If you want a real oddball of a jet engine, look no further than the RB.199 from the PA200 Tornado. Consider that normal military aircraft engines are built for simplicity, with two independent compressor and turbine sections (spools) at best for at least rudimentary efficiency and as much power as possible. And most modern engines are built with a bypass (turbofan) to increase mass flow through the engine (increasing available power) and to provide laminar air flow for cooling along the engine walls. The burner section in more modern engines is trimmed for reliability and the afterburner section is quite long to ensure proper combustion of the additional jet fuel. And there's a (flexible) nozzle with a shrinking and then expanding diameter to make the best use of the kinetic energy in the exhaust gases for maximum power.
Now you've got the cheeky little, multinational bugger in the Tornado. First, it's a turbofan, which is good and as normal as it gets with this engine. But unlike its brethren, it's a turbofan with three(!) independent compressor and turbine sections (triple spool). First oddball property. Triple spools are only found in Rolls' other modern civilian engines like the RB.211 (think TriStar, 747 and 757) and beyond. The reasoning behind this is that three spools have each compressor section rotate at its optimal velocity throughout its envelope, providing maximum efficiency in compression - in theory. Practically, during power changes, trying to get three independent compressor sections is like trying to get three kids to do chores. The eldest (high pressure section) does what you tell it to without much hesitation, but while you try get either the youngest (low pressure section) or the middle one (middle pressure section) to join in, the other of the two will smply do what it pleases. To the effect that, in the worst case, the chores won't get done as quickly as they should or, worse, that the entire process will momentarily break down. Yep, that's an operational limitation right there. One other property of three spools is a very elaborate system of lubrication because oil rules the world and everybody hates friction. In their infinite wisdom, the engineers devised a bearing and lubrication system that's only really tight at high rotation speeds, meaning that part of the engine oil takes a stroll into other engine compartments at lower power settings. When seeping into the turbine sections, it causes a mild case of combustion visible as smoke and the blackened vertical stab so typical for the Tonka.
Continuing the theme of inefficiency and oddballness, the fuel injectors in the combustion chamber inject fuel in the opposite direction of the air flow. No elaborate mixing into the direction of the flow to optimize things like in other engines, just a simple "Here's fuel, here's air, now sort yourselves out" to keep the combustion chamber as short as possible. Efficient? Not quite.
The turbine section ties a into the compressor section above, but it isn't really special. The exhaust gas bumps into the turbine rotors, basically converting a bit of velocity and pressure into rotational energy and thus driving each of the three shafts and its attached compressor section. Standard, yawn, NEXT.
Aaaand it's the afterburner, which, for a military jet engine is SHORT. So short, in fact, that the reheated exhaust gas doesn't have much time to cool down and expand, giving the Tornado its characteristic blue afterburner flame and the heat signature of an B class star. It's said that a Tonka in afterburner can be spotted with the bare eye from Proxima Centauri and that the only usable countermeasure is a tow array for an O0 (o zero) supergiant star.
As if the intense heat of the exhaust is not bad enough, the nozzle adds insult to injury because it totally does away with the standard shape of tighten-widen and just tightens, essentially trading some thrust for mechanical simplicity (shoulda simplified the compressors instead, eh?). The nozzle, however, still widens to accomodate the added exhaust gas flow when in afterburner, so it's got that going for itself, which is nice.
Just when the exhaust gas thought it was clear of this rollercoaster ride among engine construction, it slams right into the thrust reverser panels, the last oddball characteristic of the 199. The Swedes thought that putting thrust reversers on military aircraft was a superb idea because it saves some poor conscript from having to handle the mess of nylon and lines called a braking parachute or blowing on superheated brakes, so Fritz, Giovanni and Lord Mc Lordface ran the numbers and came to the conclusion that it was perfect to offset the horrendous R&D costs for getting the compressors (again: THREE SPOOLS!!!) to work by reducing the number of required wheel brake changes. Great thinking, folks! What the three musketeers didn't realize, however, is that the exhaust gas gets super miffed at being thrown out in the opposite direction it came in and therefor will merrily deposit anything remotely sooty (lubricant, partially burnt fuel) on any surface of the aircraft it can find - most prominently the vertical stabilizer. This is the reason why any Tornado looks worse than most Air France airliners and why there's absolutely no point in cleaning them around the tail end. Rumors have it that a good number of Tonkas still carry 30+ year old reverser marks...
And this concludes the general oddities about the RB.199. I didn't dive into the minor ones (the starter comes to mind...), but this shall do.
To recap, this bit of drunk powerplant engineering has a very complex compressor prone to hiccups, leaks oil at low RPM like the Exxon Valdez, has inefficient combustion (how they got it smoke free is a mystery to this day), the heat signature of the surface of the sun and a "no tractor needed" reverse gear.
On the upside (yes, rumor has it that these exist), it doesn't need any additional mechanical devices to optimize the flow through the compressors because of the three spools, it's compact, has a good power to weight ratio, a device to shorten the landing roll, hyper ultra awesome blue afterburner flames and an exceptionally sweet sound and noise level. Oh, and its concept's been proven and working for 40+ years by now.
But it's so odd when compared to the other engines, I can't help but love it.