First some terminology:[ul][li]A turbine “stage” is a single layer of fixed blades and an adjacent single layer of rotating blades. Conventions differ on whether the fixed set is immediately upstream or downstream of the rotating set. [/li][li]Multiple stages can be coupled together on a common shaft to rotate at a common RPM. Such a group is typically called a “turbine”. If there is more than one turbine in an engine they’re usually numbered 1, 2, 3 from upstream to downstream or labeled high-, medium- / intermediate-, or low-pressure = HPT, MPT/IPT, and LPT. [/li][li]The whole shebang, from the downstream end of the combustor to the upstream end of the exhaust pipe of the engine is a “turbine system.”[/ul][/li]
Many pure turbojets were/are single-turbine engines. Some, particularly in the early days or in low power applications, were/are even single-stage single-turbine engines. Recognize also that turbine systems are a necessary evil, not an inherent good. If we could get compression some other way, a turbojet wouldn’t have a turbine system at all. We call those ramjets. Our problems with those are mostly down to inadequate materials science. From a pure aero and mechanical simplicity perspective they beat the crap out of turbine-equipped engines.
The advent of turbofan engines changed the equations a bunch. Now the goal is to use the fire to drive the fan. Any thrust out the tailpipe is gravy, and inefficient gravy at that. The ideal turbine *system * in a turbofan engine will extract 100% of the thermal & pressure energy from the combustor exhaust stream. Such that the exhaust downstream from the turbine *system *is ambient air at ambient pressure just wafting gently out the back.
It is not efficient to try to do that in one stage. The input and output conditions are more radically different than can be converted by passage over just a single airfoil. And the hotter & more highly compressed the combustion scenario, the more that it true. Modern engines with modern compressors & combustors burn far hotter and at far higher pressures than the canonical science museum 1950s turbojet. And hence require more sophisticated turbine *systems *to extract the vastly greater work available per cubic inch of combustion exhaust gas generated.
From a steady-state and strictly aerodynamic POV it might well be possible or even advantageous to use a single *turbine *with multiple stages. But aero efficiency within the turbine is not the only consideration and steady-state is not the only operating point.
Prior to the advent of the geared turbofan, the fan RPM was exactly equal to the LPT RPM. And even with the latest in geared fans, the power extracted by the fan drive turbine (typically called LPT) is equal to the power applied to the fan, net of frictional losses. So the LPT has to be sized to deliver the right amount of power to the fan and at reasonable RPMs. And has to be able to accelerate and decelerate at reasonable rates, without producing excessive back pressure against the upstream turbine(s). All this leads in the direction of a large and relatively slow-turning fan-drive turbine.
Further upstream in the turbine system, the demands are different. The compressor system(s) turned by the other turbine(s) have different power, RPM, and acceleration needs. And as noted above ref ramjets, 100% of the work extracted by these turbines is “wasted” in that it’s used to run the engine, not to produce anything useful outside the engine. So the more efficiently we do this, the greater the overall combined efficiency of the overall engine. There’s really a twofer to be gained by doing this part right. As a separate matter, one or more of these turbines drive the mechanical accessory loads: fuel pump(s), hydraulic pump(s), electric generator(s), etc. Which each have their own mechanical power consumption needs and range of acceptable RPMs and accelerations. And which needs are mostly independent of the engine’s needs.
It turns out that for the current state of the art, using 2 or 3 distinct turbines is the best way to extract as much energy as possible as efficiently as possible. Efficiency also includes things like packaging diameter and weight of parts.
I suspect the ultimate in efficiency would be to have each turbine *stage *be separately freewheeling and have an embedded superconducting electrical generator in the hub. Each stage would be like this and computers would adjust the field currents to extract the appropriate increment of power from each stage according to its aerodynamics of the moment. Meantime the compressors and fans would be driven by similarly situated and controlled electric motors which consume all the energy extracted from the total turbine system, less some for ship’s services.
In effect today, the current HPT/LPT systems are a bit like a transmission, coupling a high speed high energy low volume combustion chamber to a low speed high energy high volume fan. There is an upper limit to how much gear reduction you can get in a single gear pair. Beyond that point it’s more efficient, albeit more mechanically complex, to use a two stage gear train.
Bottom line, it isn’t really sensible to talk about one stage of an existing two-stage engine without the other stage; the engine *as designed *can’t operate without both. e.g. In the current Toyota 2.0 liter 4 cyl, which is more efficient, the piston or the cylinder? Not really a logical question. The metaphor isn’t perfect, but it’s in the ballpark.