  It has previously been shown that by increasing the Reynolds number across a
channel by spatially varying the viscosity does not cause an immediate change
in the size of turbulent structures and a delay is in fact observed in both
wall shear and friction Reynolds number (Coppo Leite, V. & Merzari, E.,
Proceedings of the ASME 2020 FEDSM, p. V003T05A019). Furthermore, it is also
shown that depending on the length in which the flow condition changes,
turbulence bursts are observed in the turbulence field. For the present work we
propose a new version of the standard Reynolds Averaged Navier Stokes (RANS)
k-tau model that includes some modifications in the production term in order to
account for these effects. The new proposed model may be useful for many
engineering applications as turbulent flows featuring temperature gradients and
high heat transfer rates are often seen in heat exchangers, combustion chambers
and nuclear reactors. In these applications, thermal and viscous properties f
the working fluid are important design parameters that depende on temperature;
hence it is likely to observe strong gradients on these scalars' fields. To
accomplish our goal, the modifications for the k-tau model are implemented and
tested for a channel flow with spatial varying viscosity in the streamwise
direction. The numerical simulations are performed using Nek5000, a
spectral-element code developed at Argonne National Laboratory (ANL). Finally,
the results considering a turbulence channel using the proposed model are
compared against data obtained using Direct Numerical Simulations from the
earlier work.
