Turbulent flow in non-circular ducts. Part 1: Mean flow properties in the developing region of a square duct

Abstract

The generalized mean properties of turbulent flow in non-circular ducts are examined for the developing region of a square duct The experimental data include mean velocity profiles and peripheral wall shear distributions at several locations, as well as the longitudinal static pressure distribution, all for Reynolds numbers between 50 000 and 150 000. A similarity exists between the mean wall isovels and peripheral wall shear distributions in the developing region with those of fully developed flow. The wall shear stress rapidly assumes a value that is slightly greater than that for fully developed flow, even though the axial pressure gradient has not stabilized, due to the convective acceleration of the core fluid. This indicates that the near wall flow rapidly establishes fully developed properties. It is recommended that for engineering calculations an effective development length in conduits be defined in terms of the stabilization of wall parameters such as shear stress and heat transfer. For this square duct with a well-rounded large contraction ratio entrance, the wall shear stress had established within six hydraulic diameters, while by comparison the core fluid required a development length approximately an order of magnitude larger, and would appear to be controlled more by the Reynolds number. The Preston tube experimental shear stress data are confirmed by a momentum integral procedure which is generalized for all regular polygons. The experimental and predicted wall shear stress data are correlated to within 4 per cent of fully developed pipe data by using a new characteristic length scale which takes into account the shape of the duct.