The vanishing of strong turbulent fronts in bent pipes

Abstract

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 δ = 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 longlived 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.

Critical Point for Bifurcation Cascades and Featureless Turbulence

“…Figure 1 eter space. Transition to turbulence is subcritical at low curvatures and qualitatively similar to the one in straight pipes [30][31][32]. For larger δ, instead, transition is initiated by a supercritical Hopf bifurcation [30,[32][33][34] and all elements point towards a bifurcation cascade [33].…”

“…[30][31][32]. At this Reynolds number, in fact, we are above the intermittency range where turbulent puffs are observed [30][31][32]. An appropriate perturbation is sufficient to initiate the by-pass mechanism that renders the flow homogeneously turbulent.…”

Taming turbulent fronts by bending pipes

“…In their recent paper, Rinaldi, Canton & Schlatter (2019) address how the classical puffs and slugs of straight pipe flow are transformed in the case of bent pipes, and more broadly how the subcritical route to turbulence is potentially affected by the presence of pipe curvature. Specifically, the authors perform direct numerical simulations of flow in toroidal pipe with pipe-to-torus-diameter ratio of δ = 0.01.…”

“…The authors argue, convincingly, that the secondary flow (Dean 1927) generated in the curved pipe is responsible for this localisation, and moreover, that due to this localisation, turbulence in the front can be sustained at smaller energies than is the case for a straight pipe, thereby explaining why and how strong fronts vanish in a bent pipe. To be clear, owing in part to the numerous applications of curved pipe flow, there is a substantial literature on instabilities and turbulence in helical and toroidal pipes (see the discussion and citations in Kühnen et al (2015) and Rinaldi et al (2019)), and the secondary Dean flow is well known to play an important role in bent pipes. However, Rinaldi et al are the first to demonstrate its important role in the energy budget, not only at turbulent-laminar fronts and also in the turbulent core within toroidal pipe flow.…”

“…Potentially the most interesting observations in Rinaldi et al (2019) concern the way pipe curvature affects the route to turbulence. It is known from Kühnen et al (2015) that in toroidal pipes with pipe-to-torus-diameter ratio greater than about δ = 0.028, the transition scenario switches from subcritical to supercritical.…”