A gPC-based Global Sensitivity Analysis for Phosphate Slurry Flow in Pipelines

The present work focuses on a new application of the Generalized Polynomial Chaos (gPC) approach: the stochastic response of a three-dimensional simulation of slurry pipe flows in pipelines subject to parametric uncertainties. Initial and boundary conditions (e.g., the slurry flowrate used at the pipe entrance, initial solid concentration), material properties (e.g., particles size), model parameters (e.g., specularity coefficient when the kinetic theory of granular flow (KTGF) is coupled with the Eulerian-Eulerian model), and geometry-related factor (e.g., pipe inclination) are considered as random parameters. gPC surrogate model is built through a least angle regression (LAR) methodology in order to perform uncertainty quantification and global sensitivity analysis following a variance-based approach. The use of gPC is motivated based on its ability to estimate Sobol’ indices efficiently. These variance-based sensitivity indices are effective to perform sensitivity analysis without any assumptions about the model’s linearity or monotony. Retaining the gPC technique has the advantage of giving the global sensitivity Sobol’ indices in a straightforward manner at a lower computing cost than the usual Monte Carlo (MC) method. The first order and total Sobol’ indices of the pressure drop along the pipe are calculated and their inspection show that the variability of the pressure gradient is mainly due to the principal effects of the inlet velocity, followed by the inclination of the pipe and then the size of particles. Within the framework of uncertainty quantification, the gPC expansions will also be applied as a surrogate model, as its objective is to recreate the global behavior of the CFD model in a manner that is consistent with a polynomial decomposition.