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Statistical scale of hairpin packets in the later stage of bypass transition induced by cylinder wake

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Abstract

The hairpin packet's structure and its statistical scale in the later stage of bypass transition induced by a cylinder wake are investigated by time-resolved particle image velocimetry from the side and top view, respectively. Linear stochastic estimation is used to achieve the conditionally averaged velocity fields. For the side view case, the conditionally averaged structure consists of a series of swirling motions located along a line inclining at a large angle (18°) from the wall and a low-speed region occupied by the cylinder wake appearing right above them. In the (x, z)-plane at the wall-normal height y/δ = 0.2, the dominant structures are shown to be the large-scale regions of low momentum elongated almost over 3δ along the streamwise. The low-speed regions are consistently bordered by small-scale counter-rotating vortice pairs organized in the streamwise with a statistical spanwise width of 0.55δ. The results suggest that in the later part of the transitional zone, the upward induction of the cylinder wake enhances both the wall-normal and spanwise extent of the hairpin packets.

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Abbreviations

D :

Diameter of circular cylinder

PIV:

Particle image velocimetry

rms:

Root mean square

TBL:

Turbulent boundary layer

TR:

Time-resolved

u,v,w :

Instantaneous velocity components in x-(streamwise), y-(wall normal) and z-(spanwise) directions

u′,v′,w′:

Fluctuation velocity components

x,y,z :

Streamwise, wall normal and spanwise coordinates

x c ,y c :

Streamwise and wall-normal position of the cylinder from the leading edge of the flat plate

Re D :

Reynolds number based on diameter of circular cylinder

Re τ :

Reynolds number based on u τ and δ

δ:

Boundary layer thickness (0.99U ∞)

2D:

Two dimensional

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under grant no. 10832001 and 10872145, and the State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences.

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Authors and Affiliations

  1. Department of Mechanics, Tianjin University, Tianjin, 300072, People’s Republic of China

    Z. Q. Tang & N. Jiang

  2. Tianjin Key Laboratory of Modern Engineering Mechanics, Tianjin, 300072, People’s Republic of China

    N. Jiang

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  1. Z. Q. Tang
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  2. N. Jiang
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Correspondence to Z. Q. Tang.

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Tang, Z.Q., Jiang, N. Statistical scale of hairpin packets in the later stage of bypass transition induced by cylinder wake. Exp Fluids 53, 343–351 (2012). https://doi.org/10.1007/s00348-012-1291-7

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