Uncertainty propagation in simulation predictions of generalized Newtonian fluid flows

Abstract

We elucidate how uncertainties from rheological measurements manifest in a Generalized Newtonian Fluid (GNF) flow prediction. As specific examples, the resistance and velocity of a settling sphere under gravity in Carbopol and Polyvinylpyrrolidone (PVP) solution was predicted using a Herschel–Bulkley and a Carreau model. Uncertainties in model predictions are quantified, accounting for parametric uncertainties in geometry and rheological models. While the prediction for a settling sphere in PVP falls within the quantified uncertainty bounds, the self-consistent predictions for Carbopol do not. This quantifies the inadequacy of a GNF model for Carbopol in this configuration. Generalizing these results, a validation procedure is presented as a framework for including model-parameter uncertainties in model predictions and identifying model-form error. This information provides quantitative assessments to inform decisions.