Figure 4.5.1: SSME Combustion System^[1]

Large Throat Main Combustion Chamber

Although not technically a “turbomachine” it is still fitting to conclude this section with a discussion of the Large Throat Main Combustion Chamber (LTMCC). The preceding sections traced the thermodynamic properties of liquid hydrogen and liquid oxygen from the external tank, through the SSME turbomachinery, all the way LTMCC inlet. We are now positioned to use these results and calculate the properties of the exhaust gas generated in LTMCC. The thermodynamic conditions established in the LTMCC will be used in Section 5.3 to calculate thrust and specific impulse, and again in Section 6 to determine heat transfer through the regenerative cooling circuit.

The combustion model developed in Section 3 serves as the basis for this analysis of the LTMCC. The analysis begins by taking stock of the multiple propellant sources flowing into the combustion chamber. There are five different flows to account for which result in a total mass flow rate of 492.1 kg/sec:

Table 4.5.1

Results from the preburner analysis in the previous sections (Tables 4.2.2 and 4.4.4) show that the flows departing Stations 30 and 32 contain two different species that must be account for: gaseous hydrogen and water vapor. The resulting mass flow rates are tabulated below.

Table 4.5.2

The combustion model established in Section 3 accounts for $x$ moles of hydrogen and and $y$ moles oxygen being pumped in to the LTMCC each second. It does not include a mechanism to account for the water vapor entering from the preburner outlets. We must adapt several equations in the combustion model to account for this additional reactant. Before reading on, it might be a good idea to review Section 3.1 for a more thorough description of how these calculations are performed. We begin by adapting the four primary chemical reactions to account for the addition of $z$ moles per second of $H_2O$:

The $\sum\Delta_C$ values for Equations 3.1a-d remain unchanged, as the additional $z$ term on both the left and right sides of Equation 3.1a cancel out:

Table 4.5.3

However, the overall chemical reaction does change. A $z$ term is added in the coefficient for $H_2O$:

Adding additional $H_2O$ as a product of the reaction changes the equilibrium mass fraction of each species, as shown by the following modifications to Equations 3.1.6 - 3.1.12:

Finally, we must update the representation of the First Law of thermodynamics described by Equation 3.2.12 to account for addition of excess $H_2O$ as a reactant:

We then utilize the correlations developed in Sections 2.2, 2.3, and 2.4 to calculate the enthalpy of the reactants as they enter the combustion chamber at the pressures and temperatures listed above in Tables 4.5.1 and 4.5.2. These enthalpy values are then plugged in to the updated model of the First Law, Equation 3.2.13. It should be noted that the hydrogen at Stations 12 and 15 and the oxygen at Station 21 must be treated as “real” fluids. The Helmholtz correlation from Sections 2.2 and 2.3 must be utilized to calculate properties. The hydrogen and water departing the preburners at Stations 30 and 32 is much hotter and can be treated as an ideal gas, so the property curve fits from Section 2.4 are used.

Pressure inside the LTMCC is designed to be 2871 psia when the engine is operating at 104.5% of its rated power level.^[2] We now have enough input data to run the combustion model one final time! Results of this the calculation are tabulated below. They are in excellent agreement with actual data from the SSME. Flame temperature and specific impulse are accurate to within 1%.

Table 4.5.4

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