Comptes Rendus
Direct numerical simulation of transition to turbulence in an oscillatory channel flow
Comptes Rendus. Mécanique, Volume 331 (2003) no. 1, pp. 55-60.

In this Note, we present results of the numerical simulation of transition to turbulence for a purely oscillatory channel flow. These simulations were performed for various values of the Reynolds number, the so-called Stokes parameter being equal to 4. The methodology used for the flow simulation relies on a combination of finite element space approximations with time-discretization by operator splitting; it has shown to be very effective, even when it is applied to relatively complex domains with strong expansions at the inlet and outlet of the channel. The numerical results obtained agree qualitatively well with previous experiments by other investigators.

Dans cette Note, on présente les résultats de la simulation numérique de la transition vers la turbulence d'un écoulement oscillant dans une conduite bi-dimensionnelle. Ces simulations ont été effectuées pour diverses valeurs du nombre de Reynolds, la valeur du paramètre de Stokes restant fixée à 4. La méthodologie utilisée pour ces calculs combine approximation en espace par éléments finis et discrétisation en temps par décomposition d'opérateurs ; au vu des résultats obtenus, elle semble très efficace, en particulier pour le cas où la conduite présente de forts expansions, en entrée et en sortie. Les résultats numériques obtenus sont qualitativement en bon accord avec ceux d'autres auteurs.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-0721(03)00023-8
Keywords: Computational fluid mechanics, Turbulence transition, Oscillatory channel flow
Mot clés : Mécanique des fluides numérique, Transition à la turbulence, Écoulement oscillant

L.Héctor Juárez 1; Eduardo Ramos 2

1 Departamento de Matemáticas UAM-I, AP55-534, 09340 México D.F., Mexico
2 Centro de Investigación en Energı́a, UNAM, AP34, 62580 Temixco Mor., Mexico
@article{CRMECA_2003__331_1_55_0,
     author = {L.H\'ector Ju\'arez and Eduardo Ramos},
     title = {Direct numerical simulation of transition to turbulence in an oscillatory channel flow},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {55--60},
     publisher = {Elsevier},
     volume = {331},
     number = {1},
     year = {2003},
     doi = {10.1016/S1631-0721(03)00023-8},
     language = {en},
}
TY  - JOUR
AU  - L.Héctor Juárez
AU  - Eduardo Ramos
TI  - Direct numerical simulation of transition to turbulence in an oscillatory channel flow
JO  - Comptes Rendus. Mécanique
PY  - 2003
SP  - 55
EP  - 60
VL  - 331
IS  - 1
PB  - Elsevier
DO  - 10.1016/S1631-0721(03)00023-8
LA  - en
ID  - CRMECA_2003__331_1_55_0
ER  - 
%0 Journal Article
%A L.Héctor Juárez
%A Eduardo Ramos
%T Direct numerical simulation of transition to turbulence in an oscillatory channel flow
%J Comptes Rendus. Mécanique
%D 2003
%P 55-60
%V 331
%N 1
%I Elsevier
%R 10.1016/S1631-0721(03)00023-8
%G en
%F CRMECA_2003__331_1_55_0
L.Héctor Juárez; Eduardo Ramos. Direct numerical simulation of transition to turbulence in an oscillatory channel flow. Comptes Rendus. Mécanique, Volume 331 (2003) no. 1, pp. 55-60. doi : 10.1016/S1631-0721(03)00023-8. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00023-8/

[1] R. Akhavan; R.D. Kamm; A.H. Shapiro An investigation of transition to turbulence in bounded oscillatory Stokes flows. Part 1. Experiments, J. Fluid Mech., Volume 225 (1991), pp. 395-422

[2] M. Hino; M. Sawamoto; S. Takasu Experiments on transition to turbulence in an oscillating pipe flow, J. Fluid Mech., Volume 75 (1976), pp. 193-207

[3] S.I. Sergeev Fluid oscillations in pipes at moderate Reynolds numbers, Fluid Dynamics, Volume 1 (1966), pp. 121-122

[4] P. Hall The linear stability of flat Stokes layers, Proc. Roy. Soc. London Ser. A, Volume 359 (1978), pp. 151-166

[5] C. von Kerczek; S.H. Davis Linear stability theory of oscillatory Stokes layers, J. Fluid Mech., Volume 62 (1974), pp. 753-773

[6] R. Akhavan; R.D. Kamm; A.H. Shapiro An investigation of transition to turbulence in bounded oscillatory Stokes flows. Part 2. Numerical simulations, J. Fluid Mech., Volume 225 (1991), pp. 423-444

[7] G.I. Marchuk Splitting and alternating direction methods (P.G. Ciarlet; J.-L. Lions, eds.), Handbook of Numerical Analysis, 1, North-Holland, Amsterdam, 1990, pp. 197-462

[8] R. Glowinski; P. Le Tallec Augmented Lagrangians and Operator Splitting Methods in Nonlinear Mechanics, SIAM, Philadelphia, PA, 1989

[9] E.J. Dean; R. Glowinski A wave equation approach to the numerical simulation of the Navier–Stokes equations for incompressible viscous flows, C. R. Acad. Sci. Paris Sér. I, Volume 325 (1997), pp. 789-791

[10] E.J. Dean; R. Glowinski; T.W. Pan A wave equation approach to the numerical simulation of incompressible viscous flow modeled by the Navier–Stokes equations (J.A. De Santo, ed.), Mathematical and Numerical Aspects of Wave Propagation, SIAM, Philadelphia, PA, 1998, pp. 65-74

[11] S. Pissanetzky Sparse Matrix Technology, Academic Press, 1984

Cited by Sources:

Comments - Policy