An asymptotic analysis of the structure of the flow at high Reynolds number around a streamlined body is presented. The boundary layer is turbulent. This question is studied with the successive complementary expansion method, SCEM. The starting point is to look for a uniformly valid approximation (UVA) of the velocity field, including the boundary layer and the external flow. Thanks to the use of generalized expansions, SCEM leads to the theory of interactive boundary layer, IBL. For many years, IBL model has been used successfully to calculate aerodynamic flows. Here, the IBL model is fully justified with rational mathematical arguments. The construction of a UVA of the velocity profile in the boundary layer is also studied.
On présente une analyse asymptotique de la structure de l'écoulement à grand nombre de Reynolds en présence d'un corps profilé. La couche limite est turbulente. Avec la méthode des approximations successives complémentaires, MASC, le point de départ est la recherche d'une approximation uniformément valable, AUV, du champ de vitesse couvrant la couche limite et l'écoulement extérieur. Grâce à l'utilisation de développements généralisés, la MASC conduit à la théorie de couche limite interactive, CLI. Les modèles CLI, appliqués depuis longtemps au calcul d'écoulements aérodynamiques, sont ici pleinement justifiés à l'aide d'arguments mathématiques rationnels. La construction d'une AUV pour le profil de vitesse dans la couche limite est également étudiée.
Accepted:
Published online:
Mot clés : Turbulence, Couche limite interactive, Couplage visqueux–non visqueux, Écoulement turbulent, Analyse asymptotique
Jean Cousteix 1, 2; Jacques Mauss 3
@article{CRMECA_2007__335_9-10_590_0,
author = {Jean Cousteix and Jacques Mauss},
title = {Interactive boundary layers in turbulent flow},
journal = {Comptes Rendus. M\'ecanique},
pages = {590--605},
publisher = {Elsevier},
volume = {335},
number = {9-10},
year = {2007},
doi = {10.1016/j.crme.2007.08.014},
language = {en},
}
Jean Cousteix; Jacques Mauss. Interactive boundary layers in turbulent flow. Comptes Rendus. Mécanique, Volume 335 (2007) no. 9-10, pp. 590-605. doi : 10.1016/j.crme.2007.08.014. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.08.014/
[1] Turbulent Flows, Cambridge University Press, Cambridge, UK, 2000
[2] P.A. Bois, Joseph Boussinesq, a pioneer of Mechanical Modelling at the end of the 19th century, C. R. Mecanique 335 (2007), this issue, | DOI
[3] J.E. Carter, A new boundary layer inviscid iteration technique for separated flow, AIAA Paper 79-1450, in: 4th Computational Fluid Dynamics Conf., Williamsburg, 1979
[4] An Engineering Approach to the Calculation of Aerodynamic Flows, Horizons Publishing Inc., Springer-Verlag, Long Beach, CA, Berlin, 1999
[5] Couplage visqueux–non visqueux : analyse du problème incluant décollements et ondes de choc, La Recherche Aérospatiale, Volume 6 (1977), pp. 349-358
[6] Matched asymptotic expansions and the numerical treatment of viscous–inviscid interaction, J. Eng. Math., Volume 39 (2001), pp. 189-206
[7] Analyse asymptotique et couche limite, Mathématiques et Applications, vol. 56, Springer-Verlag, SMAI, Berlin, Heidelberg, 2006
[8] An expansion method for singular perturbation problems, J. Austral. Math. Soc., Volume 2 (1962), pp. 440-463
[9] Introduction to Singular Perturbations, Applied Mathematics and Mechanics, vol. 14, Academic Press, New York, London, 1974
[10] Review of wall turbulence as described by composite expansions, Appl. Mech. Rev., Volume 58 ( January 2005 ) no. 1, pp. 1-36
[11] Recent advancements toward the understanding of turbulent boundary layers, AIAA J., Volume 44 (2006), pp. 2435-2449
[12] The large Reynolds number asymptotic theory of turbulent boundary layers, Int. J. Eng. Sci., Volume 10 (1972), pp. 851-873
[13] Asymptotic theory of turbulent shear flows, part 2, J. Fluid Mech., Volume 42 (1970), pp. 411-427
[14] R. Michel, C. Quémard, R. Durant, Application d'un schéma de longueur de mélange à l'étude des couches limites turbulentes d'équilibre, N.T. 154, ONERA, 1969
[15] On turbulent flow near a wall, J. Aeron. Sci., Volume 23 (1956), p. 1007
[16] The turbulent boundary layer, Adv. Appl. Mech., Volume 4 (1956), pp. 1-51
[17] The law of the wake in the turbulent boundary layer, J. Fluid Mech., Volume 1 (1956), p. 191
[18] Remarks on the equilibrium turbulent boundary layer, J. Aero. Sci., Volume 24 (1957)
[19] G.L. Mellor, D.M. Gibson, Equilibrium turbulent boundary layer, FLD No. 13, Princeton University, 1963
[20] Turbulent Boundary Layers in Incompressible Flows, Progress in Aeronautical Sciences, vol. 2, Pergamon Press, 1962
[21] Asymptotic Theory of Separated Flows, Cambridge University Press, Cambridge, UK, 1998
Cited by Sources:
Comments - Policy