A comprehensive model to predict and mitigate the erosion of carbon-carbon/graphite rocket nozzles

An integrated theoretical/numerical framework is established and validated thoroughly to study the erosion of carbon-carbon/graphite nozzle material in solid rocket-motor environments. The numerical framework takes into account propellant chemistry, detailed thermofluid dynamics, homogeneous chemical kinetics in the gas phase, heterogeneous reactions at the nozzle surface, and nozzle geometry and material properties. The gas-phase flame dynamics is based on the complete conservation equations for multicomponent reacting system. Typical combustion species of AP/HTPB and AP/HTPB/Al propellants at practical motor operating conditions are considered at the nozzle inlet. Full account of variable transport and thermodynamic properties is considered. The energy equation is solved for the process in the nozzle material with appropriate species and energy boundary conditions at the gas-solid interface. Three heterogeneous reactions involving carbon-carbon/graphite and the oxidizing species of H₂O, CO₂, and OH are considered at the interface. The predicted surface recession rates compare very well with available experimental data. The results indicate that erosion is most severe at the nozzle throat with the main contribution is from the species H ₂O. The important factors that dictate the erosion process are nozzle surface temperature, concentrations of the oxidizing species at the nozzle inlet, rate of diffusion of oxidizing species towards the surface, motor operating conditions, and nozzle geometry and material properties. The erosion rate increases almost linearly with chamber pressure for both metallized and non-metallized propellants. The erosion rate decreases with propeUants with higher aluminum content since the concentration of oxidizing species such as H₂O, OH, and CO₂ reduces. Finally, a recently suggested nozzle boundary layer control system (NBLCS) has been implemented by incorporating an injection upstream of the throat. It is shown that the NBLCS helps reduce the nozzle throat erosion rate significantly by reducing the surface temperature and by lowering the detrimental oxidizing species concentrations near throat area.