Uncertainty analysis of decomposing polyurethane foam

Sensitivity/uncertainty analyses are necessary to determine where to allocate resources for improved predictions in support of our nation’s nuclear safety mission. Yet, sensitivity/uncertainty analyses are not commonly performed on complex combustion models because the calculations are time consuming, CPU intensive, nontrivial exercises that can lead to deceptive results. To illustrate these ideas, a variety of sensitivity/uncertainty analyses were used to determine the uncertainty associated with thermal decomposition of polyurethane foam exposed to high radiative flux boundary conditions. The polyurethane used in this study is a rigid closed-cell foam used as an encapsulant. The response variable was chosen as the steady-state decomposition front velocity. Four different analyses are presented, including (1) an analytical mean value (MV) analysis, (2) a linear surrogate response surface (LIN) using a constrained latin hypercube sampling (LHS) technique, (3) a quadratic surrogate response surface (QUAD) using LHS, and (4) a direct LHS (DLHS) analysis using the full grid and time step resolved finite element model. To minimize the numerical noise, 50 μm elements and approximately 1 ms time steps were required to obtain stable uncertainty results. The complex, finite element foam decomposition model used in this study has 25 input parameters that include chemistry, polymer structure, and thermophysical properties. The surrogate response models (LIN and QUAD) are shown to give acceptable values of the mean and standard deviation when compared to the fully converged DLHS model.