3 spool engine can allow a greater differential between the speed of the high pressure compressor and the fan. This should alllow for higher fuel efficiency.
2 spool engines have fewer parts and are less complicated, so they should have lower maintenance costs.
Currently not all Rolls Royce engines are triple spools, only their biggest ones which are used on the biggest planes for intercontinental flying where they will have a relatively high amount of flight hours and a relatively low number of engine cycles. In other words, where cruise efficiency is relatively more important than engine durability, compared to planes that make several more lower distance flights each day.
Pratt and Whitney is working on their own technological equivalent to the triple spool: the geared fan. Just like the triple spool, it adds complexity in order to allow the speed of the high pressure compressor to be further removed from the speed of the fan.
EDIT: I can color in some more information.
The reason that its advantageous to create a bigger difference between the fan speed and the high pressure compressor speed is because the optimal speed for the fan is tied to the speed that the airplane is flying, while the optimal speed for the high pressure compressor is as high as is possible.
The laws of propulsion are that an airplane will be propelled most efficiently when its exhuast is moving at close to the same speed as the airplane. So if the plane is flying 500 mph, you would want the engines to be pushing a large volume of air at 510mph instead of a smaller volume of air at 1000mph. In the latter scenario, even though your engine may be outputting the same exact amount of energy, a lot of it is lost so it is less efficient. This is the reason why you see those massive super-high-bypass turbofans on large planes, and many of those are the Rolls Royce three spools. They need huge fans in order to push a high enough volume of air. This is also why turbofans have completely replaced turbojet engines, even though the former is theoretically bigger, heavier, and more complex. When you think about it, a turbojet engine is essentially just the core of a turbofan without the big, heavy, drag inducing fan at the front. As far as converting fuel to raw energy output, a turbojet is theoretically more efficient than a turbofan. The problem is that the turbojet thrust might be moving at Mach 2+, so if you're trying to push a subsonic airplane, there's a ton of loss there versus the turbofan pushing a higher volume of air at a slower speed.
Interesting trivia: The Concorde's turbojets had higher propulsive efficiency than any turbojet or fan airliner of its time. This is because the Concorde combined the higher raw efficiency of a turbojet engine with cruise speeds high enough to be relatively close to the exhaust speed. The specific fuel consumption per passenger mile would still be really high though because the Concorde had much higher weight and drag per passenger.
Getting back to 2 spool vs 3 spool... the reason that you want the high pressure compressor to go as fast as feasible is because the faster it spins, the higher compression ratio you'll get, and just like your car, higher compression ratio means better efficiency. Also just like your car, the limiting factors are the technology and materials that you're willing to invest in order to achieve those higher ratios, and the amount of extra maintenance that you're willing to endure. For example, an F1 racing engine has a super high compression ratio, but they more or less have to throw it out after each race.
Last edited by tuna hp; 8th Mar 2011 at 14:31.