A Bayesian approach to estimate flame spread model parameters over the cylindrical PMMA samples under various gravity conditions

The flammability limit of cylindrical polymethyl-methacrylate (PMMA) samples in an opposed-flow was observed experimentally under various gravity levels at 1$G$ or more utilizing a centrifuge. Flame spread on the sample was observed, and the limiting oxygen concentration (LOC) was measured in various opposed-flow velocities ranging from 5 to 30 cm/s. Two rotating radii of the centrifuge were tested to assess the effects of Coriolis force on the LOC. A scale analysis model, based on an energy balance equation, was evaluated for thermally thick cylindrical samples. The buoyancy-induced flow was modeled in the analytical model. Model parameters were evaluated with a Bayesian approach: The Metropolis Hasting (a Markov Chain Monte Carlo) method. The results indicated that flames were tilted by the Coriolis force when the oxygen concentration was sufficiently rich from the LOC in 4$G$. However, the effects were negligible under the oxygen concentration conditions near LOC. No significant difference in the LOC was also observed even when the rotating radius of the centrifuge changed. At 1$G$ or higher, the LOC approached to a certain value asymptotically with decreasing the opposed-flow velocity. The LOC also increased with increasing the gravity level and sample diameter. The measured LOCs were used to sample model parameters using MCMC methods. Consequently, a suitable fitting curve of the model to the experimental LOC was obtained. Using the predicted model parameters, the LOC under microgravity, Moon, and Mars conditions were predicted as a function of the opposed-flow velocity. In microgravity, the LOC increased greatly with decreasing the forced flow velocity (the radiative extinction regime), and the minimum LOC (MLOC) was recognized. On Moon, the credible interval of LOC was rather large in the low-velocity region, and the MLOC was also recognized. Moreover, it was possible that the cylindrical PMMA sample exhibited the highest flammability not under microgravity but a partial gravity condition.

Novelty and Significance

From observing the limiting oxygen concentration of the flammability limit for cylindrical polymethyl-methacrylate (PMMA) samples in opposed-flows under various gravity conditions, we developed a model of limiting oxygen concentration (LOC) for thick cylindrical samples with the buoyancy induced flow was developed, and we estimated difficult-to-predict parameters using Bayesian statistical methods. Using this model, we can estimate the flammability limits under various gravity conditions of manned space exploration, including Moon and Mars. In addition, the present study shows that the minimum limiting oxygen concentration (MLOC) is the lowest in partial gravity. These results open a new research field for partial gravity combustions, apart from the normal gravity and microgravity and contribute to the understanding on the fire safety on manned space explorations to Moon and Mars.