[serialk11r]

Okay after a bit of research and thinking I think this is definitely possible. A turbocharger not attached to the engine usually would run at higher speeds, but mechanically linking it to the engine would change up things a bit. Ideally we'd want CVT connecting the 2, but I believe a 2 speed gearbox is probably good enough to get near peak efficiency most of the time.

A single speed link would probably be okay though. Garrett's compressor maps seem to indicate 200k rpm as the maximum allowable speed. Of course having the turbine spin at close to maximum speed isn't best because losses tend to be the greatest, but a chart I found on the BorgWarner website seemed to indicate peak efficiency at around 160k rpm, slightly lower at 180k, and climbing up consistently from lower speeds. That said, the 80k curve was still in a pretty healthy zone, within 20% of maximum efficiency, but if we extrapolate a bit we can see that the efficiency drops off quite a bit at lower speeds. This is probably why turbo-compounding has appeared in diesel engines first: they have only a small rev range to worry about, so the turbine doesn't need to operate at inefficient conditions.

If our engine has a 8000 rpm redline though, things seem rather inconvenient. With 200000rpm maximum turbine speed, we want a 25:1 gear ratio to make full use of the "useful" operating range of the turbine. At say 750rpm idle though, this is a pathetic 18000 rpm at which the turbine does barely any work, and at 2000 rpm, we are only at 50000rpm at the turbine, at which it can only achieve perhaps 50% of max efficiency. Certainly with higher gear ratios for fuel economy, if we are running 2500rpm on the highway, our turbine does not operate very efficiently. However while cruising and idle, there isn't as much exhaust either, and the pressure ratio across the turbine would be close to 1 anyways. So that brings us to acceleration. But when we get over 3000rpm the turbine can do pretty well. So for city driving, we probably want something more like a 35:1 ratio to make the turbine useful from 2000-4000rpm. But then again, you can stick to one ratio and rev a bit higher in each gear.

As far as turbo sizing goes, the Garrett website does some approximate calculations with a 2L engine that is supposed to make about 400hp. It would need about 24psi boost to do this at 8000 rpm (not intercooled though I think, but just using this for quick computations). In my previous post I used the fact that there is perhaps more than 3atm absolute pressure left in the cylinder when naturally aspirated. Let's say there's about 30% of the energy in the pressure difference that can be captured. (so use 0.75atm gauge pressure to calculate). This is about 15hp from what I said previously, so we want the turbine from a turbo with compressor that uses 15hp under peak power conditions, which would be a turbo that you'd use to generate about 7psi boost. These calculations are super super super rough, but that gives you sorta an idea of the difference between sizing of the turbines between just a turbocharger and a turbo-compound (with supercharger or not). With say 5psi boost we will have something like 30% more exhaust pressure as well, so the turbine should be from a turbo that makes about 10psi boost, and so on. However you'd want to use a smaller aspect ratio turbine housing since you're not using as much air.

Oh and the more boost you add the more useless this turbine will be at part load, of course. On a racing car though this would provide pretty significant benefit in power.

Another side note: I am honestly not too sure if manufacturers would ever consider this as an efficiency increasing measure, when it's possible to add displacement and use late intake valve closure instead, although late intake valve closure is a bit tricky to do valve timing output control with. Of course more displacement has its own issues too...I guess if it came down to cost, 25% more displacement is cheaper to do than a turbo compound setup most likely, but then with more displacement you'd run into the issue of possibly overexpanding the exhaust at part load. Dunno...