So, I want to see the effect of altitude on the compressor characteristic of a single spool & double spool turbofan engine at constant flight speed and TIT (turbine inlet temp).
I am aware that as the altitude increases, density decreases, mass flow decreases which ultimately reduces thrust.
As well as, with an increase in altitude the fuel consumption decreases, due to a decrease in inlet temperature which leads to a lesser amount of compressor work to be done* ( From Gas Turbine Theory by HIH Sarvananamuttoo, H Cohen & GFC Rogers).
But as the compressor work is directly proportional to the spool speed, I would expect the spool speed to be lower as well. (Correct me if I am wrong). But in the plot shown, the shaft speed parameter (N/$\sqrt(T_02)$) seems to increase from 0.73 to 0.89 for single spool and 0.86 to 0.91 for double spool with increase in altitude. Why does the spool speed increase with altitude?