If you were to spray a 50/50 Water/Methanol mix into the connecting chamber just upstream of the power turbine, it could be made to react in a after burner like arrangement to supply additional mass flow and power to the downstream turbine.
Assuming water/meth was sprayed in at a large volume, to consume all the remaining oxygen (stochiometric), that would give 40 parts air, 1 part hydrocarbon fuel and 8 parts of water/meth....
The theoretical adiabatic flame temperature would rise to ~3012'F.
Code WEIGHT D-H DENS COMPOSITION
0 AIR (400 K) (720 R) 400.000 23 0.00001 835 N 224 O 5 AR
0 GASOLINE (LIQUID) 10.000 -794 0.02570 46 H 21 C
0 WATER 40.000 -3792 0.03610 2 H 1 O
0 METHANOL 40.000 -1780 0.02870 4 H 1 C 1 O
THE PROPELLANT DENSITY IS 0.00001 LB/CU-IN OR 0.0003 GM/CC
THE TOTAL PROPELLANT WEIGHT IS 490.0000 GRAMS
NUMBER OF GRAM ATOMS OF EACH ELEMENT PRESENT IN INGREDIENTS
10.974320 H
1.951607 C
21.575670 N
9.256535 O
0.129196 AR
****************************CHAMBER RESULTS FOLLOW *****************************
T(K) T(F) P(ATM) P(PSI) ENTHALPY ENTROPY CP/CV GAS RT/V
1928 3012 2.04 30.00 -221.62 1147.59 1.2404 18.233 0.112
SPECIFIC HEAT (MOLAR) OF GAS AND TOTAL = 10.218 10.182
NUMBER MOLS GAS AND CONDENSED = 18.233 0.129
1.078649e+001 N2 5.426075e+000 H2O 1.866150e+000 CO2 1.291956e-001 Ar*
8.521745e-002 CO 5.766315e-002 H2 5.884373e-003 HO 2.480190e-003 NO
0.00213967 O2 0.00213967 O2 0.00213967 O2
THE MOLECULAR WEIGHT OF THE MIXTURE IS 26.685
****************************EXHAUST RESULTS FOLLOW *****************************
T(K) T(F) P(ATM) P(PSI) ENTHALPY ENTROPY CP/CV GAS RT/V
1681 2567 1.00 14.70 -268.22 1147.59 1.2472 18.227 0.055
SPECIFIC HEAT (MOLAR) OF GAS AND TOTAL = 9.989 9.954
NUMBER MOLS GAS AND CONDENSED = 18.227 0.129
1.078766e+001 N2 5.424489e+000 H2O 1.879640e+000 CO2 1.291956e-001 Ar*
7.172794e-002 CO 6.219262e-002 H2 5.726668e-004 HO 1.420500e-004 NO
0.000130622 H 0.000130622 H
THE MOLECULAR WEIGHT OF THE MIXTURE IS 26.694
Although the calculated flame temperature of 3012'F would be way too high for the turbines, the actual temperature will never get that high in practice because:
1) Propep assumes 100% perfect mixing and combustion efficiency.
We know the combustion efficiency will never come close to 100% because all that water in the mix will greatly dilute the reactants and the reaction rate.
2) Propep does not account for the enthalpy of vaporization of the reactants.
Water/methanol will act as a huge heat sink just getting it to change from a liquid to a gas phase. The enthalpy of vaporization will quench the reaction temperature significantly.
Although 50/50 water/meth can be made to burn, the burning will be marginal and weak. There is no way it will get to 3000'F. It has too much water in it. And this could be exactly what you need to make more power.
Now I havn't tested it in circumstances like this but my guess is the flame temperature will be a lot lower. Possibly in the 1200'F - 1800'F range.
By injecting 8 parts water/meth after burn mass flow into the 40:1 turbine outlet mass flow, that will give you a 19.5% increase in mass flow at the power turbine... at roughly the same overall temperature.
This means you could gain up to ~19.5% more power without burning up the turbine.
If for some reason the equilibrium flame temperature went up more than you wanted, you could simply add more water to the water/meth mix. You can even tailor the water/meth mix ratio to anything you want to achieve the flame temperature you want. The objective would be to stay within the maximum thermal limits of the turbine while increasing the mass flow as much as you can push through the turbine.
This power boost may be possible because there is so much free oxygen coming out of the upstream combustion chamber. If that oxygen can be burned and diluted to a reasonable temperature, it can be turned into more shaft power.
I am starting a turbine build myself and will test the effects of water/methanol to see what can be done with it.
