Why no reheat cycles between turbine stages?

[AeroGav]

One of (The most?) limiting factors in jet engine performance is turbine inlet temperature.

Basically, there is a limit to how hot the gases can be after leaving the combustion chamber, or they will melt the blades of the first stage turbine off. As they pass over the first stage turbine, the gases are allowed to expand, converting some of their heat energy to kinetic energy, which drives the turbine. As a result, they are cooler by the time they hit downstream turbine stages, which therefore get an easier ride.

Now, there's two ways to keep turbine inlet temperature down. The first is to lower the engine's pressure ratio - that is, don't compress the incoming air so much before you put it in the combustion chamber. Compressing any gas heats it , Expanding any gas cools it. By compressing it less, the air will be cooler before combustion occurs and post combustion temperatures will be lower too, for the same amount of fuel burned. However, reducing the pressure ratio costs efficiency.

Alternatively, you can just inject less fuel, and leave more of the available air unburned. This however, costs power. Even with today's super high temperature alloys, only about 50% of the available air is actually used for combustion. Turbine engines run very "lean". This confuses a lot of automotive types, because spark ignition piston engines run stoichiometric at lower power settings (neither surplus of fuel nor oxygen - a chemically perfect mix) but run rich - an excess of fuel - at max throttle, to prevent detonation/pinging. The excess fuel cannot find any oxygen to burn, so does not release any energy. That fuel which does burn, has to heat all these extra molecules up that aren't pulling their own weight - temperatures go down.

The excess air in inherently lean running turbine and diesel engines serves the same purpose. Highest temperatures are found at Stoichiometric mixtures, where there is no surplus of either fuel or oxidiser and everything put in the combustion chamber gets to burn. Rich OR lean of this point temperatures go down. Car engines prefer to go rich, because it means more power (every cubic inch of air your motor pulls in is being used), and also because spark plugs have a hard time igniting lean mixtures. But i digress.

The question is, if the melting point of the first stage turbine limits how much fuel you can burn in the main combustor, why not add a second stage of combustion after the first stage turbine, so that the second stage turbine is also being fully utilized - fed gases right up to its temperature limit. And so on, though many aero engines only have 2 or 3 turbine stages total?

Obviously, combustion in the main combustion chamber is the most efficient, because the gases expand though every stage of turbine before passing out the tailpipe. Secondary and Tertiary combustors are going to be burning at lower pressure ratios and pass through fewer turbine stages.

However, the engine could recruit combustors with this in mind. At lower power settings, all combustion takes place in the primary combustor. When no more fuel can be added without overheating the high pressure turbine, fuel starts to be added to the secondary etc.

Imagine it adds weight and length to the engine , but is surely going to give better SFC than just dumping everything in the afterburner. Would this have made more sense with early jet engines , which had lower temperature limits?

Or, if the engine is optimised fuel economy at partial power settings, you could run a higher than normal pressure ratio, burning less fuel in the primary combustor to avoid overheating, but having the secondary combustor to ensure you still hit desired power rating. At rated power, SFC will be worse because of the combustion taking place at reduced pressure ratio of secondary combustor, but at part throttle you'll only be using the primary and be benefitting from the higher pressure ratio.

[peadar1987]

Primarily because at some point you're going to have to expand to your heat sink temperature.

Reheat is primarily used to avoid the formation of liquid droplets in "wet" working fluids, without adding excessive superheat and ruining your overall pressure ratio.