Periodic flows through curved tubes: the effect of the frequency parameter

Publisher Website
Google Scholar
Abstract
In a previous paper we reported on the effect of Dean number, κm, on the fully developed region of periodic flows through curved tubes. In this paper we again consider a sinusoldally varying volumetric flow rate in a curved pipe of arbitrary curvature ratio, δ, and investigate the effect of frequency parameter α, and Reynolds number Rem on the flow. Specifically, we report on the flow-field development for the range 7.5 [les ] α [les ] 25, and 50 [les ] Rem [les ] 450. The results, obtained by numerical integration of the full Navier–Stokes equations, reveal a number of characteristics of the flow previously unreported. For low values of Rem the secondary flow consists of a single vortex (Dean-type motion) in the half-cross-section at all times and for all values of α studied. For higher Rem we observe inward ‘centrifuging’ (Lyne-type motion) at the centre. This motion always occurs during the accelerating period of the volumetric flow rate. It appears at lower α for higher Rem and, for the given Rem at which it appears, it occurs at earlier times in the cycle for lower a. A striking feature is observed for α = 15 for the range 315 [les ] Rem [les ] 400: period tripling. The flow field varies periodically with time for the duration of three volumetric-flow-rate cycles then repeats for the subsequent three cycles, and so on. The computed axial pressure gradient also varies periodically with time but with the same period as the volumetric flow rate.