Numerical simulations of Carreau‐model fluid flows past a circular cylinder

Abstract

Numerical simulations of shear-thinning and shear-thickening fluid flows past a circular cylinder are performed using a lattice Boltzmann method. In this study, the property of shear-thinning and shear-thickening fluids is expressed by the Carreau model. We focus on the definition of an effective (representative) Reynolds number for describing the flow of shear-thinning and shearthickening fluids past a circular cylinder. The fluid flows and viscosity profiles are clearly shown for fluids flowing across a circular cylinder depending on the Reynolds and Carreau numbers and the power index. A large value of Carreau number lead to the formation of low-viscosity regions for shear-thinning and high-viscosity regions for shear-thickening around a circular cylinder. Meanwhile, the change in the viscosity around the cylinder is not remarkable for a small Carreau number. The formulation of the effective Reynolds number defined using effective shear rate and viscosity is proposed in order to organize and understand the flow of Carreau-model fluids across a circular cylinder. The effective Reynolds number counseled in this study allows one to completely describe the flow state of Carreau-model fluids past a circular cylinder on an equal footing with Newtonian fluid flows. The usefulness of the effective Reynolds numbers is discussed, and the feature of Carreau-model fluid flows past a circular cylinder is considered in terms of the effective Reynolds number.

Dynamics of a Polymer Solution Droplet on a High‐Temperature Surface

“…Therefore, it is necessary to estimate the effective viscosity of the system, η eff . Accordingly, the effective shear rate, which determines the effective viscosity, should be carefully selected for fluid flows with non‐Newtonian fluids 36–38. Generally, the effective shear rate for droplets can be defined as 39, 40.…”

Numerical investigation of double emulsion formation in non-Newtonian fluids using double co-flow geometry

“…the Weber number (We), which compares inertia forces to surface tension, the capillary number (Ca), which measures the relative influence of viscous forces versus interfacial forces, and the Reynolds number (Re), which determines the ratio of inertial to viscous forces. Reynolds number is estimated to describe non-Newtonian fluid flows using the following relation (Ohta et al 2020):…”

Design of Artificial Neural Network for predicting the reduction in permeability of porous media as a result of polymer gel injection

“…A) By coupling equations for the kinematic viscosity of the non-Newtonian model and equation (4) shear-dependent relaxation time τ at each node can be obtained. For the Carreau model, frequency (ω) can be calculated which is the inverse of relaxation time, iteratively, with the below formula (Ohta et al, 2020):…”