The simplified relations that follow give the basic method for determining the overall specific impulse, the total propellant flow, and the overall mixture ratio as a function of the corresponding component performance terms for complete rocket engine systems. This applies to engine systems consisting of one or more thrust chambers, auxiliaries, gas generators, turbines, and evaporative propellant pressurization systems all operating at the same time.
Refer to Eqs. 2-5 and 6-1 for the specific impulse Is, propellant flow rate w or m and mixture ratio r. The overall thrust Foa is the sum of all the thrusts from thrust chambers and turbine exhausts and the overall flow m is the sum of their flows. The subscripts oa, o, and/ designate the overall engine system, the oxidizer, and the fuel, respectively. Then
These same equations should be used for determining the overall performance when more than one rocket engine is contained in a vehicle propulsion system and they are operating simultaneously. They also apply to multiple solid pro-pellant rocket motors and combinations of liquid propellant rocket engines and solid propellant rocket booster motors, as in the Space Shuttle (see Fig. 1-13).
Example 10-2. For an engine system with a gas generator similar to the one shown in Fig. 1-4, determine a set of equations that will express (1) the overall engine performance and (2) the overall mixture ratio of the propellant flows from the tanks. Let the following subscripts be used: c, thrust chamber; gg, gas generator; and tp, tank pressur-ization. For a nominal burning time t, a 1% residual propellant, and a 6% overall reserve factor, give a formula for the amount of fuel and oxidizer propellant required with constant propellant flow. Ignore stop and start transients, thrust vector control, and evaporation losses.
SOLUTION. Only the oxidizer tank is pressurized by vaporized propellant. Although this pressurizing propellant must be considered in determining the overall mixture ratio, it should not be considered in determining the overall specific impulse since it stays with the vehicle and is not exhausted overboard.
_ (m0)e + (m0)gg + (m0)tp oa / • \ i <* ■ \ VAU lu/
(mf)c + (mf)gg mf = [(rhf)c + (mf)gg\ t (1.00 + 0.01 + 0.06)
m„ = [(m0)e + (m0)gg + (m0)lp] t (1.00 + 0.01 + 0.06)
For this gas generator cycle the engine mixture ratio or roa is different from the thrust chamber mixture ratio rc = (m0)c/(mf)c. Similarly, the overall engine specific impulse is slightly lower than the thrust chamber specific impulse. However, for an expander cycle or a staged combustion cycle these two mixture ratios and two specific impulses are the same, provided that there are no gasified propellant used for tank pressurization.
The overall engine specific impulse is influenced by the nozzle area ratio and the chamber pressure, and to a lesser extent by the engine cycle, and the mixture ratio. Table 10-3 describes 11 different rocket engines using liquid oxygen and liquid hydrogen propellants designed by different companies in different countries, and shows the sensitivity of the specific impulse to these parameters. References 10-13 to 10-15 give additional data on several of these engines.
TABLE 10-3. Comparison of Rocket Engines Using Liquid Oxygen and Liquid Hydrogen Propellants
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