Direct numerical simulation of turbulent heat transfer in water with temperature-dependent viscosity and conductivity

Abstract

We study turbulent forced convection of liquid water in a plane channel by direct numerical simulation (DNS), with temperature-dependent viscosity and thermal conductivity. The simulations cover wall heating and cooling, mean-to-wall temperature ratios from 0.83 to 1.3, wall temperatures from 277 to 360\,K and wall Prandtl numbers from 2 to 12. Compared with constant-property flow at the same bulk Reynolds number, the friction coefficient changes by $-39\%$ to $+32\%$, the heat transfer coefficient referred to the wall Prandtl number changes by up to a factor of $2.3$, and empirical correlations deviate from the DNS by up to $26\%$. Instantaneous fields and spectra show that the wall friction Reynolds number misrepresents the range of turbulent scales, whereas near-wall streaks of velocity and temperature have a common spacing when scaled with the local viscous length. The density is constant, so the mean velocity and temperature defects in the core follow those of constant-property flow. To predict friction and heat transfer, we map the mean profiles onto those of constant-property flow through integral transformations derived from the mean momentum and energy balances, with empirical corrections of the eddy viscosity and diffusivity calibrated on the DNS. This approach, developed for air, is extended to liquids, whose conductivity is not proportional to the viscosity and whose Prandtl number varies across the channel. The inverse transformations predict friction and heat transfer within $2\%$ of the DNS, except at the lowest Reynolds numbers. The same corrections, introduced in the Spalart--Allmaras model, halve its friction error.