Skip to main content
SpringerLink
Log in

Analysis of two-point velocity measurements in near-wall flows

  • Originals
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

Two-point measurements of the streamwise velocity in a turbulent channel flow are performed using laser-Doppler anemometry. High spatial and temporal resolutions (about 1 Kolmogorov microscale in space and time) are achieved. Data are obtained at several distances from the wall for Re δ in the range 1500–5000. Results from correlation functions are compared with the hypotheses of Taylor and Tennekes: they reproduce the experimental data even at low Reynolds numbers and small distances from the wall, providing that convection rather than mean velocity is used. Convection velocities are computed from transfer function phase diagrams: the ratio of convection to mean flow velocity is found to decrease with increasing Reynolds number and distance from the wall. Large flow structures are convected with the local mean velocity rather than the test section mean velocity; data at small Reynolds and close to the wall exhibit convection velocities lying between the two. The good agreement between the time evolution of the envelope of space-time-correlation function with the corresponding Lagrangian correlation over one integral time scale confirms the existence of a strict relation between the Eulerian and Lagrangian descriptions of turbulence.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

A :

upstream measurement point

B :

downstream measurement point

d :

seeding particle size

f :

frequency

f * :

non-dimensional frequency (using Taylor time microscale)

H AB (f) :

transfer function between signals at points A and B

¦H AB (f)¦:

modulus of transfer function

L ɛ :

dissipation length scale

L E :

Eulerian space integral scale

N D :

valid data density

r :

distance between points A and B

R A,B (τ):

time correlation function at point A or B

R AB (τ):

space-time correlation function between points A and B

R AB (r) :

space correlation function between points A and B

Re δ :

Reynolds number based on half channel height

Re λ :

Reynolds number based on Taylor microscale

S A,B (f) :

auto-spectral power density at point A or B

S A B(f) :

cross-spectral power density between points A and B

¦S AB (f)¦:

modulus of cross-spectral power density

u′ :

rms of streamwise fluctuating velocity

u * :

friction velocity

u A,B (t) :

velocity at point A or B

U :

mean flow velocity in the entire test section

U c :

convection velocity

U l :

local mean flow velocity

t :

time

t + :

time in wall units

t * :

non-dimensional time (using Eulerian or Lagrangian integral time scale)

T :

total sampling time

T E :

Eulerian integral time scale

T L :

Lagrangian integral time scale

x,y :

z reference frame coordinates

y + :

distance from the wall in wall units

β :

ratio between Lagrangian and Eulerian integral time scales

γ AB (f) :

coherence function between signals at points A and B

δ :

half channel height

Δ r/r :

relative error on distance evaluations

ΔU/U :

relative error on velocity measurements

ɛ :

mean energy dissipation

0 AB (f) :

phase of cross-spectral power density

η :

Kolmogorov scale

λ :

Taylor length microscale

ν :

kinematic viscosity

ρ L :

Lagrangian correlation coefficient

Σ :

mean displacement of fluid particles

τ :

time lag

τ 0 :

fixed time lag

τ λ :

Taylor time microscale

φ AB (f) :

phase of transfer function

References

  • Adrian RJ (1988) Linking correlations and structure: stochastic estimation and conditional averaging. In: Near wall turbulenceZoran Zaric Memorial Conf. (Kline SJ; Afgan NH, eds.), pp 420–436. New York: Hemisphere

    Google Scholar 

  • Adrian RJ; Yao CS (1987) Power spectra of fluid velocities measured by laser Doppler velocimetry. Exp Fluids 5: 17–28

    Google Scholar 

  • Antonia RA; Browne LWB; Bisset DK (1988) Effect of Reynolds number on the organized motion in a turbulent boundary layer. In: Near wall turbulence-Zoran Zaric Memorial Conf. (Kline SJ; Afgan NH, eds.), pp 488–505. New York: Hemisphere

    Google Scholar 

  • Balint JL; Piomelli U; Wallace JM (1989) On the validity of Taylor hypothesis for wall-bounded flows. Phys Fluids Al: 609–611

    Google Scholar 

  • Bendat JS; Piersol AG (1971) Random data: analysis and measurement procedures. New York: Wiley-Interscience

    Google Scholar 

  • Benak M; Sturm M; Tropea CD (1993) Correlation estimators for two-point laser Doppler anemometry. In: Laser anemometry — advances and applications. SPIE Vol 2052, pp 613–622

    Google Scholar 

  • Berkooz G; Holmes P; Lumley JL (1993) The proper orthogonal decomposition in the analysis of turbulent flows. Ann Rev Fluid Mech 25: 539–575

    Google Scholar 

  • Buchhave P; George WK; Lumley JL (1979) The measurement of turbulence with the laser Doppler anemometry. Ann Rev Fluid Mech 11: 443–503

    Google Scholar 

  • Cenedese A; Costantini A; Romano GP (1992) LDA spectral measurements in a turbulent boundary layer. Exp Thermal Fluid Sci 5: 281–289

    Google Scholar 

  • Cenedese A; Di Felice F; Romano GP (1991) Experimental testing of Taylor's hypothesis by LDA in highly turbulent flow. Exp Fluids 11: 351–358

    Google Scholar 

  • Champagne FH; Harris G; Corssin S (1970) Experiments on nearly homogeneous turbulent shear flow. J Fluid Mech 41: 281–322

    Google Scholar 

  • Corssin S (1963) Estimates of the relations between Eulerian and Lagrangian scales in large Reynolds number turbulence. J Atm Sci 20: 115–119

    Google Scholar 

  • Dumas R (1988) Observations on the boundary layer based on measured correlations with various improvements. In: Near wall turbulence-Zoran Zaric Memorial Conf. (Kline SJ; Afgan NH, eds.), pp 437–452. Hemisphere

  • Edwards RV (1987) Report of the special panel on statistical particle bias problems in laser anemometry. J Fluids Eng 109: 89–93

    Google Scholar 

  • Favre AJ; Gaviglio JJ; Dumas R (1957) Space-time double correlations and spectra in a turbulent boundary layer. J Fluid Mech 2: 313–342

    Google Scholar 

  • Fisher MJ; Davies POAL (1963) Correlation measurements in a nonfrozen pattern of turbulence. J Fluid Mech 18: 97–116

    Google Scholar 

  • Fung JCH; Hunt JCR; Malik NA; Perkins RJ (1992) Kinematic simulation of homogeneous turbulence by unsteady random Fourier modes. J Fluid Mech 236: 281–318

    Google Scholar 

  • George WK (1974) The measurement of turbulence intensities using real-time laser-Doppler velocimetry. J Fluid Mech 66: 11–16

    Google Scholar 

  • George WK; Lumley JL (1973) The laser Doppler velocimeter and its application to the measurement of turbulence. J Fluid Mech 60: 321–362

    Google Scholar 

  • Gerosa S; Romano GP (1994) Effect of noise in Laser Doppler Anemometry. Mech Systems Signal Proces 8: 229–242

    Google Scholar 

  • Hinze JO (1975) Turbulence. New York: McGraw-Hill

    Google Scholar 

  • Moin P; Spalart PR (1989) Contributions of numerical simulation data bases to the physics, modeling and measurement of turbulence. In: Advances in turbulence (George, WK; Arndt R, eds.), pp 11–36, New York: Hemisphere

    Google Scholar 

  • Morton JB; Clark WH (1971) Measurements of two-point velocity correlations in a pipe flow using laser anemometers. J Phys E: Scient Instrum 4: 809–814

    Google Scholar 

  • Nicolaenko B; She ZS (1990) Turbulent bursts, inertial sets and simmetry-breaking homoclinic cycles in periodic Navier-Stokes flows: In: Turbulence in fluid flows — A dynamical systems approach (Sell GR; Foias C; Temam R, eds.) pp 123–136. Berlin: Springer

    Google Scholar 

  • Pedrizzetti G; Novikov EA (1994) On Markov modelling of turbulence. Accepted in: J Fluid Mech

  • Romano GP (1993) Two-point velocity measurements using LDA: spatial and temporal analysis in a turbulent boundary layer. In: Laser anemometry — Advances and applications, SPIE Vol 2052, pp 597–604

    Google Scholar 

  • Sato Y; Yamamoto K (1987) Lagrangian measurement of fluid-particle motion in an isotropic turbulent field. J Fluid Mech 175: 183–199

    Google Scholar 

  • Squires KD; Eaton JK (1991) Lagrangian and Eulerian statistics obtained from direct numerical simulations of homogeneous turbulence. Phys Fluids A3: 130–143

    Google Scholar 

  • Taylor JT (1938) The spectrum of turbulence. Proc Roy Soc A164

  • Tennekes H (1975) Eulerian and Lagrangian time microscales in isotropic turbulence. J Fluid Mech 67: 561–567

    Google Scholar 

  • Tropea CD (1993) Refined turbulence measurements using laser Doppler anemometry. In: Refined flow modelling and turbulence measurements, pp 257–268. Presses de l'Ecole Nationale des Ponts et Chaussees

  • Yeoung PK; Pope SB (1989) Lagrangian statistics from direct numerical simulations of isotropic turbulence. J Fluid Mech 207: 531–586

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanics and Aeronautics, University of Roma “La Sapienza”, Via Eudossiana18, I-00184, Roma, Italy

    G. P. Romano

Authors
  1. G. P. Romano
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The present work was supported by the Italian University, Scientific Research and Technology Office (MURST). The author is grateful to Prof. A. Cenedese for very useful suggestions and discussions, to Prof. R.A. Antonia for valuable comments on the manuscript and to Prof. G. Seminara for revision of the paper. The author would also like to thank Prof. C. Tropea for encouraging the publication of the paper. Stimulating discussions were provided by Drs. F. Di Felice, G. Leuzzi, P. Monti and G. Querzoli. Special thanks to Dr. S. Gerosa and D. Pietrogiacomi for help with the measurements.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Romano, G.P. Analysis of two-point velocity measurements in near-wall flows. Experiments in Fluids 20, 68–83 (1995). https://doi.org/10.1007/BF00189296

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00189296

Keywords

Search

Navigation