Water Tank Study of the Decay of Trailing Vortices

Abstract

Underwater towing experiments were carried out with a rectangular airfoil of aspect ratio 5.3 at 4° and 8°a ngles of attack and at chord-based Reynolds numbers between 2.2 x 10 5 and 7.5 x 10 5 . Tangential velocity measurements in the downstream region between 100 and 1000 chord lengths indicate rates of vortex decay proportional to r 7/8 at 8°, whereas previous flight tests show that the decay rate approaches £~1 /2 far downstream. The observed behavior is explained in terms of an analytical solution that includes time dependence of the turbulent eddy viscosity, V T ~ t m . It shows that, for m > 0, an isolated turbulent vortex decays faster than t~1 /2 . In this case, the decay is accompanied by increasing v r , or levels of turbulence, which corresponds to turbulent nonequilibrium flow. The special case of vortex decay with equilibrium flow (m = 0) leads to the well-known decay rate 2 . Since, in towing tank experiments at low Reynolds number, turbulent vortex decay may occur predominantly in nonequilibrium, it is doubtful that such tests correctly predict the late stage of decay of aircraft trailing vortices, when turbulence is the only dissipating mechanism. Nomenclaturea = core radius b = wing span c -wing chord AH = head loss in boundary layer p = pressure p m = fluid pressure as r -> oo p(0) = pressure on the vortex axis r = radius measured from vortex axis t = time At = time difference in velocity measurement T = time parameter, T -F^ t/c 2 U ^ -towing speed v = tangential velocity component v a = tangential velocity at r = a w = axial velocity component vv 0 = axial velocity on vortex axis z = downstream distance behind airfoil ex = angle of attack /? = constant of proportionality, Eq. (6) F = circulation F a = circulation at core radius F^ = circulation of wing 0, A0 = angle in velocity measurement v = kinematic viscosity V T = eddy viscosity (v T /v) a = eddy viscosity at core radius p = fluid density Superscripts m = exponent in expression for time-dependent V T , Eq. (7)Subscripts a = conditions at the core radius, r = a v e = effective viscosity (v T /v) 0 = eddy viscosity level after rollup 0 = conditions on the vortex axis, r -0 oo = conditions at r = GO

Mean and Turbulence Measurements in the Near Field of a Wingtip Vortex

“…Squire's (1954) is lacking, however. Lezius (1974) noticed that in towing tank tests between 100 and 1000 chords downstream of an airfoil set at 8 degrees, the vortex decayed at a rate proportional to t -7 / 8 , not the usually predicted t-'I2. The towing tank tests had Re, ranging from 2.2 x 10"o 7.5 x lo5.…”

Numerical Simulations of Commercial Aircraft Wakes Subjected to Airport Surface Weather Conditions

“…That was the approach used by Owen, 13 but he contended that the eddy viscosity should not scale simply with circulation, because it implied that the 14 yield S q = 2000 6 500, for 4 3 10 4 < G`/ n < 2 3 10 5 , while Owen 13 estimated that Sq = 5000 at G`/n ' 10 7 for the experiments of Rose and Dee. 24 Similarly, Iverson's 15 nonlinear eddy viscosity model was t through a slightly different data set that produced S q ' 10,000 at Re = G`/n = 2.6 3 10 7 .…”

“…1, for example) is true height only for one aircraft con guration (a B 757). The vertical axis of the weather data for other aircraft types represented by that simulation must be scaled for each aircraft type by the ratio of the particular value of s 0, from Table 3, to the actual reference value of s 0, i.e., 14.90 m, in the run 9 case for B 757. Hence, we can approximate the circulation decay behavior for B 727, B 757, and A 300, subjected to surface weather conditions that are similar to run 9 (Fig.…”