Experiments in Fluids

, Volume 7, Issue 2, pp 88–98

Turbulent flows with incipient separation over solid waves

  • J. D. Kuzan
  • T. J. Hanratty
  • R. J. Adrian
Originals

Abstract

Measurements of the streamwise velocity over solid sinusoidal waves with height to wavelength ratios of 2a/λ=0.05, 0.125 and with dimensionless wave numbers α+=0.00624, 0.00135 have been made. For these conditions the instantaneous flow reverses direction, but the time-averaged flow is non-separated. Many features of the flow are similar to those reported in previous papers for a time-averaged flow that is separated. Approximate agreement is obtained from an eddy viscosity model derived for flow over small amplitude waves. However, the differences are more interesting than the agreement in that they point out shortcomings of present Reynolds stress models. Comparison with other measurements in the literature shows how increasing Reynolds number decreases the size of the separated region. Measurements of pressure profiles and of drag are interpreted in terms of measured flow patterns.

List of symbols

A

van Driest parameter which is a measure of the extent of the viscous wall region

Ā

value of van Driest constant for flow over a flat plate

a

amplitude of the wave, defined by Eq. (1)

Cs

skin friction drag coefficient equal to \(\left\langle {\bar \tau _w } \right\rangle\)Ub2

Cp

form drag coefficient associated with pressure forces on the wave surface

f

fanning friction factor defined by Eq. (5)

h

half height of the channel

k1, k2

coefficients defined in Eq. (8)

kL

lag parameter defined in Eq. (9)

p

pressure

pw

pressure at the wall

p+

dimensionless pressure gradient, defined by Eq. (10)

g+

dimensionless effective pressure gradient, defined by Eq. (9)

q

root-mean of the sum of the squares of the turbulent velocity components, Eq. (12)

Re

Reynolds number equal to h UB/v

Ui

velocity in the ith direction

Ūi

time averaged velocity component

ui

velocity fluctuation, equal to UiŪi

¦Ûi¦n

magnitude of the amplitude of the nth harmonic of the wave-induced variation of Ūi

Ub

bulk-average velocity

u*

friction velocity defined using \(\bar \tau _w\) for a flat surface

ut*

friction velocity defined using the actual drag on the wave surface

x

Cartesian coordinate in the horizontal direction

y

Cartesian coordinate in the vertical direction

ys

location of wave surface

α

wavenumber, equal to 2π/λ

γ

per cent of the time the velocity has a positive value

θ

phase lag

θn

phase lag of nth harmonic

κ

von Karman constant

λ

wavelength

ν

kinematic viscosity

νt

turbulent kinematic viscosity

ρ

density of fluid

τ

shear stress

τw

wall shear stress

ψ

streamfunction

〈 〉

average along a wavelength

time average

+

as a superscript signifies a quantity made dimensionless using u* and ν

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References

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • J. D. Kuzan
    • 1
  • T. J. Hanratty
    • 1
  • R. J. Adrian
    • 2
  1. 1.Dept. of Chemical EngineeringUniversity of IllinoisUrbanaUSA
  2. 2.Dept. of Theoretical and Applied MechanicsUniversity of IllinoisUrbanaUSA

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