Laminar-to-Turbulence Transition Revealed Through a Reynolds Number Equivalence

Xiao Dong Chen

PDF(382 KB)
PDF(382 KB)
Engineering ›› 2019, Vol. 5 ›› Issue (3) : 576-579. DOI: 10.1016/j.eng.2018.09.013
Research
Research Green Chemical Engineering—Article

Laminar-to-Turbulence Transition Revealed Through a Reynolds Number Equivalence

Author information +
History +

Abstract

Flow transition from laminar to turbulent mode (and vice versa)—that is, the initiation of turbulence—is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the onset of turbulence requires sophisticated instrumentation and/or direct numerical simulation, based on observing the instantaneous flow structure formation and evolution. In this work, a local Reynolds number equivalence γ (ratio of local inertia effect to viscous effect) is seen to conform to the Universal Law of the Wall, where γ = 1 represents a quantitative balance between the abovementioned two effects. This coincides with the wall layer thickness (y+ = 1, where y+ is the dimensionless distance from the wall surface defined in the Universal Law of the Wall). It is found that the characteristic of how the local derivative of γ against the local velocity changes with increasing velocity determines the onset of turbulence. For pipe flow, γ ≈ 25, and for plate flow, γ ≈ 151.5. These findings suggest that a certain combination of γ and velocity (nonlinearity) can qualify the source of turbulence (i.e., generate turbulent energy). Similarly, a re-evaluation of the previous findings reveals that only the geometrically narrow domain can act locally as the source of turbulence, with the rest of the flow field largely being left for transporting and dissipating. This understanding will have an impact on the future large-scale modeling of turbulence.

Keywords

Local Reynolds number equivalence / Flow transition from laminar to turbulent mode / Universal Law of the Wall / Pipe flow / Plate flow / Modeling

Cite this article

Download citation ▾
Xiao Dong Chen. Laminar-to-Turbulence Transition Revealed Through a Reynolds Number Equivalence. Engineering, 2019, 5(3): 576‒579 https://doi.org/10.1016/j.eng.2018.09.013

References

[[1]]
Avila K., Moxey D., de Lozar A., Avila M., Barkley D., Hof B.. The onset of turbulence in pipe flow. Science. 2011; 333(6039): 192-196.
[[2]]
Barkley D., Song B., Mukund V., Lemoult G., Avila M., Hof B.. The rise of fully turbulent flow. Nature. 2015; 526(7574): 550-553.
[[3]]
Hof B., de Lozar A., Avila M., Tu X., Schneider T.M.. Eliminating turbulence in spatially intermittent flows. Science. 2010; 327(5972): 1491-1494.
[[4]]
Kühnen J., Song B., Scarselli D., Budanur N.B., Ried M., Willis A.P., . Destabilizing turbulence in pipe flow. Nat Phys. 2018; 14(4): 386-390.
[[5]]
Reynolds O.. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Philos Trans R Soc Lond. 1883; 174: 935-982.
[[6]]
Tokaty G.A.. A history and philosophy of fluid mechanics.
[[7]]
Bird R.B., Stewart W.E., Lightfoot E.N.. Transport phenomena. 2nd ed.
[[8]]
Laufer J. The structure of turbulence in fully developed pipe flow. NACA technical report. United States: National Bureau of Standards; 1953 Jun. Report No.: NACA-TN-2954.
[[9]]
Schlichting H., Gersten K.. Boundary-layer theory. 8th ed.
[[10]]
Churchill S.W.. Progress in the thermal sciences: AIChE Institute Lecture. AIChE J. 2000; 46(9): 1704-1722.
[[11]]
Nikuradse J.. Gesetzmassigkeiten der turbulenten stromung in glatten rohren. German
[[12]]
Pai S.I.. On turbulent flow in circular pipe. J Franklin Inst. 1953; 256(4): 337-352.
[[13]]
Çengel Y.A., Cimbala J.M.. Fluid mechanics—fundamentals and applications. 2nd ed.

Acknowledgements

The author is grateful to his father, Prof. Naixing Chen (1933–2018), who was the first to introduce him to the field of fluid mechanics over 35 years ago; the author had discussed the initial ideas of this paper with him not long before he fell terminally ill. Some 17 months were spent working on and off as a research assistant in Prof. Lixing Zhou’s laboratory at Tsinghua University in 1985–1987, on a code for simulating a two-dimensional multiphase flow in a sudden-expansion combustion chamber. The personal knowledge of Dr. Tuoc Trinh of Canterbury University and later of Fonterra New Zealand in the late 1980s to early 1990s, respectively, was a real inspiration in thinking about wall turbulence. Dr. Trinh wrote a remarkable PhD thesis in the early 2000s on his original ideas on boundary layer turbulence.
AI Summary AI Mindmap
PDF(382 KB)

Accesses

Citations

Detail

Sections
Recommended

/