Abstract
The hairpin vortex structures in the boundary layer with \({Re}_{\theta }\) = 159–239 of a square tube were studied experimentally using the moving single- frame and long-exposure image (M-SFLE) method. And the Liutex vortex identification criteria are used to confirm vortices and characterize their strength in the experimental results. The flow measurement system always moves at the same or similar speed as vortices in the boundary layer to track vortex structures continuously. The experimental results show that the secondary hairpin vortex and the tertiary hairpin vortex can be induced by the primary hairpin vortex. And the extension of the vortex packet in the flow direction can lead to the occurrence of vortex merging in the near-wall turbulent boundary layer. The Q2 event plays a key role in the formation of secondary hairpin vortices and the merging behaviors. The merging process of two vortices can be divided into three stages and the strength of the vortex structures has unique characteristics in different stages.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
S.J. Kline, W.C. Reynolds, F.A. Schraub, P.W. Runstadler, The structure of turbulent boundary layers. J. Fluid Mech. 30(4), 741–773 (1967)
H. Kim, S.J. Kline, W.C. Reynolds, The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50(1), 133–160 (1971)
T. Theodorsen, Mechanisms of turbulence, in Proceedings of the 2nd Midwestern Conference on Fluid Mechanics (1952)
M.R. Head, P. Bandyopadhyay, New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297–338 (1981)
J. Zhou, R.J. Adrian, S. Balachandar, Autogeneration of near-wall vortical structures in channel flow. Phys. Fluids 8(1), 288–290 (1996)
J. Zhou, R.J. Adrian, S. Balachandar, T. Kendall, Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396 (1999)
R.J. Adrian, C.D. Meinhart, C.D. Tomkins, Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54 (2000)
I. Marusic, On the role of large-scale structures in wall turbulence. Phys. Fluids 13(3), 735–743 (2001)
B. Ganapathisubramani, E.K. Longmire, I. Marusic, S. Pothos, Dual-plane PIV technique to determine the complete velocity gradient tensor in a turbulent boundary layer. Exp. Fluids 39(2), 222–231 (2005)
G.E. Elsinga, R.J. Adrian, B.W. Van Oudheusden, F. Scarano, Three-dimensional vortex organization in a high -Reynolds-number supersonic turbulent boundary layer. J. Fluid Mech. 644, 35–60 (2010)
D.J. Dennis, T.B. Nickels, Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 1. Vortex packets. J. Fluid Mech. 673, 180–217 (2011)
X.R. Tang, X.R. Dong, X.S. Cai, W. Zhou, Liutex identification on hairpin vortex structures in a channel based on msfle and moving-PIV. J. Hydrodyn. 33(6), 1119–1128 (2021)
W. Fan, Z. Wu, C. Xiaoshu, Image processing algorithm for particle trajectory image and reconstruction study on flow field. J. Exp. Fluid Mech. 33(4), 100–107 (2019)
A.E. Perry, M.S. Chong, A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19(1), 125–155 (1987)
J.C. Hunt, A.A. Wray, P. Moin, Eddies, streams, and convergence zones in turbulent flows, in Studying Turbulence Using Numerical Simulation Databases, 2. Proceedings of the 1988 Summer Program (1988)
J. Jeong, F. Hussain, On the identification of a vortex. J. Fluid Mech. 285, 69–94 (1995)
C. Liu, Y. Wang, Y. Yang, Z. Duan, New omega vortex identification method. Sci. China Phys. Mech. Astron. 59(8), 1–9 (2016)
C. Liu, Y. Gao, S. Tian, X. Dong, Rortex—a new vortex vector definition and vorticity tensor and vector decompositions. Phys. Fluids 30(3), 035103 (2018)
Y.S. Gao, J.M. Liu, Y.F. Yu, C. Liu, A Liutex based definition and identification of vortex core center lines. J. Hydrodyn. 31(3), 445–454 (2019)
C.R. Smith, J.D.A. Walker, A.H. Haidari, U. Sobrun, On the dynamics of near-wall turbulence. Philos. Trans. R. Soc. Lond. Ser. A: Phys. Eng. Sci. 336(1641), 131–175 (1991)
H. Li, D. Wang, H. Xu, Hairpin vortex formation mechanisms based on LXC-Liutex core line method, in Liutex and Third Generation of Vortex Definition and Identification (Springer, Cham, 2021), pp. 201–214
R.J. Adrian, S. Balachandar, Z.C. Lin, Spanwise growth of vortex structure in wall turbulence. KSME Int. J. 15(12), 1741–1749 (2001)
G.U.O. Yanang, D.O.N.G. Xiangrui, C.A.I. Xiaoshu, Z.H.O.U. Wu, Experimental studies on vortices merging based on MSFLE and Liutex. 空气动力学学报 38(3), 432–440 (2020)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Li, Y., Dong, X., Cai, X., Zhou, W., Tang, X. (2023). Experimental Studies on the Evolution of Hairpin Vortex Package in the Boundary Layer of a Square Tube. In: Wang, Y., Gao, Y., Liu, C. (eds) Liutex and Third Generation of Vortex Identification. Springer Proceedings in Physics, vol 288. Springer, Singapore. https://doi.org/10.1007/978-981-19-8955-1_9
Download citation
DOI: https://doi.org/10.1007/978-981-19-8955-1_9
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-8954-4
Online ISBN: 978-981-19-8955-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)