I know roughly how a turbine engine (let's say a gas turbine producing no jet thrust) is supposed to work:
The compressor forces fresh air into a combustion chamber, where it reacts with fuel to become hot exhaust gas. On its way out of the engine, the exhaust gas drives a turbine, and the turbine both makes the compressor go, and has enough leftover torque to do useful work.
However, how do the exhaust gases know they're supposed to push on the turbine blades to drive the shaft, rather than push back on the compressor blades to retard the drive shaft in equal measure?
In a piston engine there are valves that force things to flow in the correct direction at the right times. But with the turbine engine everything is openly connected all the time. Shouldn't that mean that the pressure differential the compressor must work against is exactly the same as that which is available to drive the turbine?
Something magical and irreversible seems to happen in the combustion chamber.
The descriptions I can find that go deeper than the three-step explanation above all seem to jump directly to a very detailed model with lots of thermodynamics and fluid dynamics that make my head spin. Is there an idealized system with fewer variables that I could think of to convince myself we're not getting something for nothing here (e.g., might the working fluid be incompressible, or massless, or have infinite heat capacity or whatever)?
Answer
I just had an epiphany. The engine works because the turbine is "larger" than the compressor.
For extreme simplicity, let's assume that the working fluid is incompressible and effectively massless (it has pressure, but its inertia is negligible compared to the pressure). Assume further that the actual combustion is so finely tuned that the pressure stays constant during the combustion -- the gas simply expands at constant pressure, doing work against its own pressure as it does so.
Then the compressor and turbine really do operate across the same pressure differential, namely the difference between ambient pressure and pressure inside the combustion chamber.
At both ends of the engine, the power delivered to (or taken from) the drive shaft is the (common) pressure difference times the volume flow through the compressor/turbine. At this ideal level they are both the same kind of thing, except that one of them runs in reverse.
However, the torque is not necessarily the same. The turbine is constructed such that one revolution of the drive shaft will allow a certain volume of air to escape from the combustion chamber. (I suppose that is a matter of the turbine blades being mounted at a different angle than the compressor blades). At the other end of the shaft, one revolution of the shaft will push a certain smaller volume of air into the combustion chamber. It must be so because the gas expands during combustion.
This difference in volume-per-revolution means that the same pressure difference translates to different torques at the two ends of the engine.
As a completely idealized toy example we can imagine that the compressor and turbine are both made of the same kind of ideal reversible fan assemblies -- for each such unit, one crank of the handle will make a certain volume of air change places, and how hard the handle is to crank depends on the pressure difference.
The units that make up the compressor are mounted such that turning the drive shaft clockwise corresponds to air moving into the engine; the ones that make up the turbine are mounted opposite. Since the pressure difference is the same everywhere, the torque output from one turbine unit can drive exactly one compressor unit. But there are more turbine units than compressor units, and the additional ones produce surplus torque that can do work.
This corresponds to the fact that there's a net outflow of air from the combustion chamber, because new volumes of gas come into being as the fuel burns.
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