Steam Wankel

Well I've tried a version of this idea before, but I've made some edits and I think I'll try again.

So wankel engines are incredibly good at making high power at high RPM. The only things they lack are torque and decent fuel economy. Well there is already a version of the wankel engine that uses steam, so why not combine the two and subtract a couple problems? My idea is relatively simple. It is to use a supercharger to scavenge the chamber of its exhaust and fill it up with new air, all in one chamber. This frees up the 3rd chamber for steam power. Now the thing is that the exhaust would have to be tuned to have basically no backpressure, otherwise the supercharger would have to work too hard and the steam power wouldn't make up for the supercharger's losses. However, if the exhaust is tuned for barely any backpressure (perhaps some kind of ram air exhaust?). The engine would be direct injected, and therefore wouldn't produce anywhere near the amount of hydrocarbon emmisions that most wankels do. The water injection (steam stroke as I call it) would be the engine's only cooling source, and I reckon it would make enough power during the steam stroke to allow the gasoline injection to be lean enough so that it wouldn't require a cat. (the european Audi A3 with direct injection doesn't need one). Now I don't have any good numbers to do any calculations, but I figure that the supercharger would rob 20HP at most, and the steam power stroke has to produce at least 60HP+ at its peak (not to mention a nice amount of torque). I figure a 40HP+ gain without the complications of a cooling system is a good gain.