Conference on Turbulence and Interactions TI2006 May June Porquerolles France

Emmanuel Leriche

Description

Niveau: Supérieur
Conference on Turbulence and Interactions TI2006, May 29 - June 2, 2006, Porquerolles, France DIRECT NUMERICAL SIMULATION IN A LID-DRIVEN CAVITY AT HIGH REYNOLDS NUMBER E. Leriche †,? † Laboratoire d'Ingenierie Numerique, Institut des Sciences de l'Energie, Section de Genie Mecanique, Faculte des Sciences et Techniques de l'Ingenieur, Ecole Polytechnique Federale de Lausanne, Station 9, CH-1015 Switzerland. ?Email: emmanuel.leriche@ep .ch ABSTRACT Direct numerical simulation of the flow in a lid-driven cubical cavity has been carried out at high Reynolds numbers (based on the maximum velocity on the lid), between 1.2 104 and 2.2 104. An efficient Chebyshev spectral method has been implemented for the solution of the incompressible Navier-Stokes equations in a cubical domain. The resolution used up to 5.0 million Chebyshev collocation nodes, which enable the detailed representation of all dynamically significant scales of motion. The mean and root-mean-square velocity statistics are briefly presented. INTRODUCTION Estimates for the attainable turbulent Reynolds number by the method of direct numerical sim- ulation (DNS) have been known for several decades. This estimate is based on the ratio be- tween the largest scales to the nest ones (i.e. Kolmogorov scales), which scales like Re3/4, where Re is the Reynolds number, and to re- solve numerically all the scales, an upper bound in term of degrees of freedom (dof) is then given by Re9/4.

• stokes solvers


• integra- tion time


• time scales


• maximum velocity


• chebyshev


• order extrapolation scheme


• high-order direct


• lid driven cavity


• direct numerical

Sujets

• École polytechnique
• Cambridge University
• Déville
• Time scale
• Pafnouti Tchebychev

Informations

• Publié par: chaeh
• Nombre de lectures: 13
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Conference on Turbulence and Interactions TI2006, May 29  June 2, 2006, Porquerolles, France

DIRECT NUMERICAL SIMULATION IN A LIDDRIVEN CAVITY AT HIGH REYNOLDS NUMBER

†,∗ E. Leriche

† Laboratoired’Inge ´ nierieNume ´ rique,InstitutdesSciencesdel’Energie,SectiondeGe ´ nieM ´ ecanique, Facult ´ edesSciencesetTechniquesdel’Ing ´ enieur,EcolePolytechniqueF ´ ede ´ raledeLausanne,Station9, ∗ CH1015 Switzerland.Email: emmanuel.leriche@ep .ch

ABSTRACT Direct numerical simulation of the flow in a liddriven cubical cavity has been carried out at high Reynolds 4 4 numbers (based on the maximum velocity on the lid), between1.2 10and2.2 10. An efficient Chebyshev spectral method has been implemented for the solution of the incompressible NavierStokes equations in a cubical domain. The resolution used up to 5.0 million Chebyshev collocation nodes, which enable the detailed representation of all dynamically significant scales of motion. The mean and rootmeansquare velocity statistics are briefly presented.

I NTRODUCTION

Estimates for the attainable turbulent Reynolds number by the method of direct numerical sim ulation (DNS) have been known for several decades. This estimate is based on the ratio be tween the largest scales to thenest ones(i.e. 3/4 Kolmogorov scales), which scales likeRe, whereReis the Reynolds number, and to re solve numerically all the scales, an upper bound in term of degrees of freedom (dof) is then given 9/4 byRe. The evolution in computer hardware and algorithmic developments makes it now pos sible to extend the direct numerical simulation to transitional and turbulento ws that are inho mogeneous in all space directions. The present contribution is concerned with the numerical and physical aspects of the direct simulation of incompressibleo wwithin a liddriven cu bical cavity. Theuid isenclosed in a cubical cavity where one wall is moved with a speci ed velocity.The goal is to reach the highest Reynolds number but in a very simple domain,

a cubical cavity and then to study in detail the threedimensional transitional and turbulento w properties within the cavity by means of direct simulation at high Reynolds numbers (based on the maximum velocity on the lid), between 4 4 1.2 10and2.2 10. Thephenomena eno w countered within such systems are many and poorly understood.

T HE GOVERNING EQUATIONS

The uid enclosedin the cavity is assumed to be incompressible, viscous, Newtonian and ho mogeneous. The equation of motion for theuid inside the cavity is given by the NavierStokes equations. The threedimensional domain, de 3 noted by, is the open interval(]−h,+h[)and its closure is written as. The NavierStokes equations are written in vector notation as

∂u + (u∙ r)u=−rp+νu ∂t

(1)