Minimal flow unit of wall-bounded high-pressure transcritical turbulence

Abstract

The minimum domain size required to maintain fully developed wall-bounded turbulent flow in high-pressure transcritical regimes is analyzed using direct numerical simulations. The computations involve carbon dioxide at supercritical conditions with pressure P=Pc ¼ 2 (subscript c denotes critical value), confined between cold (temperature T=Tc ¼ 0:85) and hot (T=Tc ¼ 1:5) isothermal walls. The corresponding friction Reynolds numbers are Res 76 and 123 for the cold and hot walls, respectively. The study considers a large baseline domain of size Lx=d ¼ 4p, Ly=d ¼ 2, and Lz=d ¼ð8=3Þp in the streamwise, wall-normal, and spanwise directions, respectively, with d the half-channel height, as well as truncated setups along the streamwise and/or spanwise directions. The results show that rather small domains are sufficient to reproduce near-wall flow motions, while larger domains are needed to properly capture large-scale structures, especially within the log-law region. Additionally, the study confirms that the distance over which thermal interactions occur is shorter than the typical size of hydrodynamic structures, particularly so in the spanwise direction. This finding suggests that the minimum periodic domain size required in the high-pressure transcritical regime is comparable to that of the minimum flow unit established by other researchers for wall-bounded flows under standard pressure-temperature conditions.