PROBABILISTIC THERMAL DESIGN OF A ROCKET CHAMBER WALL COOLING SYSTEM

The baseline design of a liquid rocket chamber wall cooling system obtained deterministically was combined with a probabilistic methodology. This procedure allowed an initial assessment on response variability to perturbations in the physics model input parameters under a fixed geometry as well as the generation of thermal probabilistic data for a complete reliability assessment on low cycle fatigue (LCF). A total of twenty random variables (inputs to the thermal code) representing the rocket engine system operating conditions and regenerative cooling model empiricism were selected. Actual test data and engineering judgement were applied in statistically characterizing the variables. Sensitivity factors for chamber wall maximum temperature, and regenerative coolant exit conditions were then determined at the median and "plus two sigma" probability design points (PDP) of the cumulative distribution function (CDF). The PDP separates the design space into "failure" and "safe" regions. The results indicate that the influence and٫or sensitivity of input variables to the variability of a given response depends on the selected PDP. The generated CDF for the baselined ۱۳۶۰ R (۷۵۵ K) copper chamber wall temperature reveals that the best estimate (i.e. ۵۰% confidence level) failure probability of not exceeding a maximum allowable wall temperature of ۱۵۴۰ R (۸۵۵.۵ K) is approximately ۲.۳%. With a ۹۰% confidence interval however, the error bounds predict a safe region probability of ۹۹.۹۹% at the lower limit and only ۴۹% at the upper limit.