A method comprises providing a combustion apparatus having an outer vessel and an inner conduit. The outer vessel has a first wall that defines an internal volume. The inner conduit is at least partially positioned within the internal volume and provides a fluid passageway that is in communication therewith. The method further comprises introducing oxygen into the internal volume in a manner such that the oxygen swirls within the internal volume and around the inner conduit. Furthermore, the method comprises introducing fuel into the internal volume, and combusting the fuel and oxygen at least partially therewithin. The combustion of the fuel and oxygen produces reaction products and the method further comprises discharging at least some of the reaction products from the internal volume via the fluid passageway of the inner conduit.