Numerical investigation of turbulent flow of Herschel–Bulkley fluids in a concentric annulus with inner cylinder rotation

In the present work, under-resolved direct numerical simulation (UDNS) is used to study the turbulent flow of Herschel–Bulkley fluids in a concentric annular region with the rotation effect of the inner cylinder. The current numerical method is verified against the first- and second-order statistics of the velocity field with the large-eddy simulation (LES) data available in the literature for the Reynolds number of 8,900. The influence of the flow behavior index ($n=$ 0.65, 0.70, and 0.75), the Bingham number ($Bn=$ 0.10, 0.25, and 0.40), and the Rotation number ($N=$ 0, 0.15 and 0.30) on the flow characteristics are explored. The instantaneous flow quantities, including contours of the axial velocity and viscosity and vortical structures, and mean flow features, such as the first- and second-order turbulence statistics, mean viscosity profiles, pressure gradient, and skin friction coefficients, are investigated. The results show that weaker Reynolds stress tensor components are generated as the $n$ value is reduced and the Bingham number increases. Moreover, raising the rotation rate increases the magnitudes of turbulent statistics and makes the velocity fluctuations more asymmetrical.