Mike Busch, in a response to the blog posting on intercoolers asks this question:
"George, could you post a graph that shows the relationships between OAT, CDT, and IAT as altitude varies from SL to FL250. In other words, how much temperature increase is produced by the turbocompressor and how much temperature decrease is produced by the intercooler as the aircraft climbs up to the Flight Levels? "
So, Mike, your wish is my command ! 
In this context, CDT is the compressor discharge air temperature (after it has been compressed and experiences the resulting temperature rise from that process.)
The IAT ( Induction Air Temperature) is the air temperature that actually enters the throttle of the engine. In the absence of an intercooler, the compressor discharge air flows directly to the throttle and the CDT will be equal to the IAT, within a very few degrees.
Frankly, doing this for Mike takes a fair bit of work. But, Mike is a good friend! So I decided to try to spend a couple of hours and model it up. The results are consistent with my actual data to a remarkable degree.
As mentioned, when looking at the graph, keep in mind that when one does not have an intercooler, then the CDT = IAT within a very few degrees, by definition.
As a result, I did not plot CDT as an extra curve, but the CDT is evident from the graphs, by reference to the non-intercooled compressor output lines (RED).
Allowing for the various issues described below, the results are consistent with actual data to a remarkable degree.
In the graph below, the assumptions are these:
1) Departure from a 5,000 foot MSL airport on a hot summer day ( OAT = ~ 100 deg F) and then a direct climb to altitude. The further assumption is made that the atmosphere (away from the surface) is an ISA + 40d F day. By making that assumption, anybody can figure the OAT at any altitude without having to plot it out. For easy of reference, at:
Altitude OAT (dF) Pres (in Hg)
10,000 63 20.6
15,000 45.5 16.9
20,000 28 13.75
25,000 10 11.1
2) Further assumptions are that there is an inherent gain in compressor inlet temperature (CIT ) of about 10d F (empirically verified) above the measured ambient (OAT) temperature, just due to the air flow going from the outside to the inside of the engine compartment. I have never seen an installation that did not have more than 10 degrees of rise from OAT to CIT. Further, it assumes some real world pressure losses from the compressor to the throttle of about 0.5" Hg for the non-intercooled configuration and about 1.5" Hg for the intercooled configuration. Those are also based on empirical experience.
3) The mis-matched compressor efficiency number is also from real world experience with older compressor designs or even more recent designs where the compressor is adapted from one design point and used in another application where the speed (RPM) or the mass flow is "off " of the normal compressor map sweet spot.
4) There are multiple well matched and well designed compressors that can operate with efficiencies well into the mid 70's percent range. An Efficiency of 0.74 was chosen as being consistent with real world experience.
5) The intercooler efficiency of 60% is actually "OK" for a single engine aircraft, but low for a twin engine aircraft (higher indicated speeds results in better intercooler efficiencies). It is realistic for a range of aircraft and climb airspeeds and it would be low for cruise for a well designed intercooler.
6) These plots assume the compressor efficiency is constant across the climb profile. That is an over simplification. They are not. One will move out of the sweet spot on the compressor at map at one end or the other of the climb.
7) I did this in a bit of a hurry, so it is possible I made a mistake somewhere!
Some observations:
1) The most significant observation is that, with a well designed turbo & intercooler combination, one can operate a piston aircraft under very hot ambient conditions and the engine will continue to see relatively modest induction air temperatures - - even all the way to 25,000 feet.
2) And, conversely, without the intercooler, one sees some difficult temperatures up into the mid or high 200 degree F range at 25,000 feet. Better compressor efficiencies mitigate this somewhat.
If the compressor is limited in its ability to deliver manifold pressure because of speed or drive shaft torque limitations, then below, is a further example of how that compressor, without an intercooler would perform. Note, the example assumes a compressor with a maximum pressure ratio of about 1.4:1.
So, Mike, is this the data that you wanted to see ?
Regards, George
Posted
15 Feb 2009 10:53
by
George Braly