4262: Rockets and Mission Analysis Assigned: September 27, 2016

Homework #3 Due: October 6, 2016

The purpose of this homework assignment is to review and apply the basics of thrust chamber model development.

Question 1

A rocket thrust chamber contains a propellant of molecular weight 25 ad specific heat ratio 1.2. The chamber pressure is 10 MPa and the combustion temperature is 3,000 K. The throat area is 0.1 m2. Determine the thrust for the following conditions and discuss your results:

Case / Ambient Pressure (MPa) / Exhaust Area (m2)
1 / 0 / 0.1
2 / 0 / 4.06
3 / 0.101 / 0.1
4 / 0.101 / 4.06

Question 2

Consider the performance of a solid-propellant rocket under conditions that change with time. The stagnation temperature is constant at 3,000 K. The stagnation pressure changes with time according to:

P0 = 20 – 0.04t / 0 < t < 100

This equation is for P0 in MPa and t in seconds. The nozzle has an area ratio of 5 and a throat area of 0.3 m2. The rocket is operating in a vacuum. The fluid may be considered to have specific heat ration of 1.4 and average molecular weight of 20. Plot the (a) exhaust velocity versus time, (b) mass flow rate versus time, and (c) thrust versus time.

Question 3

A rocket operates at sea level with a chamber pressure of 20 atm, a chamber temperature of 2000 K, and a mass flow of =1 kg/s. Gas properties are taken as constant and are known to be Cp/Cv=1.3, Cp=0.36 kcal/kg K and R=350 J/kg K.

1.  Show graphically the variation of the area, A, density, r, velocity, V, and Mach Number, M, with respect to pressure in the system. Can the throat location be identified from these plots?

2.  Comment on plotting the results vs. pressure instead of position. What is the utility in plotting vs. pressure?

3.  Calculate the ideal thrust and the ideal specific impulse.

Question 4

Design the nozzle exit and throat area for an ideal rocket that has to operate at a 25 km altitude and provide 5 kN thrust at a chamber pressure and temperature of 20 atm and 2800 K, respectively. Take Cp/Cv=1.3 and R=350 J/Kg K. Determine the throat area, exit area, and exit temperature.

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