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.
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References
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
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
Batchelor G (1967) An introduction to fluid dynamics. Cambridge Mathematical Library, Cambridge University Press. https://books.google.ca/books?id=Rla7OihRvUgC
Benjamin TB (1986) Note on added mass and drift. J Fluid Mech 169:251–256. https://doi.org/10.1017/S0022112086000617
Brennan CE (1982) A review of added mass and fluid inertial forces. Tech report CR 82.010, Department of the Navy
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
Darwin C (1953) Note on hydrodynamics. Math Proc Camb Philos Soc 49(2):342–354. https://doi.org/10.1017/S0305004100028449
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
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
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
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
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
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
Lighthill MJ (1956) Drift. J Fluid Mech 1(1):3153. https://doi.org/10.1017/S0022112056000032
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
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
Raffel M, Willert C, Wereley S, Kompenhans J (2007) Particle image velocimetry: a practical guide, 2nd edn. Springer, Berlin
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
Schanz D, Gesemann S, Schröder A (2016) Shake-The-Box: Lagrangian particle tracking at high particle image densities. Exp Fluids 57:70
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
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
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
Yih CS (1985) New derivations of Darwin’s theorem. J Fluid Mech 152:163–172. https://doi.org/10.1017/S0022112085000623
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The authors acknowledge the financial support from the Ontario Graduate Scholarship and the Natural Sciences and Engineering Research Council of Canada.
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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
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DOI: https://doi.org/10.1007/s00348-018-2515-2