An engine contains at least one pulse detonation combustor which is surrounded by a bypass flow air duct, through which bypass air flow is directed. The bypass air duct contains at least one converging-diverging structure to dampen or choke the upstream propagation of shock waves from the pulse detonation combustor through the bypass flow air duct. The bypass air also serves to cool the outer surfaces of the pulse detonation combustor. The bypass air flow is controlled in tandem with the heat release from the PDC to provide the appropriate amount of thermal energy to a downstream energy conversion device, such as a turbine. A mixing plenum is positioned downstream of the pulse detonation combustor and bypass flow air duct.