# Asymmetry Propagation in a Pipe Flow Downstream of a 90\({}^{\circ}\) Sharp Sarp Elbow Bend  
[PERSON]  
1 Reactor Engineering Division, Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia; [EMAIL_ADDRESS] (K.C. ); [EMAIL_ADDRESS] (I.T.) [PERSON]  
1 Reactor Engineering Division, Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia; [EMAIL_ADDRESS] (K.C. ); [EMAIL_ADDRESS] (I.T.) [PERSON]  
1 Reactor Engineering Division, Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia; [EMAIL_ADDRESS] (K.C. ); [EMAIL_ADDRESS] (I.T.) Footnote 1: email: {[EMAIL_ADDRESS]}, {klemen. to the flow deflection, secondary flows, coherent structures or even a separation bubble [4]. Downstream of a bend, the asymmetry is gradually damped until the flow achieves a fully developed flow condition and forgets the presence of the bend. In many industrial systems, it is important to know how far the flow asymmetry behind the pipe bend propagates. For example, flow meters are usually calibrated to measure flow that is fully developed and undisturbed, as found in long straight pipes. Therefore, in a complex system, it is important to understand the appropriate distance downstream of a bend where such a device should be installed to ensure accurate measurements. In straight pipes, an entrance length is defined as the segment of a pipe, starting from the inlet, where the flow is in the process of developing, and extending up to the point where a fully developed flow is established. The entrance lengths in straight pipes vary widely, typically between 25 D to 60 D for mean velocity profiles and from 70 D to 90 D when higher-order statistics are being specified as criterions [5]. However, the entrance length increases further when large-scale turbulent structures are present [6] or in a laminar-turbulent transition regime [7; 8]. An additional complexity is introduced with the pipe bend, which is described with the curvature ratio \(\gamma=R/R_{c}\), with \(R\) and \(R_{c}\) denoting pipe and bend radius, respectively. A straight pipe corresponds to \(\gamma=0\), whereas, in the other extreme case, \(\gamma=1\) corresponds to a sharp internal edge of the pipe bend as shown in Figure 1b. The latter is usually referred to as the pipe elbow and can be found in numerous applications where one has limited space for pipe installation. This study investigates the velocity asymmetry propagation downstream of a 90\({}^{\circ}\) elbow with \(\gamma=0.93\) (\(R_{c}=1.08R\)), a sharp elbow that is, to the best of the authors' knowledge, still missing in the existing literature. Most experimental and numerical studies of flow behaviour focus on low \(\gamma\) and relatively short pipe sections. For example, flow downstream of a 90\({}^{\circ}\) pipe bend with \(\gamma=0.25\) was measured at \(Re=60,000\), showing a recovery length of 10 D needed for a symmetrical velocity profile [9]. Similar measurements for a 180\({}^{\circ}\) bend revealed longer recovery lengths [10]. Time-resolved stereoscopic Particle Image Velocimetry (PIV) with Proper Orthogonal Decomposition (POD) downstream of a 90\({}^{\circ}\) bend with \(\gamma=0.5\) revealed that the dominant structures were not the well-known Dean vortices, but bimodal single-cell structures with alternating directions of rotation, i.e., the swirl-switching mode [11], which was first visualized by [PERSON] and [PERSON] [12]. The analysis indicated that Dean vortices act as a transitional phase in swirl-switching, where one Dean vortex is suppressed, leading to a single swirl. Turbulent swirling flow at the exit of a 90\({}^{\circ}\) pipe bend with  
Figure 1: **(a)** Dean vortices downstream of the pipe bend; **(b)** Pipe bends with different bend angles and bend radii. \(\gamma=0.63\) was investigated for various \(Re\) in the range 14,000-34,000 [13; 14; 15]. A wide range of imposed swirl flows was employed by axially rotating the pipe section upstream of the bend, and it was found that the secondary motion in a curved pipe gradually diminishes as the swirl flow increases.