Quote:
Originally Posted by drmiller100
saturated does indeed follow ideal gas laws at higher temps.
Therefore, you are wrong.
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Hello drmiller100,
No, the part of the steam table where the ideal gas law applies is where the steam is "dry" and at relatively low pressure. In the graph posted by t vago the blue dots are the percent error from an ideal gas. At the critical point the error is 330% But you can use the ideal gas law for supercritical steam at low pressures and accept some error. The error is away from gas properties (PV=nRT) and towards incompressibility where the volume is independent from pressure.
The problem I see with advocating for the gas law is that in terms of increasing efficiency it is a non-starter. If you want to use an ideal gas, inject air, or recycle exhaust or any other gas. All the increased power you get from the additional expansion is only equal to the amount of power it takes to pump the gas in against the pressure in the cylinder.
The putative advantage of water is that it goes from a very small volume liquid to a high volume gas. The power to pump the liquid into the cylinder should be less than the power you get back by it's expansion. This part works OK but only well below the critical temperature.
Above the critical temperature saturated steam is neither liquid nor gas. Liquid and gas properties are indistinguishable. The volume and pressure of the gas phase and liquid phase are the same. To put it in other terms, above the critical temperature compressing the "vapor" does not condense it to a liquid, and adding heat to the "liquid" does not cause it to evaporate.
Again, this is for saturated steam above the critical temperature.
However, below the critical temperature, even the phase change advantage is lost because the amount of energy as heat absorbed by the water as it expands into gas is larger than the amount of energy as expansion and pressurization due to evaporation. The phase change energy is only recovered by condensing the gas again.
Common combustion pressures run about 2 to 3 MPa and temperatures are around 2000 K. So using small amounts of water is a waste, assuming the water doesn't disassociate, it will be dry steam above the critical temperature and behave as an ideal gas. Using enough water to move into the saturated region is a waste because above the critical temperature (and below 22 MPa) steam behaves worse than an ideal gas. Adding enough water to move below the critical point is a waste because more heat goes into the phase change than you get from the expansive force, so the pressure of the water plus exhaust mixture is lower than if you hadn't added the water.
-mort