It sounds like you know your way around a turbofan, but you wrote some confusing stuff, mainly this: > Now, as this compressed air exits from the back of the e

It sounds like you know your way around a turbofan, but you wrote some confusing stuff, mainly this: > Now, as this compressed air exits from the back of the engine, it provides a forward thrust. This is something you generally don't want to happen in a reaction engine. If you eject above-atmospheric-pressure out of your engine, the expansion takes place downstream, in the wake, and that energy is mostly wasted (some pressure thrust is still created, but it's minuscule). You always want all the expansion to happen inside your engine, in a properly designed propelling nozzle, which should always result in a flow of low-pressure high-speed air leaving the engine. If the nozzle fails to expand the air (choked flow, nozzle too short, wrong shape), you're losing thrust (and efficiency).