After much work by CodenameJack and also some great assistance by Concorde fans and users, there appears to be a potential fix ready for Concorde. The alterations by Asobo in the depths of the new fuel_system affect fuel pressure lines, hence the reheats cutting out and the failure of fuel transfer (fuel line pressure too low in both cases).
If all works well, the update will be rolled out within a day or two across all platforms. Other aircraft have not been affected as they don't use the new fuel system yet or their fuel systems are far simpler than Concorde's immense set up (181 lines, 48 junctions, 33 valves and 37 pumps). There is no documentation in the SDK on what Asobo changed or why. The fault created by the change was reported by Concorde users during the SU9 beta, but nothing was done and no feedback was provided either to us or to them, so we cannot tell if it's a sim-bug or intentional.
I will post again when the update goes live. We won't change anything else, this emergency update will be just to ensure that Concorde is operating correctly again.
