# ENAE 483/788D Principles of Space Systems Design Fall, 2002

## Question 10:

For both ENAE 483 and ENAE 788D:

a) The NERVA rocket engine used hydrogen (H2) as propellants, heated by a nuclear reactor. Assuming the Isp for an ideally expanded NERVA engine was 900 sec, reverse engineer the engine to estimate the temperature of the hydrogen in the reactor. (Hint: since no combustion takes place, assume the ratio of specific heat for H2 is the ideal value of 1.4)

b) It would be nice to use a simple, easy to handle material like water as propellant for a nuclear engine. Based on the data for the NERVA from (a), estimate the Isp available using water for the propellant.

c) You need to design a pressure-fed system to supply LOX to a hybrid rocket engine. The LOX tank contains 10,000 kg initially. You need to pressurize the tank to 300 psi. Due to the regulator used, the minimum pressure drop between the helium pressurant tank and the LOX tank is 100 psi. Find the volume and mass of helium required for this pressurization, assuming the initial He tank pressure is 3000 psi and the initial temperature is 300°K.

For ENAE 788D only:

d) An upper stage (operating in vacuum) contains 15,000 kg of LOX/LH2 at a stochiometic mixture ratio. The inert mass of the stage, including everything except the rocket nozzle, is 1000 kg. Assume the throat diameter of the rocket engine is 0.1 m, and the nozzle is a hollow cone with a 15° half-angle. The nozzle has a mass of 10 kg per square meter of surface area. The rocket engine has a chamber pressure of 1000 psi and a combustion temperature of 3800°K. Find the exit pressure Pe and expansion ratio Ae/At that maximizes total delta-V for the stage. What is the maximum delta-V?