Near-wall passive scalar transport at high Prandtl numbers

Abstract

Very accurate numerical simulations of a passive scalar field in the turbulent channel and flume flow were performed at friction Reynolds numbers Reτ=150 and Reτ=395 and Prandtl numbers Pr=100, Pr=200. Direct numerical simulation is used for description of the velocity field. The temperature field is described with the LES-like approach with the smallest resolved temperature scales equal to the smallest scales of the velocity field. The consistency of the applied physical modelling and pseudospectral scheme is first tested with comparison of the results with the existing DNS simulations of F. Schwertfirm and M. Manhart [Proceedings of Turbulence, Heat, and Mass Transfer (2006)] at Reτ=180 and Pr=25. The sensitivity of the method to the grid refinement and time step variations is performed with simulations at Reτ=150 and Pr=200. Both tests show that the proposed approach produces very accurate mean temperature profiles, heat transfer coefficients, and other low-order moments of the turbulent thermal field. It is shown that the mean temperature profiles near the wall can be accurately predicted even when the temperature scales between the Batchelor and Kolmogorov scale are not resolved. The key to the success of the proposed approach lies in the fact that the large-scale structures govern the turbulent heat transfer at high Prandtl numbers. Resolved spectra of the temperature fluctuations and the rms temperature fluctuations in the diffusive sublayer and the thermal buffer layer (y+<5) are practically unaffected by the unresolved temperature scales. The contribution of the sub-Kolmogorov thermal scales becomes relevant above the thermal buffer layer (y+>5), where the unresolved temperature scales affect spectra and rms temperature fluctuations, but not the log-law shape of the mean temperature profile and the mean heat transfer coefficient. Further results are obtained at Reτ=150, Pr=100, Pr=500, and Reτ=395, Pr=100, Pr=200. These results are compared with Kader empirical temperature profiles and other available experimental and numerical results. Significant difference in the mean temperature profiles is demonstrated between the profiles calculated at friction Reynolds numbers 150 and 395. Kader correlation is shown to be very accurate at higher Reynolds number but underpredicts temperatures at low Reynolds number.