Turbulent Channel Flow With Spatially Dependent Viscosity: A Numerical Study

In this study, we examine in detail the effect of spatially dependent viscosity on wall-bounded flow. For this purpose, direct numerical simulations (DNS) are performed considering a channel flow with a viscosity change along the streamwise direction. The DNS were performed using NEK5000, a computational fluid dynamics code developed at Argonne National Laboratory. The channel is divided into three different regions: in the first one, the flow is at a constant Reynolds number of Re ¼ 5000; in the second region, the Reynolds number is imposed to linearly increase as viscosity decreases through a ramp; and finally, in the third region, the flow is again at a constant Reynolds number, this time at Re ¼ 10,000. Since the temperature field is not evaluated, the proposed setup is a simplification of a heated channel. Nevertheless, the outcomes of this study may be valuable for future works considering variable-viscosity effects, especially for cooling and heating applications. Four test cases with different ramp inclinations were analyzed. The results from this study were compared with a correlation available in the literature for the friction Reynolds number as a function of the Reynolds number. We observe that in all cases the ramp does not cause an immediate change in the characteristics of turbulent structures, and a delay is in fact observed in both wall shear and friction. Finally, in order to characterize and understand these effects, streaks from the viscous region and turbulence statistics for the turbulent kinetic energy (TKE) budget terms are analyzed.