A pulsatile developing flow in a bend
Résumé
Low frequency pulsatile flow of an incompressible viscous fluid has been numerically investigated in a rigid 90° bend of circular cross-section, using the finite-volume method. The governing parameters are as follows : amplitude ratio of 1.25, Womersley parameter of 4, peak Reynolds number of 358, peak Dean number of 113, Strouhal number ranging from 0.05 to 0.45. With this set of input data, no flow reversal is observed and a single axial vortex occurs in the half cross-section. Upstream and downstream effects of the bend are mainly characterized by an inward shift of the peak axial velocity in the upstream straight tube and the persistency of the secondary motions several diameters down the exit straight pipe. Secondary motions, present in steady flow, weaken greatly when the unsteady axial component of the flow (W) is lower than the mean flow $\bar{W}$. The axial shear stress τa, whose maximum is more often located at the outer part of the bend, increases and remains nearly constant about 8 diameters downstream from the bend inlet. The circumferential shear stress τc maximum, located slightly towards the outer bend, is 28% of τa maximum, and 20% when $W < \bar{W}$. The magnitude of both τa and τc increases during the accelerative phase. The low shear region is more often located near the inner tube wall. However, the existence of bends in a tube network might increase the deposit of solid particles, with respect to straight pipes, only when W (t)>W, and locally at the inner edge.
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