Figure 4.4.1: SSME Oxidizer System Schematic ^[1]

The high-pressure oxidizer system is slightly more complex than the low-pressure system. Combustion gas exits the Oxidizer Preburner at Station 31 and spins the blades of the High Pressure Oxidizer turbine. The shaft on this turbine drives two pumps: the High-Pressure Oxidizer Boost Pump and the Preburner Oxidizer Boost Pump. We will begin the analysis by determining the power requirement of these two pumps. Next, we will calculate the output enthalpy from the Oxidizer Preburner. This data will then allow us to calculate the optimal mass flow rate through the High-Pressure Oxidizer Turbine.

High Pressure Oxidizer Turbopump

Liquid oxygen enters this device at Station 19 with a known temperature and pressure. The desired pressure on the output side of the pump (Station 20) is known, but all other output state variables are unknown. The input and output mass flow rates are known. Output conditions are found with a similar procedure to that described for the Low Pressure Fuel Turbopump in Section 4.1. Results of this calculation are displayed below.

Figure 4.4.2

Table 4.4.2

Preburner Oxidizer Boost Pump

Analysis for this pump is very similar to the pumps discussed previously. Liquid oxygen enters this device at Station 24 with a known temperature, pressure and mass flow rate. The desired pressure on the output side of the pump (Station 25) is known, but all other output state variables are unknown. These unknown values are calculated in the same manner as previously discussed. Results of this calculation are shown below.

Figure 4.4.3:

Table 4.4.3

Oxidizer Preburner

The oxidizer preburner is a combustion chamber that converts liquid hydrogen and oxygen into a gaseous mixture of hydrogen and water vapor that is used to drive the blades of the High Pressure Oxidizer Turbine. The desired pressure in the preburner is known, along with the temperature, pressure, and mixture ratio of the reactants entering at Stations 14 and 26. The combustion model developed in Section 3 is then utilized to compute temperature and thermodynamic properties of the resulting gaseous mixture. Input and exit conditions are shown below.

Figure 4.4.4:

The mixture ratio selected for this combustion chamber, $\dot m_{26} / \dot m_{14}$, was selected based on the maximum allowable turbine inlet temperature at Station 31. In this case, this temperature is approximately 721 K. As in described in Section 4.2, we work backward from this temperature to determine the corresponding mixture ratio and output enthalpy from the preburner. Plots to accomplish this task are shown below. There is some minor turbulence on these charts due to the solution scheme used in the combustion model. This model utilizes Gauss elimination to solve a system of linear equations represented in matrix form. Unfortunately the determinant of this matrix tends to approach zero for small mixture ratios. The solution scheme can encounter difficulty solving these near-singular systems. The results remain accurate to within 2% of actual values found in the SSME, but the resulting plots are not too pretty.

Figure 4.4.5:

Figure 4.4.6:

Table 4.4.4

High Pressure Oxidizer Turbine Mass Flow Rate

The preceding calculations enabled us to determine the relative proportions of liquid hydrogen and oxygen required to feed the oxidizer preburner. Although we selected a mixture ratio of 0.592, this number does not tells us anything about overall mass flow rate required to power the system ($\dot m_{26}$ and $\dot m_{14}$). We can determine these values utilizing the same procedure discussed in Section 4.2 Again, we assume the desired output pressure from the turbine at Station 32 is known (22.03 MPa). Mole fractions of the gas entering the turbine are known based on the results of the combustion calculation described above (0.926 for hydrogen and 0.074 for water). One difference from Section 4.2 is that the high pressure oxidizer turbine powers two pumps: the High Pressure Oxidizer Turbopump and the Oxidizer boost pump. To account for this the $\dot W$ term in Equation 4.2.1 must be adjusted include the power requirement for both of these pumps: 22,880 HP and 1588 HP respectively. The results from this calculation displayed below on Figure 4.4.7. Once again the model gives excellent results, predicting mass flow rates within 5% of actual values.

Figure 4.4.7

Table 4.4.5

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