how is ITT peak temperature affected by altitude during an airstart?

Question

another T-6 Texan II (turboprop aircraft) question. When reading the airstart prodedure in the engine failure during flight section of the manual, I found something that Id appreciate the clarification. It mentions, "The higher the altitude, and the slower the airspeed, the warmer the starting ITT peak temperature."

By airspeed, I believe it is referring to KIAS (all graphs and useful data for pilots is in KIAS, at least in this manual) so no arguments there. now, we know that the higher the altitude the less dense air gets to keep up with a relatively constant KIAS, then TAS has to increase.

If TAS increased at this higher altitude, (relative to the air the plane is passing faster) and the plane is making up for the less dense air, why would we expect a higher peak ITT compared to an airstart at a lower altitude? Shoudnt be about the same peak temp?

Also the higher you go the colder it gets at least for a good 20,000 ft MSL which is a major portion of the flight envelope for this aircraft. (max ceiling 31,000 ft MSL). I guess getting colder air has zero impact on ITT? I appreciate the discussion. TY all!

Answer 1

ITT is affected by the heat dissipating effect of airflow: The less air flowing through the turbine section the hotter it can get.

So, you are correct in that IAS is the parameter that is being referred to by term "airspeed". However, I think you are confusing things by bringing TAS into the discussion. Keep the same unit of measure - if IAS increases then there will be a higher volume of air, and more heat dissipation; lower IAS means less airflow and higher ITT.

The reason you might get higher ITT at the same IAS but a higher altitude isn't because of TAS, it is because the air is less dense. (yes, I understand that TAS and density are related...) Air has thermal mass, and the less dense it is the less mass there is available to absorb heat from the turbine.

It might seem odd as cold as it is up high, but when performing environmental qualification testing of electronic equipment we often had more difficulty with heat dissipation during the high altitude chamber tests, (despite the sub-freezing temperatures) simply because the air was so thin.

Answer 2

Heat dissipation is roughly proportional to mass flow times temperature difference.

Mass flow through the intercooler is $\dot{m}=\textrm{TAS}\times \rho$. Since $\textrm{TAS}\approx\textrm{EAS}\sqrt{\dfrac{\rho_0}{\rho}}$ we get that $\dot{m}\approx\textrm{EAS}\sqrt{\rho_0 \rho}$. In words: the effect of increasing TAS and decreasing density don't exactly cancel out.

The temperature at altitude is only a few tens of degrees lower whereas the turbocharged air is a few hundred degrees. So not much of a factor.