DNS of passive scalars in turbulent pipe flow

We study the statistics of passive scalars at Pr=1, for turbulent flow within a smooth straight pipe of circular cross--section up to Reτ ≈ 6000 using direct--numerical-simulation (DNS) of the Navier--Stokes equations. While featuring a general organization similar to the axial velocity field, passive scalar fields show additional energy at small wavenumbers, resulting in higher mixedness, and in a k-4/3 spectral inertial range. The DNS results highlight logarithmic growth of the inner-scaled bulk and mean centreline scalar values with the friction Reynolds number, implying an estimated scalar von Karman constant kθ ≈ 0.459, which also nicely fits the mean scalar profiles. The DNS data are used to synthesize a modified form of the classical predictive formula of Kader & Yaglom, which points to some shortcomings of the original formulation. Universality of the mean core scalar profile in defect form is recovered, with very nearly parabolic shape. Logarithmic growth of the buffer-layer peak of the scalar variance is found in the Reynolds number range under scrutiny, which well conforms with Townsend's attached-eddy hypothesis, whose validity is also supported by the spectral maps. The behavior of the turbulent Prandtl number shows good universality in the outer wall layer, with values Prt ≈ 0.84, as also found in previous studies, but closer to unity near the wall, where existing correlations do not reproduce the observed trends.