Skip to main content

Applications: Transonic Flows

  • 7180 Accesses


Solid surfaces in like actuators, fluid mechanical models and surrounding walls can influence the fluid flow and/or can be deformed or displaced by it. The knowledge of the actual surface shape and location is therefore important for many fluid mechanical investigations. In compressible fluids density variations is another important fluid parameter besides velocity. Both, the measurement of density gradients in a flow and the detection of the deformation and position of solid surfaces in contact with the fluid can be easily obtained based on PIV imaging hard- and software. The correlation based procedures for deformation, displacement, and strain analysis have been developed and applied more and more frequently during the past decade. The most common method, the deformation measurement by Digital Image Correlation (DIC) is described first together with examples of applications. The later section describes the theory of the Background-Oriented Schlieren Technique (BOS), which determines density gradients without using any sophisticated optical equipment. Practical aspect of the technique are addressed by the description of its application to a helicopter in hovering flight and to the transonic flow behind a cylinder.

An overview of the Digital Content to applications on transonic flows can be found at [DC12.1].

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

Buying options

USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-68852-7_12
  • Chapter length: 38 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
USD   169.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-68852-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   219.99
Price excludes VAT (USA)
Hardcover Book
USD   299.99
Price excludes VAT (USA)
Fig. 12.1
Fig. 12.2
Fig. 12.3
Fig. 12.4
Fig. 12.5
Fig. 12.6
Fig. 12.7
Fig. 12.8
Fig. 12.9
Fig. 12.10
Fig. 12.11
Fig. 12.12
Fig. 12.13
Fig. 12.14
Fig. 12.15
Fig. 12.16
Fig. 12.17
Fig. 12.18
Fig. 12.19
Fig. 12.20
Fig. 12.21
Fig. 12.22
Fig. 12.23
Fig. 12.24
Fig. 12.25
Fig. 12.26
Fig. 12.27
Fig. 12.28
Fig. 12.29
Fig. 12.30
Fig. 12.31
Fig. 12.32
Fig. 12.33


  1. Arunajatesan, S., Barone, M.F., Wagner, J.L., Casper, K.M., Beresh, S.J.: Joint experimental/computational investigation into the effects of finite width on transonic cavity flow. AIAA Pap. 3027 (2014). DOI 10.2514/6.2014-3027. URL

  2. Beresh, S., Kearney, S., Wagner, J., Guildenbecher, D., Henfling, J., Spillers, R., Pruett, B., Jiang, N., Slipchenko, M., Mance, J., Roy, S.: Pulse-burst PIV in a high-speed wind tunnel. Meas. Sci. Technol. 26(9), 095,305 (2015). DOI 10.1088/0957-0233/26/9/095305. URL

  3. Beresh, S.J., Henfling, J.F., Spillers, R.W.: Planar velocimetry of a fin trailing vortex in subsonic compressible flow. AIAA J. 47(7), 1730–1740 (2009). DOI 10.2514/1.42097. URL

  4. Beresh, S.J., Henfling, J.F., Spillers, R.W.: Turbulence of a fin trailing vortex in subsonic compressible flow. AIAA J. 50(11), 2609–2622 (2012). DOI 10.2514/1.J051904. URL

  5. Beresh, S.J., Smith, J.A., Henfling, J.F., Grasser, T.W., Spillers, R.W.: Interaction of a fin trailing vortex with a downstream control surface. J. Spacecr. Rockets 46(2), 318–328 (2009). DOI 10.2514/1.40294. URL

  6. Beresh, S.J., Wagner, J.L., Henfling, J.F., Spillers, R.W., Pruett, B.O.M.: Width effects in transonic flow over a rectangular cavity. AIAA J. 53(12), 3831–3834 (2015)

    CrossRef  Google Scholar 

  7. Beresh, S.J., Wagner, J.L., Pruett, B., Spillers, R., McWithey, M., Gary, J., Chankaya, K.: Deployment of particle image velocimetry into the Lockheed Martin High Speed Wind Tunnel. In: 52nd Aerospace Sciences Meeting, p. 1238 (2014). DOI 10.2514/6.2014-1238. URL

  8. Beresh, S.J., Wagner, J.L., Smith, B.L.: Self-calibration performance in stereoscopic PIV acquired in a transonic wind tunnel. Exp. Fluids 57(4), 1–17 (2016). DOI 10.1007/s00348-016-2131-y. URL

  9. Elsinga, G.E., van Oudheusden, B.W., Scarano, F.: Evaluation of aero-optical distortion effects in PIV. Exp. Fluids 39(2), 246–256 (2005). DOI 10.1007/s00348-005-1002-8. URL

  10. Fitzgerald, E.J., Mueller, T.J.: Measurements in a separation bubble on an airfoil using laser velocimetry. AIAA J. 28(4), 584–592 (1990). DOI 10.2514/3.10433. URL

  11. Förster, W., Karpinsky, G., Krain, H., Röhle, I., Schodl, R.: 3-component Doppler laser-two-focus velocimetry applied to a transonic centrifugal compressor. In: Laser Techniques for Fluid Mechanics, pp. 55–74. Springer, Berlin (2002). DOI 10.1007/978-3-662-08263-8_4. URL

  12. Foucaut, J.M., Carlier, J., Stanislas, M.: Piv optimization for the study of turbulent flow using spectral analysis. Meas. Sci. Technol. 15(6), 1046 (2004). DOI 10.1088/0957-0233/15/6/003. URL

  13. Göttlich, E., Neumayer, F., Woisetschläger, J., Sanz, W., Heitmeir, F.: Investigation of stator-rotor interaction in a transonic turbine stage using laser-doppler-velocimetry and pneumatic probes. In: ASME Turbo Expo 2003, collocated with the 2003 International Joint Power Generation Conference, pp. 163–172. American Society of Mechanical Engineers (2003). DOI 10.1115/1.1649745. URL

  14. Göttlich, E., Woisetschläger, J., Pieringer, P., Hampel, B., Heitmeir, F.: Investigation of vortex shedding and wake-wake interaction in a transonic turbine stage using laser-doppler-velocimetry and particle-image-velocimetry. J. Turbomach. 128(1), 178–187 (2006). DOI 10.1115/1.2103092. URL

  15. Hannemann, K., Lüdeke, H., Pallegoix, J.F., Ollivier, A., Lambaré, H., Maseland, H., Geurts, E., Frey, M., Deck, S., Schrijer, F., Scarano, F., Schwane, R.: Launch vehicle base buffeting-recent experimental and numerical investigations. In: 7th European Symposium on Aerothermodynamics, Brugge, Belgium, vol. 692, p. 102 (2011)

    Google Scholar 

  16. Heineck, J.T., Schairer, E.T., Walker, S.M.: Piv measurements of flow past the space shuttle ascent configuration in the nasa ames 9-by 7-foot supersonic wind tunnel. In: Proceedings of the 6th International Symposium on Particle Image Velocimetry (PIV 2005), Pasadena, CA (2005)

    Google Scholar 

  17. Hergt, A., Klinner, J., Steinert, W., Grund, S., Beversdorff, M., Giebmanns, A., Schnell, R.: The effect of an eroded leading edge on the aerodynamic performance of a transonic fan blade cascade. J. Turbomach. 137(2), 021,006–021,006–11 (2014). DOI 10.1115/1.4028215. URL

  18. Klinner, J., Hergt, A., Willert, C.E.: Experimental investigation of the transonic flow around the leading edge of an eroded fan airfoil. Exp. Fluids 55(9), 1800 (2014). DOI 10.1007/s00348-014-1800-y. URL

  19. Kompenhans, J., Raffel, M.: Application of PIV technique to transonic flows in a blow-down wind tunnel. In: Cha, S.S., Trolinger, J.D. (eds.) Optical Techniques in Fluid, Thermal, and Combustion Flow, San Diego, CA, United States, vol. 2005, pp. 425–436 (1993). DOI 10.1117/12.163727. URL

  20. Lee, B.H.K.: Self-sustained shock oscillations on airfoils at transonic speeds. Prog. Aerosp. Sci. 37(2), 147–196 (2001). DOI 10.1016/S0376-0421(01)00003-3. URL

    Google Scholar 

  21. Raffel, M., Höfer, H., Kost, F., Willert, C.E., Kompenhans, J.: Experimental aspects of PIV measurements of transonic flow fields at a trailing edge model of a turbine blade. In: 8th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon (Portugal) (1996)

    Google Scholar 

  22. Raffel, M., Kompenhans, J.: PIV measurements of unsteady transonic flow fields above a NACA0012 airfoil. In: 5th International Conference on Laser Anemometry, Veldhoven (the Netherlands), pp. 527–535 (1993)

    Google Scholar 

  23. Ragni, D., Schrijer, F., van Oudheusden, B.W., Scarano, F.: Particle tracer response across shocks measured by PIV. Exp. Fluids 50(1), 53–64 (2011). DOI 10.1007/s00348-010-0892-2. URL

  24. Ray, J., Lefantzi, S., Arunajatesan, S., Dechant, L.: Bayesian parameter estimation of a k-\(\epsilon \) model for accurate jet-in-crossflow simulations. AIAA J. pp. 1–17 (2016). DOI 10.2514/1.J05 4758. URL

  25. Scarano, F.: Overview of PIV in supersonic flows, pp. 445–463. Springer, Berlin (2008). DOI 10.1007/978-3-540-73528-1_24. URL

  26. Sciacchitano, A., Scarano, F.: Elimination of PIV light reflections via a temporal high pass filter. Meas. Sci. Technol. 25(8), 084,009 (2014). DOI 10.1088/0957-0233/25/8/084009. URL

  27. Soloff, S.M., Adrian, R.J., Liu, Z.C.: Distortion compensation for generalized stereoscopic particle image velocimetry. Meas. Sci. Technol. 8(12), 1441 (1997). DOI 10.1088/0957-0233/8/12/008. URL

  28. Voges, M., Beversdorff, M., Willert, C., Krain, H.: Application of particle image velocimetry to a transonic centrifugal compressor. Exp. Fluids 43(2–3), 371–384 (2007). DOI 10.1007/s00348-007-0279-1. URL

  29. Wagner, J.L., Casper, K.M., Beresh, S.J., Arunajatesan, S., Henfling, J.F., Spillers, R.W., Pruett, B.O.: Relationship between acoustic tones and flow structure in transonic cavity flow. In: 45th AIAA Fluid Dynamics Conference (2015). DOI 10.2514/6.2015-2937. URL

  30. Wernet, M.P.: Development of digital particle imaging velocimetry for use in turbomachinery. Exp. Fluids 28(2), 97–115 (2000). DOI 10.1007/s003480050015. URL

  31. Wernet, M.P.: A flow field investigation in the diffuser of a high-speed centrifugal compressor using digital particle imaging velocimetry. Meas. Sci. Technol. 11(7), 1007 (2000). DOI 10.1088/0957-0233/11/7/316. URL

  32. 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

  33. Woisetschläger, J., Lang, H., Hampel, B., Göttlich, E., Heitmeir, F.: Influence of blade passing on the stator wake in a transonic turbine stage investigated by particle image velocimetry and laser vibrometry. Proc. Inst. Mech. Eng. Part A: J. Power. Energy 217(4), 385–391 (2003). DOI 10.1243/095765003322315441. URL

  34. Woisetschläger, J., Mayrhofer, N., Hampel, B., Lang, H., Sanz, W.: Laser-optical investigation of turbine wake flow. Exp. Fluids 34(3), 371–378 (2003). DOI 10.1007/s00348-002-0568-7. URL

  35. Woisetschläger, J., Pecnik, R., Göttlich, E., Schennach, O., Marn, A., Sanz, W., Heitmeir, F.: Experimental and numerical flow visualization in a transonic turbine. J. Vis. 11(1), 95–102 (2008). DOI 10.1007/BF03181919. URL

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Markus Raffel .

Rights and permissions

Reprints and Permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Verify currency and authenticity via CrossMark

Cite this chapter

Raffel, M., Willert, C.E., Scarano, F., Kähler, C.J., Wereley, S.T., Kompenhans, J. (2018). Applications: Transonic Flows. In: Particle Image Velocimetry. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68851-0

  • Online ISBN: 978-3-319-68852-7

  • eBook Packages: EngineeringEngineering (R0)