Characteristic stages of heat transfer for supercritical CO₂ flowing downward in a vertical tube under cooling conditions

The present work investigates the streamwise development stages of supercritical carbon dioxide downward cooling flow and heat transfer in a vertical tube through direct numerical simulation. The tube has a diameter of 2 mm and an inlet Reynolds number of 5400. The formation mechanisms of flow stages are investigated by studying turbulence statistics and momentum balance analysis. The results indicate that there are three distinct development stages for both flow and heat transfer, including a deterioration stage, a recovery stage, and a re-deterioration stage. The last stage only occurs in some flows and is less well-understood than the first two stages. In the flow deterioration stage, both the weakening of the external buoyancy effect (due to mean flow modification) and the negative influence of the structural effect (direct interactions between the fluctuating density and the thermal field) contribute to flow laminarization. In the flow recovery stage, the increase in buoyancy further reduces the streamwise pressure gradient, increasing near-wall velocity. At this point, the velocity profile becomes M-shaped, accompanied by turbulence regeneration. As the bulk temperature drops around pseudo-critical temperature, a sudden global deceleration occurs due to the increased fluid density, which weakens both the external and structural effects and causes a decrease in turbulence, and hence the flow and heat transfer enter the re-deterioration stage. Moreover, the inlet temperature and wall heat flux have a pronounced effect on the development stages, which affects the duration distance of the deterioration stage and the corresponding enthalpy value at the beginning of the recovery stage.