# zbMATH — the first resource for mathematics

Lift and the leading-edge vortex. (English) Zbl 1284.76059
Summary: Flapping wings often feature a leading-edge vortex (LEV) that is thought to enhance the lift generated by the wing. Here the lift on a wing featuring a leading-edge vortex is considered by performing experiments on a translating flat-plate aerofoil that is accelerated from rest in a water towing tank at a fixed angle of attack of 15$$^\circ$$. The unsteady flow is investigated with dye flow visualization, particle image velocimetry (PIV) and force measurements. Leading- and trailing-edge vortex circulation and position are calculated directly from the velocity vectors obtained using PIV. In order to determine the most appropriate value of bound circulation, a two-dimensional potential flow model is employed and flow fields are calculated for a range of values of bound circulation. In this way, the value of bound circulation is selected to give the best fit between the experimental velocity field and the potential flow field. Early in the trajectory, the value of bound circulation calculated using this potential flow method is in accordance with Kelvin’s circulation theorem, but differs from the values predicted by Wagner’s growth of bound circulation and the Kutta condition. Later the Kutta condition is established but the bound circulation remains small; most of the circulation is contained instead in the LEVs. The growth of wake circulation can be approximated by Wagner’s circulation curve. Superimposing the non-circulatory lift, approximated from the potential flow model, and Wagner’s lift curve gives a first-order approximation of the measured lift. Lift is generated by inertial effects and the slow buildup of circulation, which is contained in shed vortices rather than bound circulation.

##### MSC:
 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing 76B47 Vortex flows for incompressible inviscid fluids 76-05 Experimental work for problems pertaining to fluid mechanics
##### Keywords:
vortex dynamics; vortex flows
Full Text:
##### References:
 [1] DOI: 10.1103/PhysRevE.66.051907 · doi:10.1103/PhysRevE.66.051907 [2] DOI: 10.2514/1.4922 · doi:10.2514/1.4922 [3] Aeronaut. J. 105 pp 135– (2001) · doi:10.1017/S0001924000092058 [4] A. Angew. Math. pp 17– (1925) [5] Prog. Electromagnetics 19 pp 113– (2010) [6] DOI: 10.1242/jeb.022269 · doi:10.1242/jeb.022269 [7] DOI: 10.2514/1.C031184 · doi:10.2514/1.C031184 [8] J. Expl Biol. 202 pp 3439– (1999) [9] J. Aircraft 47 (2010) [10] DOI: 10.1016/j.jfluidstructs.2007.09.001 · doi:10.1016/j.jfluidstructs.2007.09.001 [11] DOI: 10.1126/science.284.5422.1954 · doi:10.1126/science.284.5422.1954 [12] DOI: 10.2514/3.7913 · Zbl 0479.76018 · doi:10.2514/3.7913 [13] J. Expl Biol. 174 pp 45– (1993) [14] DOI: 10.1016/j.ast.2010.05.003 · doi:10.1016/j.ast.2010.05.003 [15] DOI: 10.1088/0950-7671/44/1/302 · doi:10.1088/0950-7671/44/1/302 [16] DOI: 10.1088/0957-0233/12/9/307 · doi:10.1088/0957-0233/12/9/307 [17] DOI: 10.2514/3.25250 · doi:10.2514/3.25250 [18] DOI: 10.2514/3.8967 · doi:10.2514/3.8967 [19] Aero. Res. Counc. R&M pp 90– (1933) [20] DOI: 10.4050/JAHS.48.80 · doi:10.4050/JAHS.48.80 [21] DOI: 10.1038/384626a0 · doi:10.1038/384626a0 [22] DOI: 10.1038/35089071 · doi:10.1038/35089071 [23] J. Aerosp. Engng G 220 pp 61– (2006) [24] J. Expl Biol. 205 pp 1547– (2002) [25] Aerodynamics of Low Reynolds Number Flyers vol. 1 (2008) [26] DOI: 10.1007/s10409-008-0164-z · Zbl 1271.76285 · doi:10.1007/s10409-008-0164-z [27] Stud. Appl. Maths 57 pp 107– (1977) · Zbl 0385.76033 · doi:10.1002/sapm1977572107 [28] Particle Image Velocimetry: A Practical Guide (2001) [29] DOI: 10.1017/jfm.2011.490 · Zbl 1241.76055 · doi:10.1017/jfm.2011.490
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.