3 results
The vanishing of strong turbulent fronts in bent pipes
- Enrico Rinaldi, Jacopo Canton, Philipp Schlatter
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- Journal:
- Journal of Fluid Mechanics / Volume 866 / 10 May 2019
- Published online by Cambridge University Press:
- 13 March 2019, pp. 487-502
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Isolated patches of turbulence in transitional straight pipes are sustained by a strong instability at their upstream front, where the production of turbulent kinetic energy (TKE) is up to five times higher than in the core. Direct numerical simulations presented in this paper show no evidence of such strong fronts if the pipe is bent. We examine the temporal and spatial evolution of puffs and slugs in a toroidal pipe with pipe-to-torus diameter ratio $\unicode[STIX]{x1D6FF}=D/d=0.01$ at several subcritical Reynolds numbers. Results show that the upstream overshoot of TKE production is at most one-and-a-half times the value in the core and that the average cross-flow fluctuations at the front are up to three times lower if compared to a straight pipe, while attaining similar values in the core. Localised turbulence can be sustained at smaller energies through a redistribution of turbulent fluctuations and vortical structures by the in-plane Dean motion of the mean flow. This asymmetry determines a strong localisation of TKE production near the outer bend, where linear and nonlinear mechanisms optimally amplify perturbations. We further observe a substantial reduction of the range of Reynolds numbers for long-lived intermittent turbulence, in agreement with experimental data from the literature. Moreover, no occurrence of nucleation of spots through splitting could be detected in the range of parameters considered. Based on the present results, we argue that this mechanism gradually becomes marginal as the curvature of the pipe increases and the transition scenario approaches a dynamical switch from subcritical to supercritical.
The three-dimensional structure of swirl-switching in bent pipe flow
- Lorenz Hufnagel, Jacopo Canton, Ramis Örlü, Oana Marin, Elia Merzari, Philipp Schlatter
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- Journal:
- Journal of Fluid Mechanics / Volume 835 / 25 January 2018
- Published online by Cambridge University Press:
- 27 November 2017, pp. 86-101
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Swirl-switching is a low-frequency oscillatory phenomenon which affects the Dean vortices in bent pipes and may cause fatigue in piping systems. Despite thirty years worth of research, the mechanism that causes these oscillations and the frequencies that characterise them remain unclear. Here we show that a three-dimensional wave-like structure is responsible for the low-frequency switching of the dominant Dean vortex. The present study, performed via direct numerical simulation, focuses on the turbulent flow through a $90^{\circ }$ pipe bend preceded and followed by straight pipe segments. A pipe with curvature 0.3 (defined as ratio between pipe radius and bend radius) is studied for a bulk Reynolds number $Re=11\,700$, corresponding to a friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}\approx 360$. Synthetic turbulence is generated at the inflow section and used instead of the classical recycling method in order to avoid the interference between recycling and swirl-switching frequencies. The flow field is analysed by three-dimensional proper orthogonal decomposition (POD) which for the first time allows the identification of the source of swirl-switching: a wave-like structure that originates in the pipe bend. Contrary to some previous studies, the flow in the upstream pipe does not show any direct influence on the swirl-switching modes. Our analysis further shows that a three-dimensional characterisation of the modes is crucial to understand the mechanism, and that reconstructions based on two-dimensional POD modes are incomplete.
Modal instability of the flow in a toroidal pipe
- Jacopo Canton, Philipp Schlatter, Ramis Örlü
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- Journal:
- Journal of Fluid Mechanics / Volume 792 / 10 April 2016
- Published online by Cambridge University Press:
- 08 March 2016, pp. 894-909
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The modal instability encountered by the incompressible flow inside a toroidal pipe is studied, for the first time, by means of linear stability analysis and direct numerical simulation (DNS). In addition to the unquestionable aesthetic appeal, the torus represents the smallest departure from the canonical straight pipe flow, at least for low curvatures. The flow is governed by only two parameters: the Reynolds number $\mathit{Re}$ and the curvature of the torus ${\it\delta}$, i.e. the ratio between pipe radius and torus radius. The absence of additional features, such as torsion in the case of a helical pipe, allows us to isolate the effect that the curvature has on the onset of the instability. Results show that the flow is linearly unstable for all curvatures investigated between 0.002 and unity, and undergoes a Hopf bifurcation at $\mathit{Re}$ of about 4000. The bifurcation is followed by the onset of a periodic regime, characterised by travelling waves with wavelength $\mathit{O}(1)$ pipe diameters. The neutral curve associated with the instability is traced in parameter space by means of a novel continuation algorithm. Tracking the bifurcation provides a complete description of the modal onset of instability as a function of the two governing parameters, and allows a precise calculation of the critical values of $\mathit{Re}$ and ${\it\delta}$. Several different modes are found, with differing properties and eigenfunction shapes. Some eigenmodes are observed to belong to groups with a set of common characteristics, deemed ‘families’, while others appear as ‘isolated’. Comparison with nonlinear DNS shows excellent agreement, confirming every aspect of the linear analysis, its accuracy, and proving its significance for the nonlinear flow. Experimental data from the literature are also shown to be in considerable agreement with the present results.