High-temperature gradient effect on a turbulent channel flow using thermal large-eddy simulation in physical and spectral spaces

Abstract

This paper studied nonisothermal plane channel flows using the method of thermal large-eddy simulations (TLES). Several temperature ratios (T_R =T_H /T_C ) were investigated, where T_C and T_H are the temperatures of the cold and hot sides, respectively. Each T_R case is further considered for two wall Reynolds numbers (Re _τm ), 180 and 395, where the wall Reynolds number was defined as the average of the local wall Reynolds number values obtained for the cold and hot sides, Re _τC and Re _τH . For a given wall Reynolds number Re _τm , it was demonstrated that the increased temperature ratio directly led to an enhanced disparity between the local wall Reynolds numbers of the cold and hot sides. Essentially, the wall Reynolds number for the cold side (Re _τC ) is increased, but its companion value for the hot side (Re _τH ) is decreased. In the case of large temperature ratio, the asymmetry of the mean velocity and temperature profiles is also increased. The major findings are that for high-temperature ratios, the flow on the hot side could relaminarize, as indicated by the parabolicity of the axial flow profile on the hot side; however, this process can be overcome if the flow has a greater turbulent intensity, as illustrated for the higher-Reynolds-number case studied in the paper. Finally, the impact of the temperature gradient on the turbulent fluctuations is investigated by controlling the influence of the Reynolds number. Four nonisothermal energy spectra on the cold and the hot side are compared and contrasted with eight isothermal flows. Here, the isothermal flows were chosen so that their Reynolds numbers have the same values as those Re _τC and Re _τH previously evaluated from the nonisothermal flows. The isothermal spectra reproduced the classical Kolmogorov spectra when the Reynolds numbers were sufficiently high. As a result, any observed deviation of the spectra index of the nonisothermal spectra from that of the isothermal one is a direct consequence of the temperature gradient.

Keywords:

• thermal large-eddy simulations
• plane channel
• nonisothermal turbulent flow
• low-Mach-number equations
• turbulent fluctuation spectra

Acknowledgements

The authors wish to acknowledge the support of the CINES (France), for providing computer resources to carry out simulations. The authors are also thankful to the CEA (France Atomic Agency), for their support with TrioU code. The last author (Y.Z.) is extremely grateful to University of Perpignan, which provided support for his visit during which some of his work was carried out.