Two-dimensional fluid dynamics in a sharply bent channel: Laminar flow, separation bubble, and vortex dynamics

Abstract

Understanding the hydrodynamic properties of fluid flow in a curving pipe and channel is important for controlling the flow behavior in technologies and biomechanics. The nature of the resulting flow in a bent pipe is extremely complicated because of the presence of a cross-stream secondary flow. In an attempt to disentangle this complexity, we investigate the fluid dynamics in a bent channel via the direct numerical simulation of the Navier-Stokes equation in two spatial dimensions. We exploit the absence of secondary flow from our model and systematically investigate the flow structure along the channel as a function of both the bend angle and Reynolds number of the laminar-to-turbulent regime. We numerically suggest a scaling relation between the shape of the separation bubble and the flow conductance, and construct an integrated phase diagram.

The Role of Elasticity in the Vortex Formation in Polymeric Flow around a Sharp Bend

“…For Reynolds number values larger than 30, a clear vortex forms downstream of the bend corner. This critical Reynolds number value is in line with other numerical work [1,2].…”

“…This ratio is more than enough to obtain a fully developed flow well upstream of the corner bend and for the exit, being far enough away to prevent any upstream effect from the outlet boundary conditions, see references [19,20], and also Appendix A. The geometry used follows the experimental work of Gulati et al [5] and is typical of benchmark cases and similar configurations that have been evaluated both numerically and experimentally, see [1,6,21,22]. The bend used in the simulations has a ten to one ratio of length to channel height, H, in both branches.…”

“…Sci. 2021, 11, x FOR PEER REVIEW 9 of 20 that this Newtonian inertial vortex would become unstable at a sufficiently high Reynolds number value [1].…”

“…One such effect is the formation of recirculation zones, or vortices in abrupt, changes of flow direction as in contractions and bends. These vortices are a feature where some amount of the fluid becomes trapped in a cyclone like structure near or around corners, justifying those authors that refer to them as separation bubbles [1]. Recirculation zones can have detrimental effects on the flow of polymers and polymer solutions, affecting their manufacturing processes.…”

“…Even in purely Newtonian fluid flow, understanding the hydrodynamic behavior in a bend channel or a pipe elbow remains relevant today. Matsumoto et al [1] investigated the flow dynamics for a Newtonian fluid in a bent channel via two-dimensional direct numerical simulations. They investigated the flow structure along the channel as a function of both the bend angle and the Reynolds number.…”