Abstract
AbstractIt has previously been shown that the transient flow in a channel following a step increase of Reynolds number from 2800 to 7400 (based on channel half-height and bulk velocity) is effectively a laminar–turbulent bypass transition even though the initial flow is turbulent (He & Seddighi, J. Fluid Mech., vol. 715, 2013, pp. 60–102). In this paper, it is shown that the transient flow structures exhibit strong contrasting characteristics in large and small flow perturbation scenarios. When the increase of Reynolds number is large, the flow is characterized by strong elongated streaks during the initial period, followed by the occurrence and spreading of isolated turbulent spots, as shown before. By contrast, the flow appears to evolve progressively and the turbulence regeneration process remains largely unchanged during the flow transient when the Reynolds number ratio is low, and streaks do not appear to play a significant role. Despite the major apparent differences in flow structures, the transient flow under all conditions considered is unambiguously characterized by laminar–turbulent transition, which exhibits itself clearly in various flow statistics. During the pre-transition period, the time-developing boundary layers in all the cases show a strong similarity to each other and follow closely the Stokes solution for a transient laminar boundary layer. The streamwise fluctuating velocity also shows good similarity in the various cases, irrespective of the appearance of elongated streaks or not, and the maximum energy growth exhibits a linear rate similar to that in a spatially developing boundary layer. The onset of transition is clearly definable in all cases using the minimum friction factor, and the critical time thus defined is strongly correlated with the free-stream turbulence in a power-law form.
Highlights
An interesting question is how will the behaviour of the transient flow change when the initial and final Reynolds numbers are increased or decreased? In particular, what happens when the Reynolds number ratio is very small? Assuming that the flow rate is increased by only 20 %, for example, is the response of the flow still a distinct transition process? The purpose of this paper is to provide some answers to these questions by analysing results of direct numerical simulation (DNS) of a series of transient flows with systematically varied initial and final Reynolds numbers
The flow structures at several instants during the transient period in selected cases are shown in figure 1 using three-dimensional isosurface plots of u /Ub0 and λ2/(Ub0/δ
All the cases shown in the figure have the same initial Reynolds number (Re0 = 2800) but very different final Reynolds numbers, namely 12 600, 5000 and 3100 for S11, S13 and S16 respectively
Summary
Unsteady turbulent flow remains a topic of great interest in fluid mechanics due to its many intriguing characteristics that remain not fully understood as well as its broad practical applications in many engineering systems and natural environments, S For example, the transient startup and shutdown of a power station, the closure or opening of a valve of a large water pipeline, sea waves over beaches, the blood flow in a vascular system and the unsteady flow in a turbo machine. Unsteady flows can be usefully classified into periodic and non-periodic flows, albeit similar underlying physics is often present in both cases.
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