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Streamwise Vortices and Velocity Streaks in a Locally Drag-Reduced Turbulent Boundary Layer

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Abstract

This work aims to understand the changes associated with the near-wall streaky structures in a turbulent boundary layer (TBL) where the local skin-friction drag is substantially reduced. The Reynolds number is R e 𝜃 = 1000 based on the momentum thickness or R e τ = 440 based on the friction velocity of the uncontrolled flow. The TBL is perturbed via a local surface oscillation produced by an array of spanwise-aligned piezo-ceramic (PZT) actuators and measurements are made in two orthogonal planes using particle image velocimetry (PIV). Data analyses are conducted using the vortex detection, streaky structure identification, spatial correlation and proper orthogonal decomposition (POD) techniques. It is found that the streaky structures are greatly modified in the near-wall region. Firstly, the near-wall streamwise vortices are increased in number and swirling strength but decreased in size, and are associated with greatly altered velocity correlations. Secondly, the velocity streaks grow in number and strength but contract in width and spacing, exhibiting a regular spatial arrangement. Other aspects of the streaky structures are also characterized; they include the spanwise gradient of the longitudinal fluctuating velocity and both streamwise and spanwise integral length scales. The POD analysis indicates that the turbulent kinetic energy of the streaky structures is reduced. When possible, our results are compared with those obtained by other control techniques such as a spanwise-wall oscillation, a spanwise oscillatory Lorentz force and a transverse traveling wave.

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Abbreviations

Latin symbols :

ᅟ

A o :

Peak-to-peak oscillation amplitude at the actuator tip

\(A_{\omega _{x} } \) :

Size of streamwise vortex

D y z :

Velocity gradient tensor

f o :

Oscillation frequency

H c :

Height of vortex center

H 12 :

= δ ∗/𝜃, Shape factor, where δ ∗ and 𝜃 are displacement and momentum thicknesses, respectively

L c :

Transverse spacing of adjacent vortex centers

N c :

Number of vortex center

Re 𝜃 :

= U ∞ 𝜃/ν, Reynolds number based on momentum thickness

Re τ :

= u τ δ/ν, Reynolds number based on friction velocity

S :

Spacing of adjacent streaks

U, U ∞ :

Local mean and free-stream streamwise velocities, respectively

u :

Streamwise fluctuating velocity

u τ :

\(= \sqrt {\overline \tau _{w} /\rho } ,\) friction velocity

W :

Streak width

W p :

Perturbed spanwise velocity

w :

Spanwise fluctuating velocity

x :

Streamwise direction

y :

Wall-normal direction

z :

Spanwise direction

δ 99 :

Boundary layer thickness defined by the location where U = 99% U ∞

𝜃 :

Momentum thickness

Λ c i :

= (ω x / |ω x |)λ c i , signed swirling strength

λ r :

Real eigenvalue

λ c i :

Vortex strength as indicated by eigenvalue of the local velocity gradient tensor

λ z :

Wavelength

v :

Wall-normal fluctuating velocity

ρ :

Flow density

\(\overline \tau _{w} \) :

Averaged wall shear stress

ϕ i, i+1 :

(i = 1, 2, …, 15), phase shift between adjacent actuator

ω x :

Streamwise vorticity

ω y :

Wall-normal vorticity

PIV:

Particle image velocimetry

POD:

Proper orthogonal decomposition

TBL:

Turbulent boundary layer

TKE:

Turbulent kinetic energy

+:

Normalization by wall units

−:

Ensemble average

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Acknowledgements

YZ wishes to acknowledge support given to him from NSFC through grant 11632006, from RGC of HKSAR through grant PolyU 5329/11E. H.L.B. would like to acknowledge support given to him from NSFC through grant 11302062 and from State Key Laboratory of Aerodynamics through grant SKLA20130102.

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Authors and Affiliations

  1. Institute for Turbulence-Noise-Vibration Interaction and Control, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, 518055, China

    H. L. Bai & Y. Zhou

  2. State Key Laboratory of Aerodynamics, Mianyang, 621000, China

    H. L. Bai & W. G. Zhang

  3. Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR, China

    H. L. Bai

  4. School of Engineering, University of Newcastle, Callaghan, NSW, 2308, Australia

    R. A. Antonia

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  1. H. L. Bai
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Correspondence to Y. Zhou.

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Bai, H.L., Zhou, Y., Zhang, W.G. et al. Streamwise Vortices and Velocity Streaks in a Locally Drag-Reduced Turbulent Boundary Layer. Flow Turbulence Combust 100, 391–416 (2018). https://doi.org/10.1007/s10494-017-9860-8

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