The Law of the Wall for Swirling Flow in Annular Ducts

Abstract

Expressions for the logarithmic portion of the law of the wall are derived for the axial and tangential velocity components of swirling flow in annular ducts. These expressions involve new shear-velocity scales and curvature terms. They are shown to agree well with experiment over a substantial portion of the flow near both walls of an annulus. The resultant velocity data also agree with the law of the wall. The success of the proposed logarithmic expressions implies that the mixing-length model used in deriving them correctly describes flow-velocity behavior. This model indicates that the velocity gradient at any height y in the near-wall region is determined by the wall shear stress, not by the local shear stress. This suggests that the influence of wall shear stress is dominant and that it determines the near-wall wall flow even in flows with curvature and pressure gradient. A physical explanation is suggested for this.