Vortex topology of a pitching and rolling wing in forward flight
Tóm tắt
Vortex topology is analyzed from measurements of flow over a flat, rectangular plate with an aspect ratio of 2 which was articulated in pitch and roll, individually and simultaneously. The plate was immersed into a
$$\text {Re} = 10,000$$
flow (based on chord length). Measurements were made using a 3D–3C plenoptic PIV system to allow for the study of complete vortex topology of the entire wing. The prominent focus is the early development of the leading-edge vortex (LEV) and resulting topology. The effect of the wing kinematics on the topology was explored through a parameter space involving multiple values of pitch rate and roll rate at pitch and roll angles up to
$${50}^{\circ }$$
. Characterization and comparisons across the expansive data set are made possible through the use of a newly defined dimensionless parameter,
$${\textit{k}_{\text {Rg}}}$$
. Termed the effective reduced pitch rate,
$${\textit{k}_{\text {Rg}}}$$
, is a measure of the pitch rate that takes into account the relative rolling motion of the wing in addition to the pitching motion and freestream velocity. This study has found that for a purely pitching wing, increasing the reduced pitch rate
$${\textit{k}}$$
delays the vortex evolution with respect to
$$\alpha _\mathrm {eff}$$
. For a purely rolling wing, as the advance coefficient
$${\textit{J}}$$
is increased, the vortex evolution is advanced with respect to nondimensionalized time and the bifurcation point of the LEV shifts inboard. For a pitching and rolling wing, the addition of roll stabilizes and delays the evolution of the LEV in both nondimensionalized time and effective angle of attack.
Tài liệu tham khảo
Akkala JM, Buchholz JH (2017) Vorticity transport mechanisms governing the development of leading-edge vortices. J Fluid Mech 829:512–537. https://doi.org/10.1017/jfm.2017.559
Aono H, Liang F, Liu H (2008) Near- and far-field aerodynamics in insect hovering flight: an integrated computational study. J Exp Biol 211(2):239–257. https://doi.org/10.1242/jeb.008649
Birch JM, Dickinson MH (2001) Spanwise flow and the attachment of the leading-edge vortex on insect wings 412(August):4
Birch JM, Dickson WB, Dickinson MH (2004) Force production and flow structure of the leading edge vortex on flapping wings at high and low Reynolds numbers, pp 1063–1072. https://doi.org/10.1242/jeb.00848
Borazjani I, Daghooghi M (2013) The fish tail motion forms an attached leading edge vortex. In: Proceedings of biological sciences/The Royal Society, p 280. https://doi.org/10.1098/rspb.2012.2071
Bridges DH (2010) Toward a theoretical description of vortex wake asymmetry. Prog Aerosp Sci 46(2–3):62–80. https://doi.org/10.1016/j.paerosci.2009.11.005
Bross M, Ozen CA, Rockwell D (2013) Flow structure on a rotating wing: effect of steady incident flow. Phys Fluids. https://doi.org/10.1063/1.4816632
Carr ZR, Chen C, Ringuette MJ (2012) The effect of aspect ratio on the three-dimensional vortex formation of rotating flat-plate wings. In: 50th AIAA aerospace sciences meeting (January):1–26. https://doi.org/10.2514/6.2012-912. http://arc.aiaa.org/doi/pdf/10.2514/6.2012-912
Chin DD, Lentink D (2016) Flapping wing aerodynamics: from insects to vertebrates. J Exp Biol 219(7):920–932. https://doi.org/10.1242/jeb.042317
Dickinson MH, Götz K (1993) Unsteady aerodynamic performance of model wings at low reynolds numbers. J Exp Biol 174:45–64. https://doi.org/10.1242/jeb.00739
Eldredge J, Wang C (2010) High-fidelity simulations and low-order modeling of a rapidly pitching plate. In: 40th fluid dynamics conference and exhibit (June 2010). https://doi.org/10.2514/6.2010-4281. http://arc.aiaa.org/doi/10.2514/6.2010-4281
Eldredge JD, Jones AR (2019) Leading-edge vortices: mechanics and modeling. Annu Rev Fluid Mech 51:1. https://doi.org/10.1146/annurev-fluid-010518-040334
Ellington CP, van den Berg C, Willmott AP, Thomas ALR (1996) Leading-edge vortices in insect flight. Nature 384(6610):626–630. https://doi.org/10.1038/384626a0
Eslam Panah A, Akkala JM, Buchholz JH (2015) Vorticity transport and the leading-edge vortex of a plunging airfoil. Exp Fluids 56(8):1–15. https://doi.org/10.1007/s00348-015-2014-7
Fahringer TW, Lynch KP, Thurow BS (2015) Volumetric particle image velocimetry with a single plenoptic camera. Meas Sci Technol 26(11):1–25. https://doi.org/10.1088/0957-0233/26/11/115201. http://stacks.iop.org/0957-0233/26/i=11/a=115201?key=crossref.324b3a85fc9196137efd1fa4ec233b89
Garmann DJ, Visbal MR (2011) Numerical investigation of transitional flow over a rapidly pitching plate. Phys Fluids 23:9. https://doi.org/10.1063/1.3626407
Garmann DJ, Visbal MR, Orkwis PD (2013) Three-dimensional flow structure and aerodynamic loading on a revolving wing. Phys Fluids 25:3. https://doi.org/10.1063/1.4794753
Garmann DJ, Visbal MR (2014) Dynamics of revolving wings for various aspect ratios. J Fluid Mech 748(2014):932–956. https://doi.org/10.1017/jfm.2014.212. http://www.journals.cambridge.org/abstract_S0022112014002122
Granlund KO, Ol MV, Bernal LP (2013) Unsteady pitching flat plates. J Fluid Mech 733(2013):1–13. https://doi.org/10.1017/jfm.2013.444
Gursul I, Gordnier R, Visbal M (2005) Unsteady aerodynamics of nonslender delta wings. Prog Aerosp Sci 41(7):515–557. https://doi.org/10.1016/j.paerosci.2005.09.002
Hall EM, Fahringer TW, Thurow BS, Guildenbecher DR (2017) Volumetric calibration of a plenoptic camera. In: 55th AIAA aerospace sciences meeting (January):1–14. https://doi.org/10.2514/6.2017-1642. http://arc.aiaa.org/doi/10.2514/6.2017-1642
Hartloper C, Rival D (2013) Vortex development on pitching plates with lunate and truncate planforms. Jfm 732(2013):332–344. https://doi.org/10.1017/jfm.2013.400
Hord K, Lian Y (2016) Leading edge vortex circulation development on finite aspect ratio pitch-up wings. AIAA J 54(9):1–13. https://doi.org/10.2514/1.J053911. http://arc.aiaa.org/doi/10.2514/1.J053911
Jantzen RT, Taira K, Granlund KO, Ol MV (2014) Vortex dynamics around pitching plates. Phys Fluids 26:5. https://doi.org/10.1063/1.4879035
Jardin T (2017) Coriolis effect and the attachment of the leading edge vortex. J Fluid Mech 820:312–340. https://doi.org/10.1017/jfm.2017.222
Lee HM, Wu Y (2014) A Tomo-PIV study of the effects of freestream turbulence on stall delay of the blade of a horizontal-axis wind turbine. Wind Energy 17(April 2013):1185–1205. . http://wileyonlinelibrary.com/doi/10.1002/we.1754, arXiv:1006.4405v1
Lehmann FO (2004) The mechanisms of lift enhancement in insect flight. Naturwissenschaften 91(3):101–122. https://doi.org/10.1007/s00114-004-0502-3
Lentink D, Dickinson MH (2009) Biofluiddynamic scaling of flapping, spinning and translating fins and wings. J Exp Biol. https://doi.org/10.1242/jeb.022251
Limacher E, Morton C, Wood D (2016) On the trajectory of leading-edge vortices under the influence of Coriolis acceleration. J Fluid Mech 800:R1. https://doi.org/10.1017/jfm.2016.395. http://www.journals.cambridge.org/abstract_S0022112016003955
Lynch K (2015) Advances in time-resolved tomographic particle image velocimetry. Phd, TU Delft
Mendez MA, Raiola M, Masullo A, Discetti S, Ianiro A, Theunissen R, Buchlin JM (2017) POD-based background removal for particle image velocimetry. Exp Thermal Fluid Sci 80:181–192. https://doi.org/10.1016/j.expthermflusci.2016.08.021
Mulleners K, Kindler K, Raffel M (2012) Dynamic stall on a fully equipped helicopter model. Aerosp Sci Technol 19(1):72–76. https://doi.org/10.1016/j.ast.2011.03.013
Olivier M, Dumas G (2016) A parametric investigation of the propulsion of 2D chordwise-flexible flapping wings at low Reynolds number using numerical simulations. J Fluids Struct 63:210–237. https://doi.org/10.1016/j.jfluidstructs.2016.03.010
Ozen CA, Rockwell D (2011) Vortical structures on a flapping wing. Exp Fluids 50(1):23–34. https://doi.org/10.1007/s00348-010-0888-y
Phillips N, Knowles K, Bomphrey RJ (2015) The effect of aspect ratio on the leading-edge vortex over an insect-like flapping wing. Bioinspir Biomimet 10(5):056020. https://doi.org/10.1088/1748-3190/10/5/056020. http://stacks.iop.org/1748-3190/10/i=5/a=056020?key=crossref.670af6abfcf482b0fa381358fa14e798
Polet DT, Rival DE, Weymouth GD (2015) Unsteady dynamics of rapid perching manoeuvres. J Fluid Mech 767(2014):323–341. https://doi.org/10.1017/jfm.2015.61
Raghav V, Komerath N (2013) An exploration of radial flow on a rotating blade in retreating blade stall. J Am Helicopter Soc 58(2):1–10. https://doi.org/10.4050/jahs.58.022005. http://www.ingentaconnect.com/content/ahs/jahs/2013/00000058/00000002/art00005%255Cndx.doi.org/10.4050/JAHS.58.022005
Raghav V, Komerath N (2015) Advance ratio effects on the flow structure and unsteadiness of the dynamic-stall vortex of a rotating blade in steady forward flight. Phys Fluids 27:2. https://doi.org/10.1063/1.4906803
Ramesh K, Gopalarathnam A, Granlund K (2014) Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding. J Fluid Mech 751:500–538. https://doi.org/10.1017/jfm.2014.297
Sane SP (2003) The aerodynamics of insect flight. J Exp Biol 206(Pt 23):4191–4208. https://doi.org/10.1242/jeb.00663
Scarano F, Poelma C (2009) Three-dimensional vorticity patterns of cylinder wakes. Exp Fluids 47(1):69–83. https://doi.org/10.1007/s00348-009-0629-2
Shih C, Ho CM (1994) Vorticity balance and time scales of a two-dimensional airfoil in an unsteady free stream. Phys Fluids 6(2):710–723. https://doi.org/10.1063/1.868310
Shyy W, Aono H, Chimakurthi SK, Trizila P, Kang CK, Cesnik CE, Liu H (2010) Recent progress in flapping wing aerodynamics and aeroelasticity. Prog Aerosp Sci 46(7):284–327. https://doi.org/10.1016/j.paerosci.2010.01.001
Shyy W, Aono H, Kang CK, Liu H (2013) An introduction to flapping wing aerodynamics. Cambridge Univeristy Press, Cambridge
Stevens PRRJ, Babinsky H (2017) Experiments to investigate lift production mechanisms on pitching flat plates. Exp Fluids 58(1):7. https://doi.org/10.1007/s00348-016-2290-x. http://link.springer.com/10.1007/s00348-016-2290-x
Sun M, Tang J (2002) Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion. J Exp Biol 205(Pt 1):55–70
Thomas ALR, Taylor GK, Srygley RB, Nudds RL, Bomphrey RJ (2004) Dragonfly flight : free-flight and tethered flow visualizations reveal a diverse array of unsteady lift-generating mechanisms , controlled primarily via angle of attack, pp 4299–4323. https://doi.org/10.1242/jeb.01262
Usherwood JR (2010) The aerodynamic forces and pressure distribution of a revolving pigeon wing. Anim Locomot. https://doi.org/10.1007/978-3-642-11633-9_33
Usherwood JR, Ellington CP (2002) The aerodynamics of revolving wings I. Model hawkmoth wings. J Exp Biol 205(Pt 11):1547–1564
Van den Berg C, Ellington CP (1997) The three-dimensional leading-edge vortex of a ’hovering’ model hawkmoth. Philos Trans R Soc B Biol Sci 352(1351):329–340. https://doi.org/10.1098/rstb.1997.0024. http://rstb.royalsocietypublishing.org/cgi/doi/10.1098/rstb.1997.0024
Visbal MR (2014a) Analysis of the onset of dynamic stall using high-fidelity large-eddy simulations (January):1–25
Visbal MR (2014b) Numerical exploration of flow control for delay of dynamic stall on a pitching airfoil (June):1–28
Visbal MR, Shang JS (1989) Investigation of the flow structure around a rapidly pitching airfoil. AIAA J 27(8):1044–1051. https://doi.org/10.2514/3.10219
Wang ZJ (2005) Dissecting insect flight. Annu Rev Fluid Mech 37(1):183–210. https://doi.org/10.1146/annurev.fluid.36.050802.121940. http://www.annualreviews.org/doi/10.1146/annurev.fluid.36.050802.121940
Wojcik CJ, Buchholz JH (2014a) Parameter variation and the leading-edge vortex of a rotating flat plate. AIAA J 52(2):348–357
Wojcik CJ, Buchholz JHJ (2014b) Vorticity transport in the leading-edge vortex on a rotating blade. J Fluid Mech 743(2014):249–261. https://doi.org/10.1017/jfm.2014.18. http://www.journals.cambridge.org/abstract_S0022112014000184
Wolfinger M, Rockwell D (2015) Transformation of flow structure on a rotating wing due to variation of radius of gyration. Exp Fluids 56:7. https://doi.org/10.1007/s00348-015-2005-8
Yilmaz T, Ol M, Rockwell D (2010) Scaling of flow separation on a pitching low aspect ratio plate. J Fluids Struct 26(6):1034–1041. https://doi.org/10.1016/j.jfluidstructs.2010.07.003
Yilmaz TO, Rockwell D (2012) Flow structure on finite-span wings due to pitch-up motion. J Fluid Mech 691(2012):518–545. https://doi.org/10.1017/jfm.2011.490
Zhou J, Adrian RJ, Balachandar S, Kendall TM (1999) Mechanisms for generating coherent packets of hairpin vortices in channel flow. J Fluid Mech 387(October):353–396. https://doi.org/10.1017/S002211209900467X