Asymmetry Propagation in a Pipe Flow Downstream of a 90° Sharp Elbow Bend

Featured Application Sharp pipe elbows are commonly used in industrial applications where space is constrained. The flow downstream of a sharp elbow is highly asymmetric, and it is crucial in some cases to determine how far this asymmetry extends. For example, accurate flow meters are usually calibrated based on a fully developed symmetric flow profile. We showed that in turbulent pipe flows, the recovery length is systematically shorter at higher Reynolds numbers (Re) regardless of the criteria used. Specifically, a recovery length of 10-40 pipe diameters (D) is observed at Re=5600 and 10-30 D at Re=10,000. However, for a laminar flow, even a length of 100 D might not be sufficient for the flow to fully recover to a symmetric profile.Abstract Pipe bends disrupt the flow, resulting in an asymmetric velocity field across the pipe diameter (D). We examined the recovery length required for the flow to return to a symmetric velocity profile downstream of a sharp elbow. The wall-resolved Large Eddy Simulation (LES) approach was applied to reproduce turbulent fluid flow at Reynolds numbers (Re) of 5600 and 10,000. An additional case in the transitional laminar-turbulent-laminar regime was analyzed at Re=1400. This analysis explored the behavior of the Dean vortices downstream of the elbow and revealed that, in turbulent cases, these vortices reverse their vorticity direction in the region between 8 D and 10 D. However, they eventually decay in structure as far as 25 D from the elbow. Flow asymmetry was analyzed in a 100 D long pipe section downstream of the elbow using four different criteria: wall shear stress (WSS), streamwise velocity, its fluctuations, and vorticity fields. This study found that in turbulent flows, the distance required for flow recovery is a few tens of D and decreases with increasing Re. However, in the transitional case, the flow separation within the elbow induces instabilities that gradually diminish downstream, and flow asymmetry persists even longer than the 100 D length of our outlet pipe section. WSS proved sensitive for detecting asymmetry near walls, whereas flow profiles better revealed bulk asymmetry. It was also shown that asymmetry indicators derived from velocity fluctuations and vorticity were less sensitive than those obtained from streamwise velocity.