Post-processing of PIV Data

  • Markus Raffel
  • Christian E. Willert
  • Fulvio Scarano
  • Christian J. Kähler
  • Steven T. Wereley
  • Jürgen Kompenhans
Chapter

Abstract

While the previous chapter have dealt with recording and evaluation of PIV images, the extracted data require further post-processing in the context of data validation and further data reduction to retrieve fluid mechanical relevant information. This chapter introduces a variety of validation schemes that operate either globally or locally on the data along with methods of data interpolation to fill in data gaps in both space and time. The validated data can then be subjected to differentiation to, for instance, extract gradient information such as vorticity fields. Issues and errors arising through applying differentials to the finitely-spaced data grid are discussed and illustrated. Alternatively, the velocity data can be integrated to retrieve streamlines, body forces or even pressure fields.

References

  1. 1.
    Agüí, J.C., Jiménez, J.: On the performance of particle tracking. J. Fluid Mech. 185, 447–468 (1987). DOI 10.1017/S0022112087003252. URL http://journals.cambridge.org/article_S0022112087003252
  2. 2.
    Baur, T., Köngeter, J.: PIV with high temporal resolution for the determination of local pressure reductions from coherent turbulent phenomena. In: Third International Workshop on Particle Image Velocimetry, Santa Barbara (USA) (1999)Google Scholar
  3. 3.
    de Kat, R., van Oudheusden, B.W.: Instantaneous planar pressure determination from PIV in turbulent flow. Exp. Fluids 52(5), 1089–1106 (2012). DOI 10.1007/s00348-011-1237-5. URL http://dx.doi.org/10.1007/s00348-011-1237-5
  4. 4.
    Dieterle, L.: Entwicklung eines abbildenden Messverfahrens (PIV) zur Untersuchung von Mikrostrukturen in turbulenten Strömungen. Ph.D. thesis, Technische Universität Clausthal (1997)Google Scholar
  5. 5.
    Duncan, J., Dabiri, D., Hove, J., Gharib, M.: Universal outlier detection for particle image velocimetry (PIV) and particle tracking velocimetry (PTV) data. Meas. Sci. Technol. 21(5), 057002 (2010). DOI 10.1088/0957-0233/21/5/057002. URL http://stacks.iop.org/0957-0233/21/i=5/a=057002
  6. 6.
    Etebari, A., Vlachos, P.P.: Improvements on the accuracy of derivative estimation from DPIV velocity measurements. Exp. Fluids 39(6), 1040–1050 (2005). DOI 10.1007/s00348-005-0037-1. URL http://dx.doi.org/10.1007/s00348-005-0037-1
  7. 7.
    Foucaut, J.M., Stanislas, M.: Some considerations on the accuracy and frequency response of some derivative filters applied to particle image velocimetry vector fields. Meas. Sci. Technol. 13(7), 1058 (2002). DOI 10.1088/0957-0233/13/7/313. URL http://stacks.iop.org/0957-0233/13/i=7/a=313
  8. 8.
    Fouras, A., Soria, J.: Accuracy of out-of-plane vorticity measurements derived from in-plane velocity field data. Exp. Fluids 25(5–6), 409–430 (1998). DOI 10.1007/s003480050248. URL http://dx.doi.org/10.1007/s003480050248
  9. 9.
    Gurka, R., Liberzon, A., Hefetz, D., Rubinstein, D., Shavit, U.: Computation of pressure distribution using PIV velocity data. In: 3rd International Workshop on PIV, 16–18 September, Santa Barbara (USA), pp. 671–676 (1999)Google Scholar
  10. 10.
    Hain, R., Kähler, C.J.: Fundamentals of multiframe particle image velocimetry (PIV). Exp. Fluids 42(4), 575–587 (2007). DOI 10.1007/s00348-007-0266-6. URL http://dx.doi.org/10.1007/s00348-007-0266-6
  11. 11.
    Higham, J.E., Brevis, W., Keylock, C.J.: A rapid non-iterative proper orthogonal decomposition based outlier detection and correction for PIV data. Meas. Sci. Technol. 27(12), 125303 (2016). DOI 10.1088/0957-0233/27/12/125303. URL http://stacks.iop.org/0957-0233/27/i=12/a=125303
  12. 12.
    Imaichi, K., Ohmi, K.: Numerical processing of flow-visualization pictures - measurement of two-dimensional vortex flow. J. Fluid Mech. 129, 283–311 (1983). DOI 10.1017/S0022112083000774. URL http://journals.cambridge.org/article/S0022112083000774
  13. 13.
    Kurtulus, D.F., Scarano, F., David, L.: Unsteady aerodynamic forces estimation on a square cylinder by TR-PIV. Exp. Fluids 42(2), 185–196 (2007). DOI 10.1007/s00348-006-0228-4. URL http://dx.doi.org/10.1007/s00348-006-0228-4
  14. 14.
    Liu, X., Katz, J.: Instantaneous pressure and material acceleration measurements using a four-exposure PIV system. Exp. Fluids 41(2), 227–240 (2006). DOI 10.1007/s00348-006-0152-7. URL http://dx.doi.org/10.1007/s00348-006-0152-7
  15. 15.
    Lourenco, L., Krothapalli, A.: On the accuracy of velocity and vorticity measurements with PIV. Exp. Fluids 18(6), 421–428 (1995). DOI 10.1007/BF00208464. URL http://dx.doi.org/10.1007/BF00208464
  16. 16.
    Noca, F., Shiels, D., Jeon, D.: A comparison of methods for evaluating time-dependent fluid dynamic forces on bodies, using only velocity fields and their derivatives. J. Fluids Struct. 13(5), 551–578 (1999). DOI 10.1006/jfls.1999.0219. URL http://www.sciencedirect.com/science/article/pii/S0889974699902190
  17. 17.
    Nogueira, J., Lecuona, A., Rodr’iguez, P.A.: Data validation, false vectors correction and derived magnitudes calculation on PIV data. Meas. Sci. Technol. 8(12), 1493 (1997). DOI 10.1088/0957-0233/8/12/012. URL http://stacks.iop.org/0957-0233/8/i=12/a=012
  18. 18.
    Novara, M., Scarano, F.: A particle-tracking approach for accurate material derivative measurements with tomographic PIV. Exp. Fluids 54(8), 1584 (2013). DOI 10.1007/s00348-013-1584-5. URL http://dx.doi.org/10.1007/s00348-013-1584-5
  19. 19.
    Pröbsting, S., Tuinstra, M., Scarano, F.: Trailing edge noise estimation by tomographic particle image velocimetry. J. Sound Vib. 346, 117–138 (2015). DOI 10.1016/j.jsv.2015.02.018. URL http://www.sciencedirect.com/science/article/pii/S0022460X15001522
  20. 20.
    Raben, S.G., Charonko, J.J., Vlachos, P.P.: Adaptive gappy proper orthogonal decomposition for particle image velocimetry data reconstruction. Meas. Sci. Technol. 23(2), 025303 (2012). DOI 10.1088/0957-0233/23/2/025303. URL http://stacks.iop.org/0957-0233/23/i=2/a=025303
  21. 21.
    Raiola, M., Discetti, S., Ianiro, A.: On PIV random error minimization with optimal POD-based low-order reconstruction. Exp. Fluids 56(4), 75 (2015). DOI 10.1007/s00348-015-1940-8. URL http://dx.doi.org/10.1007/s00348-015-1940-8
  22. 22.
    Rival, D.E., van Oudheusden, B.W.: Load-estimation techniques for unsteady incompressible flows. Exp. Fluids 58(3), 20 (2017). DOI 10.1007/s00348-017-2304-3. URL http://dx.doi.org/10.1007/s00348-017-2304-3
  23. 23.
    Scarano, F., Moore, P.: An advection-based model to increase the temporal resolution of PIV time series. Exp. Fluids 52(4), 919–933 (2012). DOI 10.1007/s00348-011-1158-3. URL https://doi.org/10.1007/s00348-011-1158-3
  24. 24.
    Schanz, D., Gesemann, S., Schröder, A.: Shake-The-Box: Lagrangian particle tracking at high particle image densities. Exp. Fluids 57(5), 1–27 (2016). DOI 10.1007/s00348-016-2157-1. URL http://dx.doi.org/10.1007/s00348-016-2157-1
  25. 25.
    Schiavazzi, D., Coletti, F., Iaccarino, G., Eaton, J.K.: A matching pursuit approach to solenoidal filtering of three-dimensional velocity measurements. J. Comput. Phys. 263, 206–221 (2014). DOI 10.1016/j.jcp.2013.12.049. URL https://doi.org/10.1016/j.jcp.2013.12.049
  26. 26.
    Schneiders, J.F.G., Scarano, F.: Dense velocity reconstruction from tomographic PTV with material derivatives. Exp. Fluids 57(9), 139 (2016). DOI 10.1007/s00348-016-2225-6. URL http://dx.doi.org/10.1007/s00348-016-2225-6
  27. 27.
    Schneiders, J.F.G., Dwight, R.P., Scarano, F.: Time-supersampling of 3D-PIV measurements with vortex-in-cell simulation. Exp. Fluids 55(3), 1692 (2014). DOI 10.1007/s00348-014-1692-x. URL https://doi.org/10.1007/s00348-014-1692-x
  28. 28.
    Schneiders, J.F.G., Scarano, F., Elsinga, G.E.: Resolving vorticity and dissipation in a turbulent boundary layer by tomographic PTV and VIC+. Exp. Fluids 58(4), 27 (2017). DOI 10.1007/s00348-017-2318-x. URL https://doi.org/10.1007/s00348-017-2318-x
  29. 29.
    Schram, C., Rambaud, P., Riethmuller, M.L.: Wavelet based eddy structure eduction from a backward facing step flow investigated using particle image velocimetry. Exp. Fluids 36(2), 233–245 (2004). DOI 10.1007/s00348-003-0695-9. URL http://dx.doi.org/10.1007/s00348-003-0695-9
  30. 30.
    Schröder, A.: Untersuchung der Struktur des laminaren Zylindernachlaufs mit Hilfe der Particle Image Velocimetry. Technical report, Diploma thesis, Universität Göttingen (Germany) (1996). DLR, Göttingen, GermanyGoogle Scholar
  31. 31.
    Shinneeb, A.M., Bugg, J.D., Balachandar, R.: Variable threshold outlier identification in PIV data. Meas. Sci. Technol. 15(9), 1722 (2004). DOI 10.1088/0957-0233/15/9/008. URL http://stacks.iop.org/0957-0233/15/i=9/a=008
  32. 32.
    Suzuki, T.: Reduced-order Kalman-filtered hybrid simulation combining particle tracking velocimetry and direct numerical simulation. J. Fluid Mech. 709, 249–288 (2012). DOI 10.1017/jfm.2012.334. URL https://doi.org/10.1017/jfm.2012.334
  33. 33.
    Symon, S., Dovetta, N., McKeon, B.J., Sipp, D., Schmid, P.J.: Data assimilation of mean velocity from 2D PIV measurements of flow over an idealized airfoil. Exp. Fluids 58(5), 61 (2017). DOI 10.1007/s00348-017-2336-8. URL https://doi.org/10.1007/s00348-017-2336-8
  34. 34.
    Taylor, J.R.: An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, 2nd edn. University Science Books, Sausalito (1997). URL https://archive.org/details/TaylorJ.R.IntroductionToErrorAnalysis2ed
  35. 35.
    Unal, M.F., Lin, J.C., Rockwell, D.: Force prediction by PIV imaging: a momentum-based approach. J. Fluids Struct. 11(8), 965–971 (1997). DOI 10.1006/jfls.1997.0111. URL http://www.sciencedirect.com/science/article/pii/S0889974697901110
  36. 36.
    van Gent, P.L., Michaelis, D., van Oudheusden, B.W., Weiss, P.É., de Kat, R., Laskari, A., Jeon, Y.J., David, L., Schanz, D., Huhn, F., Gesemann, S., Novara, M., McPhaden, C., Neeteson, N.J., Rival, D.E., Schneiders, J.F.G., Schrijer, F.F.J.: Comparative assessment of pressure field reconstructions from particle image velocimetry measurements and Lagrangian particle tracking. Exp. Fluids 58(4), 33 (2017). DOI 10.1007/s00348-017-2324-z. URL http://dx.doi.org/10.1007/s00348-017-2324-z
  37. 37.
    van Oudheusden, B.W.: Principles and application of velocimetry-based planar pressure imaging in compressible flows with shocks. Exp. Fluids 45(4), 657–674 (2008). DOI 10.1007/s00348-008-0546-9. URL http://dx.doi.org/10.1007/s00348-008-0546-9
  38. 38.
    van Oudheusden, B.W.: PIV-based pressure measurement. Meas. Sci. Technol. 24(3), 032001 (2013). DOI 10.1088/0957-0233/24/3/032001. URL http://stacks.iop.org/0957-0233/24/i=3/a=032001
  39. 39.
    van Oudheusden, B.W., Scarano, F., Casimiri, E.W.F.: Non-intrusive load characterization of an airfoil using PIV. Exp. Fluids 40(6), 988–992 (2006). DOI 10.1007/s00348-006-0149-2. URL http://dx.doi.org/10.1007/s00348-006-0149-2
  40. 40.
    van Oudheusden, B.W., Scarano, F., Roosenboom, E.W.M., Casimiri, E.W.F., Souverein, L.J.: Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows. Exp. Fluids 43(2–3), 153–162 (2007). DOI 10.1007/s00348-007-0261-y. URL http://dx.doi.org/10.1007/s00348-007-0261-y
  41. 41.
    Vlasenko, A., Steele, E.C.C., Nimmo-Smith, W.A.M.: A physics-enabled flow restoration algorithm for sparse PIV and PTV measurements. Meas. Sci. Technol. 26(6), 065301 (2015). DOI 10.1088/0957-0233/26/6/065301. URL http://stacks.iop.org/0957-0233/26/i=6/a=065301
  42. 42.
    Vollmers, H.: Detection of vortices and quantitative evaluation of their main parameters from experimental velocity data. Meas. Sci. Technol. 12(8), 1199 (2001). DOI 10.1088/0957-0233/12/8/329. URL http://stacks.iop.org/0957-0233/12/i=8/a=329
  43. 43.
    Wereley, S.T., Meinhart, C.D.: Second-order accurate particle image velocimetry. Exp. Fluids 31(3), 258–268 (2001). DOI 10.1007/s003480100281. URL http://dx.doi.org/10.1007/s003480100281
  44. 44.
    Westerweel, J.: Digital particle image velocimetry: theory and application. Ph.D. thesis, Mechanical Maritime and Materials Engineering, Delft University of Technology (1993). URL http://repository.tudelft.nl/islandora/object/uuid:85455914-6629-4421-8c77-27cc44e771ed/datastream/OBJ/download
  45. 45.
    Westerweel, J.: Efficient detection of spurious vectors in particle image velocimetry data. Exp. Fluids 16(3–4), 236–247 (1994). DOI 10.1007/BF00206543. URL http://dx.doi.org/10.1007/BF00206543
  46. 46.
    Westerweel, J.: Theoretical analysis of the measurement precision in particle image velocimetry. Exp. Fluids 29(1), S003–S012 (2000). DOI 10.1007/s003480070002. URL http://dx.doi.org/10.1007/s003480070002
  47. 47.
    Westerweel, J., Scarano, F.: Universal outlier detection for PIV data. Exp. Fluids 39(6), 1096–1100 (2005). DOI 10.1007/s00348-005-0016-6. URL http://dx.doi.org/10.1007/s00348-005-0016-6
  48. 48.
    Willert, C.E.: The interaction of modulated vortex pairs with a free surface. Ph.D. thesis, Department of Applied Mechanics and Engineering Sciences, University of California, San Diego (USA) (1992)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Markus Raffel
    • 1
  • Christian E. Willert
    • 2
  • Fulvio Scarano
    • 3
  • Christian J. Kähler
    • 4
  • Steven T. Wereley
    • 5
  • Jürgen Kompenhans
    • 1
  1. 1. Institut für Aerodynamik und StrömungstechnikDeutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)GöttingenGermany
  2. 2. Institut für AntriebstechnikDeutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)KölnGermany
  3. 3.Department of Aerospace EngineeringDelft University of TechnologyDelftThe Netherlands
  4. 4.Institut für Strömungsmechanik und AerodynamikUniversität der Bundeswehr MünchenNeubibergGermany
  5. 5.Department of Mechanical Engineering, Birck Nanotech CenterPurdue UniversityWest LafayetteUSA

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