[serialk11r]

Today I was pondering this question instead of doing homework, and I've almost come to the conclusion that it is viable (although perhaps expensive).

We can analyze the (gas cycle) efficiency of a Roots blower run against a negative pressure gradient by looking at the only non-isentropic process that happens in this scenario, when the atmospheric pressure gas "blows down" into the manifold via free adiabatic expansion. This entropy increase is somewhat easy to quantify.

Now looking at it from a pressures point of view, after the blowdown is complete and the pressure against the lobe has equalized with the manifold, the rotor will turn 1/2 of 1/n revolutions (where n is the number of lobes), displacing 1/2 of 1/n of its rated displacement, and work will be done on the rotor. In the real world it's a bit more complicated but just working off this for now...

My problem with this is that if we're actually putting work into the rotor, then the intake temperature and pressure should end up lower than before (for the same air density), except that means the atmospheric pressure air coming in is blowing down to a lower pressure than it would with a throttle plate...which means more losses to the free expansion. Can someone point out the flaw in my reasoning?

Is it perhaps that at the same pressure, the throttle plate is allowing less air mass through?

EDIT: okay thought about it a little more, if the Roots blower is displacing x volume for every 1 unit volume the engine is displacing, then the Roots blower is having slightly less than x * the amount of pumping work the engine is doing since the negative pressure acts on the blower for x times the volume it acts on the engine. So the engine is expending ideally about the same amount of pumping work, but in real life more? The entropy accounting is so much easier...
If the plenum volume is small enough that each atmospheric pressure pulse from the blower increases the pressure appreciably, then the pressure will drop more as each piston descends on the intake stroke and reduce the net work required, and it's easy to see that having the pressure drop less during the blowdown and then having reversible expansion on the intake stroke increases entropy less, but this is pretty iffy. If plenum volume gets really low then it gets interesting and you can probably recover a fairly large amount of energy but that's not practical.