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.
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References
Adrian RJ, Westerweel J (2011) Particle image velocimetry. Cambridge University Press
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
Betz A (1925) A method for the direct determination of profile drag (in German). Zeitschrift für Flugtechnik und Motorluftschifffahrt 16:42–44
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
Dabiri JO (2005) On the estimation of swimming and flying forces from wake measurements. J Exp Biol 208:3519–3532
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
Darwin CG (1953) Note on hydrodynamics. Math Proc Cambridge Philos Soc 49(2):342–354
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
DeVoria AC, Ringuette M (2013) On the flow generated on the leeward face of a rotating flat plate. Exp Fluids 54:1495
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
Elsinga GE, Scarano F, Wieneke B, van Oudheusden BW (2006) Tomographic Particle Image Velocimetry. Exp Fluids 41:933–947
Fernando JFF, Rival DE (2016) Reynolds-number scaling of vortex pinch-o on low-aspect-ratio propulsors. J Fluid Mech 799:R3
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
Gharali K, Johnson DA (2014) Piv-based load investigation in dynamic stall for different reduced frequencies. Exp Fluids 54:1–14
Graziani G, Bassanini P (2002) Unsteady viscous flows about bodies: Vorticity release and forces. Meccanica 37:283–303
Haller G (2002) Lagrangian coherent structures from approximate velocity data. Phys Fluids 14(6):1851–1861
Huang Y, Green MA (2015) Detection and tracking of vortex phenomena using lagrangian coherent structures. Exp Fluids 56:147
Hubel TY, Hristov NI, Swartz SM, Breuer KS (2009) Time-resolved wake structure and kinematics of bat flight. Exp Fluids 46:933–943
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
Jones BM (1936) Measurement of profile drag by the pitot-traverse method. ARC R&M No. 1688
Kähler CJ, Scharnowski S, Cierpka C (2012a) On the resolution limit of digital particle image velocimetry. Exp Fluids 52(6):1629–1639
Kähler CJ, Scharnowski S, Cierpka C (2012b) On the uncertainty of digital PIV and PTV near walls. Exp Fluids 52(6):1641–1656
Koochesfahani MM (1989) Vortical patterns in the wake of an oscillating airfoil. AIAA J 27:1200–1205
Kriegseis J, Rival D (2014) Vortex force decomposition in the tip region of impulsively-started flat plates. J Fluid Mech 756:758–770
Kurtulus DF, Scarano F, David L (2007) Unsteady aerodynamics force estimation on a square cylinder by TR-PIV. Exp Fluids 42:185–196
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
Lighthill MJ (1986) Fundamentals concerning wave loading on offshore structures. J Fluid Mech 173:667–681
Lin J-C, Rockwell D (1996) Force identification by vorticity fields: techniques based on flow imaging. J Fluids Struct 10:663–668
Mackowski AW, Williamson CHK (2011) Developing a cyber-physical fluid dynamics facility for fluid-structure interaction studies. J Fluids Struct 27:748–757
Mendelson L, Techet AH (2015) Quantitative wake analysis of a freely swimming fish using 3D synthetic aperture PIV. Exp Fluids 56:135
Minotti FO (2011) Determination of the instantaneous forces on flapping wings from a localized fluid velocity field. Phys Fluids s1-9(1):91–93
Mohebbian A, Rival D (2012) Assessment of the derivative-moment transformation method for unsteady-load estimation. Exp Fluids 53:319–330
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
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
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
Onoue K, Breuer KS (2016) Vortex formation and shedding from a cyber-physical pitching plate. J Fluid Mech 793:229–247
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
Polet DT, Rival DE (2015) Rapid area change in pitch-up manoeuvres of small perching birds. Bioinsp Biomimet 10(1):066004
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
Protas B, Styczek A, Nowakowski A (2000) An effective approach to computation of forces in viscous incompressible flows. J Comput Phys 159:231–245
Quartapelle L, Napolitano M (1983) Force and moment in incompressible flows. AIAA J 21:911–913
Rival DE, Manejev R, Tropea C (2010) Measurement of parallel blade-vortex interaction at low Reynolds numbers. Exp Fluids 49:89–99
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
Saffman P (1992) Vortex Dynamics. Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge University Press
Schanz D, Gesemann S, Schroeder A (2016) Shake The Box: Lagrangian particle tracking at high particle image densities. Exp Fluids 57-70
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
Unal M, Lin J-C, Rockwell D (1997) Force prediction by PIV imaging: a momentum-based approach. J Fluids Struct 11:965–971
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
van Oudheusden BW (2013) PIV-based pressure measurement. Measure Sci Technol 24(032001):1–32
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
Villegas A, Diez F (2014) Evaluation of unsteady pressure fields and forces in rotating airfoils from time-resolved piv. Exp Fluids 55:1697
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
Westerweel J (2008) On velocity gradients in PIV interrogation. Exp Fluids 44:831–842
Wu JC (1981) Theory for aerodynamic force and moment in viscous flows. AIAA J 19:432–441
Wu J-Z, Ma H-Y, Zhou J-Z (2006) Vorticity and vortex dynamics. Lecture notes in mathematics. Springer, Berlin Heidelberg
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
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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
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DOI: https://doi.org/10.1007/s00348-017-2304-3