "acoustics". Kadenacy action is the driving mechanism for all acoustic pipes, from a penny whistle to an Argus valved pulsejet engine. Kadenacy action simply means that, because air has mass, whenever air rushes out of a tight space, it will not stop when the pressure equalizes but will continue until it is slowed and stopped by the force caused by lowered pressure left behind it. Then, the direction reverses because of that pressure difference. As air rushes in, again it doesn't instantaneously stop when the pressure equalizes, but keeps rushing in until sufficient internal pressure is reached to slow it down and stop it. Then, the cycle repeats.

Because the action of moving air is not "lossless", the process will wind down in some finite number of cycles UNLESS outside energy is added. In the penny whistle you keep blowing; in the pulsejet you keep pumping fuel.

L Cottrill

[paul fellows]

I am not swearing that I am right but please think about this.
As a half wave resonator being driven at its second harmonic, when the pressure at one quarter of the length from the intake is high, then the pressure three quarters of the length of the tube will be low.

The gasses released by combustion will in part flow down to the pressure of the outside air, and in part flow towards the low pressure point half a wavelength further down the tube.

By the time it gets there this will be the high pressure point, but the gas will continue passed this point driven by its own momentum and acoustical energy.

There is one good way to tell the difference 1/4 or 1/2.
Compare the sound of a Lockwood to a valved pulse jet of about half of the exhaust pipe length.
if the Lockwood is a quarter wave resonator like the valved pulse jet then the Lockwood will have a deeper sound. If the Lockwood is acting like a half wave resonator resonating at its second harmonic, then it will have a higher pitch.
Also here viewtopic.php?f=3&t=3104&st=0&sk=t&sd=a ... FFT#p38146
and here viewtopic.php?f=3&t=4085&p=57624&hilit= ... FFT#p57624
seem to suggest that some pulse jet produce even harmonics and a quarter wavelength resonator can not do that, or have I misread the data

[paul fellows]

". Seeing them in this way does not invalidate also seeing the whole thing as a half-wave resonator IF you take into account that the antinode is NOT at the halfway point in the overall length..... This "asymmetry" can be clearly shown."

an intreguing idea a half wave resonator, but of two very unequel halves.
but can the speed of sound be shifted that far?

[larry cottrill]

Paul -

At the high gas temps and low densities at some locations within the pulsejet pipe, the speed of sound is MUCH higher than in normal air. The quarter wave will propagate much faster in the tail section (always hot) than in the front end (intake, almost always full of cool outdoor air). It is a profound asymmetry, NOT a small detail.

Also, in your diagram, you have shown a full wave, not a half wave. It is actually a picture of what would be the second harmonic (twice the fundamental frequency) in a straight pipe of constant temperature. There is no time in the cycle that a pressure wave would resemble that form in a running pulsejet.

L Cottrill

[larry cottrill]

Paul -

You might want to see an animation of the waveforms in a real engine. Go here:
viewtopic.php?f=10&t=4761
and run the second little movie file. The first part of this is two brief animations of the waveforms in my Lady Anne Boleyn engine. First there is a slow animation, then a few cycles of a livelier version of the same frames. These are frames captured from a UFLOW1D run; I have superimposed a little scale drawing of the engine so you can see how the wave alterations fit the engine contours. The upper left pane is the pressure wave; the lower left is density. The upper right is gas velocity (in Mach numbers) and the lower right is mass flow. These little animated sequences are very brief, and some other junk follows. You will probably have to view it several times to really get the sense of it.

This is a good example of an "unfolded" design (what you would call a half wave pipe) for a "folded" FWE (what you would call a quarter wave pipe). There is no acoustic difference. I have designed many folded FWEs this way and gotten them to work. I recently designed a big unfolded one which worked nicely after lengthening the tailpipe very slightly (hey - nobody's perfect ;-).

Enjoy!

L Cottrill

[paul fellows]

Hi I'm still looking at the animation.

The reason I drew a full wave in the pipe, is that that is what I am talking about. A half wave resonator driven at its second harmonic.

Picture this, a one meter long pipe stopped at one end will resonate as follows,
first harmonic four meters in wavelength
second harmonic not possible
third harmonic one meter in wavelength

for an open tube of one meter in length the resonances are
first harmonic two meters in wavelength
second harmonic one meter in wavelength.

[larry cottrill]

Oops ... my apologies. You did say "second harmonic".

I think everything you've just stated above would be correct. Keep in mind that the wavelength in the pulsejet and thje wavelength of the radiated noise will be vastly different, because of the temperature difference between the jet interior and the surrounding air. The frequency will be the same, of course.

L Cottrill

[paul fellows]

Hi Larry

I'm afraid I'm not seeing three reversals (positive to negative and back) which of the of the four graphs should I be concentrating on.
Possibly as you cut to the beat it got lessoned.

Re the video may I suggest for next time, Norwegian wood is in three four tine. Or better still Souza's liberty bell march, the Monty python theam tune is in six eight time, might highlight the third harmonic of a pulse to a bar a bit better. Just a thought.

Any way
I see your beautiful commuter animation, and raise you a set of bad MS Paint drawings such that people can animate them in there minds.

Because both waves have to travel through both sides of the tube to get back to compress the gas for the next pulse the different speeds of sound are applied to both more or less equally

[paul fellows]

Keep in mind that the wavelength in the pulsejet and thje wavelength of the radiated noise will be vastly different, because of the temperature difference between the jet interior and the surrounding air. The frequency will be the same, of course.

one posible way to test between th two theories would be to compair the sound of a Lockwood to that of a valved pulsejet that is half the length.
if my rambelings are right then the Lockwood will be the higher pitched of the two, if i am wrong (and i posibly am ) then the Lockwood will be the deeper of the two sounds

[PyroJoe]

I like the paint,
It is good to see how you picked up the pressure pulse splitting and the 2 seperate wave travels.

From what I have seen the rarefaction wave can be weak compared to the compression wave (although strong enough to collapse heated tailpipes in certain engines). This doesn't appear to have much consequence until one observes what occurs with the related density traveling to and fro in a tube. One thing to consider is the tailpipe at approximately the center of the engine will see very little, if any, (internal) ambient air contact while the intake will see ambient air well over half the cycle time.

I often consider the possibility of some "drift" velocity setup within valveless linear engines, but haven't found much mention of it.

Aerodynamic valving, cavity resonance and pressurized fuel flow IMO can add to the complexity of trying to estimate a specific length, therefore I abandoned the harmonic lengths and started using a method of driving a length/diameter of tailpipe with a relative combustor volume/length.

I think this could make things easier for newcomers, as it basically simplifying the theory in that the engine is building pressure, and releasing it in a controlled manner based on dimensions.

Joe

[paul fellows]

imo

newbi

joe do you have a fleshed version of your theory anywhere?

[PyroJoe]

Not sure what your looking for in a fleshed version.

As metiz once said, after about thirty engines, you lose count. Many engines(and jars) a builder will modify and have 6 or so renditions from a single engine. Patterns start emerging, I learn almost as much from engines that fail or are difficult, as those that bust off and run fine.

Joe


Experience: that most brutal of teachers. But you learn, my God do you learn. C.S. Lewis

[PyroJoe]

This was posted in the forum past, I hold it in high regard:

"you cannot speak of anything in absolutes when you speak of pulsejets. What you have is a hugely complex reaction between chemical processes, thermodynamical processes, flud flow mechamics and acoustics. Up until very recently, researchers literally despaired of describing the processes inside in exact mathematical way. The whole thing was simply too complex.

So, whenever a simple statement on something inside a pulsejet is made, take it as a simplification, never as a solid fact or as a strict rule."