# Asymmetry Propagation in a Pipe Flow Downstream of a 90\({}^{\circ}\) Sharp Sarp Elbow Bend
Unfortunately, the velocity field was measured only at one cross-section at the bend outlet, thus, the asymmetry propagation downstream of the flow was not measured. High-fidelity simulations, such as Direct Numerical Simulations (DNS) and Large Eddy Simulation (LES), provide deeper insights into flow behaviour. Global stability of laminar flow in curved toroidal pipes has shown that a very small curvature is sufficient to make the flow linearly unstable via a Hopf bifurcation that leads the flow to a periodic regime [16]. Typically, as the curvature increases, the onset of turbulence occurs at lower \(Re\). Specifically, at a fixed curvature (i.e., \(\gamma=0.33\)), the Hopf bifurcation occurs at \(Re=3290\) for evenly curved toroidal pipes [16], but at considerably lower \(Re=2531\)[17] and \(Re=2528\)[18] in the flow downstream of \(90^{\circ}\) and \(180^{\circ}\) pipe bends, respectively. The primary source of the flow instability in pipe bends is attributed to a strong shear resulting from the backflow in the separation bubble [17]. Interestingly, turbulent flows at higher \(Re\) in curved pipes reveal that overall turbulence decreases with increasing curvature [19; 20]. Coherent structures in toroidal pipes [20] resemble the swirl-switching previously observed downstream of pipe bends [11], which originates from a wave-like structure in the bend [21]. Turbulent flow in a \(90^{\circ}\) pipe bend was studied with LES and the Reynolds-Averaged Navier-Stokes (RANS) approach [22]. LES revealed a correlation between secondary flow motion and wall shear stresses [23], relevant for erosion wear [24; 25; 26], solid particle accumulation in curved pipes [27] and agglomerate breakage in particle-laden flow [28]. Detached Eddy Simulation (DES) was used to simulate turbulent flow downstream of a \(90^{\circ}\) bend with \(\gamma=0.5\)[29], as well as in the Wellborn S-duct [30]. Pipe flow in bends with \(\gamma\) from 0.17 to 0.5 was investigated at \(Re\) from 5000 to 27,000 [31], and low frequency oscillations of the Dean vortices were detected at largest \(Re\). Similarly, a numerical study of flow in a short, 90-degree elbow with a sharp internal edge also reported that the bend induced low-frequency velocity fluctuations at \(Re=51,000\)[32]. A recent study [33] used LES to examine the decay of secondary motion downstream of \(180^{\circ}\) pipe bends with \(\gamma\) from 0.15 to 0.5. Results showed that increased curvature enhanced turbulence intensity immediately downstream, reducing the recovery length for restoring the velocity profile. The role of Dean vortices in thermal fatigue was studied in a T-junction with an upstream pipe bend [34], which represents a safety concern in nuclear plant thermal-hydraulic systems, as it may cause unforeseen piping failures as the plant ages. Similarly, thermally stratified flow in a horizontally oriented \(90^{\circ}\) pipe bend was investigated [35], and the risk of material damage due to thermal fatigue was evaluated for pipe bends with \(\gamma\) from 0.16 to 0.63, finding that thermal fatigue damage increases as the pipe bend radius decreases. This is attributed to enhanced turbulent mixing in pipes with high curvature, underscoring the need for a comprehensive understanding of flow behaviour, especially in sharp pipe elbows. Although understanding the unsteady nature of flow instabilities downstream of a sharp pipe elbow is important, our present analysis focuses on information that can be derived from time-averaged flow fields. Therefore, special care has been taken to ensure sufficiently long time-averaging to eliminate any transient characteristics of the flow. In the present study, we investigated the propagation length of flow asymmetry, which was generated by a sharp pipe elbow with a curvature ratio of \(\gamma=0.93\). In Section 2, the numerical setup is described for the LES approach to three different cases with \(Re\) of 1400, 5600 and 10,000, which correspond to the laminar-turbulent transition regime as well as the fully turbulent regime.