The flow through the core of a hybrid pulse detonation combustion system is passed through a compressor and then separated into a primary flow, that passes directly to the combustor, and a bypass flow, which is routed to a portion of the system to be used to cool components of the system. The bypass flow is routed to a nozzle of the pulse detonation combustor. The flow is then passed back into the primary flow through the core downstream of where it was extracted.