Comptes Rendus
no. 9
On the accuracy of analytical methods for turbulent flows near smooth walls
Rafik Absi1  ; Carmine Di Nucci2
1 EBI, Inst. Polytech. St-Louis, UPGO – Université Paris Grand Ouest, 32 Bd du Port, 95094 Cergy-Pontoise Cedex, France
2 Dipartimento di Ingegneria delle Strutture, delle Acque e del Terreno, University of LʼAquila, 67040 LʼAquila, Italy
Comptes Rendus. Mécanique, Volume 340 (2012) no. 9, pp. 641-645.

This Note presents two methods for mean streamwise velocity profiles of fully-developed turbulent pipe and channel flows near smooth walls. The first is the classical approach where the mean streamwise velocity is obtained by solving the momentum equation with an eddy viscosity formulation [R. Absi, A simple eddy viscosity formulation for turbulent boundary layers near smooth walls, C. R. Mecanique 337 (2009) 158–165]. The second approach presents a formulation of the velocity profile based on an analogy with an electric field distribution [C. Di Nucci, E. Fiorucci, Mean velocity profiles of fully-developed turbulent flows near smooth walls, C. R. Mecanique 339 (2011) 388–395] and a formulation for the turbulent shear stress. However, this formulation for the turbulent shear stress shows a weakness. A corrected formulation is presented. Comparisons with DNS data show that the classical approach with the eddy viscosity formulation provides more accurate profiles for both turbulent shear stress and velocity gradient.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2012.09.001
Mots clés : Fluid mechanics, Turbulence, DNS
Rafik Absi 1 ; Carmine Di Nucci 2

1 EBI, Inst. Polytech. St-Louis, UPGO – Université Paris Grand Ouest, 32 Bd du Port, 95094 Cergy-Pontoise Cedex, France
2 Dipartimento di Ingegneria delle Strutture, delle Acque e del Terreno, University of LʼAquila, 67040 LʼAquila, Italy 
@article{CRMECA_2012__340_9_641_0,
     author = {Rafik Absi and Carmine Di Nucci},
     title = {On the accuracy of analytical methods for turbulent flows near smooth walls},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {641--645},
     publisher = {Elsevier},
     volume = {340},
     number = {9},
     year = {2012},
     doi = {10.1016/j.crme.2012.09.001},
     language = {en},
}
TY  - JOUR
AU  - Rafik Absi
AU  - Carmine Di Nucci
TI  - On the accuracy of analytical methods for turbulent flows near smooth walls
JO  - Comptes Rendus. Mécanique
PY  - 2012
SP  - 641
EP  - 645
VL  - 340
IS  - 9
PB  - Elsevier
DO  - 10.1016/j.crme.2012.09.001
LA  - en
ID  - CRMECA_2012__340_9_641_0
ER  - 
%0 Journal Article
%A Rafik Absi
%A Carmine Di Nucci
%T On the accuracy of analytical methods for turbulent flows near smooth walls
%J Comptes Rendus. Mécanique
%D 2012
%P 641-645
%V 340
%N 9
%I Elsevier
%R 10.1016/j.crme.2012.09.001
%G en
%F CRMECA_2012__340_9_641_0
Rafik Absi; Carmine Di Nucci. On the accuracy of analytical methods for turbulent flows near smooth walls. Comptes Rendus. Mécanique, Volume 340 (2012) no. 9, pp. 641-645. doi : 10.1016/j.crme.2012.09.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.09.001/

[1] J.P. Monty; N. Hutchins; H.C.H. Ng; I. Marusic; M.S. Chong A comparison of turbulent pipe, channel and boundary layer flows, J. Fluid Mech., Volume 632 (2009), pp. 431-442

[2] M.H. Buschmann; T. Indinger; M. Gad-el-Hak Near-wall behavior of turbulent wall-bounded flows, Int. J. Heat Fluid Flow, Volume 30 (2009), pp. 993-1006

[3] S.B. Pope Turbulent Flows, University Press, Cambridge, 2000

[4] H. Schlichting; K. Gersten Boundary Layer Theory, Springer, 2000

[5] F. Laadhari On the evolution of maximum turbulent kinetic energy production in a channel, Phys. Fluids, Volume 14 (2002) no. 10, p. L65-L68

[6] E.-S. Zanoun; F. Durst; H. Nagib Evaluating the law of the wall in two-dimensional fully developed turbulent channel flows, Phys. Fluids, Volume 15 (2003) no. 10, pp. 3079-3089

[7] R. Absi A simple eddy viscosity formulation for turbulent boundary layers near smooth walls, C. R. Mecanique, Volume 337 (2009), pp. 158-165

[8] C. Di Nucci; E. Fiorucci Mean velocity profiles of fully-developed turbulent flows near smooth walls, C. R. Mecanique, Volume 339 (2011), pp. 388-395

[9] R. Absi Analytical solutions for the modeled k-equation, ASME J. Appl. Mech., Volume 75 (2008), p. 044501

[10] E.R. van Driest On turbulent flow near a wall, J. Aeronaut. Sci., Volume 23 (1956), p. 1007

[11] K. Iwamoto; Y. Suzuki; N. Kasagi Reynolds number effect on wall turbulence: toward effective feedback control, Int. J. Heat Fluid Flow, Volume 23 (2002), p. 678

[12] G. Bucci; E. Fiorucci; A. Russo Spena; C. Di Nucci Analysis of turbulent flow speed profiles in pressure pipes using the dissimilar similitude technique applied to an electrolytic tank: implementation and experimental characterization, IEEE Trans. Instrum. Meas., Volume 57 (2008) no. 8, pp. 1547-1553

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Mean velocity profiles of fully-developed turbulent flows near smooth walls

C. Di Nucci; E. Fiorucci

C. R. Méca (2011)

Mean velocity profiles of two-dimensional fully developed turbulent flows

Carmine Di Nucci; Aniello Russo Spena

C. R. Méca (2012)

A simple eddy viscosity formulation for turbulent boundary layers near smooth walls

Rafik Absi

C. R. Méca (2009)