Skip to main content
SpringerLink
Log in

Analysis of errors in the measurement of energy dissipation with two-point LDA

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

Abstract

In the present study, an attempt has been made to identify and quantify, with a rigorous analytical approach, all possible sources of error involved in the estimation of the fluctuating velocity gradients \(\overline {\left( {\partial u_i /\partial x_j } \right)^2 } \) when a two-point laser Doppler velocimetry (LDV) technique is employed. Measurements were carried out in a grid-generated turbulence flow where the local dissipation rate can be calculated from the decay of kinetic energy. An assessment of the cumulative error determined through the analysis has been made by comparing the values of the spatial gradients directly measured with the gradient estimated from the decay of kinetic energy. The main sources of error were found to be related to the length of the two control volumes and to the fitting range, as well as the function used to interpolate the correlation coefficient when the Taylor length scale \(\left( {{\text{or }}\overline {\left( {\partial u_i /\partial x_j } \right)^2 } } \right)\) are estimated.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8a, b
Fig. 9
Fig. 10

Similar content being viewed by others

Notes

  1. The perfect symmetry of the correlation curve is caused by the fact that R ii (Δx i ) has been set equal to R ii (−Δx i ).

Abbreviations

C f :

Calibration factor (m)

D :

Grid wire diameter (mm)

L :

Test section length (m)

L ij :

Integral length scale in the ith direction of the u j velocity component (m)

M :

Grid mesh size (m)

N :

Number of points in the fitting range

N tot :

Number of particles in coincidence

R ii (Δx j ):

Correlation coefficient of the ith velocity component in the jth direction

R mii :

Measured correlation coefficient of the ith velocity component

R rii :

Real correlation coefficient of the ith velocity component

Re :

Reynolds number

Re M :

Reynolds number based on M

t :

Particle arrival time (s)

U i :

Velocity component in the i direction (ms−1)

u i :

Turbulent velocity component in the i direction (ms−1)

\(\overline {U_i }\) :

Mean velocity in the i direction (ms−1)

W :

Width of the test section (m)

x 0 :

Position where the two control volumes overlap completely (m)

x i :

Coordinate in the i direction (m)

x M :

Non-dimensionalised distance from the grid

Δx j :

Displacement in the j direction (m)

Δxmax:

Upper limit of the fitting range (m)

Δxmin:

Lower limit of the fitting range (m)

ε :

Viscous dissipation rate of turbulent kinetic energy (m2s−3)

η :

Kolgomorov length scale (m)

Λ:

Control volume length (m)

λ ij :

Taylor length scale in the i direction of the u j velocity component (m)

ν :

Kinematic viscosity (m2s−1)

σ :

Grid solidity ratio

τ w :

Coincidence window (s)

HWA:

Hot wire anemometry

LDA/LDV:

Laser Doppler anemometry/velocimetry

PIV:

Particle image velocimetry

References

  • Absil LHJ (1988) Laser Doppler measurements of mean turbulence quantities, time- and spatial-correlation coefficients in the wake of a circular cylinder. In: Proceedings of the 4th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, July 1988, paper 1.1

  • Belmabrouk H (2000) A theoretical investigation of the exactness of Taylor length scale estimates from two-point LDV. Exp Therm Fluid Sci 22:45–53

    Google Scholar 

  • Belmabrouk H (2001) Accuracy of Taylor length scale measurements by two-point laser Doppler velocimetry: a theoretical study. Flow Measur Instrum 12:9–16

    Google Scholar 

  • Belmabrouk H, Michard M (1998) Taylor length scale measurement by laser Doppler velocimetry. Exp Fluids 25:69–76

    Google Scholar 

  • Benak M, Sturm M, Tropea C, Nobach H, Fuchs W, Müller E (1993) Correlation estimators for two-point laser Doppler anemometry. Proc SPIE 2052:613–621

    Google Scholar 

  • Bendat JS, Piersol AG (1987) Random data: analysis and measurement procedures, 2nd edn. Wiley-Interscience, New York

    Google Scholar 

  • Benedict LH, Gould RD (1998) Concerning time and length scale estimates made from burst-mode LDA autocorrelation measurements. Exp Fluids 24:246–253

    Google Scholar 

  • Benedict LH, Gould RD (1999) Understanding biases in the near-field region of two-point correlation measurements using LDA. Exp Fluids 26:381–388

    Google Scholar 

  • Browne LWB, Antonia RA, Shah DA (1987) Turbulent energy dissipation in a wake. J Fluid Mech 179:307–326

    CAS  Google Scholar 

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

    Google Scholar 

  • Corrsin S (1943) Experimental investigation and analysis of the velocity variations in turbulent flow. NACA, war-time report W-94, Washington, DC

  • Eriksson JG, Karlsson RI (1995) An investigation on the spatial resolution requirements for two-point correlation measurement using LDV. Exp Fluids 18(5):393–396

    Google Scholar 

  • Fraser RA, Bracco FV (1988) Cycle-resolved LDV integral length scale measurements in an IC engine. SAE paper 880381, Society of Automotive Engineers, Warrendale, PA

  • Gan CL, Djenidi L, Antonia RA (1996) Spanwise vorticity measurements in a turbulent boundary layer using LDV. In: Proceedings of the 8th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, July 1996, paper 17.2

  • Gould RD, Benedict LH, Nejad AS, Ahmed SA (1992) Two-point velocity correlation measurements in an axisymmetric sudden expansion using LDV. In: Proceedings of the 6th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, July 1992, paper 7.1

  • Groth J, Johansson AV (1988) Turbulence reduction by screens. J Fluid Mech 197:139–155

    Google Scholar 

  • Hinze JO (1975) Turbulence, 2nd edn. McGraw-Hill, New York

  • Johansson G, Klingmann J (1994) An LDA-based method for accurate measurements of the dissipation rate tensor with application to a circular jet. In: Proceedings of the 7th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, July 1994, paper 25.2

  • Johns RJR, Pitcher GF, Winklhofer E (1986) Measurement of spatial correlations in turbulent flow with a two-component backscatter LDA system. In: Proceedings of the 3rd international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, July 1986, paper 10.2

  • Kang S, Patil B, Roy RP (2001) Effects of coincidence window and measuring volume size on laser Doppler velocimetry measurement of turbulence. Exp Fluids 30:365–370

    Google Scholar 

  • Kline SJ, McClintock FA (1953) Describing uncertainties in single-sample experiments. Mech Eng 75:3–8

    Google Scholar 

  • Michelet S (1998) Turbulence et dissipation au sein d’un réacteur agité par une turbine Rushton—vélocimétrie laser Doppler à deux volumes de mesure. PhD thesis, Institut National Polytechnique de Lorraine, France

  • Mohamed MS, LaRue JC (1990) The decay power law in grid-generated turbulence. J Fluid Mech 219:195–214

    Google Scholar 

  • Müller E, Nobach H, Tropea C (1998) A refined reconstruction-based correlation estimator for two-channel, non-coincidence laser Doppler anemometry. Meas Sci Technol 9 (3):442–451

    Google Scholar 

  • Nakatani N, Tokita M, Maegawa M, Yamada T (1985) Multi-point LDVs using phase diffraction gratings and optical fiber probes—measurements of coherent structures in premixed flame. In: Proceedings of the 2nd international symposium on laser anemometry, Miami, Florida, November 1985, pp 111

  • Romano GP (1995) Analysis of two-point velocity measurements in near-wall flows. Exp Fluids 20(2):68–83

    Google Scholar 

  • Schenk T, Jovanović J (2002) Measurement of the instantaneous velocity gradients in plane and axisymmetric turbulent wake flows. ASME J Fluids Eng 124:143–153

    Google Scholar 

  • Simmons LFG, Salter C (1934) Experimental investigation and analysis of the velocity variations in turbulent flow. Proc R Soc Lon Ser A 145:145–212

    Google Scholar 

  • Tennekes H, Lumley JL (1973) A first course in turbulence, 2nd edn. MIT Press, Cambridge, Massachusetts

  • Townsend AA (1948) Local isotropy in the turbulent wake of a cylinder. Aus J Sci Res Ser A 1:161–174

    Google Scholar 

  • Tresso R, Munoz DR (2000) Homogeneous, isotropic flow in grid generated turbulence. ASME J Fluids Eng 122:51–56

    Google Scholar 

  • Trimis D, Melling A (1995) Improved laser Doppler anemometry techniques for two-point turbulent flow correlations. Meas Sci Technol 6:663–673

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Experimental and Computational Laboratory for the Analysis of Turbulence (ECLAT), Department of Mechanical Engineering, King’s College London, Strand, London, WC2R 2LS, UK

    A. Ducci & M. Yianneskis

Authors
  1. A. Ducci
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Yianneskis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Yianneskis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ducci, A., Yianneskis, M. Analysis of errors in the measurement of energy dissipation with two-point LDA. Exp Fluids 38, 449–460 (2005). https://doi.org/10.1007/s00348-004-0924-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00348-004-0924-x

Keywords

Search

Navigation