Why are low-bypass turbofan engines used for supersonic flight and not high-bypass turbofans? Aren’t high-bypass turbofan engines more efficient?

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Jet engines take air in the front and spit air out the back.

If the engine takes in air at mach 2 and only spits it out at mach 1, your engine is actually slowing you down. The force of drag is stronger than the thrust.

To put this more generally, your airplane can never travel faster than your engine exhaust.

There is a tradeoff here, though. A faster exhaust uses more energy. Twice as fast is four times as much energy, which means that it’s more efficient to have a lot of slow exhaust than to get the same thrust from a bit of fast exhaust.

The purpose of the bypass in the engine is to get more air blown out the back, and as a result slower exhaust, and more efficiency/thrust for the same fuel use.

You see the issue, though, right? Now your exhaust is slower, so your thrust drops off more at high speeds. No matter how big you build your engine you’re limited by that.

By reducing the bypass or getting rid of it entirely, you get a higher exhaust velocity and so a higher top speed before your engine really starts to lose thrust.

The fan part of a turbofan is essentially a ducted propeller. Propellers lose their efficiency very quickly at high speeds, so they don’t really work at higher than mach speeds and that may also generate shock waves that tear them apart.