Can motorjets be a viable means of propulsion?
Internal combustion engines (ICE) have great thermal efficiency, so driving a fan or compressor using an ICE is on paper very appealing indeed.


  It is well known that internal combustion engines are capable of achieving higher thermal efficiency than gas turbine engines.


NASA even looked at it in 1976. The proposal was to substitute a jet engine's combustor with an ICE. Two problems with that (according to Rolls-Royce) are the need for a gearbox and "component aerodynamic mismatching under certain engine operating conditions" due to the single-shaft design.

R-R filed a patent in 1995 that according to them fixes the problems with NASA's engine. So far we know why motorjets will have a hard time making a comeback.

R-R's solution is, more shafts, of course. They propose to have an ICE in place of the combustor, but this time it has its own shaft, fed by its spool's compressor, and the exhaust would drive a turbine (too many parts already) that drives a ducted fan (think turbofan but with ICE thermal efficiency).


  According to the present invention, an aircraft compound cycle propulsion engine comprises a propulsive fan and a core engine to power said fan core engine comprising an air compressor downstream of said fan, at least one rotary internal combustion engine configured to receive compressed air from said air compressor, a power turbine positioned to receive and to be powered by the exhaust efflux of said at least one rotary internal combustion engine, a first shaft drivingly interconnecting said power turbine and said propulsive fan, and a second shaft drivingly interconnecting said at least one rotary internal combustion engine and said air compressor.






Source: https://patents.google.com/patent/US5692372A/en