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Structure evolution at early stage of boundary-layer transition: simulation and experiment

Published online by Cambridge University Press:  11 March 2020

X. Y. Jiang ,
C. B. Lee Open the ORCID record for C. B. Lee [Opens in a new window] ,
X. Chen Open the ORCID record for X. Chen [Opens in a new window] ,
C. R. Smith  and
P. F. Linden
X. Y. Jiang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, No. 5 Yiheyuan Road Haidian District, Beijing100871, PR China
C. B. Lee*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, No. 5 Yiheyuan Road Haidian District, Beijing100871, PR China
X. Chen
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, Sichuan Province, 621000, PR China
C. R. Smith
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, 19 Memorial Drive West, Bethlehem, PA18015, USA
P. F. Linden
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, CambridgeCB3 0WA, UK
*
†Email address for correspondence: cblee@mech.pku.edu.cn
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Abstract

The beginning of laminar–turbulent transition is usually associated with a wave-like disturbance, but its evolution and role in precipitating the development of other flow structures are not well understood from a structure-based view. Nonlinear parabolized stability equations (NPSE) were solved numerically to simulate the transition of K-regime, N-regime and O-regime. However, only the K-regime transition was examined experimentally using both hydrogen bubble visualization and time-resolved tomographic particle image velocimetry (tomo-PIV). Based on the ‘NPSE visualization’ and ‘tomographic visualization’, at least four common characteristics of the generic transition process were identified: (i) inflectional regions representing high-shear layers (HSL) that develop in vertical velocity profiles, accompanied by ejection–sweep behaviours; (ii) low-speed streak (LSS) patterns, manifested in horizontal timelines, that seem to consist of several three-dimensional (3-D) waves; (iii) a warped wave front (WWF) pattern, displaying multiple folding processes, which develops adjacent to the LSS in the near-wall region, prior to the appearance of 𝛬-vortices; (iv) a coherent 3-D wave front, similar to a soliton, in the upper boundary layer, accompanied by regions of depression along the flanks of the wave. It was determined that the amplification and lift-up of a 3-D wave causes the development of the HSL, WWF and multiple folding behaviour of material surfaces, that all contribute to the development of a 𝛬-vortex. The amplified 3-D wave is hypothesized as a soliton-like coherent structure. Based on our results, a path to transition is proposed, which hypothesizes the function of the WWF in boundary-layer transition.

JFM classification

Boundary Layers: Boundary layer structure Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 890 , 10 May 2020 , A11
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Jiang et al. supplementary movie 1

Evolution of timelines initiated at 𝑦 = 1.71 for K-regime transition. The upper row is the side view of timelines, the middle row is the plane view of timelines, and the lower row is the plane view of the timeline surface, with contour lines and color indicating the wall-normal distance (𝑦). The sections of A-A and B-B show the end views of the cross section curves at 𝑥 = 1180 and 1240.

Download Jiang et al. supplementary movie 1(Video)
Video 4.6 MB

Jiang et al. supplementary movie 2

Evolution of timelines initiated at 𝑦 = 3.83 for K-regime transition. The upper row is the side view of timelines, the middle row is the plane view of timelines, and the lower row is the plane view of the timeline surface, with contour lines and color indicating the wall-normal distance (𝑦).

Download Jiang et al. supplementary movie 2(Video)
Video 2.6 MB

Jiang et al. supplementary movie 3

Evolution of timelines initiated at 𝑦 = 1.71 for O-regime transition. The upper row is the side view of timelines, the middle row is the plane view of timelines, and the lower row is the plane view of the timeline surface, with contour lines and color indicating the wall-normal distance (𝑦). The sections of A-A and B-B show the end views of the cross section curves at 𝑥 = 1000 and 1080.

Download Jiang et al. supplementary movie 3(Video)
Video 6.4 MB

Jiang et al. supplementary movie 4

Evolution of timelines initiated at 𝑦 = 3.83 for O-regime transition. The upper row is the side view of timelines, the middle row is the plane view of timelines, and the lower row is the plane view of the timeline surface, with contour lines and color indicating the wall-normal distance (𝑦). The low-speed streak is observed to consist of several 3D waves.
Download Jiang et al. supplementary movie 4(Video)
Video 4.4 MB

Jiang et al. supplementary movie 5

Evolution of timelines initiated at 𝑦 = 1.71 for N-regime transition. The upper row is the side view of timelines, the middle row is the plane view of timelines, and the lpwer row is the plane view of the timeline surface, with contour lines and color indicating the wall-normal distance (𝑦). The sections of A-A and B-B show the end views of the cross section curves at 𝑥 = 1175 and 1280.

Download Jiang et al. supplementary movie 5(Video)
Video 4.2 MB

Jiang et al. supplementary movie 6

Evolution of timelines initiated at 𝑦 = 3.83 for N-regime transition. The upper row is the side view of timelines, the middle row is the plane view of timelines, and the lower row is the plane view of the timeline surface, with contour lines and color indicating the wall-normal distance (𝑦).

Download Jiang et al. supplementary movie 6(Video)
Video 2.3 MB

Jiang et al. supplementary movie 7

Evolution of vertical (wall-normal) timelines initiated at 𝑥 = 1010, 𝑧 = 126 for K-, O-, and N-regime transition.

Download Jiang et al. supplementary movie 7(Video)
Video 4.9 MB

Jiang et al. supplementary movie 8

Evolution of hydrogen bubble timelines initiated at 𝑦=0.35 δ, for K-regime transition. Flow is left to right

Download Jiang et al. supplementary movie 8(Video)
Video 6.2 MB