Numerical Analysis of Steady Flow in a 90° Circular Section Bend

Abstract

Laminar‐viscous flow around a bend of radius twice the conduit diameter, preceded and succeeded by a straight conduit, is calculated via primitive variables for a Reynolds number of 100. The nature of the finite‐difference equations and the solution approach used are indicated. In the solution, pressure is evaluated via the Poisson equation involving velocity components. Initially, axial velocities are found to shift toward inside of bend; later they shift toward outer wall. Secondary flows initiate upstream of the bend proper and continue in the downstream conduit. They maximize and level off about one‐third the way around the bend and decrease after another third. Detailed information on pressure field indicates appreciable modification in the bend proper together with significant modification in the upstream and downstream straight conduit. Wall shear stresses are found to vary greatly in the bend. Axial components are largest and vary most in the junction region between the bend and the straight conduit.