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 e.g. seventh edition Gas Turbine Theory by H.I.H. Sarvananamuttoo, G.F.C. Rogers, H. Cohen, P.V. Straznicky and A.C. Nix).

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?

Compressor Characteristic of Single Shaft (Blue) & Double shaft (Brown)

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    $\begingroup$ I searched my documents but couldn't find a clear answer right away. My gut feeling tells that with a fixed turbine inlet temperature, and a lower environmental temperature the temperature difference is greater and thus the turbine work and the compressor work are a little bit higher resulting in an increased rotation speed... The mass flow of the compressor is roughly the mass flow of the turbine so they pretty much cancel out from the equation and thus the equilibrium of the compressor and turbine power mostly depends on the temperatures... could be mistaken though, not an expert myself :) $\endgroup$ – Jan Sep 1 '19 at 10:15
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    $\begingroup$ Hey Jan! Thanks for digging in your doc for answering this. I think you are right, I believe this is how it happens- As the altitude increases, density decreases, drag reduces and lesser resistance is experienced, thus, same cruise speed can be attained at lower thrust which also reduces due to reduction in mass flow, hence lower fuel flow rate. In a way, thermal efficiency is increased at higher altitude. As far as the operating line to moving towards design point is concerned, a jet engine is designed to operate in cruise i.e. the design point. But still, even I am not sure about this. $\endgroup$ – Topcatmki Sep 3 '19 at 6:27
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    $\begingroup$ @Topcatmki you may check to see if indicated airspeed is constant for that data. It may be they "let it rip" at higher altitudes where conditions favor greatest fuel efficiency (right up to the Mach limit). $\endgroup$ – Robert DiGiovanni Sep 3 '19 at 13:32
  • $\begingroup$ @Robert DiGiovanni the indicated airspeed/flight cruise speed is constant as the altitude varies for this case. $\endgroup$ – Topcatmki Sep 3 '19 at 13:54
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    $\begingroup$ @Jan this might vary based on no. of spools. As far as I know, as the spool speed increases beyond design value, at a certain point inlet is choked, that is when the surge line. But as you go from design point to a lower spool speed, the velocity at first few stages in the compressor is lower than the rear stages (because of converging portion downstream), this leads to increase in incidence angle at the first few stages and reduction in the incidence angle at last stages. For the case you have stated, assuming it to be acceleration, incidence angle in rear stage is increased- stall of rear. $\endgroup$ – Topcatmki Sep 4 '19 at 8:10

As you note - as altitude increases, air density decreases.

The work done by the compressor stages therefore also decreases at any given rotational speed. If we assume constant power applied to the compressor stages (not entirely correctly) then the speed will increase until the work done matches the power input.

The overall work done by the engine will still decrease, due to decreased combustion, but the spool speed is going to increase a certain amount.

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