MAE 5495: Launch Vehicle Analysis

MAE 5495: Launch Vehicle Analysis

Homework #4

Due: 24 Apr 2008

1.  (20%) You have designed a solid propulsion system that utilizes the following solid propellants: 18% Aluminum, 71% Ammonium Perchlorate, and 11% HTPB. The pressure vessel design limits the stagnation pressure to Po = 3.447 MPa. A thermochemistry code has predicted values for the products of g = 1.190 and molecular weight = 31.01 kg/kmol. The propulsion system must deliver a constant thrust of F = 3113.76 N. Using Propellant B (Table 6.9 of the course text, pg. 330), calculate the following parameters:

A.  (2%) Propellant regression rate

B.  (5%) System specific impulse for ideal expansion at sea level

C.  (2%) Propellant mass flow rate

D.  (5%) Burn area

E.  (3%) Nozzle throat area

F.  (3%) Nozzle expansion ratio for ideal expansion at sea level

2.  (60%) Your company has secured funding to develop a solid rocket motor for missile defense applications. The motor will use the readily available TP-H-3340 (18% Aluminum, 71% Ammonium Perchlorate, and 11% HTPB) as propellant. Your job is to perform the preliminary sizing of the motor case and nozzle to predict the thruster’s performance. The following data is given to you as requirements:

Mission DV: 550 m/sec

Initial Mass of the Missile (max): 45.36 kg

Initial Po: 12.410 MPa

Initial Thrust: 2224.1 N

Atmospheric Pressure: 0.07584 MPa

Grain Geometry: Center port cylindrical burning tube. L/D = 8.5 (for the grain)

Motor Case: r = 1500 kg/m3, Ftu = 1.34 GPa, Safety Factor = 1.25, Diameter = 0.092 m

Insulation: r = 1100 kg/m3

Nozzle: e = 21.297, qcn = 15°, Lsub = 20%

Propellant Product Parameters: g = 1.190, molecular weight = 31.01 kg/kmol

A.  (9%) Size the mass, inner radius and length of the solid propellant grain.

B.  (9%) Size the nozzle (throat diameter, exit diameter, diverging section length)

C.  (15%) Accomplish a burn simulation to determine the burn time such that the propellant burns completely from inner radius to outer radius. Use a Dt = 0.1 sec. In doing so, you should generate data for the mass flow, stagnation pressure and thrust as a function of time. Use this data to generate plots of the motor’s performance.

D.  (3%) Calculate the nozzle mass.

E.  (9%) Design the motor case, pressure vessel, and insulation.

F.  (5%) Find the resultant Finert.

G.  (10%) Calculate the resulting DV. How does this compare with the original design requirement? If it is not the same, what should be done with the preliminary design?

3.  (20%) Design a hybrid rocket motor that provides an initial thrust of 355.86 N with a total burn time of 50 sec. The motor will be ideally expanded at an ambient pressure of 0.0748 MPa. The propellants are HTPB and liquid oxygen (a = 0.00002, n = 0.8, m = -0.2). At the design point, you are targeting an O/F = 1.6 and a Po = 1.361 MPa. Size a single-port grain (center port) as follows:

A.  (5%) Determine the required mass flow rates for the propellants.

B.  (5%) Design an ideal nozzle that will provide the required thrust level.

C.  (5%) Assume a reasonable number for the initial oxidizer mass flux and determine the port’s cross-sectional dimensions.

D.  (5%) Determine the port length required.