Similarity solution of fuel mass transfer, port mass flux coupling in hybrid propulsion

• Published in: Journal of engineering mathematics 2014-02, Vol.84 (1), p.19-40
• Main Author: Cantwell, B. J.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Cylinders; Flux; Fuels; Liquids; Mass transfer; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Oxidizers; Ports; Rockets; Theoretical and Applied Mechanics
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-013-9624-y

Boundary layer combustion is the primary mechanism of hot gas generation in hybrid rockets. The idea of a hybrid rocket is to store the oxidizer as a liquid and the fuel as a solid, producing a design that is less susceptible to chemical explosion than conventional solid and bipropellant liquid designs. The fuel is contained within the rocket combustion chamber in the form of a cylinder, with a circular channel called a port hollowed out along its axis. Upon ignition, a diffusion flame forms over the fuel surface along the length of the port. The combustion is sustained by heat transfer from the flame to the solid fuel causing continuous fuel vaporization until the oxidizer flow is turned off. Theory shows that the fuel mass transfer rate is proportional to the mass flux averaged across the port. The mass flow rate increases with axial distance, leading to coupling between the local fuel regression rate and the local mass flux. For proper design, accurate expressions are needed for both the time-dependent oxidizer-to-fuel ratio at the end of the port and the time at which all the fuel is consumed. As the fuel is depleted, the flame approaches the motor case, at which point the burn must be terminated. The purpose of this paper is to present a similarity solution for the coupled problem and a brief discussion of current practice.