HTPB Fuel Grain Flow Rate, Sizing, and Thrust

Regression Rate Governs Size The faster the solid propellant is burned, the “fatter” the rocket must be to accommodate such a burn. Several parameters must be known to size a rocket –Fuel Mass –Regression Rate Once regression rate and fuel mass have been determined, mass flow rate and thrust can be found.

Fuel Mass Total fuel mass can be found using Tsiolkovsky’s basic rocket equation. –Assuming complete burn of the fuel. Propellant mass is simply a fraction of the total fuel mass due to an oxidizer-fuel ratio of 8:1.

Regression Rate A general formula taken from a paper by Chiaverini, M. J. is: This equation is based off a pipe-type fuel grain geometry.

Fuel Grain Sizing The amount of solid propellant burned in one second was estimated using the regression rate, which then leads to an approximate mass flow rate for HTPB. Using this, total time for the fuel to burn up can be estimated and an outside diameter for the fuel grain calculated. L = 0.3 m d i = 0.03 m d o = m

Fuel Grain Sizing cont’d The outside diameter of the fuel grain, however, was increased to m. –Allow extra fuel to insulate combustion chamber walls –Utilize standard pipe sizes during ground testing

Mass Flow Rate Mass flow rate is an essential calculation: Oxidizer flow during testing Nozzle design Thrust Oxidizer flow rate can be found using the following relationship:

Thrust The calculation of thrust is very basic. During ground testing, we can assume atmospheric pressure to be equivalent to exit pressure (p e = p a ). –The new equation is as follows: This results in a thrust of approximately 550N.

Thrust cont’d In a vacuum, we can assume p a << p e. –The new thrust equation is as follows: The pressure differential in a vacuum generates an even greater thrust. How much extra thrust is generated will depend on the design of the nozzle.

Final Notes Regression rate is an inexact science which relies on multiple parameters. It is based off experimental data,theoretical predictions, and correlation of parameters. The sizing calculations performed will give our team the ability to conduct our first test. Testing of the engine and measurements of actual regression rate will determine the true size of the final rocket design.