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.

This work is funded by the European Union (ERC, SCRAMBLE, 101040379). Views and opinions expressed are, however, those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. The authors also acknowledge support from the SGR program (2021-SGR-01045) of the Generalitat de Catalunya (Spain), the PID2023-150840OA-I00 grant of the Agencia Estatal de Investigación (AEI, Spain), and the computer resources at FinisTerrae III & MareNostrum and the technical support provided by CESGA & Barcelona Supercomputing Center (RES-IM-2023-1-0005, RES-IM-2023-2-0005). F.M. acknowledges support from the PID2020-114043GB-I00 and PID2023-150029NB-I00 grants of the AEI.

Peer Reviewed

Postprint (published version)