Aberlin
Most people want to get rid of pulsations!!
You could try creating the situation which others have to avoid, which is basically to have an exhaust tube with a single diameter which is long enough to generate a resonant sound wave (you can calculate the probable frequency by assuming a node at the burner end and an antinode at the open end). If you get the parameters right, the sound (pressure) wave produces an interference on the inflow of air and fuel (it only works at low pressures) and that causes a momentary increase in flame temperature which surges the flue gas. By tweaking the flows you can probably find a condition which allows the surges to lock in with the sound wave. It probably works more easily if flame doesn't quite fill the exhaust tube and you need to avoid other turbulence raisers which can disturb or retune the sound wave.
(Putnam wrote a whole book about it)
David