Compression and Expansion of Cabin Air

[hawk37]

The Lear series corporate jets have an emergency pressurization system where air can be tapped off between the high and low pressure compressors, and fed directly into the cabin. So this air does not going through an ECU, and doesn't have any temperature control except the engine rpm. While testing on the ground, if one puts the throttles up to a mid point, the air coming in is quite warm, though not at an excessive rate or speed, even in the winter.

So here is my dilemma; the air starts out at -20 degrees C, and maybe 1 atmosphere of pressure. It gets compressed to a higher pressure and temperature, and then reduces pressure to gently enter the cabin. The flow is smooth and seemingly of a pressure very close to ambient, ie 1 atmosphere again. However, the temperature of the incoming air has not cooled to - 20 degrees C, it is maybe 35 deg C. Shouldn't the amount of heating due to compression equal the amount of cooling due to expansion?

Sorry for what seems a simple question. Anyone with ideas?

Hawk

[DaveReidUK]

Originally Posted by hawk37

So here is my dilemma; the air starts out at -20 degrees C, and maybe 1 atmosphere of pressure. It gets compressed to a higher pressure and temperature, and then reduces pressure to gently enter the cabin. The flow is smooth and seemingly of a pressure very close to ambient, ie 1 atmosphere again. However, the temperature of the incoming air has not cooled to - 20 degrees C, it is maybe 35 deg C. Shouldn't the amount of heating due to compression equal the amount of cooling due to expansion?

Would that not imply that the pressure inside the cabin would be then equal to ambient? But it obviously isn't.

[flypaddy]

You’re absolutely right that in an “ideal fluid” theoretically you could compress and expand the gas and it would return to its original temperature. In real life, the process of compressing the air is not 100% efficient (entropy; due in part to friction) and so you will introduce heat to the air. This means you end up with a higher temperature even after expansion to the original pressure.

In flight your objective is to compress the low density ambient air but there is no need to expand it. Therefore your air temperature will be higher primarily because of compression and secondarily because of entropy. This is not such a bad thing because the ambient air you start with can be pretty chilly!

Not sure what your background is so apologies if I’m teaching you to suck eggs.

[Goldenrivett]

Originally Posted by hawk37

While testing on the ground, if one puts the throttles up to a mid point, the air coming in is quite warm, though not at an excessive rate or speed, even in the winter.
Shouldn't the amount of heating due to compression equal the amount of cooling due to expansion?
Sorry for what seems a simple question. Anyone with ideas?
Hawk

Yes. Except you have not done the whole process adiabatically.
The air has been given a huge amount of Kinetic Energy by the compressors as well as the static pressure rise. The KE is responsible for the temperature rise.

[hawk37]

Thanks for the responses

DaveReid, you say "Would that not imply that the pressure inside the cabin would be then equal to ambient? But it obviously isn't."

I think your point is that since the air is ** flowing** into the cabin, there must be some pressure differential. However, I think the pres differential is almost zero, for example I would still get some air with the cabin door open, and there is no pressure bump on ears or showing on the cabin rate of climb.

Flypaddy and Goldenrivett, thanks for your explanation. Goldenrivett you say

"The air has been given a huge amount of Kinetic Energy by the compressors as well as the static pressure rise. The KE is responsible for the temperature rise."

There is also a decrease in kinetic energy almost back to zero, as the air entering the cockpit is very slow, and I'm on the ground with the engines running. Does the air also cool as the kinetic energy decreases?

[Chu Chu]

I can't answer these question in any depth, but when air slows down, the kinetic energy is converted into heat. So the temperature increases. I suspect most of the heating occurs due to turbulence in the compressor itself rather than slowing of flow downstream, but don't know for sure.

I think folks are assuming you're asking about what happens at altitude when, of course, the cabin pressure is significantly higher than ambient. Your question isn't really clear, but -20C is a pretty cold day in most places.

[Goldenrivett]

Does the air also cool as the kinetic energy decreases?

No. The Kinetic energy is "wasted" as heat. Same way the brakes get hot because they have dissipated the aircraft K.E. during landing roll out.

[flypaddy]

In response to the kinetic energy comments, it’s all governed by the simplified Bernoulli equations. When high speed air is brought to rest, the kinetic energy is converted into static pressure. The primary effect of this pressure rise is a temperature rise because of the ideal gas law. A secondary effect is the heating from the friction which may have caused the air to come to rest in the first place.

So for a static test on the ground:

Static ambient air is drawn into the engine and compressed. Both its static pressure and kinetic energy rise because of the action of the compressor blades on the air. This static pressure rise results in the major rise in temperature. Additionally the compressor is hot because of bearing friction and some of this heat will also be conducted to the air. The air friction on the surface of the compressor blades will give a rise in temperature too.

When the air is brought to rest in the cabin it expands back to its previous pressure. It will not cool back to the same ambient temperature for three reasons:

1) Entropy increase because the gas is not “ideal”.
2) The heat transferred from the compressor metal itself.
3) The heat due to air friction against the compressor blades and through the ducting.

[hawk37]

Chu, I was considering on the ground, not moving, for simplicity. I used -20 to indicate on a cold day the original air, once back at ambient pressure in the cabin was still appreciably warmer despite the cold temperature it started out at.

Flypaddy, great explanation. Appreciate it

Hawk