The Garrett ATF3 is one of the most unusual triple spool jet engines there is. In most triple spool engines all 3 shafts are concentric. That is, the high-pressure shaft is inside a hollow intermediate shaft which is inside the low-pressure shaft. In the ATF3 the intermediate is still inside the low, but the high-pressure shaft, while colinear with the other 2 it is behind them.
As you can see from the ATF3 below, the front section outlined in green is very similar to the twin-spool engine but where the combustion chamber is the hot gas is piped off to the rear of the engine, turned through 90 degrees and through a centrifugal compressor. Only then does it hit the combustion chambers. From there it flows through the high-pressure turbine before flowing backwards through various turbines, turning 180 degrees and exiting, mixed with the bypass stream.
It is slightly unorthodox here as the turbine driving the low-pressure compressor is actually at a higher pressure than the one driving the high pressure.
The back-to-forward flow helps keep the engine length down and minimises losses from the hot gas. The centrifugal compressor and reverse flow combustion also help keep the length down but make the entire thing rather wide.
The original Whittle engine had a very similar arrangement for very similar reasons, and on small engines, centrifugal compressors are not unheard of.
 | |
| ATF3 |
Base drawing from here
Quad spool and beyond
To make a quad spool all you would need to do is replace the front twin spool with a triple spool or convert the aft section to double. In theory you could get pent or oct spool engines before hitting the 3 concentric spool limit.
I can only assume the benefit still isn't worth the extra weight and complexity.
