Jane-DoH
Thin-walled high operating temperature heat exchanger and now methanol injection. This is one incredibly complex engine. What is the reliability over how many re-usage cycles?
Why do you have the air going through the pre-cooler from the sides and in a spiral-trajectory rather than just straight through? I don't really get it.
I've had a chance to examine the references you gave and the spiral construction of the pre-cooler appears to be an attempt to make it behave like a
counterflow heat exchanger. A conventional counterflow heat exchanger is continuous in that one fluid is gradually heated along its length as the other fluid travelling in the opposite direction is gradually cooled, At all points along the heat exchanger the temperature difference between fluids is the same, yielding the best performance. In the Sabre pre-cooler, the flow temperatures are stepped but tend towards the counterflow ideal. See spiralflow/crossflow in the wiki link above.
The formula does look ambiguous, but if you look carefully is Mn^2.
Check out the admiring video on jetblast/hamsterwheel, sung by heart-throb Christofer Drew / Never Shout Never.