Black smoke = too much fuel. White (pure white) smoke which disipates into thin air = steam. Whitish (bluish) smoke that wafts away in the wind or hangs around = unburned fuel/oil burning.

Black smoke without the engine exceeding idle, and assuming good compression/mechanicals, is most likely a bad injector or something at the IP such as a stuck delivery valve.

The cylinder responsible "may" be able to be isolated by cracking individual lines at each injector, in turn, and listening to the engine and watching the exhaust.

Black smoke could also be caused by air getting into the pump and the air can delay injection because of contraction, then diesel (explode) inside the injection line and blow excess fuel into the cylinder late, and cause all kinds of weird running problems. That it ran better on the purge may in fact point to that issue.