The -N *does* have water injection, meaning it's displacing gas in the cylinders to cool them off (water cools it to prevent premature detonation, allowing greater compression in the cylinder, creating more power with less gas, as Hitech stated).
That's why the F4U-4 and the P-47N have less fuel consumption on WEP. I think they have the same engine, or at least different versions of the same engine.
As for the -D models, it's possible the water injection just works to a lesser extent than on the -N, maybe not so efficient. The Bf109s had WM (water-methanol mix) for the same reason, but on THEIR engines they increased fuel consumption by ungodly amounts.
Depends on the engine and the circumstances on how it works. I suppose it varries from plane to plane.