# Asymmetry Propagation in a Pipe Flow Downstream of a 90\({}^{\circ}\) Sharp Sarp Elbow Bend
## 4 Conclusions  
This study investigates propagation of flow asymmetry downstream of a sharp pipe elbow with a bend curvature ratio \(\gamma=0.93\). Numerical simulations of incompressible turbulent flow at \(Re\) of 1400, 5600 and 10,000 were performed using the LES approach. Results of the turbulent cases were first validated against the DNS results of pipe flow in straight pipes. We examined the dynamics of the Dean vortices downstream of the elbow and discovered that, in turbulent cases, these vortices reversed their vorticity direction within the region between 8 D and 10 D, but they persisted up to a distance of 25 D from the elbow. Then, we introduced profile asymmetry parameters and analysed flow asymmetry in a 100 D long pipe section downstream of the elbow using four different criteria, which resulted in similar observations. Figure 11: Asymmetry parameter for streamwise velocity fluctuations \(\overline{u_{x}{}^{2}}\) calculated in y- and z-profiles at different \(Re\): (**a**) \(Re=1400\); (**b**) \(Re=5600\); (**c**) \(Re=10,000\). Red curve indicates same quantity calculated in the recycling inlet pipe section, where no asymmetry is expected. Figure 12: Asymmetry parameter for vorticity field \(\overline{\|\omega\|}\) calculated in y- and z-profiles at different \(Re\): (**a**) \(Re=1400\); (**b**) \(Re=5600\); (**c**) \(Re=10,000\). Red curve indicates same quantity calculated in the recycling inlet pipe section, where no asymmetry is expected. The recovery length to symmetric flow is defined as the distance downstream of the elbow where the asymmetry parameter reaches the value expected in a long straight pipe. However, since the asymmetry parameter does not always decrease monotonically with distance from the elbow, we slightly relaxed this criterion. As a result, we now consider a broader range of values, from nearly symmetric (lower value) to fully symmetric flow profiles (higher value). In the turbulent cases, the recovery length is systematically shorter at larger \(Re\) regardless of the criteria applied. Specifically, a recovery length of 10-40 D was observed at \(Re=5600\) and 10-30 D at \(Re=10,000\). This analysis involved investigation into asymmetries of the wall shear stress, streamwise velocity component, streamwise velocity fluctuations and vorticity fields. Wall shear stress turned out to be a sensitive indicator of flow asymmetry in the near-wall region; however, it offers very limited or no information on the flow behaviour in the core (bulk) flow region. Contrarily, analysing flow profiles across the pipe diameter offers an improved understanding of flow asymmetry in the bulk region. It was found that the asymmetry parameter, when based on velocity fluctuations and vorticity, did not yield significantly more sensitive results compared to those based on the streamwise velocity component. At \(Re=1400\), the flow is laminar at the inlet; however, flow separation inside the elbow triggers flow instabilities which can be described as non-developed turbulence. After that, the vortices are gradually damped as the flow approaches laminar again. Nevertheless, the flow asymmetry is so persistent and the laminarization so slow that the 100 D long pipe is not long enough for the flow to recover back to a fully developed symmetric profile. Conceptualization, B.M. and I.T. ; methodology, B.M., K.C. and I.T. ; software, K.C. ; validation, B.M. and K.C. ; formal analysis, B.M. and K.C. ; investigation, B.M., K.C. and I.T. ; resources, I.T. ; data curation, K.C. ; writing--original draft preparation, B.M. ; writing--review and editing, K.C. and I.T. ; visualization, K.C. ; supervision, I.T. ; project administration, B.M. ; funding acquisition, I.T. All authors have read and agreed to the published version of the manuscript. This research was funded by the Slovenian Research Agency, grants P2-0026 and NC-0026. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.