An algebraic model for the turbulent flux of a passive scalar

TLDR

The authors performed direct numerical simulations of homogeneous turbulent shear flow (128 × 128 × 128 grid) to study passive‑scalar transport and used the results to fit a dimensionless coefficient for a tensor turbulent diffusivity model as a function of Reynolds and Péclet numbers. The study shows that pressure‑, velocity‑, and time‑derivative contributions to the turbulent scalar‑flux balance are all approximately aligned with the flux vector, enabling a tensor‑diffusivity gradient‑transport model that accurately predicts scalar flux across the entire channel.

Abstract

The behaviour of passive-scalar fields resulting from mean scalar gradients in each of three orthogonal directions in homogeneous turbulent shear flow has been studied using direct numerical simulations of the unsteady incompressible Navier-Stokes equations with 128 × 128 × 128 grid points. It is found that, for all orientations of the mean scalar gradient, the sum of the pressure-scalar gradient and velocity gradient-scalar gradient terms in the turbulent scalar flux balance equation are approximately aligned with the scalar flux vector itself. In addition, the time derivative of the scalar flux is also approximately aligned with the flux vector for the developed fields (corresponding to roughly constant correlation coefficients). These alignments lead directly to a gradient transport model with a tensor turbulent diffusivity. The simulation results are used to fit a dimensionless model coefficient as a function of the turbulence Reynolds and Péclet numbers. The model is tested against two different passive-scalar fields in fully developed turbulent channel flow (also generated by direct numerical simulation) and is found to predict the scalar flux quite well throughout the entire channel.