This sounds very similar to what happened to both a mates Zafira a few years back and my sisters old Volvo V40. There is probably a leak on the high pressure side of the air intake between the turbo and where it goes into the engine. When the turbo spins up, air leaks out of here, rather than being forced into the engine. The black smoke will be due to the airflow sensor thinking there is more air going into the engine than there is and the injectors then putting the wrong amount of fuel in.

If you're lucky, the leak will be on an air pipe rather than the turbo itself. It was on my mates car, and was a pretty cheap fix as it only needed a short section of pipe and a couple of jubilee clips.