Load-estimation techniques for unsteady incompressible flows

Abstract

In a large variety of fluid-dynamic problems, it is often impossible to directly measure the instantaneous aerodynamic or hydrodynamic forces on a moving body. Examples include studies of propulsion in nature, either with mechanical models or living animals, wings, and blades subjected to significant surface contamination, such as icing, sting blockage effects, etc. In these circumstances, load estimation from flow-field data provides an attractive alternative method, while at the same time providing insight into the relationship between unsteady loadings and their associated vortex-wake dynamics. Historically, classical control-volume techniques based on time-averaged measurements have been used to extract the mean forces. With the advent of high-speed imaging, and the rapid progress in time-resolved volumetric measurements, such as Tomo-PIV and 4D-PTV, it is becoming feasible to estimate the instantaneous forces on bodies of complex geometry and/or motion. For effective application under these conditions, a number of challenges still exist, including the near-body treatment of the acceleration field as well as the estimation of pressure on the outer surfaces of the control volume. Additional limitations in temporal and spatial resolutions, and their associated impact on the feasibility of the various approaches, are also discussed. Finally, as an outlook towards the development of future methodologies, the potential application of Lagrangian techniques is explored.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

References

  1. Adrian RJ, Westerweel J (2011) Particle image velocimetry. Cambridge University Press

  2. Ben-Gida H, Kirchhefer A, Taylor ZJ, Bezner-Kerr W, Guglielmo CG, Kopp GA, Gurka R (2013) Estimation of unsteady aerodynamics in the wake of a freely flying european starling (sturnus vulgaris). PLOS One 8(11):e80086

    Article  Google Scholar 

  3. Betz A (1925) A method for the direct determination of profile drag (in German). Zeitschrift für Flugtechnik und Motorluftschifffahrt 16:42–44

    Google Scholar 

  4. Bohl DG, Koochesfahani MM (2009) MTV measurements of the vortical field in the wake of an airfoil oscillating at high reduced frequency. J Fluid Mech 620:63–88

    Article  MATH  Google Scholar 

  5. Dabiri JO (2005) On the estimation of swimming and flying forces from wake measurements. J Exp Biol 208:3519–3532

    Article  Google Scholar 

  6. Dabiri JO, Bose S, Gemmell BJ, Colin SP, Costello JH (2013) An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements. J Exp Biol 217:331–336

    Article  Google Scholar 

  7. Darwin CG (1953) Note on hydrodynamics. Math Proc Cambridge Philos Soc 49(2):342–354

    MathSciNet  Article  MATH  Google Scholar 

  8. David L, Jardin T, Farcy A (2009) On the non-intrusive evaluation of fluid forces with the momentum equation approach. Measure Sci Technol 20:095401

    Article  Google Scholar 

  9. DeVoria AC, Ringuette M (2013) On the flow generated on the leeward face of a rotating flat plate. Exp Fluids 54:1495

    Article  Google Scholar 

  10. DeVoria ACJ, Carr ZR, Ringuette MJ (2014) On calculating forces from the flow field with application to experimental volume data. J Fluid Mech 749:297–319

    Article  Google Scholar 

  11. Elsinga GE, Scarano F, Wieneke B, van Oudheusden BW (2006) Tomographic Particle Image Velocimetry. Exp Fluids 41:933–947

    Article  Google Scholar 

  12. Fernando JFF, Rival DE (2016) Reynolds-number scaling of vortex pinch-o on low-aspect-ratio propulsors. J Fluid Mech 799:R3

    Article  Google Scholar 

  13. Ferreira CJS, van Bussel GJW, van Kuik GAM, Scarano F (2011) On the use of velocity data for load estimation of a vawt in dynamic stall. J Solar Energy Eng 133:011006

    Article  Google Scholar 

  14. Gharali K, Johnson DA (2014) Piv-based load investigation in dynamic stall for different reduced frequencies. Exp Fluids 54:1–14

    Google Scholar 

  15. Graziani G, Bassanini P (2002) Unsteady viscous flows about bodies: Vorticity release and forces. Meccanica 37:283–303

    MathSciNet  Article  MATH  Google Scholar 

  16. Haller G (2002) Lagrangian coherent structures from approximate velocity data. Phys Fluids 14(6):1851–1861

    MathSciNet  Article  MATH  Google Scholar 

  17. Huang Y, Green MA (2015) Detection and tracking of vortex phenomena using lagrangian coherent structures. Exp Fluids 56:147

    Article  Google Scholar 

  18. Hubel TY, Hristov NI, Swartz SM, Breuer KS (2009) Time-resolved wake structure and kinematics of bat flight. Exp Fluids 46:933–943

    Article  Google Scholar 

  19. Jardin T, Chatellier L, Farcy A, David L (2009) Correlation between vortex structures and unsteady loads for flapping motion in hover. Exp Fluids 47:655–664

    Article  Google Scholar 

  20. Jones BM (1936) Measurement of profile drag by the pitot-traverse method. ARC R&M No. 1688

  21. Kähler CJ, Scharnowski S, Cierpka C (2012a) On the resolution limit of digital particle image velocimetry. Exp Fluids 52(6):1629–1639

    Article  Google Scholar 

  22. Kähler CJ, Scharnowski S, Cierpka C (2012b) On the uncertainty of digital PIV and PTV near walls. Exp Fluids 52(6):1641–1656

    Article  Google Scholar 

  23. Koochesfahani MM (1989) Vortical patterns in the wake of an oscillating airfoil. AIAA J 27:1200–1205

    Article  Google Scholar 

  24. Kriegseis J, Rival D (2014) Vortex force decomposition in the tip region of impulsively-started flat plates. J Fluid Mech 756:758–770

    Article  Google Scholar 

  25. Kurtulus DF, Scarano F, David L (2007) Unsteady aerodynamics force estimation on a square cylinder by TR-PIV. Exp Fluids 42:185–196

    Article  Google Scholar 

  26. Lentink D, Haselsteiner AF, Ingersoll R (2015) In vivo recording of aerodynamic force with an aerodynamic force platform: from drones to birds. J R Soc Interface 12:20141283

    Article  Google Scholar 

  27. Lighthill MJ (1986) Fundamentals concerning wave loading on offshore structures. J Fluid Mech 173:667–681

    Article  Google Scholar 

  28. Lin J-C, Rockwell D (1996) Force identification by vorticity fields: techniques based on flow imaging. J Fluids Struct 10:663–668

    Article  Google Scholar 

  29. Mackowski AW, Williamson CHK (2011) Developing a cyber-physical fluid dynamics facility for fluid-structure interaction studies. J Fluids Struct 27:748–757

    Article  Google Scholar 

  30. Mendelson L, Techet AH (2015) Quantitative wake analysis of a freely swimming fish using 3D synthetic aperture PIV. Exp Fluids 56:135

    Article  Google Scholar 

  31. Minotti FO (2011) Determination of the instantaneous forces on flapping wings from a localized fluid velocity field. Phys Fluids s1-9(1):91–93

  32. Mohebbian A, Rival D (2012) Assessment of the derivative-moment transformation method for unsteady-load estimation. Exp Fluids 53:319–330

    Article  Google Scholar 

  33. Neeteson NJ, Bhattacharya S, Rival DE, Michaelis D, Schanz D, Schroeder A (2016) Pressure-field extraction from Lagrangian flow measurements: first experiences with 4D-PTV data. Exp Fluids 57:102

    Article  Google Scholar 

  34. Noca F, Shiels D, Jeon D (1997) Measuring instantaneous fluid dynamic forces on bodies, using only velocity fields and their derivatives. J Fluids Struct 11:345–350

    Article  Google Scholar 

  35. Noca F, Shiels D, Jeon D (1999) A comparison of methods for evaluating time-dependent fluid dynamic forces on bodies, using only velocity fields and their derivatives. J Fluids Struct 13:551–578

    Article  Google Scholar 

  36. Onoue K, Breuer KS (2016) Vortex formation and shedding from a cyber-physical pitching plate. J Fluid Mech 793:229–247

    Article  Google Scholar 

  37. Poelma C, Dickson WB, Dickinson MH (2006) Time-resolved reconstruction of the full velocity field around a dynamically-scaled flapping wing. Exp Fluids 41:213–225

    Article  Google Scholar 

  38. Polet DT, Rival DE (2015) Rapid area change in pitch-up manoeuvres of small perching birds. Bioinsp Biomimet 10(1):066004

    Article  Google Scholar 

  39. Protas B (2007) On an attempt to simplify the Quartapelle Napolitano approach to computation of hydrodynamic forces in open flows. J Fluids Struct 23:1207–1214

    Article  Google Scholar 

  40. Protas B, Styczek A, Nowakowski A (2000) An effective approach to computation of forces in viscous incompressible flows. J Comput Phys 159:231–245

    Article  MATH  Google Scholar 

  41. Quartapelle L, Napolitano M (1983) Force and moment in incompressible flows. AIAA J 21:911–913

    Article  MATH  Google Scholar 

  42. Rival DE, Manejev R, Tropea C (2010) Measurement of parallel blade-vortex interaction at low Reynolds numbers. Exp Fluids 49:89–99

    Article  Google Scholar 

  43. Rival DE, Schoenweitz D, Tropea C (2011) Vortex interaction of tandem pitching and plunging plates: a two-dimensional model of hovering dragonfly-like flight. Bioinspir Biomimet 6(1):016008

    Article  Google Scholar 

  44. Saffman P (1992) Vortex Dynamics. Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge University Press

  45. Schanz D, Gesemann S, Schroeder A (2016) Shake The Box: Lagrangian particle tracking at high particle image densities. Exp Fluids 57-70

  46. Sterenborg JJHM, Lindeboom RCJ, Ferreira CJS, van Zuijlen AH, Bijl H (2013) Assessment of piv-based unsteady load determination of an airfoil with actuated flap. J Fluids Struct 45:79–95

    Article  Google Scholar 

  47. Unal M, Lin J-C, Rockwell D (1997) Force prediction by PIV imaging: a momentum-based approach. J Fluids Struct 11:965–971

    Article  Google Scholar 

  48. van de Meerendonk R, Percin M, van Oudheusden B (2016) Three-dimensional flow and load characteristics of flexible revolving wings at low Reynolds number. In: 18th International Symposium on Applications of Laser Techniques to Fluid Mechanics, 4–7 July, Lisbon, Portugal

  49. van Oudheusden BW (2013) PIV-based pressure measurement. Measure Sci Technol 24(032001):1–32

    Google Scholar 

  50. van Oudheusden BW, Scarano F, Roosenboom EWM, Casimiri EWF, Souverein LJ (2007) Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows. Exp Fluids 43(2–3):153–162

    Article  Google Scholar 

  51. Villegas A, Diez F (2014) Evaluation of unsteady pressure fields and forces in rotating airfoils from time-resolved piv. Exp Fluids 55:1697

    Article  Google Scholar 

  52. Violato D, Moore P, Scarano F (2011) Lagrangian and Eulerian pressure field evaluation of rod-airfoil flow from time-resolved tomographic PIV. Exp Fluids 50:1057–1070

    Article  Google Scholar 

  53. Westerweel J (2008) On velocity gradients in PIV interrogation. Exp Fluids 44:831–842

    Article  Google Scholar 

  54. Wu JC (1981) Theory for aerodynamic force and moment in viscous flows. AIAA J 19:432–441

    Article  MATH  Google Scholar 

  55. Wu J-Z, Ma H-Y, Zhou J-Z (2006) Vorticity and vortex dynamics. Lecture notes in mathematics. Springer, Berlin Heidelberg

    Google Scholar 

  56. Wu J-Z, Pan Z-L, Lu X-Y (2005) Unsteady fluid-dynamic force solely in terms of control-surface integral. Phys Fluids 17:098102

    Article  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to David E. Rival.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Rival, D.E., Oudheusden, B.v. Load-estimation techniques for unsteady incompressible flows. Exp Fluids 58, 20 (2017). https://doi.org/10.1007/s00348-017-2304-3

Download citation

Keywords

  • Vorticity
  • Control Volume
  • Control Surface
  • Aerodynamic Loading
  • Load Estimation