The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer


To investigate the accuracy of tomographic particle image velocimetry (Tomo-PIV) for turbulent boundary layer measurements, a series of synthetic image-based simulations and practical experiments are performed on a high Reynolds number turbulent boundary layer at Reθ = 7,800. Two different approaches to Tomo-PIV are examined using a full-volume slab measurement and a thin-volume “fat” light sheet approach. Tomographic reconstruction is performed using both the standard MART technique and the more efficient MLOS-SMART approach, showing a 10-time increase in processing speed. Random and bias errors are quantified under the influence of the near-wall velocity gradient, reconstruction method, ghost particles, seeding density and volume thickness, using synthetic images. Experimental Tomo-PIV results are compared with hot-wire measurements and errors are examined in terms of the measured mean and fluctuating profiles, probability density functions of the fluctuations, distributions of fluctuating divergence through the volume and velocity power spectra. Velocity gradients have a large effect on errors near the wall and also increase the errors associated with ghost particles, which convect at mean velocities through the volume thickness. Tomo-PIV provides accurate experimental measurements at low wave numbers; however, reconstruction introduces high noise levels that reduces the effective spatial resolution. A thinner volume is shown to provide a higher measurement accuracy at the expense of the measurement domain, albeit still at a lower effective spatial resolution than planar and Stereo-PIV.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29


  1. Adrian RJ (1991) Particle-imaging techniques for experimental fluid mechanics. Annu Rev Fluid Mech 23:261–304

    Article  Google Scholar 

  2. Atkinson C, Soria J (2009) Efficient simultaneous reconstruction and direct cross-correlation techniques for tomographic particle image velocimetry (tomo-piv). Exp Fluids (submitted)

  3. Atkinson CH, Dillon-Gibbons CJ, Herpin S, Soria J (2008) Reconstruction techniques for tomographic piv (tomo-piv) of a turbulent boundary layer. In: 14th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal

  4. Baur T, Koengeter J (2000) High-speed piv and the post-processing of time-series results. Euromech 411

  5. Carlier J (2001) Etude des structures coh erentes d’une couche limite turbulente à grand nombre de reynolds. PhD thesis, Univ. de Lille, France

  6. Carlier J, Stanislas M (2005) Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry. J Fluid Mech 535:143–188

    Article  MATH  MathSciNet  Google Scholar 

  7. Chong MS, Perry AE, Cantwell BJ (1990) A general classification of three-dimensional flow fields. Phys Fluids 2(5):765–777

    Article  MathSciNet  Google Scholar 

  8. Elsinga GE (2008) Tomographic particle image velocimetry and its application to turbulent boundary layers. PhD thesis, Technische Universiteit Delft

  9. Elsinga GE, van Oudheusden BW, Scarano F (2006a) Experimental assessment of tomographic-piv accuracy. In: 13th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal

  10. Elsinga GE, Scarano F, Wieneke B, van Oudheusden BW (2006) Tomographic particle image velocimetry. Exp Fluids 41:933–947

    Article  Google Scholar 

  11. Elsinga GE, Westerweel J, Scarano F, Novara M (2009) On the velocity of ghost particles. In: 8th international symposium on particle image velocimetry—PIV09, Melbourne, Australia

  12. Foucaut JM, Stanislas M (2002) Some considerations on the accuracy and frequency response of some derivative filters applied to particle image velocimetry vector fields. Meas Sci Technol 13:1058–1071

    Article  Google Scholar 

  13. Foucaut JM, Milliat B, Perenne N, Stanislas M (2003) Characterisation of different piv algorithms using the europiv synthetic image generator and real images from a turbulent boundary layer. In: Particle image velocimetry: recent improvements, proceedings of the EUROPIV2 workshop, Zaragoza, Spain

  14. Foucaut JM, Carlier J, Stanislas M (2004) Piv optimization for the study of turbulent flow using spectral analysis. Meas Sci Technol 15:1046–1058

    Article  Google Scholar 

  15. Foucaut JM, Coudert S, Stanislas M (2009) Unsteady characteristics of near-wall turbulence using high repetition stereoscopic particle image velocimetry (piv). Meas Sci Technol 20(7):1–12

    Article  Google Scholar 

  16. Herpin S (2009) Study of the influence of the Reynolds number on the organization of wall-bounded turbulence. PhD thesis, Ecole Centrale de Lille and Monash University

  17. Herpin S, Wong C, Stanislas M, Soria J (2008) Stereoscopic piv measurements of a turbulent boundary layer with a large spatial dynamic range. Exp Fluids 45(4):745–763

    Article  Google Scholar 

  18. Hinze JO (1975) Turbulence. McGraw-Hill, New York

    Google Scholar 

  19. Huang H, Dabiri D, Gharib M (1997) On errors of digital particle image velocimetry. Meas Sci Technol 8:1427–1440

    Article  Google Scholar 

  20. Huang HT, Fiedler HE, Wang JJ (1993) Limitations and improvements of piv; part ii: particle image distortion, a novel technique. Exp Fluids 15:263–273

    Google Scholar 

  21. Keane RD, Adrian RJ (1990) Optimization of particle image velocimeters, part i: double pulsed systems. Meas Sci Technol 1:1202–1215

    Article  Google Scholar 

  22. Kim BJ, Sung HJ (2006) A further assessment of interpolation schemes for window deformation in piv. Exp Fluids 41:499–511

    Article  Google Scholar 

  23. Meng H, Pan G, Pu Y, Woodward SH (2004) Holographic particle image velocimetry: from film to digital recording. Meas Sci Technol 15:673–685

    Article  Google Scholar 

  24. Michael YC, Yang KT (1991) Recent developments in axial tomography for heat transfer and fluid flow studies. Exp Ther Fluid Sci 4:637–647

    Article  Google Scholar 

  25. Moffat RJ (1988) Describing the uncertainties in experimental results. Exp Ther Fluid Sci 1:3–17

    Article  Google Scholar 

  26. Nogueira J, Lecuona A, Rodriguez PA (2001) Identification of a new source of peak locking, analysis and its removal in conventional and super-resolution piv techniques. Exp Fluids 30:309–316

    Article  Google Scholar 

  27. Raffel M, Willert C, Kompenhans J (1998) Particle image velocimetry: a practical guide. Springer, New York

    Google Scholar 

  28. Scarano F (2002) Iterative image deformation methods in piv. Meas Sci Technol 13(R1–R19)

  29. Scarano F, Elsinga GE, Bocci E, van Oudheusden BW (2006) Investigation of 3-d coherent structures in the turbulent cylinder wake using tomo-piv. In: 13th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal

  30. Schröder A, Geisler R, Staack K, Wieneke B, Elsinga GE, Scarano F, Henning A (2008) Lagrangian and Eulerian views into a turbulent boundary layer flow using time-resolved tomographic piv. In: 14th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal

  31. Soloff SM, Adrian RJ, Liu ZC (1997) Distortion compensation for generalized stereoscopic particle image velocimetry. Meas Sci Technol 8:144–1454

    Article  Google Scholar 

  32. Soria J, Atkinson C (2008) Towards 3c-3d digital holographic fluid velocity vector field measurement - tomographic digital holographic piv (tomo-hpiv). Meas Sci Technol 19:1–12

    Article  Google Scholar 

  33. Westerweel J, Scarano F (2005) Universal outlier detection for piv data. Exp Fluids 39:1096–1100

    Article  Google Scholar 

  34. Wieneke B (2008) Volume self-calibration for 3d particle image velocimetry. Exp Fluids 45(4):549–556

    Article  Google Scholar 

  35. Wieneke B, Taylor S (2006) Fat-sheet piv with computation of gull 3d-strain tensor using tomographic reconstruction. In: 13th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal

  36. Willert C (1997) Stereoscopic digital particle image velocimetry for application in wind tunnel flows. Meas Sci Technol 8:1465–1479

    Article  Google Scholar 

  37. Worth NA, Nickels TB (2008) Acceleration of tomo-piv by estimating the initial volume intensity distribution. Exp Fluids 45(5):847–856

    Article  Google Scholar 

  38. Worth NA, Nickels TB, Swaminathan N (2010) A tomographic piv resolution study based on homogeneous isotropic turbulence dns data. Exp Fluids. doi:10.1007/s00348-010-0840-1

Download references


C. Atkinson was supported by an Eiffel Fellowship and an Australian Postgraduate Scholarship while undertaking this research. The support of the Australian Research Council is gratefully acknowledged. Experiments presented in this paper were carried out using the Grid’5000 experimental testbed, being developed under the INRIA ALADDIN development action with support from CNRS, RENATER and several Universities as well as other funding bodies (see This work was also supported by the ANR VIVE 3D and CISIT programs.

Author information



Corresponding author

Correspondence to Callum Atkinson.



See Tables 11 and 12.

Table 11 Average boundary layer velocity errors in reconstruction of a 180-pixel-thick volume, starting at the wall
Table 12 Average boundary layer velocity errors in reconstruction of a 70-pixel-thick volume, starting 55 pixels above the wall

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Atkinson, C., Coudert, S., Foucaut, JM. et al. The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer. Exp Fluids 50, 1031–1056 (2011).

Download citation


  • Particle Image Velocimetry
  • Turbulent Boundary Layer
  • Seeding Density
  • Bias Error
  • Interrogation Window