Transition to turbulence in shear flows

Eckhardt, Bruno

doi:10.1016/j.physa.2018.01.032

Cited by 25 publications

(10 citation statements)

References 113 publications

(134 reference statements)

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“…The present findings are interesting in the light of recent advances on the understanding of transition in shear flow. Indeed the present work is motivated by the recent insight that the transition in shear flows bounded from two sides, such as plane-Poiseuille flow and plane-Couette flow, might be continuous, and that the discontinuous behavior around the critical Reynolds number is probably due to finite-size effects [29][30][31][32]. The obtained results in the present investigation, which are relatively easy to understand, can then serve as a test case of, perhaps, the simplest possible turbulent system exhibiting a continuous transition, against which more complicated flows such as the above mentioned shear flows can be assessed.…”

Section: Discussionmentioning

confidence: 99%

Linearly forced isotropic turbulence at low Reynolds numbers

2020

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We investigate the forcing strength needed to sustain a flow using linear forcing. A critical Reynolds number R c is determined, based on the longest wavelength allowed by the system, the forcing strength and the viscosity. A simple model is proposed for the dissipation rate, leading to a closed expression for the kinetic energy of the flow as a function of the Reynolds number. The dissipation model and the prediction for the kinetic energy are assessed using direct numerical simulations and two-point closure integrations. An analysis of the dissipationrate equation and the triadic structure of the nonlinear transfer allows to refine the model in order to reproduce the low-Reynolds-number asymptotic behavior, where the kinetic energy is proportional to R − R c .

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Section: Discussionmentioning

confidence: 99%

Linearly forced isotropic turbulence at low Reynolds numbers

2020

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“…This seems to be more difficult with other methods (such as VoF), because the underlying equations must be formulated as a system of smooth partial differential equations, such as (9)-(11). Dynamical-system approaches have helped in elucidating the transition to turbulence in wall-bounded (single-phase) flows [7], and may prove useful to tackle the rich nonlinear dynamics exhibited by two-phase pipe flows [13].…”

Section: Discussionmentioning

confidence: 99%

Phase-field simulation of core-annular pipe flow

Song

Plana

Lopez

et al. 2019

International Journal of Multiphase Flow

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Phase-field methods have long been used to model the flow of immiscible fluids. Their ability to naturally capture interface topological changes is widely recognized, but their accuracy in simulating flows of real fluids in practical geometries is not established. We here quantitatively investigate the convergence of the phase-field method to the sharp-interface limit with simulations of two-phase pipe flow. We focus on core-annular flows, in which a highly viscous fluid is lubricated by a less viscous fluid, and validate our simulations with an analytic laminar solution, a formal linear stability analysis and also in the fully nonlinear regime. We demonstrate the ability of the phase-field method to accurately deal with non-rectangular geometry, strong advection, unsteady fluctuations and large viscosity contrast. We argue that phase-field methods are very promising for quantitatively studying moderately turbulent flows, especially at high concentrations of the disperse phase.

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“…Other high-precision experiments on the air flow in smooth pipes focused on the transition zone where "slugs" and "puffs" signalled an intermittently turbulent flow (Wygnanski and Champagne 1973). Like fully developed turbulence, the transition to turbulence in pipe flow remained a persistent challenge-both from an experimental and from a theoretical perspective (Darbyshire and Mullin 1995;Kerswell 2005;Eckhardt et al 2007;Mullin 2011;Eckhardt 2018).…”

Section: Later Developmentsmentioning

confidence: 99%

Pipe flow: a gateway to turbulence

Eckert

2020

Arch. Hist. Exact Sci.

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Pipe flow has been a challenge that gave rise to investigations on turbulence—long before turbulence was discerned as a research problem in its own right. The discharge of water from elevated reservoirs through long conduits such as for the fountains at Versailles suggested investigations about the resistance in relation to the different diameters and lengths of the pipes as well as the speed of flow. Despite numerous measurements of hydraulic engineers, the data could not be reproduced by a commonly accepted formula, not to mention a theoretical derivation. The resistance of air flow in long pipes for the supply of blast furnaces or mine air appeared even more inaccessible to rational elaboration. In the nineteenth century, it became gradually clear that there were two modes of pipe flow, laminar and turbulent. While the former could be accommodated under the roof of hydrodynamic theory, the latter proved elusive. When the wealth of turbulent pipe flow data in smooth tubes was displayed as a function of the Reynolds number, the empirically observed friction factor served as a guide for the search of a fundamental law about turbulent skin friction. By 1930, a logarithmic “wall law” seemed to resolve this quest. Yet pipe flow has not been exhausted as a research subject. It still ranks high on the agenda of turbulence research—both the transition from laminar to turbulent flow and fully developed turbulence at very large Reynolds numbers.

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Transition to turbulence in shear flows

Cited by 25 publications

References 113 publications

Linearly forced isotropic turbulence at low Reynolds numbers

Linearly forced isotropic turbulence at low Reynolds numbers

Phase-field simulation of core-annular pipe flow

Pipe flow: a gateway to turbulence

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