Expert: Paul Soderman - 2/18/2001

Question
Dear Sir,

Excuse me, but this is rather long and takes some explanation.  I have run into the problem of determining the dimensions of a novel gas burner I have "invented".

The burner is a tube that ends with conical constriction and a short tubular nozzle at either end (like a funnel slapped on each end of a straight tube).  A propane gas jet sticks into each nozzle, so that each nozzle is used as a Bunsen burner, to produce a good gas/air mixture.

Gas is squirted into the tube from both ends.  Before the tube is completely filled with gas, the mixture is ignited at one end by a spark plug. The explosion drives hot combustion products out of the nozzle but also slams into the mixture at the other end of the tube, compresses it and ignites it.

While the compression and ignition take place at the other end, the first end of the tube is evacuated (due to inertia of the expanding gas) and the vacuum draws fresh gas/air mixture in.  This fresh charge fills its part of the burner just as the hot pressure wave hits it from the explosion in the opposite end and the cycle repeats itself.  It could happen with very high frequency, perhaps a couple of hundred Hz.

My theory is that the funnel-type constriction will not let the charge escape from the nozzle quickly enough when the hot pressure front hits.  Instead, the charge will suffer compression and ignition, with only a minor amount blown out.

What I will get is a blowing burner without a blower (indeed, without a single moving part!), with good fuel-air mixing, very good efficiency because of compression etc.  The tube can be bent into an U-shape, so that the hot gases blow in the same direction.  Even the ignition is only required for that first blast, so that it can be done with a small battery, and the thing would not need an outside power source.  With proper design, it might even function as a small and cheap jet engine for flying models, like the flap-valve pulsejet engines.

However, my physics fails me when I try to calculate the relative lengths of the nozzles vs. the main tube.  Their relationship must obviously be exact, so that the precise timing of the hot and cold fronts in the engine is achieved.  Any ideas?  Of course, I could build the thing long and start cutting off bit by bit, but would like to have at least a rough idea before I start.

Thank you very much!

Answer
Bruno

You need the speed of the detonation wave in the tube.  A good discussion of this can be found in Zucrow and Hoffman:  Gas Dynamics Vol. 1 (John Wiley and Sons), page 473.  The computation is not trivial but can be made if the various factors are known such as the gaseous mixture.  On page 484 are calculations for different fuel mixtures that result in speeds ranging from 1926 to 3627 m/s.  

Good luck.

Paul