High-precision surrogate modeling for uncertainty quantification in complex slurry flows

Abstract

Slurry transportation via pipelines is essential for global industries, offering efficiency and environmental benefits. Specifically, the precise calibration of physical parameters for transporting raw phosphate material to fertilizer plants is crucial to minimize energy losses and ensure secure operations. Computational fluid dynamics is commonly employed to understand solid concentration, velocity distributions, and flow pressure along the pipeline. However, numerical solutions for slurry flows often entail uncertainties from initial and boundary conditions, emphasizing the need for quantification. This study addresses the challenge by proposing a framework that combines proper orthogonal decomposition and polynomial chaos expansions to quantify uncertainties in two-dimensional phosphate slurry flow simulations. The use of surrogate modeling methods, like polynomial chaos expansion, proves effective in reducing computational costs associated with direct stochastic simulations, especially for complex flows with high spatial variability, as observed in phosphate slurries. Unlike most studies that consider 0D or 1D quantities of interest, our approach analyzes the results of the UQ process in a two-dimensional spatial context while relying on fully three-dimensional simulations that capture secondary flows, turbulence effects, and other three-dimensional phenomena. Numerical results demonstrate the accuracy of the non-intrusive reduction method in reproducing mean and variance distributions. Moreover, the uncertainty quantification analysis shows that the reduced-order model significantly reduces computational costs compared to the full-order model.