The rheology dependent region in turbulent pipe flow of a Generalised Newtonian fluid

Direct numerical simulations (DNS) of turbulent pipe flow of a Generalised Newtonian (GN) fluid at Re_τ = 323 are analysed to identify the region where GN rheology has the major influence. The flow domain is divided into two parts: in y⁺ < y⁺_up and y⁺ > y⁺_up, with the viscosity modelled using a power-law rheology for y⁺ < y⁺_up and a uniform viscosity for y⁺ > y⁺_up. Values for y⁺_up of 35 and 70 are considered. Results show that beyond y⁺ = 70, the GN rheology has no significant effect on the mean flow or turbulence statistics, and that the effect of GN rheology is confined to the near wall. To understand these results, the turbulent kinetic energy budget of the GN fluid and a Newtonian fluid at the same Re_τ = 323 are compared. The comparison shows that the GN viscosity-dependent terms in the balance either vanish or do not show rheology dependence beyond y⁺ = 70. The current results imply that in Reynolds averaged Navier–Stokes and Large eddy simulations the GN rheology’s effects can be taken care of by modifying the wall functions.