Uncertainty quantification for the squeeze flow of generalized Newtonian fluids

TL;DR

This paper applies Uncertainty Quantification to improve rheological modeling of generalized Newtonian fluids in squeeze flow, demonstrating enhanced prediction accuracy and deeper insight into complex flow behaviors through Bayesian inference.

Contribution

It introduces a semi-analytical three-region truncated power law model combined with UQ techniques for better rheological parameter estimation in complex flows.

Findings

Bayesian inference updates rheological parameters with experimental data.

Uncertainty quantification improves model predictions for squeeze flow.

The approach reveals unobservable flow regime distributions.

Abstract

The calibration of rheological parameters in the modeling of complex flows of non-Newtonian fluids can be a daunting task. In this paper we demonstrate how the framework of Uncertainty Quantification (UQ) can be used to improve the predictive capabilities of rheological models in such flow scenarios. For this demonstration, we consider the squeeze flow of generalized Newtonian fluids. To systematically study uncertainties, we have developed a tailored squeeze flow setup, which we have used to perform experiments with glycerol and PVP solution. To mimic these experiments, we have developed a three-region truncated power law model, which can be evaluated semi-analytically. This fast-to-evaluate model enables us to consider uncertainty propagation and Bayesian inference using (Markov chain) Monte Carlo techniques. We demonstrate that with prior information obtained from dedicated experiments - most importantly rheological measurements - the truncated power law model can adequately predict the experimental results. We observe that when the squeeze flow experiments are incorporated in the analysis in the case of Bayesian inference, this leads to an update of the prior information on the rheological parameters, giving evidence of the need for recalibration in the considered complex flow scenario. In the process of Bayesian inference we also obtain information on quantities of interest that are not directly observable in the experimental data, such as the spatial distribution of the three flow regimes. In this way, besides improving the predictive capabilities of the model, the uncertainty quantification framework enhances the insight into complex flow scenarios.