Skip to main content
Log in

Dual-plane PIV technique to determine the complete velocity gradient tensor in a turbulent boundary layer

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

Abstract

Simultaneous dual-plane PIV experiments, which utilized three cameras to measure velocity components in two differentially separated planes, were performed in streamwise-spanwise planes in the log region of a turbulent boundary layer at a moderate Reynolds number (Reτ ∼ 1100). Stereoscopic data were obtained in one plane with two cameras, and standard PIV data were obtained in the other with a single camera. The scattered light from the two planes was separated onto respective cameras by using orthogonal polarizations. The acquired datasets were used in tandem with continuity to compute all 9 velocity gradients, the complete vorticity vector and other invariant quantities. These derived quantities were employed to analyze and interpret the structural characteristics and features of the boundary layer. Sample results of the vorticity vector are consistent with the presence of hairpin-shaped vortices inclined downstream along the streamwise direction. These vortices envelop low speed zones and generate Reynolds shear stress that enhances turbulence production. Computation of inclination angles of individual eddy cores using the vorticity vector suggests that the most probable inclination angle is 35° to the streamwise-spanwise plane with a resulting projected eddy inclination of 43° in the streamwise-wall-normal plane.

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

Access this article

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

Similar content being viewed by others

Notes

  1. This is consistent with Brodkey et al. (1973) who provided an interpretation of production, based on instantaneous Reynolds shear stress and instantaneous wall-normal gradient, where the production term almost exactly balances dissipation. Other definitions have also been proposed (see Bradshaw 1974).

References

  • Adrian RJ, Christensen KT, Liu ZC (2000a) Analysis and interpretation of instantaneous turbulent velocity fields. Exp Fluids 29:275–290

    Google Scholar 

  • Adrian RJ, Meinhart CD, Tomkins CD (2000b) Vortex organization in the outer region of the turbulent boundary layer. J Fluid Mech 422:1–53

    Google Scholar 

  • Balint J-L, Wallace JM, Vukoslavcevic P (1987) A study of vortical structure of the turbulent boundary layer. In: Comte-Bellot G, Mathieu J (eds) Advances in Turbulence. Springer, Berlin Heidelberg New York, pp 456–464

  • Balint J-L, Wallace JM, Vukoslavcevic P (1991) The velocity and vorticity vector fields of a turbulent boundary layer. Part 2. Statistical properties. J Fluid Mech 228:53–86

    Google Scholar 

  • Barnhart DH, Adrian RJ, Meinhart CD, Papen GC (1994) Phase-conjugate holographic system for high resolution particle image velocimetry. Appl Opt 33:7159–7169

    Google Scholar 

  • Bradshaw P (1974) Comments on turbulent energy production, dissipation and transfer. Phys Fluids 17(11):2149

    Google Scholar 

  • Brodkey RS, Nychas SG, Taraba JL, Wallace JM (1973) Turbulent energy production, dissipation and transfer. Phys Fluids 16(11):2010–2011

    Google Scholar 

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

    Google Scholar 

  • Christensen KT, Adrian RJ (2002) Measurement of instantaneous Eulerian acceleration fields by particle image accelerometry: method and accuracy. Exp Fluids 33:759–769

    Google Scholar 

  • Dallmann U (1983) Topological structures of three-dimensional flow separations. In: DFVLR Report No. IB 221-82-A07, Göttingen, Germany

  • Ganapathisubramani B (2004) Investigation of turbulent boundary layer structure using stereoscopic particle image velocimetry. Ph.D. thesis, University of Minnesota, USA

  • Ganapathisubramani B, Longmire EK, Marusic I (2002) Investigation of three dimensionality in the near field of a round jet using stereo PIV. J Turbulence 3:17

    Google Scholar 

  • Ganapathisubramani B, Longmire EK, Marusic I (2003) Characteristics of vortex packets in turbulent boundary layers. J Fluid Mech 478:35–46

    Google Scholar 

  • Head MR, Bandyopadhyay P (1981) New aspects of turbulent boundary-layer structure. J Fluid Mech 107:297–337

    Google Scholar 

  • Honkan A, Andreopoulos Y (1997) Vorticity, strain-rate and dissiipation characteristics in the near-wall region of turbulent boundary layers. J Fluid Mech 350:29–96

    Google Scholar 

  • Hu H, Saga T, Kobayashi T, Taniguchi N, Yasuki M (2001) Dual-plane stereoscopic particle image velocimetry: system set-up and its application on a lobed jet mixing flow. Exp Fluids 31:277–293

    Google Scholar 

  • Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 258:69–94

    Google Scholar 

  • Kähler CJ (2004) Investigation of the spatio-temporal flow structure in the buffer region of a turbulent boundary layer by means of multiple plane stereo PIV. Exp Fluids 36:114–130

    Google Scholar 

  • Kähler CJ, Kompenhans J (2000) Fundamentals of multiple plane stereo particle image velocimetry. Exp Fluids (Suppl):S70–S77

    Google Scholar 

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

    Google Scholar 

  • Meng H, Hussain F (1995) Instantaneous flow field in an unstable vortex ring measured by HPIV. Phys Fluids 7:9–11

    Google Scholar 

  • Mullin JA, Dahm WJA (2005) Dual-plane stereo particle image velocimetry (DSPIV) for measuring velocity gradient fields at intermediate and small scales of turbulent flows. Exp Fluids 38:185–196

    Google Scholar 

  • Ötügeny MV, Su W, and Papadopoulosz G (1998) A new laser-based method for strain rate and vorticity measurements. Meas Sci Technol 9:267–274

    Google Scholar 

  • Raffel M, Willert C, Kompenhans J (1998) Particle image velocimetry - A practical guide. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Scherer JO, Bernal LP (1997) In-line holographic particle image velocimetry for turbulent flows. Appl Opt 36:9309–9318

    Google Scholar 

  • Spalart PR (1988) Direct simulation of turbulent boundary layer up to Reθ=1410. J Fluid Mech 187:61–98

    Google Scholar 

  • Wereley ST, Meinhart CD (2001) Second-order accurate particle image velocimetry. Exp Fluids 31:258–268

    Google Scholar 

  • Westerweel J (1994) Digital Particle Image Velocimetry - Theory and Applications. Delft University Press

  • Zhang J, Tao B, Katz J (1997) Turbulent flow measurement in a square duct with hybrid holographic PIV. Exp Fluids 23:373–381

    Google Scholar 

  • Zhou J, Adrian RJ, Balachandar S, Kendall TM (1999) Mechanisms for generating coherent packets of hairpin vortices in channel flow. J Fluid Mech 387:353–396

    Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge support from the National Science Foundation through Grants ACI-9982274, CTS-9983933 and CTS-0324898, the Graduate School of University of Minnesota and the David and Lucile Packard Foundation. We are indebted to Dr. Nicholas Hutchins, William Hambleton and Aizaz Bhuiyan for their help in data acquisition and many discussions during the course of this study.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ellen K. Longmire.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ganapathisubramani, B., Longmire, E.K., Marusic, I. et al. Dual-plane PIV technique to determine the complete velocity gradient tensor in a turbulent boundary layer. Exp Fluids 39, 222–231 (2005). https://doi.org/10.1007/s00348-005-1019-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00348-005-1019-z

Keywords

Navigation