Uncertainty in Modeling Ablation Heat Transfer in Rocket Nozzles

The ablation of carbon cloth phenolic insulators used in solid rocket motor (SRM) nozzles involves highly complex phenomena that are difficult to accurately predict. Historical and even more modern ablation predictions rely heavily on anchoring to SRM test data to improve predictability and SRM reliability. Accelerated schedules, reductions in static SRM testing prior to flight, and a highly competitive global market are placing a substantial onus on computational capability and predictive uncertainty. Quantifying uncertainty in SRM nozzle ablation predictions is essential for motor reliability. This paper provides the details of a modern uncertainty quantification methodology applied to ablation predictions in carbon cloth phenolic insulators exposed to SRM nozzle environments. A particular historical test motor is used as a demonstration case. The system response quantities of interest are the erosion depth and char depth. A representative model and input uncertainty are provided, and a sensitivity analysis is performed to identify influential parameters. Uncertainties in the numerical models and inputs are propagated through a two dimensional uncertainty quantification methodology using a Latin Hypercube Sampling approach. The results show that the primary sources of uncertainty in SRM nozzle thermal modeling are the heat transfer coefficient, incident radiation heat flux, char material thermal conductivity, virgin material density, char material density, char material specific heat, and pyrolysis gas enthalpy. Uncertainties in the predictions of nozzle insulation erosion and char for the test case are provided relative to the nozzle location at the 99th percentile and 95th confidence interval. Uncertainty in the char depth is roughly +/- 28% along the entire axial length of the nozzle. Uncertainty in the erosion depth ranges from about +/- 45% for the entrance and throat regions to +/- 80% at the nozzle exit.