The European Physical Journal Special Topics

, Volume 220, Issue 1, pp 91–100 | Cite as

Deriving forces from 2D velocity field measurements

  • Thomas Albrecht
  • Vanessa del Campo
  • Tom Weier
  • Hans Metzkes
  • Jörg Stiller
Regular Article


We discuss how to derive a force or a force density from a measured velocity field. The first part focuses on the integral force a fluid exerts on a body, e.g. lift and drag on an airfoil. Obtaining the correct pressure is crucial; however, it cannot be measured within the flow non-intrusively. Using numerical and experimental test cases, we compare the accuracy achievable with three methods: pressure reconstruction from velocity fields via (1) the differential momentum equation, or (2) the Poisson equation, furthermore, (3) Noca’s momentum equation [Noca, JFS 13(5), 1999], which does not require pressure explicitly. The latter gives the best results for the lift, whereas the first or second approach should be used for the drag. The second part deals with obtaining the distribution of a body force density generated by an actuator. Using a stream function ansatz, we obtain a Laplace equation that allows us to compute the solenoidal part of the force distribution; however, the irrotational part is lost. Furthermore, the wall pressure must be known. We validate this approach using numerical data from a wall jet flow in a rectangular box, driven by a fictitious, solenoidal body force. Reconstructing the force distribution yields an error of less than 10−2 for most of the domain.


Particle Image Velocimetry Direct Numerical Simulation European Physical Journal Special Topic Particle Track Velocimetry Plasma Actuator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Raffel, C. Willert, S. Wereley, J. Kompenhans, Particle Image Velocimetry, a Practicle Guide (Springer, Berlin, 2007)Google Scholar
  2. 2.
    J. Barlow, W. Rae, A. Pope, Low-speed wind tunnel testing (Wiley, New York, 1999)Google Scholar
  3. 3.
    T.C. Corke, C.L. Enloe, S.P. Wilkinson, Ann. Rev. Fluid Mech. 42, 505 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    M.F. Unal, J.C. Lin, D. Rockwell, J. Fluid. Struct. 11, 965 (1997)CrossRefGoogle Scholar
  5. 5.
    B. van Oudheusden, F. Scarano, E. Casimiri, Exp. Fluids 40, 988 (2006)CrossRefGoogle Scholar
  6. 6.
    T. Baur, J. Köngeter, in Proc. of the 3rd Int. Workshop on Particle Image Velocimetry (Santa Barbara, CA, 1999)Google Scholar
  7. 7.
    B. van Oudheusden, Exper. Fluids 45, 657 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    X. Liu, J. Katz, Exper. Fluids 41, 227 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    R. Gurka, A. Liberzon, D. Hefetz, D. Rubinstein, U. Shavit, in Proc. of the 3rd Int. Workshop on Particle Image Velocimetry (Santa Barbara, CA, 1999)Google Scholar
  10. 10.
    R. de Kat, B. van Oudheusden, F. Scarano, in 14th Int. Symp. on Applications of Laser Techniques to Fluid Mechanics (Lisbon, 2008)Google Scholar
  11. 11.
    D. Ragni, B.W. van Oudheusden, F. Scarano, Meas. Sci. Technol. 22, 017003 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    D. Kurtulus, F. Scarano, L. David, Exper. Fluids 42, 185 (2007)ADSCrossRefGoogle Scholar
  13. 13.
    F. Noca, D. Shiels, D. Jeon, J. Fluid. Struct. 11, 345 (1997)CrossRefGoogle Scholar
  14. 14.
    F. Noca, D. Shiels, D. Jeon, J. Fluid. Struct. 13, 551 (1999)ADSCrossRefGoogle Scholar
  15. 15.
    J.Z. Wu, Z.L. Pan, X.Y. Lu, Phys. Fluids 17, 098102 (2005)ADSCrossRefGoogle Scholar
  16. 16.
    T. Albrecht, V. del Campo, T. Weier, G. Gerbeth, in Proc. of the 16th Int. Symp. on Applications of Laser Techniques to Fluid Mechanics (Lisbon, 2012)Google Scholar
  17. 17.
    A. Sciacchitano, R.P. Dwight, F. Scarano, Exp. Fluids 53, 1421 (2012)CrossRefGoogle Scholar
  18. 18.
    J.B. Wilke, Ph.D. thesis, TU Darmstadt, 2009Google Scholar
  19. 19.
    M. Kotsonis, S. Ghaemi, L. Veldhuis, F. Scarano, J. Phys. D: Appl. Phys. 44, 045204 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    T. Albrecht, T. Weier, G. Gerbeth, H. Metzkes, J. Stiller, Phys. Fluids 23, 1702 (2011)CrossRefGoogle Scholar
  21. 21.
    G. Mutschke, A. Bund, Electrochem. Commun. 10, 597 (2008)CrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  • Thomas Albrecht
    • 1
  • Vanessa del Campo
    • 2
  • Tom Weier
    • 1
  • Hans Metzkes
    • 3
  • Jörg Stiller
    • 3
  1. 1.Institute of Fluid DynamicsHelmholtz-Zentrum Dresden-RossendorfDresdenGermany
  2. 2.ETSEIAT, UPCPolytechnic University of CatalunyaTerrassaSpain
  3. 3.Institute of Fluid MechanicsTechnische Universität DresdenDresdenGermany

Personalised recommendations