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Three-dimensional boundary layer and vortex wake over a cone at high angle of attack: study of asymmetries

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Abstract

An experimental investigation of the flow over a one at a large angle of attack is reported. First, the study was focused on the wall shear stress measurement, including the localization of the separation. Secondly, the mean flow field in the whole wake of the cone was measured, as well as the velocity fluctuations. Results indicate that the separation and the fluctuations are asymmetrical in a certain way, whereas the mean flow field is approximately symmetrical. Finally, the different parts of the flow can be easily determined using vorticity calculations.

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Abbreviations

C :

vortex core

D :

diffusion coefficient for the polarographic solution

D :

cone diameter for the rotation plane of the electrochemical probes

D :

separation point

F :

function F (sin α) = (K 1-K 2)/(K 1+K 2)

G :

function G(sin α) = (K 1+K 2)/(K 1+K 2)(α = 90dg)

g :

bidimensional gain of the electrochemical probe (constant for each probe)

K 1, K 2 :

mass transfer coefficients for differential probes

Re x :

Reynolds number based on the X length, and relative to the forward upstream velocity

\(\vec S\) :

wall velocity gradient vector

S :

wall velocity gradient modulus

S :

enclosing saddle point

S x :

azimuthal component of the wall velocity gradient (perpendicular to a generator)

S z :

longitudinal component of the wall velocity gradient (along a generator)

U :

mean value of the forward upstream velocity

U i :

component number i of the velocity vector in the (X, Y, Z) coordinates

X, Y, Z :

cone cartesian coordinates

\(\tilde X,\tilde Y,\tilde Z\) :

non-dimensional cone cartesian coordinates (relative to D)

α:

incidence (part 1) angle between the wall velocity gradient and the neutral axis of the electrochemical probe (except part 1)

α r :

relative incidence α/0 c

Γ:

velocity circulation

λ:

wavelength of the laser beam

ν:

kinematic viscosity

θ:

azimuthal angle

θ c :

cone semi-apex angle

References

  1. Adrian, R. J.; Fingerson, L. M. 1987: Laser anemometry theory, application and techniques. Publication TSI Incorporated

  2. Chapman, G. T.; Keener, E. R.; Malcolm, G. N. 1975: Asymmetric forces on aircraft forebodies at high angles of attack. Some design guides. A.G.A.R.D. CP 199

  3. Coe, P. L.; Chambers, J. R.; Letko, W. 1972: Asymmetric lateral directional characteristics of pointed bodies of revolution at high angles of attack. N.A.S.A. T.N. TND-7095, 1–41

  4. Cornish, J. J.; Jenkins, M. W. 1978: The application of spanwise blowing for high angles of attack spin recovery. A.G.A.R.D. CP 247

  5. Durrani, T. S.; Greated, C. A 1977: Laser systems in flow measurement. Plenum Press

  6. Durst, F.; Melling, A.; Whitelaw, J. H. 1981: Principles and practice laser-Doppler anemometry. Academic Press, 2nd Edition

  7. Ericsson, L. E.; Reding, J. P. 1981: Steady and unsteady vortex-induced asymmetric loads on slender vehicles. J. Spacecraft 18, 97–109

  8. Gregoriou, G. 1982: Modern missile design for high angles-of-attack. A.G.A.R.D. LS 121

  9. Labraga, L.; Tournier, C.; Florent, P. 1991: Experimental study of the frequency response of electrochemical split probes to transversal velocity fluctuations. Exp. Fluids 11, 325–332

  10. Lamont, P. J.; Hunt, B. L. 1976: Pressure and force distributions on sharp-nosed circular cylinder at large angles of inclination to a uniform subsonic stream. J. Fluid Mech. 76, 519–559

  11. Menet, J.-L. 1991: Elude de la couche limite tridimensionnelle et du sillage tourbillonnaire autour d'un cône à forte incidence par tribométrie électrochimique et anémométrie laser. Thèse de doctorat, Université de Valenciennes, France

  12. Menet, J.-L.; Labraga, L.; Tournier, C. 1989: Etude des structures pariétales sur un cône à forte incidence. Contrat D.R.E.T. n∘ 85/114 (Direction Générale pour l'Armement), France

  13. Mitchell, J. E.; Hanratty, T. J. 1966: A study of turbulence at a wall using an electrochemical wall shear stress meter. J. Fluid Mech. 26, 199–221

  14. Modi, V. J.; Ries, T.; Kwan, A.; Leung, E. 1984: Aerodynamics of pointed forebodies at high angles of attack. J. Aircraft 21, 428–432

  15. Mourtos, M. J.; Roberts, L. 1987: Control of vortical separation on conical bodies. U.A.A. TR-78, 1–8

  16. Peake, D. J.; Owen, F. K.; Higuchi, H. 1978: Symmetrical and asymmetrical separation about a yawed cone. A.G.A.R.D. CP 247

  17. Py, B.; Gosse, J. 1969: Sur la réalisation d'une sonde polarographiquc pariétale sensible à la vitesse et à la direction de l'écoulement. C.R. Acad. Sci. Paris 169, 401–405

  18. Rainbird, W. J.; Crabbe, R. S.; Peake, D. J.; Meyer, R. F. 1966: Some examples of separation in three-dimensional flows. C.A.S.J., 409–424

  19. Rao, D. H. 1978: Side force alleviation on slender, pointed fore-bodies at high angles of attack. A.I.A.A. P 78-1339, 92–99

  20. Reiss, L. P.; Hanratty, T. J. 1963: An experimental study of the unsteady nature of the viscous sublayer. A.I.Ch.E. J. 9, 154–160

  21. Riahi-Morteveille, A. 1987: Etude de la structure pariétale de l'ecoulement autour des cônes en incidence. Thèse de 3ème cycle. Université de Valenciennes, France

  22. Sarpkaya, T. 1966: Separated flow about lifting bodies and impulsive flow about cylinders. A.I.A.A. J. 4, 414–420

  23. Skow, A. M.; Peake, D. J. 1982: Control of forebody vortex orientation by asymmetric air injection. Part A: Application to enhance departure/spin recovery of fighter aircraft. Part B: Details of the flow structure. A.G.A.R.D. LS 121

  24. Stahl, W. 1990: Suppression of vortex asymmetry behind circular cones. A.I.A.A. J. 28, 1138–1140

  25. Tournier, C.; Py, B. 1978: The behaviour of naturally oscillating three-dimensional flow around a cylinder. J. Fluid Mech. 85, 161–186

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Menet, J.L., Menart, B. & Tournier, C. Three-dimensional boundary layer and vortex wake over a cone at high angle of attack: study of asymmetries. Experiments in Fluids 14, 224–232 (1993). https://doi.org/10.1007/BF00194012

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Keywords

  • Vortex
  • Boundary Layer
  • Shear Stress
  • Vorticity
  • Flow Field