Continuing with the idea I presented a while ago about a turbine generator directly connected to the crankshaft, I discovered this has been done on aircraft before, it's called turbo compounding, and exists on some diesel trucks...and I dug up some info.
Deere claims 20% increase in power (for free obviously, intake, combustion, expansion are not affected!) on a diesel engine. They used variable geometry turbo and electrical coupling, but Scania has a mechanically coupled one with fluid coupling (to partially isolate turbine from the crankshaft). Now let's examine the Detroid DD15 that has this system...
18.4:1 compression ratio, but max power at under 2000 rpm. Diesel engines injecting fuel as the piston moves reduces the effective compression a bit more than a gasoline engine, but at low speed this effect is less pronounced. Before anyone gets confused, my goal is to approximate the residual pressure at the bottom of the compression stroke. More precisely, finding a very loose lower bound, because these diesel engines are turbocharged already and have even lower exhaust pressure available for recovery. Let's say a comparable gasoline engine would have 17:1 compression ratio at its own power peak (by CR, I am more concerned with the expansion part of this, not the compression part...because gas engines have much higher speeds, the effect of the rate of combustion being relatively slower at high speed is much greater). Now diesel fuel has more specific heat of combustion than gasoline, so the residual pressure in a diesel of the same effective compression is higher. However at a say, 17:1 CR, you would have more than 10% less residual pressure than at say 12:1, so it's safe to say a diesel engine has no more residual pressure than a typical gas engine. But I think we all knew that? Anyways...
Let's assume turbocharging is more power increasing oriented and doesn't do much in the way of collecting exhaust energy (which is what it is most of the time). Now some of these turbo compounding engine building companies are claiming a 20% increase in power just by sticking a turbine into the exhaust...imagine what happens with a gasoline engine.
Reality check: Instead of running say 7psi boost, we just put all that power back into the engine. This means for each liter of air aspirated we get 50J. In a 2L engine running at 8000 rpm, this is 8000L/min (for every 2 revolutions of the crankshaft we get 1 full cycle), or 400kJ/min = 6.7kW, about 10 horsepower.
You might say, this power isn't actually there because there is exhaust backpressure. The thing is that turbochargers typically found on cars are designed to create backpressure! This way they can provide more power to the compressor, at the cost of taking away more power from the engine. In addition, a higher pressure ratio increases the efficiency of the turbine, of course at the cost of extra work the engine has to provide. A portion of the energy does however come from the velocity of the exhaust as the gases speed up coming out of the exhaust valves. A turbine can be designed to create almost no backpressure and instead rely on just the momentum of the exhaust. With a piston engine, the exhaust comes in "pulses", which can be exploited, so theoretically we could have the exhaust designed so that these waves hit turbine blades at the optimal time.
Side comment: turbos in normal cars usually do very little for efficiency alone because all of the energy from the turbine necessarily goes to the compressor, which does not directly do useful work.
Okay anyways, you might also be saying, isn't 10hp not very much? You have to remember, the compressor is only at most 70% efficient, and intercooling removes a great portion of the remaining energy, so in fact a LOT more energy went into this 7psi than I just calculated. At full throttle, a naturally aspirated engine's cylinders are at signficant pressure when the exhaust valves open. In this paper
http://www.hcs.harvard.edu/~jus/0303/kuo.pdf, if you look at the graph at the very end, it looks like in their particular example it was about 300kPa, although that engine had relatively low compression ratio. At higher speed, there is less thermal loss though, so 200kPa over atmospheric is not too bad of an assumption. 200kPa means we can theoretically get 30 horsepower out of the exhaust, when the engine is only producing perhaps 210 horsepower in the first place!
Realistically you might say, this is stupid, all this trouble for 30hp? However I think the real benefit is that if the exhaust turbine is sized to produce more power than the compressor consumes, we can actually increase efficiency at all operating conditions, and this would have very predictable behavior due to being coupled to the crankshaft. In addition, this would require no tuning whatsoever. We could add a supercharger to this, to make it like a lag-less, more efficient turbocharger, but if we pick a supercharger that uses less power than the turbo produces, we can see more horsepower for the same amount of boost. Why is this important again? Well we can run a high compression engine on just 4psi boost, and route the extra exhaust energy into the crankshaft. In addition, the supercharger and turbine being separate units would make piping more flexible, and zero lag makes it very suitable for all performance applications.
Just to play around a little bit, we can make 4psi boost with just 10hp from the crankshaft (I'll skip the calculations). If we intercool, this 4psi represents more than just a 28% increase in air density though, so we can most likely get more than 10hp more from the exhaust turbine as well to due a higher pressure ratio. Remember theoretically we can get 30hp out of the exhaust without the boost, now there is perhaps up to 45hp in the exhaust, which say, we can recover 25hp of (a fairly reasonable number...). Then we have a 15hp improvement over just a turbocharger throwing that 15hp away, which is pretty good, considering you get this gain for free in terms of fuel, and without much weight penalty over just a turbo (possibly saving weight due to less piping?)
The main idea is that with just a turbo we are only manipulating gas pressure at intake and exhaust, but not changing what is attached to the crankshaft. There is always more energy in the exhaust than we could possibly use to pump air back into the intake, so we can just route this straight into the crankshaft for useful work! The reason it hasn't been done is because it's more complex and expensive than a single turbocharger unit, and matching turbine speed to the engine might be a little tricky perhaps needing a CVT, although I doubt it would need that. Another possible advantage is since the turbine reduces the energy in the exhaust significantly, a better flowing exhaust muffler can be used, another direct efficiency improvement.
Something to note is this doesn't do very much for part load efficiency, we still need manufacturers to give us those better intake valve control systems! But for people who track their cars, this would give a pretty large fuel consumption decrease, especially people running superchargers.
Sorry this is really long, I'm pretty bored today since I'm procrastinating on homework lol.
EDIT: Oh and I forgot to mention, someone has done this with a Mazda 13b adapted for use on an airplane I think.