How does a lean die-out occur in a turbine engine?
With these conditions, how would this exist?


The comment by @mins appears to answer the question for modern engines, although I'm not quite sure if I'm interpreting your question as you intended, but if your intent is to find out how this happens from an operational standpoint, here's an answer for the P&amp;W JT9D-3 through -7 engines as used on 747-100/200 aircraft. In 10 years of flying with these engines, I only had a flameout once, so it wasn't a major problem, and the -3 engines were more susceptible than the later variants.

The scenario is that you're above 35,000 and you've reached your descent point and need to reduce power from full cruise to idle. We were taught to first lower the nose to ensure that we wouldn't lose any airspeed (a little gain was okay) and then to slowly bring the thrust levers all the way back. As I remember, we typically took at least 5 seconds to get the levers back.

In other words, if you suddenly reduced power or lost airspeed, you risked a flameout.

From the pilot's standpoint, if you had a flameout, all you did was tell the flight engineer to restart it when low enough that that was possible.