Mixed convection in turbulent channels with unstable stratification

TL;DR

This paper investigates turbulent channel flows with unstable stratification through direct numerical simulations, revealing unique flow patterns, deviations from classical scaling laws, and providing empirical formulas for heat flux and friction coefficients.

Contribution

It introduces new insights into mixed convection turbulence, including flow structures and deviations from classical theories, along with practical empirical predictive formulas.

Findings

Quasi-streamwise rollers significantly redistribute temperature and momentum.

Flow variables do not follow Prandtl's scaling near free convection.

Empirical formulas predict heat flux and friction coefficients with about 10% error.

Abstract

We study turbulent flows in planar channels with unstable thermal stratification, using direct numerical simulations in a wide range of Reynolds and Rayleigh numbers and reaching flow conditions which are representative of asymptotic developed turbulence. The combined effect of forced and free convection produces a peculiar pattern of quasi--streamwise rollers occupying the full channel thickness with aspect--ratio considerably higher than unity; it has been observed that they have an important redistributing effect on temperature and momentum. The mean values and the variances of the flow variables do not appear to follow Prandtl's scaling in the flow regime near free convection, except for the temperature and vertical velocity fluctuations, which are more affected by turbulent plumes. Nevertheless, we find that the Monin--Obukhov theory still yields a useful representation of the main flow features. In particular, the widely used Businger--Dyer relationships provide a convenient way of accounting for the bulk effects of shear and buoyancy, although individual profiles may vary widely from the alleged trends. Significant deviations are found in DNS with respect to the commonly used parametrization of the mean velocity in the light-wind regime, which may have important practical impact in models of atmospheric dynamics. Finally, for modelling purposes, we devise a set of empirical predictive formulas for the heat flux and friction coefficients which can be used with about $10\%$ maximum error in a wide range of flow parameters.