An eddy-viscosity model for turbulent flows of Herschel–Bulkley fluids

S Lovato,J.W Settels,G.H Keetels,S.L Toxopeus

doi:10.1016/j.jnnfm.2021.104729

Abstract

This article presents a new turbulence closure based on the k-ω SST model for predicting turbulent flows of Herschel–Bulkley fluids, including Bingham and power-law fluids. The model has been calibrated with direct numerical simulations (DNS) data for fully-developed pipe flow of shear-thinning and viscoplastic fluids. The new model shows good agreement in the mean velocity, average viscosity, mean shear stress budget and friction factor. The latter compares well also against correlations from the literature for a wide range of Reynolds numbers. With the new model, improvements are also observed in the iterative convergence, which is often difficult for calculations with yield-stress fluids. Additionally, three eddy-viscosity models for Newtonian fluids, namely the k-ω SST, k-kL and Spalart–Allmaras model, have been tested on turbulent Herschel–Bulkley flows. Results show that (i) the new model produces the best prediction; (ii) the standard SST model may be considered for simulations of weakly shear-thinning/viscoplastic fluids at high Reynolds numbers; (iii) the k-kL and the Spalart–Allmaras models appear to be unsuitable for turbulent Herschel–Bulkley flows. The new model is simple and appealing for engineering applications concerned with turbulent wall-bounded flows and is presented in a formulation that can be easily adapted to other generalised Newtonian fluids.

Highlights

Numerical simulations of turbulent Herschel–Bulkley flows are of great interest for several industrial applications, such as open channel flows of ore tailings in the mining industry or pipe flows of drilling mud in the oil industry
Numerical studies of turbulent Herschel–Bulkley flows have become of interest even for the maritime sector, with regard to the effects of muddy seabeds on marine vessels navigating in harbours and rivers [1,2]
The prohibitive costs of Direct Numerical Simulations (DNS) for predicting turbulent flows makes turbulence modelling the only feasible alternative for most engineering applications as it offers an acceptable compromise between cost and accuracy

Summary

Introduction

Numerical simulations of turbulent Herschel–Bulkley flows are of great interest for several industrial applications, such as open channel flows of ore tailings in the mining industry or pipe flows of drilling mud in the oil industry. The prohibitive costs of Direct Numerical Simulations (DNS) for predicting turbulent flows makes turbulence modelling the only feasible alternative for most engineering applications as it offers an acceptable compromise between cost and accuracy. The most widespread modelling technique is the so-called Reynolds-averaging, which makes use of the Reynolds-averaged Navier–Stokes (RANS) equations. These models are usually referred to as RANS models. RANS models for Herschel–Bulkley fluids have not yet received enough recognition in the CFD community, CFD practitioners often apply Newtonian RANS models to non-Newtonian fluids, and this continued to happen until very recently (e.g., [1,2,3,4,5])

Objectives

Results

Conclusion