DNS and LES with an extended Smagorinsky model for wall turbulence in non-Newtonian viscous fluids

• A turbulent flow field can be investigated generally with the variable viscosity.
• A proposed extended Smagorinsky model can realize LES of non-Newtonian viscous fluid.
• The extended model can predict the SGS stress in shear-thinning and shear-thickening.
• We can expect accurate LES in general by using the spatial scale correction.

To develop better computer modeling methods for wall turbulence in non-Newtonian viscous fluids, we performed direct numerical simulations (DNS) and large eddy simulations (LES) of turbulent channel flow of various non-Newtonian fluids, with viscosity described by the power-law model and the Casson model. We focused on low-Reynolds-number wall turbulence of non-Newtonian viscous fluid close to Newtonian fluid to observe the deviation of the turbulence structures of fully developed turbulent flow near a wall from Newtonian fluid. From the results of the DNS, we found that, as for Newtonian fluid, the turbulence structures of these viscous fluids could be generally normalized but with locally varying viscosity. Performing the LES with the Smagorinsky model as a subgrid scale (SGS) model extended according to the results of the DNS, we evaluated the reliability of the extended SGS model. For the various non-Newtonian viscous fluids considered, the mean velocity profiles obtained by these LESs with the extended model rather than the LES with the standard model corresponded closely with those obtained by DNS. Consequently, we demonstrated that the Smagorinsky model of turbulent flows for non-Newtonian viscous fluid can be treated universally via spatial scaling of the locally varying viscosity.