If the pipe is narrow, the amount of energy running up the tube and back will be small, and a greater proportion will go out the exhaust. Efficiency increase small. Thrust higher.your comment on halving the engine.
I had the same idea a few years back.
I even made a first prototype that didn't work.
Which doesn't mean much because its the only
VPJ prototype I have ever made, and my failure rate is 100%
But the theory sounds good.
another way to look at it is:-
take any old basically working VPJ (ha)
Add a closed end pipe sticking out of the combustion chamber.
The pipe's lengh, allowing for temperature, etc. should transmit the pressure pulse and reflect it back just in time for the next combusion.
In all practicality, better make that pipe slide adjustable.
Will probably need different lengths for starting and running temperatures.
Now, is that a BCVP, a Half BCVP, or something else?
If the pipe is wide, as wide as the combustion chamber, then most of the energy will go up the tube and back, with little available for exhaust/thrust. However, the large returning pulse should improve the efficiency.
If we look at limiting factors (ah, some maths!)
Then with an infinitely small tube, its just the standard engine.
Nominal thrust, Nominal efficiency.
With an large diameter tube (one that captures and reflects all of the combusiton pressure wave, we have increased efficiency, but zero direct thrust.
(Direct thrust is the momentum change from the energy that goes out the exhaust or other orifice, rather than up the resonance tube).
Even if we modify the direct thrust by its efficiency factor to get an actual thrust, its still zero.
Presumably with a positive pressure gain on each pulse, the combustion pressure will rise with each pulse until it reaches some steady-state value limited by the "Q" of the engine.
But, in the limiting case, thrust is stil eficinecy times zero, = zero.
So, we can plot tube diameter against efficiency and effective thrust.
At zero tube, we have nominal thrust and efficiency.
At large tube, we have a highly efficient noise machine whose only real output could best be described as leakage.
There may be an optimum point somewhere in between, or not.
This optimum point would produce greater efficiency (I'm talking about fuel efficiency), enough thrust to make the machine viable.
Unfortunately I can't tell without lots of maths or simulation or building one or ten.
For simulation purposes, this engine would probably map out as a T shape,
and would need to simulate multiple pulses to see where the pressure builds to. Well beyond anything we have available.
As for maths, a spreadsheet should be possible for some simple stuff.
Just black box stuff - energy in resonance vs energy through exhaust, (Q)etc.
Might be enough to indicate if there curve shape will have a useful maximum point or not.
On the construction side, does someone have a nice healthy reliable pulseject that they could cut a hole in the combustion chamber?
Might be able to screw in a variety of tubes, of different lengths, or adjustable. Smaller tubes shouldn't destroy the engine operation (much),
so hopefully it would still start. Then the tube could be successively crimped to shorter and shorter lengths, measuring thrust for each length.
Measuring sound levels should be a good indicator of optimal length also.
I'd expect wider tubes to be more of a problem.
Ideally, the end of the tube should be at the "front", so that when the pressure pulse is reflected back, we get momentum transferred from it in the right direction.
Smoothly curved pipes would be ok.
in the extreme case, the engine might consist of
A long cylinder, closed at the front end.
Combustion occurs at the rear end.
There are enough funny shaped pipes and thingies around teh combustion area to ensure good breathing. i.e. get rid of burnt gass thoroughly, and suck in a good healthy charge for the next pulse.
The "breathing apparatus" can be curved to point forwards or backwards as appropriate, to optimise thrust.
The bulk of the thrust comes from the main pulse hitting the front of the cylinder and reflecting back.
Phew. Hows that for a brain dump.