I had an idea of how a modern two-stroke engine, meant for a car or motorcycle, could work. Here is a gif of a regular two-stroke, carbureted oil burner: The problem with this is that due to the use of crankcase compression, some power is lost, and unburnt fuel escapes through the exhaust and causes pollution. Here is how I would solve that problem: rework the fuel system. Step one: The cylinder has a certain amount of air in it, which is compressed by the piston. Step two: As the piston approaches top dead center, an injector fires a precise amount of aerosolized fuel into the engine under high pressure. (Some kind of forced induction would need to be used here.) Step three: The spark plug ignites the compressed air-fuel mixture, delivering power and burning the fuel. A longer stroke would be used to give the fuel more time to burn, thereby eliminating some waste. Step four: The exhaust valve opens and the injector fires a blast of air into the cylinder, expelling some of the exhaust. A certain amount remains, so you get EGR for free. Is this feasible? Has this been done before? Could something similar be applied to rotary engines, which are conceptually similar to a two-stroke engine? Update: Ah, piss... I'm describing direct injection, aren't I? Every time I have an idea, someone's beaten me to it.
You've just described the traditional Detroit diesel engine and the powerplants of huge amounts of heavy industry, plus an experimental engine Renault made. You're missing a part though. You still need a scavenge cycle. In the engines I mention, this is supplied by supercharging (and sometimes turbo on top of that, for various reasons can't use turbo alone). This is far simpler than having an injector inject air and fuel, particularly with the quantity of fuel needed. And yes, it's usually combined with traditional direct injection