Stages of turbulence generation and decay in a T-shaped mixer

Abstract: The T-shaped mixer is widely used in fundamental studies of chemical engineering. Its transitional regime is well understood, whereas the turbulent dynamics has received scarce attention so far. Here we perform direct numerical simulations of the turbulent regime for Reynolds numbers up to $Re=2000$ at Schmidt number $Sc=1$. Our analysis reveals two distinct stages along the mixing channel prior to relaxation toward duct flow. Near the junction, a jet-like flow forms and exhibits the approximately self-similar behaviour of transitional planar jets. Subsequently, a decay region characterised by power-law decay of turbulent kinetic energy, dissipation and scalar variance emerges. For the velocity field, the observed exponents are consistent with those of decaying turbulence in bounded domains, whereas the scalar-variance exponent is consistent with that of unbounded turbulence. We argue that this apparent discrepancy is a consequence of the mixing process progressing from the center of the channel toward the side walls in the decay region, while turbulence already fills the channel cross-section entirely at the end of the jet region.The time-averaged mixing state presents error-function profiles of the scalar in the transverse direction, similar to the laminar cases, and is quantified here through a stream-wise evolving effective diffusion coefficient.