Intermittency, Moments, and Friction Coefficient during the Subcritical Transition of Channel Flow.

Jinsheng Liu,Mogeng Li,Shengjin Xu,Yue Xiao,Jianjun Tao

doi:10.3390/e22121399

Abstract

The intermittent distribution of localized turbulent structures is a key feature of the subcritical transitions in channel flows, which are studied in this paper with a wind channel and theoretical modeling. Entrance disturbances are introduced by small beads, and localized turbulent patches can be triggered at low Reynolds numbers (Re). High turbulence intensity represents strong ability of perturbation spread, and a maximum turbulence intensity is found for every test case as Re ≥ 950, where the turbulence fraction increases abruptly with Re. Skewness can reflect the velocity defects of localized turbulent patches and is revealed to become negative when Re is as low as about 660. It is shown that the third-order moments of the midplane streamwise velocities have minima, while the corresponding forth-order moments have maxima during the transition. These kinematic extremes and different variation scenarios of the friction coefficient during the transition are explained with an intermittent structure model, where the robust localized turbulent structure is simplified as a turbulence unit, a structure whose statistical properties are only weak functions of the Reynolds number.

Highlights

Plane Poiseuille flow (PPF), the flow driven by a pressure gradient between two parallel plates, displays a parabolic velocity profile at its laminar state and becomes linearly unstable when the Reynolds number is larger than the critical value, Rec = 5772 [1]
∗ U∗2 is measured at different Reynolds numbers, The friction coefficient C f = 8 h∗ dP
The velocity defect of localized turbulent structure leads to a negative skewness, and for all tested cases, the smallest Re where the skewness of the midplane velocity starts to be negative is about 660

Summary

Introduction

Plane Poiseuille flow (PPF), the flow driven by a pressure gradient between two parallel plates, displays a parabolic velocity profile at its laminar state and becomes linearly unstable when the Reynolds number is larger than the critical value, Rec = 5772 [1]. PPF may become turbulent at much lower Reynolds numbers than Rec due to the subcritical transition, where the finite-amplitude disturbances are necessary and the nonlinear effect cannot be ignored [2,3,4]. It was shown that the critical Reynolds number of the subcritical transition increases with the ratio between the entrance length and the channel height, and it remains at 667.5 when the entrance length is larger than 108h. Carlson et al [8]

Methods

Results

Conclusion