Direct numerical simulation and in-depth analysis of thermal turbulence in square annular duct

Abstract

The thermal turbulence in an infinitely-long square annular duct (SAD) was studied by the direct numerical simulation with the Reynolds (Re) number Reb≈6400 based on the bulk velocity. The isothermal boundary condition was applied to the side walls in SAD with the higher and lower temperatures on the outer and inner walls, respectively. As one of the most fascinating features for the corner turbulence, the turbulent-driven secondary flow (TDSF) presented the twin counter-rotating vortex pairs symmetrically located at the outer concave and inner convex corners. The TDSF was found significantly increase the spatially-averaged Nusselt (Nu) number comparing to the laminar flow. The instantaneous vortex structures were visualized by the third-generation vortex-identification method based on Liutex. The budget analyses of the governing-equation for the turbulent boundary layer (TBL) in SAD distinguished the balancing mechanisms from the one in the traditional flat-plate TBL, which justified the necessity to classify the generic TBLs into their sub-categories of Type-A, B and C TBLs. Moreover, the current study focused on a number of issues in the thermal TBL, such as the TDSF structures with their thermal effects and the TBL law formulations. For the present TBL in SAD, it was found that the buffer layer located in between the inner and the semi-log layers tended to be wider than that in a flat-plate TBL, and an outer linear conduction layer was, for the first time, found for the Type-B temperature TBL. Based on the indicator function, the quantitative sublayer partitions were first conducted for both the velocity and temperature TBLs and then the applicable ranges for the linear and semi-log sublayers were rigorously determined. Further, the profound damping mechanism was first introduced and applied to the traditional linear and semi-log laws to derive more accurate analytical law formulations for the entire velocity and temperature TBL sublayers.