Technology

even overcoming the parasitic portion of extra energy needed during the compression cycle and the exhaust cycle against the turbocharger impeller?

Let's assume the contrary. Let's assume it can't. Let's assume the turbocharger is a net drag on the engine, and any gains are only from enabling the engine to burn more fuel. If this is all true, then the turbocharger should not be able to function without the reciprocating engine. Without the "push" from the pistons during the exhaust stroke, the turbo shouldn't be able to turn.

If we can show that the turbo can not only spin without the piston engine, but that additional energy can be harvested, we will have disproven this assumption.

So, let's get rid of the pistons. Plumb the intake manifold directly to the exhaust manifold. We have one combined intake/exhaust manifold. We stick a couple spark plugs into that manifold and turn it into a combustion chamber.

Now we have air passing through a compressor turbine, into a combustion chamber and then through an exhaust turbine. Sound familiar?

Engineers discovered that some turbos were capable of producing more power than the engines they were attached to. They discovered that the reciprocating engine was a drag on the turbo. The only reason to keep the reciprocating engine was because material science hadn't caught up. We didn't have turbos capable of directly handling the heat of combustion.

That discovery gave us the jet engine.