Study of accelerating and decelerating turbulent flows in a channel

Accelerating and decelerating turbulent channel flows are investigated to study the response of the turbulence dynamics. The objective of these investigations is to further enhance the understanding on the behaviour of turbulence and wall friction under transient conditions. Large-Eddy Simulations (LES) are carried out for step-like accelerating flows with significantly higher ratios of Reynolds number than previously covered. An experimental investigation is carried out for ramp-like accelerating flows using Particle-Image Velocimetry (PIV) and Constant-Temperature Anemometry (CTA) techniques to reproduce and validate the findings in numerical simulations. Step- and ramp-like decelerating flows are studied using Direct Numerical Simulations (DNS), the results of which are compared with observations in accelerating flows.
Step-like high Re-ratio and ramp-like accelerating flows are shown to exhibit essentially the same three-stage laminar-turbulent transitional response as that described in He & Seddighi (J. Fluid Mech. 715:60-102, 2013), resembling bypass transition of boundary layer flows. The first stage is characterised by elongation and enhancement of streaks. The growing instabilities of the streak structures lead to breakdown and formation of isolated turbulent patches in the second stage, which grow in time and eventually merge with each other. The third stage is marked by the entire wall surface being covered by the newly generated turbulence. It is shown in the present study that the features of transition become more striking when the Re-ratio increases ― the elongated streaks in the pre-transitional period become increasingly longer and stronger, and the turbulent spots generated at the initial stage at the onset of transition become increasingly sparse. In a slower ramp-like flow excursion, on the other hand, the onset of transition is delayed making the flow development slower. In a step-like acceleration, a new boundary layer is formed instantly over the wall which develops into the flow with time. In a ramp-like case, however, the boundary layer development is shown to be described as an integral consequence of a continuous change of the flow. During the pre-transition stage, the time-development of the boundary layer in the step- and ramp-like accelerating flows bears strong resemblance to a time-developing laminar boundary layer described by the solution to Stokes’ first problem and can be represented by its analytical solution with a small correction.
The streamwise fluctuation velocity profile in a high Re-ratio accelerating flow is shown to exhibit two peaks immediately following the onset of transition. A conditional sampling technique, based on a λ_2-criterion, is used to show that the two peaks are separate contributions of the active and inactive regions of turbulence generation. The peak closer to the wall is attributed to the ‘newly’ generated turbulence in the active region; while the peak farther from the wall is attributed to the enhanced streaks in the inactive region.
Decelerating flows are shown to be also characterised by a time-developing boundary layer, similar to that in accelerating flows, bearing strong resemblance to the time-developing laminar boundary layer. The mean flow and wall friction in the early stages of the transient can be represented by the laminar analytical solution of the Stokes’ first problem. The streamwise fluctuations are shown to respond immediately following the commencement of the transient, while the response of the ‘real’ turbulence is shown to respond after a delay. Although the decay of turbulence and flow structures appear to be a gradual development herein, the decelerating flows may also undergo a transition process. However, the mechanism and stages of any such process are not clear in the present investigation.
In addition, a brief investigation on the performance of the low-Reynolds number Launder-Sharma k-ε model in predicting unsteady turbulent flows is undertaken using different CFD codes. It is shown that the model performance itself is robust and insensitive to the numerical/coding framework, while slight changes in the formulation of the model have significant effect on the performance of the model.