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Measurement of turbulent wall velocity gradients using cylindrical waves of laser light

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Abstract

A new optical instrument has been developed for direct measurement of instantaneous velocity gradients at the bounding wall. Light emerging from two tiny optical slits in the surface is used to form a “fan of fringes” in the region very near the wall. Doppler frequency of the light scattered by the seed particles is directly proportional to the velocity gradient. The system has been used to measure the statistics of the streamwise and spanwise velocity gradients in a turbulent boundary layer. The streamwise and spanwise rms fluctuations were found to be 38% and 11% of the mean streamwise value respectively. The latter result is subject to a large uncertainty.

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Abbreviations

a :

slit width

B :

transfer function of the instrument

B * :

normalized transfer function

\(\overline B *\) :

path-averaged value of the normalized transfer function

c :

constant in logarithmic velocity profile

C f :

skin friction coefficient

d f :

fringe spacing

f 1,f2 :

frequencies at the downstream and upstream slits resp.

f d :

heterodyne Doppler frequency of the signal

g(t) :

instantaneous wall velocity gradient

G :

Clauser shape factor

\(\overline g \) :

mean wall velocity gradient

g′ :

rms value of the wall velocity gradient

H :

boundary layer shape factor

i, j, k :

unit vectors along x, y, z axes

κ :

wavenumber of laser light

L :

major axis of the elliptic cross-section of the laser sheet at the slit

l :

length of each slit

N :

number of cycles in a signal

N 0 :

number of cycles without frequency-shifting

n :

difference of the unit vectors u 1and u 2

P :

power transmitted through a slit

P o :

power incident on a slit

Re δ 1 :

Reynolds number based on displacement thickness and free-stream velocity

Re δ 2 :

Reynolds number based on momentum thickness and free-stream velocity

S :

spacing between the slits

S * :

normalized spacing between the slits

u :

streamwise velocity

u 1,u2 :

unit vectors along the local directions of propagation of the two cylindrical waves

u l :

linear term in the streamwise velocity profile

u nl :

nonlinear terms in the streamwise velocity

u nl * :

normalized value of nonlinear streamwise velocity

u nl * :

mean streamwise velocity

u τ :

friction velocity

u+ :

mean velocity normalized with friction velocity

v :

velocity component normal to the wall

v * :

normal velocity normalized with streamwise velocity

V :

velocity vector

w :

spanwise component of velocity

W :

minor axis of the elliptic cross-section of the laser sheet at the slit

x :

streamwise distance

± x m :

limiting values of streamwise distance for a signal

x * :

normalized streamwise distance

x * :

normalized value of x m

y :

normal distance

y + :

normal distance normalized with friction length scale

z :

spanwise distance

z + :

spanwise distance normalized with friction length scale

α :

half-spreading angle of the cylindrical waves

δ :

boundary layer thickness in Coles' profile

δ 1 :

displacement thickness of the boundary layer

δ 2 :

momentum thickness of the boundary layer

δ 3 :

energy thickness of the boundary layer

ξ :

constant in logarithmic velocity profile

λ :

wavelength of laser light

ν :

kinematic viscosity

π :

coefficient of wake function in Coles' profile

References

  • Alfredsson, P. H.; Johansson, A. V.; Haritonidis, J. H.; Eckelmann, H. 1988: On the fluctuating wall shear stress and the velocity field in the viscous sublayer. Phys. Fluids 31, 1026–1033

    Google Scholar 

  • Chapman, D. R.; Kuhn, G D. 1985: Navier-Stokes computation of viscous sublayer flow and the limiting behavior of turbulence near a wall. AIAA 7th Computational Fluid Dynamics Conference, Cincinnati, Ohio

  • Coles, D. 1957: The law of the wake in turbulent boundary layer. J. Fluid Mech. 2, 191–226

    Google Scholar 

  • Coles, D. 1962: The turbulent boundary layer in a compressible fluid. RAND Corp., Rep. R-403-PR

  • Coles, D. 1978: A model for flow in the viscous sublayer. Proc. of the Workshop on Coherent Structure of Turbulent Boundary Layers. Lehigh University, Bethlehem, PA, 462–468

    Google Scholar 

  • Durst, F.; Melling, A.; Whitelaw, J. H. 1976: Principles and practice of laser-Doppler anemometry. Academic Press

  • Eckelmann, H. 1974: The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow. J. Fluid Mech. 65, 439–459

    Google Scholar 

  • Jayaraman, R.; Parikh, P.; Reynolds, W. C. 1982: An experimental study of the dynamics of an unsteady, turbulent boundary layer. Report TF-18, Dept. Mech. Engng. Stanford University, Calif.

    Google Scholar 

  • Jenkins, F. A.; White, H. E. 1957: Fundamentals of Optics. Mc-Graw-Hill Inc.

  • Kim, H. T.; Kline, S. J.; Reynolds, W. C. 1971: The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50, 133–160

    Google Scholar 

  • Kim, J.; Moin P.; Moser, R. 1987: Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166

    Google Scholar 

  • Klebanoff, P. S. 1954: Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA TN 3178

  • Kline, S. J.; Reynolds, W. C.; Schraub, F. A.; Runstadler, P. W. 1967: The structure of turbulent boundary layers.J. Fluid Mech. 30, 741–773

    Google Scholar 

  • Kreplin, H.; Eckelmann, H. 1979: Behavior of the three fluctuating velocity components in the wall region of a turbulent channel flow. Phys. Fluids. 22, 1233–1239

    Google Scholar 

  • Laufer, J. 1953: The structure of turbulence in fully developed pipe flow. NACA TN 2954

  • Ludwieg, H.; Tillmann, W. 1949: Investigation of the wall shearing stress in turbulent boundary layers. NACA TM 1285

  • Mitchell, J. E.; Hanratty, T. J. 1966: A study of turbulence at a wall using an electrochemical wall shear-stress meter. J. Fluid Mech. 26, 199–221

    Google Scholar 

  • Naqwi, A. A.; Reynolds, W. C. 1987: Dual cylindrical wave laser Doppler method for measurement of skin friction in fluid flow. Report TF-28, Dept. Mech. Engng. Stanford Univ., Stanford, Calif.

    Google Scholar 

  • Py, B. 1973: Étude tridimensionelle de la sous-couche visqueuse dans une veine rectangulaire par des mesures de transfert de matiére en paroi. Int. J. Heat Mass Transfer 16, 129–143

    Google Scholar 

  • Sirkar, K. K.; Hanratty, T. J. 1970: The limiting behavior of the turbulent transverse velocity component close to a wall. J. Fluid Mech., 44, 605–614

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Mechanical Engineering, Stanford University, 94305, Stanford, CA, USA

    A. A. Naqwi & W. C. Reynolds

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  1. A. A. Naqwi
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  2. W. C. Reynolds
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Currently at LSTM, Universitat Erlangen-Nürnberg, Cauerstraße 4, W-8520 Erlangen, BRD

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Naqwi, A.A., Reynolds, W.C. Measurement of turbulent wall velocity gradients using cylindrical waves of laser light. Experiments in Fluids 10, 257–266 (1991). https://doi.org/10.1007/BF00202458

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