Measurements of the Periodic Velocity Oscillations Near the Wall in Unsteady Turbulent Channel Flow

  • G. Binder
  • J. L. Kueny
Conference paper

Abstract

Measurements in turbulent channel flow with forced velocity oscillations of small amplitude have been performed over a wide range of frequencies. The results show that the mean flow and the mean turbulent intensity are not affected by the forced oscillations. The amplitude and the phase shift of the periodic velocity fluctuation follow the laminar Stokes solution at high frequency. At low frequencies near the wall the gradient of the amplitude becomes steeper than in the Stokes flow and the phase shift decreases to slightly negative values. Further from the wall a phase lead is again observed. The results also show that the phase averaged longitudinal turbulent intensity is not simply proportional to the velocity oscillations; the amplitude ratio is position and frequency dependent. It is shown that the Stokes thickness l + s non-dimensionalized with the mean viscous sublayer thickness is the important parameter.

Keywords

Peri 

Nomenclature

Anq

amplitude of nth mode of q

f

frequency of forced oscillations

ft

characteristic frequency of turbulence

fv

frequency of validation of the laser Doppler signal

h

channel half-height

\({{l}_{s}} = \sqrt {{2v/\omega }}\)

Stokes length

\({{l}_{v}} = v/{{u}_{\tau }}\)

viscous wall-length scale

t

time

T

period of forced oscillations

u

longitudinal velocity

uτ

shear velocity

Ωh =

ωh/ūc

x, y

longitudinal and transverse coordinates

φnq

phase lead of nth mode of q

υ

kinematic viscosity

τ

wall shear stress

ω=

f

ys=

y/l s

()+=

()/lυ

()c

centerline

(¯)

time mean

(~)

periodic fluctuation

( )

turbulent fluctuation

∣ ∣

amplitude of periodic fluctuation

\(\langle ( )\rangle = {{(}^{ - }}) + {{(}^{ \sim }})\)

ensemble average

\(q = \bar{q} + \tilde{q} + q\prime\)

for any quantity q

\(\langle q\rangle\)

\(\bar{q} + \sum\limits_{{n = 1}}^{\infty } {{{A}_{{nq}}}\cos (n\omega t + {{\phi }_{{nq}}})}\)

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • G. Binder
    • 1
  • J. L. Kueny
    • 1
  1. 1.Institut de Mécanique, Institut National PolytechniqueUniversité Scientifique et Médicale de GrenobleGrenoble-CedexFrance

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