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The transition from laminar to turbulent flow is of great interest since it is one of the most difficult and unsolved problems in fluids engineering. The transition processes are significantly important because the transition has a huge impact on almost all systems that come in contact with a fluid flow by altering the mixing, transport, and drag properties of fluids even in simple pipe and channel flows. Generally, in most transportation systems, the transition to turbulence causes a significant increase in drag force, energy consumption, and, therefore, operating cost. Thus, understanding the underlying mechanisms of the laminar-to-turbulent transition can be a major benefit in many ways, especially economically. There have been substantial previous studies that focused on testing the stability of laminar flow and finding the critical amplitudes of disturbances necessary to trigger the transition in various wall-bounded systems, including circular pipes and square ducts. However, there is still no fundamental theory of transition to predict the onset of turbulence. In this study, we perform direct numerical simulations (DNS) of the transition flows from laminar to turbulence in a channel flow. Specifically, the effects of different magnitudes of perturbations on the onset of turbulence are investigated. The perturbation magnitudes vary from 0.001 (0.1%) to 0.05 (5%) of a typical turbulent velocity field, and the Reynolds number is from 5,000 to 40,000. Most importantly, the transition behavior in this study was found to be in good agreement with other reported studies performed for fluid flow in pipes and ducts. With the DNS results, a finite amplitude stability curve was obtained. The critical magnitude of perturbation required to cause transition was observed to be inversely proportional to the Reynolds number for the magnitude from 0.01 to 0.05. We also investigated the temporal behavior of the transition process, and it was found that the transition time or the time required to begin the transition process is inversely correlated with the Reynolds number only for the magnitude from 0.02 to 0.05, while different temporal behavior occurs for smaller perturbation magnitudes. In addition to the transition time, the transition dynamics were investigated by observing the time series of wall shear stress. At the onset of transition, the shear stress experiences an overshoot, then decreases toward sustained turbulence. As expected, the average values of the wall shear stress in turbulent flow increase with the Reynolds number. The change in the wall shear stress from laminar to overshoot was, of course, found to increase with the Reynolds number. More interestingly was the observed change in wall shear stress from the overshoot to turbulence. The change in magnitude appears to be almost insensitive to the Reynolds number and the perturbation magnitude. Because the change in wall shear stress is directly proportional to the pumping power, these observations could be extremely useful when determining the required pumping power in certain flow conditions. Furthermore, the stability curve and wall shear stress changes can be considered robust features for future applications, and ultimately interpreted as evidence of progress toward solving the unresolved fluids engineering problem.
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Dynamics of laminar and transitional flows over slip surfaces: effects on the laminar–turbulent separatrix
The effect of slip surfaces on the laminar–turbulent separatrix of plane Poiseuille flow is studied by direct numerical simulation. In laminar flows, the inclusion of the slip surfaces results in a drag reduction of over 10 %, which is in good agreement with previous studies and the theory of laminar slip flows. Turbulence lifetimes, the likelihood that turbulence is sustained, is investigated for transitional flows with various slip lengths. We show that slip surfaces decrease the likelihood of sustained turbulence compared to the no-slip case, and the likelihood is further decreased as slip length is increased. A more deterministic analysis of the effects of slip surfaces on a transition to turbulence is performed by using nonlinear travelling-wave solutions to the Navier–Stokes equations, also known as exact coherent solutions. Two solution families, dubbed P3 and P4, are used since their lower-branch solutions are embedded on the boundary of the basin of attraction of laminar and turbulent flows (Park & Graham, J. Fluid Mech. , vol. 782, 2015, pp. 430–454). Additionally, they exhibit distinct flow structures – the P3 and P4 are denoted as core mode and critical-layer mode, respectively. Distinct effects of slip surfaces on the solutions are observed by the skin-friction evolution, linear growth rate and phase-space projection of transitional trajectories. The slip surface appears to modify the transition dynamics very little for the core mode, but quite considerably for the critical-layer mode. Most importantly, the slip surface promotes different transition dynamics – an early and bypass-like transition for the core mode and a delayed and H- or K-type-like transition for the critical-layer mode. We explain these distinct transition dynamics based on spatio-temporal and quadrant analyses. It is found that slip surfaces promote the prevalence of strong wall-toward motions (sweep-like events) near vortex cores close to the channel centre, inducing an early transition, while long sustained ejection events are present in the region of the $$\unicode[STIX]{x1D6EC}$$ -shaped vortex cores close to the critical layer, resulting in a delayed transition. This should motivate flow control strategies to fully exploit these distinct transition dynamics for transition to turbulence.
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- Award ID(s):
- 1832976
- PAR ID:
- 10194993
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 894
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2020.282
