Problems

1. Enumerate and explain the merits and disadvantages of pressurized and turbopump feed systems.

2. In a turbopump it is necessary to do more work in the pumps if the thrust chamber operating pressure is raised. This of course requires an increase in turbine gas flow which, when exhausted, adds little to the engine specific impulse. If the chamber pressure is raised too much, the decrease in performance due to an excessive portion of the total propellant flow being sent through the turbine and the increased mass of the turbopump will outweigh the gain in specific impulse that can be attained by increased chamber pressure and also by increased thrust chamber nozzle exit area. Outline in detail a method for determining the optimum chamber pressure where the sea level performance will be a maximum for a rocket engine that operates in principle like the one shown in Fig. 1-4.

3. The engine performance data for a turbopump rocket system are as follows:

Engine system specific impulse 272 sec

Engine system mixture ratio 2.52

Engine system thrust 40,000 N

Oxidizer vapor flow to pressurize oxidizer 0.003% of total tank oxidizer flow

Propellant flow through turbine 2.1% of total propellant flow

Gas generator mixture ratio 0.23

Gas generator specific impulse 85 sec

Determine performance of the thrust chamber /,, r, F (see Sect. 10-2).

4. For a pulsing rocket engine, assume a simplified parabolic pressure rise of 0.005 sec, a steady-state short period of full chamber pressure, and a parabolic decay of 0.007 sec approximately as shown in the sketch. Plot curves of the following ratios as a function of operating time t from t = 0.013 to t = 0.200 sec; (a) average pressure to

ideal steady-state pressure (with zero rise or decay time); (b) average Is to ideal steady-state Is; (c) average F to ideal steady-state F.

5. For a total impulse of 100 lbf-sec compare the volume and system weights of a pulsed propulsion system using different gaseous propellants, each with a single spherical gas storage tank (at 3500 psi and 0°C). A package of small thrust nozzles with piping and controls is provided which weighs 5.2 lb. The gaseous propellants are hydrogen, nitrogen, and argon (see Table 7-3).

6. Compare several systems for a potential roll control application which requires four thrusters of 1 lbf each to operate for a cumulative duration of 2 min each. Include the following:

Pressurized helium Cold Pressurized nitrogen Cold Pressurized krypton Cold Pressurized helium at 500°F (electrically heated)

The pressurized gas is stored at 5000 psi in a single spherical fiber-reinforced plastic tank; use a tensile strength of 200,000 psi and a density of 0.050 lbm/in.3 with a 0.012 in. thick aluminum inner liner as a seal against leaks. Neglect the gas volume in the pipes, valves, and thrusters, but assume the total hardware mass of these to be about 1.3 lbm. Use Table 7-3. Make estimates of the tank volume and total system weight. Discuss the relative merits of these systems.

7. Make tables comparing the merits and disadvantages of engines using the gas generator cycle and engines having the staged combustion cycle.

8. Prepare dimensioned rough sketches of the two propellant tanks needed for operating a single RD253 engine (Table 10-5) for 80 sec at full thrust and an auxiliary rocket system using the same propellants, with eight thrust chambers, each of 100 kg thrust, but operating on the average with only two of the eight firing at any one time, with a duty cycle of 12 percent (fires only 12% of the time), but for a total flight time of 4.00 hours. Describe any assumptions that were made with the propellant budget, the engines, or the vehicle design, as they affect the amount of propellant.

9. Table 10-5 shows that the RD 120 rocket engine can operate at 85% of full thrust and with a mixture ratio variation of ±10.0%. Assume a 1.0% unavailable residual propellant. The allowance for operational factors, loading uncertainties, off-nominal rocket performance, and a contingency is 1.27% for the fuel and 1.15% for the oxidizer.

(a) In a particular flight the average thrust was 98.0% of nominal and the mixture ratio was off by + 2.00% (oxidizer rich). What percent of the total fuel and oxidizer loaded into the vehicle will remain unused at thrust termination?

(b) If we want to run at a fuel-rich mixture in the last 20% of the flight duration (in order to use up all the intended flight propellant), what would the mixture ratio have to be for this last period?

(c) In the worst possible scenario with maximum throttling and extreme mixture ratio excursion (but operating for the nominal duration), what is the largest possible amount of unused oxidizer or unused fuel in the tanks?

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