Reynolds Stress

crossflow velocity for α = 5° was 0.29U∞ at x/c

= 0, a 42% decrease from α = 10°. Both the numerical and experimental vortices had a maximum crossflow velocity of 0.25 U∞ at x/c = 1 for α = 5°, which remained constant for the experimental vortex but decreased slightly to 0.22U∞ for the numerical vortex. The vortex core diameter was estimated by calculating the distance between the peaks of crossflow velocity taken on a line through the vortex centre.

4.4 Reynolds Stress

The ‹u′v′› Reynolds shear stress component was obtained from x-wire measurements and predicted from the Reynolds stress numerical model coupled with the vorticity confinement model. The ‹u′v′› component was normalised by the square of the free-stream velocity and is shown in Fig. 7 at a location of x/c = 0 for α = 5°. Both the numerical and experimental ‹u′v′›

component exhibited positive and negative values across the core of the vortex similar to the work of Chow et al [6]. Peak experimental stress levels of 0.0007 and -0.0007 were measured at x/dc = 0.25 and 0.5 respectively, where dc is the vortex core diameter. Peak numerical stresses of -0.0003 and 0.0002 were

measured at x/dc = -0.16 and 0.33. The stresses were found to decrease with increasing downstream distance and the maximum experimental stress by x/c = 1 had decayed to -0.0002, while the numerical stress was an order of magnitude smaller. The numerical values of

‹u′v′› for α = 10° were an order of magnitude smaller than experiment at all downstream locations (x/c = 0-3).

Fig. 7 Normalised Reynolds shear stress ‹u′v′›

across vortex core diameter for α = 5° at x/c = 0.

5 Conclusions

The near-field of a wingtip vortex has been investigated both numerically using a Reynolds stress turbulence model coupled with a vorticity confinement model and experimentally using a five-hole probe and x-wire anemometer. The vortex trajectory, shape and size of the vortex correlate extremely well with experiment. An upward and inboard movement was characteristic to both vortices. The same inboard shift was noted for the numerical and experimental vortices. The circulation parameters agreed with Prandtl’s lifting line theory and the numerical vortex strength was in close agreement for both angles of attack. The numerical vortex attained its maximum strength quicker than the experimental vortex which indicates that the numerical model predicts the vortex rollup too quickly. It also shows that the experimental vortex is continually trapping the wing boundary layer vorticity further

downstream. A linear trend between the circulation and angle of attack was noted and the magnitude of crossflow velocities was also thought to be linked to the discrepancy in axial velocities. The maximum crossflow velocities were obtained at a location of x/c = 0 for all cases and angles of attack. The crossflow velocities were found to decrease at x/c = 1 but stabilised thereafter up to the last measurement location of x/c = 3. The experimental vortex core diameter became slightly smaller with downstream distance for α = 5° but remained unchanged for α = 10°. The numerical vortex core diameter remained unchanged with downstream distance for α = 10° but increased slightly for α = 5°. The slight increase in vortex core diameter could be the result of decaying crossflow velocities, which ultimately would lead to the vortex becoming less tightly wound.

The numerical model was found to slightly under predict the axial velocity excess and deficit for α = 5 and 10°. The lower crossflow velocities predicted by the numerical model were thought to have had a direct effect on the discrepancy between axial velocities. The magnitude of the Reynolds stress component

‹u′v′› was in relatively good agreement at x/c = 0 for α = 5°. The Reynolds stress displayed both positive and negative values across the vortex core. This result is promising, showing that the Reynolds stress and turbulent fluctuations in the vortex core can be reasonably accurately predicted just aft of the trailing edge for α = 5°.

The numerical Reynolds stresses were found to dissipate extremely quickly further downstream and to be an order of magnitude smaller than the experimental values from x/c = 1-3 for α = 5°

and at all locations for α = 10°.

References

[1] Gerz, T., Holzӓpfel, F., and Darracq, D.,

“Commercial aircraft wake vortices” Prog. Aero.

Sci., Vol. 38, 2002, pp. 181-208

[2] Yu, Y.H., “Rotor blade-vortex interaction noise”, Prog. Aero. Sci., Vol. 36, 2000, pp. 97-115 [3] Yu, Y.H., Gmelin, B., Splettstoesser, W.,

Philippe, J.J., Prieur, J., and Brooks, T.F.,

“Reduction of helicopter blade-vortex interaction noise by active rotor control technology”, Prog.

Aero. Sci., Vol. 33, 1997, pp. 647-687

Micheál S. O’Regan, Philip C. Griffin and Trevor M. Young

[4] Beaumier, P., and Delrieux, Y., “Description and validation of the ONERA computational method for the prediction of blade-vortex interaction noise”, Aero. Sci. Tech. Vol. 9, 2005, pp. 31-43 [5] Ramaprian, B.R., and Zheng, Y., “Measurements

in Rollup Region of the Tip Vortex from a Rectangular Wing", AIAA Journal, Vol. 35, No.12, 1997, pp. 1837-1843.

[6] Chow, J.S., Zilliac, G.G., and Bradshaw, P.,

“Mean and Turbulence Measurements in the Near Field of a Wingtip Vortex”, AIAA Journal, Vol. 35, No.10, 1997, pp. 1561-1567

[7] Chigier, N.A., and Corsiglia, V.R., “Wind-Tunnel Studies of Wing Wake Turbulence”, J.

Aircraft, Vol. 9, No. 12, 1972, pp. 820-825.

[8] McAlister, K.W., and Takahashi, R.K., “NACA 0015 Wing Pressure and Trailing Vortex Measurements”, NASA TP-3151, Nov. 1991.

[9] Gerontakos, P., and Lee, T., “Near-field Tip Vortex behind a swept wing model”, Experiments in Fluids, Vol. 40, 2006, pp. 141-155.

[10] Anderson, E.G., and Lawton, T.A., “Correlation between Vortex Strength and Axial Velocity in a Trailing Vortex”, AIAA Journal, Vol. 40, No.4, 2003, pp. 699-704.

[11] Birch, D., Lee, T., Mokhtarian, F., and Kafyke, F., “Structure and Induced Drag of a Tip Vortex”, AIAA Journal, Vol. 41, No. 5, 2004, pp.

1138-1145.

[12] Devenport, W.J., Rife, M.C., Liapis, S.I., and Follin, G.J., “The Structure and development of a Wingtip Vortex”, J. Fluid Mech., Vol. 312, 1996, pp. 67-106.

[13] .Churchfield, M. J., and Blaisdell, G.A.,

“Numerical simulations of a wingtip vortex in the near field”, J. Aircraft, Vol. 46, No. 1, pp.

230-243.

[14] Dacles-Mariani, J., Zilliac, G.G., Chow, J., and Bradshaw, P., “Numerical/Experimental Study of a Wingtip Vortex in the Near Field”, AIAA Journal, Vol. 33, No.9, 1995, pp. 1561-1568.

[15] Craft, T.J., Gerasimov, A.V., Launder, B.E., and Robinson, C.M.E., “A computational study of the near-field generation and decay of wingtip vortices”, Inter. J. Heat Fluid Flow, Vol. 27, 2006, pp. 684-695.

[16] Steinhoff, J., Lynn, N., and Wang, L.

“Computation of high Reynolds number flows using vorticity confinement”, UTSI Preprint, 2005.

[17] Loehmer, R. “On limiter for minimal vorticity dissipation”, Proceedings of the 47^th AIAA Aerospace Sciences Meeting, Orlando, 2009, pp.

1-7.

[18] Kimbrell, A.B., “Development and verification of a Navier-Stokes solver with vorticity confinement using OpenFOAM” Master’s Thesis, University of Tennessee, USA, 2012.

[19] Czech, M., Miller, G., Crouch, J., and Strelets,

M., “Predicting the near-field evolution of airplane trailing vortices”, Com. Rend. Phys., Vol. 6, 2005, pp. 451-466.

[20] Spalart, P.R., and Shur, M., “On the sensitization of turbulence models to rotations and curvature”, Aero. Sci. Tech. Vol. 5, 1997, pp.

297-302.

[21] Gibson, M.M., and Launder, B.E., “Ground effects on pressure fluctuations in the atmospheric boundary layer”, J. Fluid Mech.

Vol. 86, No. 3, 1978, pp. 491-511.

[22] Shekarriz, A., Fu, T.C., Katz, J., and Huang, T.,

“Near-field behavior of a tip vortex”, AIAA Journal, Vol. 31, No. 1, 1993, pp. 112-118.

Abstract

Application of drag reduction technology based on laminar flow in a commercial environment is still being hindered by unanswered questions regarding its operational reliability. A malfunction of a laminar flow system, even if temporary, could have a considerable effect (depending on the extent of its application) on the overall fuel planning; and, for more ambitious designs, possibly even on the handling characteristics of a correspondingly equipped aircraft. Nevertheless, a first small scale application has recently been introduced into routine commercial airline service. The encounter of ice crystals, as occurring in cirrus cloud, is known to result in performance degradations or even a temporary complete loss of laminar flow. Actually occurring mechanisms are not well understood and previously proposed critical parameters have not yet been verified experimentally. Difficulties encountered while attempting to recreate conditions in the laboratory that are representative of the real occurrences have led to several alternative experimental methods. This study presents results from a relatively simple method, in terms of its complexity, providing for further insight into the phenomenon that a small particle is

capable of producing a turbulent event while travelling through an initially laminar boundary layer. Using this method, for a smooth spherical particle, a critical Reynolds number in the order of 300 has been determined above which the generation of a turbulent-spot-like disturbance will occur.

1 Introduction

The depletion of cheap fossil fuel reserves has focused research attention on improving aircraft efficiencies within a short time frame, and this has revived the interest in laminar flow technology due to its great potential to reduce fuel consumption. If applied to all aircraft components that are currently rated as being practical, namely the wings’ upper surfaces, the empennage and the engine nacelles, overall drag reductions of approximately 16% [1] are thought to be realistic. This would translate into a reduction of fuel consumption in the order of 10% [2].

The principles to achieve such benefits are Natural Laminar Flow (NLF), a passive technique based on extended regions of accelerated flow over specifically designed contours, and the active method of Laminar Flow Control (LFC) based on suction through a perforated or slotted surface, which prevents the