A new viscous sublayer influx (VSI) concept for near-wall turbulent momentum, heat and mass transfer

Abstract

This paper presents a new viscous sublayer influx (VSI) concept to describe near-wall turbulent momentum, heat and mass transfer. Based on visual studies, this concept takes account of a viscous sublayer adjacent to the wall, which is not directly affected by the bursts occurring in the wall region. Fluid penetrates only due to a wallward flow into this viscous sublayer. Thus, in contrast to the known surface renewal concept, the new VSI concept is consistent with visual flow studies and, in addition, makes it possible to meet the experimentally found limiting condition Sh ∼ ³√Sc_Sc→∞ for mass transfer. In this work, two models have been developed from the new VSI concept. The simplified viscous sublayer influx model follows the known models in literature and provides analytical equations for the profiles in the wall region. This model gives an explanation for the varying experimental results on the time intervals between successive bursts and predicts them in quantity by using measured Sherwood numbers at very high Schmidt numbers. The second, more detailed viscous sublayer influx model approximates the wallward flow in the viscous sublayer with a spherical stagnation point flow. The profiles are calculated from two ordinary differential equations. Using measured Sherwood numbers at very high Schmidt numbers, this model provides normal velocity fluctuations at the wall that agree well with experimental data. Furthermore, both models provide axial velocity fluctuations near the wall and Nusselt/Sherwood numbers in the range 0.5 ≤ Pr, Sc≤ 10⁵ that both correspond with experimental data.