A simple approach for effective CFD simulation of turbulent pipe transport of shear-thinning, power-law fluids

Abstract

This study presents a simple, efficient approach for the CFD simulation of turbulent pipe transport of shear-thinning, power-law fluids. The method is developed within the Newtonian-based Reynolds-Averaged Navier-Stokes (RANS) framework, and it relies on a modification to the Reynolds-averaged apparent viscosity function to compensate for errors induced by the non-decomposition of the instantaneous apparent viscosity, as well as for the use of turbulence models developed for Newtonian fluids. Specifically, the Reynolds-averaged apparent viscosity switches from a power law to a logarithmic function for averaged shear rates below a threshold value, called the “critical shear rate”, which becomes a calibration parameter of the model. The new framework was tested against DNS data reported in the literature for different pipe-flow conditions, covering combinations of flow index $n=\{1.0,0.8,0.6\}$ and friction Reynolds number ${\mathrm{Re}}_{\tau }=\{323,500,750\}$, as well as against well-established correlations for the friction factor, with the analysis extended to cases up to $n=0.4$ and ${\mathrm{Re}}_{\tau }=2,500$. The analysis was conducted by employing three different turbulence models, namely Lam-Bremhorst k-ε, two-layer k-ε, and k-ω SST, which all rely on a low-Reynolds number treatment to obtain a detailed flow description in the near-wall region. The proposed approach appears attractive from an engineering standpoint, as it allows obtaining reasonably accurate prediction of main features of turbulent pipe transport of shear-thinning, power-law fluids, with a simple mathematical formulation and a robust and easy-to-converge character that can make a difference for the application to more complex flows.