Experiments in Fluids

, Volume 42, Issue 6, pp 893–902 | Cite as

A correction method for measuring turbulence kinetic energy dissipation rate by PIV

Validated by random Oseen vortices synthetic image test
Research Article

Abstract

The accuracy of turbulent kinetic energy (TKE) dissipation rate measured by PIV is studied. The critical issue for PIV-based dissipation measurements is the strong dependency on the spatial resolution, Δx, as reported by Saarenrinne and Piirto (Exp Fluids Suppl:S300–S307, 2000). When the PIV spacing is larger than the Kolmogorov scale, η, the dissipation is underestimated because the small scale fluctuations are filtered. For the case of Δx smaller than the Kolmogorov scale, the error rapidly increases due to noise. We introduce a correction method to eliminate the dominant error for the small Δx case. The correction method is validated by using a novel PIV benchmark, random Oseen vortices synthetic image test (ROST), in which quasi-turbulence is generated by randomly superposing multiple Oseen vortices. The error of the measured dissipation can be more than 1,000% of the analytical dissipation for the small Δx case, while the dissipation rate is underestimated for the large Δx case. Though the correction method does not correct the underestimate due to the low resolution, the dissipation was accurately obtained within a few percent of the true value by using the correction method for the optimal resolution of η/10 < Δx < η/2.

References

  1. Antonia RA, Mi J (1993) Corrections for velocity and temperature derivatives in turbulent flows. Exp Fluids 14:203–208CrossRefGoogle Scholar
  2. Antonia RA, Pearson BR (2000) Effect of initial conditions on the mean energy dissipation rate and the scaling exponent. Phys Rev E 62(6):8086–8090CrossRefGoogle Scholar
  3. Antonia RA, Zhu Y, Kim J (1993) On the measurement of lateral velocity derivatives in turbulent flows. Exp Fluids 15:65–69Google Scholar
  4. Antonia RA, Zhu Y, Kim J (1994) Corrections for spatial velocity derivatives in a turbulent shear flow. Exp Fluids 16:411–413CrossRefGoogle Scholar
  5. Bendat JS, Piersol AG (2000) Random data analysis and measurement procedures. Wiley, CanadaMATHGoogle Scholar
  6. Burattini P, Lavoie P, Antonia RA (2005) On the normalized turbulent energy dissipation rate. Phys Fluids 17:098103CrossRefMathSciNetGoogle Scholar
  7. Chen J, Katz J (2005) Elimination of peak-locking error in PIV analysis using the correlation mapping method. Meas Sci Technol 16:1605–1618CrossRefGoogle Scholar
  8. Eaton JK, Tanaka T (2006) Particle interaction with homogeneous turbulence. Forty Fourth AIAA Aerosp Sci Meet Exhibit 44:1–3Google Scholar
  9. Ferziger JH (1981) Numerical methods for engineering application. Wiley, LondonGoogle Scholar
  10. Gui L, Wereley ST (2002) A correlation-based continuous window-shift technique to reduce the peak-locking effect in digital PIV image evaluation. Exp Fluids 32:506–517CrossRefGoogle Scholar
  11. Hart DP (2000) PIV error correction. Exp Fluids 29:13–22CrossRefGoogle Scholar
  12. Huang H, Fiedler H, Wang J (1993) Limitation and improvement of PIV: part II. Particle image distortion, a novel technique. Exp Fluids 15(263):73Google Scholar
  13. Kaneda Y, Ishihara T, Yokokawa M, Itakura K, Uno A (2003) Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box. Phys Fluids 15(2):L21–L24CrossRefGoogle Scholar
  14. Liu X, Thomas FO (2004) Measurement of the turbulent kinetic energy budget of a planar wake flow in pressure gradients. Exp Fluids 37:469–482CrossRefGoogle Scholar
  15. Lumley JL (1992) Some comments on turbulence. Phys Fluids 4:203–211MATHCrossRefGoogle Scholar
  16. Pearson BR, Krogstad PA, Water W (2002) Measurements of the turbulent energy dissipation rate. Phys Fluids 13(3):1288–1290CrossRefGoogle Scholar
  17. Pearson BR, Yousef TA, Haugen NEL, Brandenburg A, Krogstad PA (2004) Delayed correlation between turbulent energy injection and dissipation. Phys Rev E 70:056301CrossRefGoogle Scholar
  18. Raffel M, Willert C, Kompenhans J (1998) Particle image velocimetry. Springer, Heidelberg, p 144Google Scholar
  19. Roth GI, Katz J (2001) Five techniques for increasing the speed and accuracy of PIV interrogation. Meas Sci Technol 12:238–245CrossRefGoogle Scholar
  20. Saarenrinne P, Piirto M (2000) Turbulent kinetic energy dissipation rate estimation from PIV vector fields. Exp Fluids Suppl:S300–S307CrossRefGoogle Scholar
  21. Saarenrinne P, Piirto M, Eloranta H (2001) Experiences of turbulence measurement with PIV. Meas Sci Technol 8:1393–1398Google Scholar
  22. Sreenivasan KR (1984) On the scaling of the turbulence energy dissipation rate. Phys Fluids 27(5):1048–1051CrossRefMathSciNetGoogle Scholar
  23. Sreenivasan KR (1998) An update on the energy dissipation rate in isotropic turbulence. Phys Fluids 10(2):528–529CrossRefMathSciNetGoogle Scholar
  24. Westerweel J (1997) Fundamentals of digital particle image velocimetry. Meas Sci Technol 8:1379–1392CrossRefGoogle Scholar
  25. Willert CE, Gharib M (1991) Digital particle image velocimetry. Exp Fluids 10:181–193CrossRefGoogle Scholar
  26. Wyngaard JC (1968) Measurement of small-scale turbulence structure with hot wires. J Sci Instrum (J Phys E) 1:1105–1108CrossRefGoogle Scholar
  27. Wyngaard JC (1969) Spatial resolution of the vorticity meter and other hot wire arrays. J Sci Instrum (J Phys E) 2:983–987CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department Mechanical EngineeringStanford UniversityStanfordUSA
  2. 2.Department Mechanical EngineeringStanford UniversityStanfordUSA

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