So can someone explain why low by-pass ratio engines produce so much black smoke?
Nothing to do with bypass ratio. Look at photos of, say, F-86 and B-47, both powered by straight jets. Black smoke is unburnt carbon from incomplete combustion. The US engine technology of the time was not capable of full combustion. Compare British engines of the same time, e.g. Derwent, Ghost, Avon, Sapphire - little or no smoke because of better combustion technology.
Standing by for incoming from the West!