Unsteady force estimation using a Lagrangian drift-volume approach

Abstract

A novel Lagrangian force estimation technique for unsteady fluid flows has been developed, using the concept of a Darwinian drift volume to measure unsteady forces on accelerating bodies. The construct of added mass in viscous flows, calculated from a series of drift volumes, is used to calculate the reaction force on an accelerating circular flat plate, containing highly-separated, vortical flow. The net displacement of fluid contained within the drift volumes is, through Darwin’s drift-volume added-mass proposition, equal to the added mass of the plate and provides the reaction force of the fluid on the body. The resultant unsteady force estimates from the proposed technique are shown to align with the measured drag force associated with a rapid acceleration. The critical aspects of understanding unsteady flows, relating to peak and time-resolved forces, often lie within the acceleration phase of the motions, which are well-captured by the drift-volume approach. Therefore, this Lagrangian added-mass estimation technique opens the door to fluid-dynamic analyses in areas that, until now, were inaccessible by conventional means.

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
Fig. 8
Fig. 9

References

  1. Babinsky H, Stevens RJ, Jones AR, Bernal LP, Ol MV (2016) Low order modelling of lift forces for unsteady pitching and surging wings. AIAA SciTech Forum, American Institute of Aeronautics and Astronautics. DOIurlhttps://doi.org/10.2514/6.2016-0290

  2. Baik Y, Bernal L, Granlund K, Ol M (2012) Unsteady force generation and vortex dynamics of pitching and plunging aerofoils. J Fluid Mech 709:37–68

    MathSciNet  Article  MATH  Google Scholar 

  3. Batchelor G (1967) An introduction to fluid dynamics. Cambridge Mathematical Library, Cambridge University Press. https://books.google.ca/books?id=Rla7OihRvUgC

  4. Benjamin TB (1986) Note on added mass and drift. J Fluid Mech 169:251–256. https://doi.org/10.1017/S0022112086000617

    Article  MATH  Google Scholar 

  5. Brennan CE (1982) A review of added mass and fluid inertial forces. Tech report CR 82.010, Department of the Navy

  6. Dabiri JO (2005) On the estimation of swimming and flying forces from wake measurements. J Exp Biol 208:3519–3532. https://doi.org/10.1242/jeb.01813

    Article  Google Scholar 

  7. Darwin C (1953) Note on hydrodynamics. Math Proc Camb Philos Soc 49(2):342–354. https://doi.org/10.1017/S0305004100028449

    MathSciNet  Article  MATH  Google Scholar 

  8. Eames I, Belcher SE, Hunt JCR (1994) Drift, partial drift and Darwin’s proposition. J Fluid Mech 275:201–223. https://doi.org/10.1017/S0022112094002338

    MathSciNet  Article  MATH  Google Scholar 

  9. Fernando JN, Rival DE (2016) Reynolds-number scaling of vortex pinch-off on low-aspect-ratio propulsors. J Fluid Mech 799. https://doi.org/10.1017/jfm.2016.396

  10. Fernando JN, Rival DE (2017) On the dynamics of perching manoeuvres with low-aspect-ratio planforms. Bioinspir Biomim 12(4):046007. http://stacks.iop.org/1748-3190/12/i=4/a=046007

  11. Kähler CJ, Scharnowski S, Cierpka C (2012) On the uncertainty of digital PIV and PTV near walls. Exp Fluids 52(6):1641–1656. https://doi.org/10.1007/s00348-012-1307-3

    Article  Google Scholar 

  12. Karanfilian SK, Kotas TJ (1978) Drag on a sphere in unsteady motion in a liquid at rest. J Fluid Mech 87(1):8596. https://doi.org/10.1017/S0022112078002943

    Article  Google Scholar 

  13. Leonard A, Roshko A (2001) Aspects of flow-induced vibration. J Fluids Struct 15(3):415–425. https://doi.org/10.1006/jfls.2000.0360

    Article  Google Scholar 

  14. Lighthill MJ (1956) Drift. J Fluid Mech 1(1):3153. https://doi.org/10.1017/S0022112056000032

    MathSciNet  Article  Google Scholar 

  15. Odar F, Hamilton WS (1964) Forces on a sphere accelerating in a viscous fluid. J Fluid Mech 18(2):302–314. https://doi.org/10.1017/S0022112064000210

    Article  MATH  Google Scholar 

  16. Polet DT, Rival DE (2015) Rapid area change in pitch-up manoeuvres of small perching birds. Bioinspir Biomim 10(6):066004. http://stacks.iop.org/1748-3190/10/i=6/a=066004

  17. Raffel M, Willert C, Wereley S, Kompenhans J (2007) Particle image velocimetry: a practical guide, 2nd edn. Springer, Berlin

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  20. Weymouth G, Triantafyllou MS (2012) Global vorticity shedding for a shrinking cylinder. J Fluid Mech 702:470–487. https://doi.org/10.1017/jfm.2012.200

    Article  MATH  Google Scholar 

  21. Weymouth G, Triantafyllou MS (2013) Ultra-fast escape of a deformable jet-propelled body. J Fluid Mech 721:367–385. https://doi.org/10.1017/jfm.2013.65

    MathSciNet  Article  MATH  Google Scholar 

  22. Wong JG, Rosi GA, Rouhi A, Rival DE (2017) Coupling temporal and spatial gradient information in high-density unstructured Lagrangian measurements. Exp Fluids 58(10):140. https://doi.org/10.1007/s00348-017-2427-6

    Article  Google Scholar 

  23. Yih CS (1985) New derivations of Darwin’s theorem. J Fluid Mech 152:163–172. https://doi.org/10.1017/S0022112085000623

    MathSciNet  Article  MATH  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the financial support from the Ontario Graduate Scholarship and the Natural Sciences and Engineering Research Council of Canada.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Cameron J. McPhaden.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (MP4 15087 kb)

Supplementary material 1 (MP4 15087 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

McPhaden, C.J., Rival, D.E. Unsteady force estimation using a Lagrangian drift-volume approach. Exp Fluids 59, 64 (2018). https://doi.org/10.1007/s00348-018-2515-2

Download citation