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Parametric investigation of friction drag reduction in turbulent flow over a flexible wall undergoing spanwise transversal traveling waves

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Abstract

Active friction drag reduction by spanwise transversal traveling surface waves is investigated experimentally in a fully developed zero-pressure gradient (ZPG) turbulent boundary layer (TBL). The spanwise transversal traveling wave of an aluminum surface is generated by an electromagnetic actuator system. A parametric study focusing on the influence of the wave amplitude (A+) and wave period (T+) is performed to analyze the impact of the wave parameters on drag reduction. Within the range of the parameters investigated, the maximum local drag reduction of 4.5% is found at A+ = 11.8 and T+ = 110. Furthermore, the TBL flows above the wave crest and trough are investigated by phase-locked PIV and µ-PTV measurements. The results evidence that the drag reduction effect is not only enhanced by increasing the amplitude, but also by reducing the period in the range of the current parameters. The turbulence statistics show that the velocity fluctuations and the Reynolds shear stresses in the streamwise and in the wall-normal direction are damped by the traveling surface wave motion in the near-wall region. The outer velocity distribution deviates from the inner scaling based on the actuated friction velocity, i.e., it possesses a slight tendency of a varying slope in the log region. The phase-locked measurements of the velocity profiles above the crest and the trough show that only above the crest the inner scaling property is valid. Above the moving surface a non-zero spanwise secondary flow is induced. The quadrant decomposition of the turbulent productions shows that the sweep and ejection events are weakened.

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Abbreviations

A :

Wave amplitude, mm

A + = Au τ/ν :

Normalized wave amplitude

c f :

Friction coefficient

d :

Particle diameter, µm

d + = du τ /ν :

Normalized particle size

f :

Wave frequency, 1/s

f + = fv/u τ 2 :

Normalized wave frequency

l + = lu τ /ν :

Normalized spatial resolution

P :

Probability density function

Re θ :

Reynolds number based on momentum thickness

Re τ :

Reynolds number based on the friction velocity

t :

Laser pulse delay, s

t + = tu τ 2/ν :

Normalized laser pulse delay

T :

Wave period, s

T + = Tu τ 2/ν :

Normalized wave period

u, v, and w :

Streamwise, wall-normal, and spanwise velocity, m/s

u τ :

Friction velocity of the non-actuated flow, m/s

u τ, local :

Friction velocity of the actuated case, m/s

U ∞ :

Freestream velocity, m/s

U + = U/u τ :

Normalized streamwise velocity

x, y, and z :

Streamwise, wall-normal, and spanwise distance, mm

y + = yu τ /ν :

Normalized wall distance

u′rms, v′rms :

Root-mean square of the streamwise and wall-normal velocity fluctuation, m/s

τ w :

Wall-shear stress, N/m2

θ :

Momentum thickness, mm

µ :

Dynamic viscosity, kg/(m s)

ν :

Kinematic viscosity, m2/s

DNS:

Direct numerical simulation

DR:

Drag reduction

LES:

Large eddy simulation

PIV:

Particle-image velocimetry

µ-PTV:

Micro-particle tracking velocimetry

TBL:

Turbulent boundary layer

ZPG:

Zero-pressure gradient

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Acknowledgements

The support of this research by the Deutsche Forschungsgemeinschaft DFG in the frame of FOR1779 is gratefully acknowledged.

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Authors and Affiliations

  1. Institute of Aerodynamics, RWTH Aachen University, Aachen, Germany

    Wenfeng Li, Dorothee Roggenkamp, Tobias Hecken, Wilhelm Jessen, Michael Klaas & Wolfgang Schröder

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  1. Wenfeng Li
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  2. Dorothee Roggenkamp
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  3. Tobias Hecken
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  4. Wilhelm Jessen
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  5. Michael Klaas
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  6. Wolfgang Schröder
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Correspondence to Wenfeng Li.

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Li, W., Roggenkamp, D., Hecken, T. et al. Parametric investigation of friction drag reduction in turbulent flow over a flexible wall undergoing spanwise transversal traveling waves. Exp Fluids 59, 105 (2018). https://doi.org/10.1007/s00348-018-2559-3

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