Finite Element Solution for Flow in Noncircular Conduits

Typical solutions for conduits of various shapes are presented. For turbulent flow the solution is based on the validity of the use of an eddy viscosity concept to account for the Reynolds stresses. The solution procedure allows the quantitative isolation of the effects of secondary flows on the velocity and boundary shear distributions. However, the effect of secondary flows has been considered herein only for a square duct because of the present dearth of knowledge about their distribution in other conduit shapes. For the square duct the solution shows that the secondary flow is responsible for a 6% increase in the friction factor and an 11% decrease in the maximum boundary shear. The inclusion of the secondary flows in the analysis allows satisfactory agreement to be achieved between the calculated and experimental velocity and boundary shear distributions and illustrates the limitations that must accompany any solution that ignores the effects of secondary flows.