You have to distinguish the conventional (high efficiency) cycle of a jet engine at low Mach, from the reheat (low efficiency) operation usually used for high Mach.

No engine (of which I am aware) has air flowing past the fan blades at supersonic speeds, because the trans-sonic transitions tear engines apart. There is one prototype aircraft (a naval derivative of the F-84) which did have a supersonic propeller, but it was very inefficient and loud. All jet engines compress sub-Mach 1 flows, then expand them at the very back of the engine to produce supersonic exhaust.