The engine (10) includes a low spool (16) disposed aft of an air inlet (12) and a high spool (34) disposed aft of the low spool (16). An intake reverse-duct (44) is disposed radially outward of the high spool (34) and reverses direction of low pressure compressed air from the low spool (16) into a forward-flow high pressure compressor (40) of the high spool (34). A discharge reverse-manifold (48) directs flow of an exhaust gas stream (50} from a forward-flow low pressure turbine (20) into a rearward-flow direction and into at least one pulse detonation firing tube (54). An annular bypass air duct (72) directs cooling air along the engine (10)—The at least, one firing tube is positioned radially outward of the high spool (34), overlies the high spool (34) and is also positioned within the bypass air duct (72).