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Rocket nozzles are used to convert slow moving gas under high pressure and temperature into hypersonic gas under approximately ambient pressure. From many videos of experimental Pulse Detonation Engines (PDE), or a subgroup of thereof - Rotation Detonation Engines (RDE) engines seems that avoid using nozzles. Here are some videos of PDE & RDE without nozzles: 1, 2, 3
Do pulse detonation rocket engines (PDE & RDE) require any type of nozzle at all?
One certainly doesn't want a converging nozzle because the flow is already supersonic.
None have made use of converging or converging-diverging nozzles, because the exhaust is typically flowing at supersonic velocities and thus could be choked through the converging cross-section. This would result in a loss of energy that would decrease the overall efficiency of the system.
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Like all jet-thrust reaction-based engines, the exhaust from a RDE may be channelled through a nozzle to increase thrust. Outlet and nozzle designs have varied across different RDEs. Many have not attached any nozzle, whilst some have chosen to utilise an aerospike [30, 31, 52]. The use of an aerospike increases performance through higher expansion area ratios, although the increased surface area results in higher heat flux and thus a loss of efficiency from the additional heat transfer [53]. Aerospikes may be directly attached to the end of the reaction chamber [31]. A diverging nozzle was found to increase the specific impulse, although the thrust increase was small, and for angles greater than 10°, the increase with angle was negligible.
(Quoted out of order)
Source: https://www.intechopen.com/online-first/a-theoretical-review-of-rotating-detonation-engines
