Turbulence Models In Cfd

lsUniversity of Ljubljana
Faculty for mathematics and physics
Department of physics

Turbulence models in CFD
Jurij SODJA
Mentor: prof. Rudolf PODGORNIK

March 2007

INDEX
1

INTRODUCTION .................................................................................................3

2

GENERALREMARKS.........................................................................................3
2.1
2.2

Complexity of the turbulence model..............................................................4

2.3
3

Ideal turbulence model...................................................................................3

Classification of turbulent models .................................................................4

REYNOLDS-AVERAGED NAVIER-STOKESMODELS.................................6
3.1

Reynolds’s decomposition .............................................................................6

3.1.1

Equations describing instantaneous fluid motion ..................................6

3.1.2

Reynolds averaging................................................................................7

3.2

The closure problem......................................................................................9

3.2.1
3.3
4

Laminar flow, infinitesimal fluctuations and superposition ..................9

Reynolds stress models ................................................................................10

COMPUTATION OF FLUCTUATING QUANTITIES.....................................12
4.1

Direct numericalsimulation.........................................................................12

4.2

Large-Eddy simulation.................................................................................13

5

RANS versus LES................................................................................................14

6CONCLUSION....................................................................................................17

7

REFERENCES ....................................................................................................18

2

1

INTRODUCTION

The abbreviation CFD stands for computational fluid dynamics. It represents a vast
area of numerical analysis in the field of fluid’s flow phenomena. Headway in the
field of CFD simulations is strongly dependent on thedevelopment of computerrelated technologies and on the advancement of our understanding and solving
ordinary and partial differential equations (ODE and PDE). However CFD is much
more than “just” computer and numerical science. Since direct numerical solving of
complex flows in real-like conditions requires an overwhelming amount of
computational power success in solving such problems is very muchdependent on the
physical models applied. These can only be derived by having a comprehensive
understanding of physical phenomena that are dominant in certain conditions.[1], [8]
Why turbulence?
Whenever turbulence is present in a certain flow it appears to be the dominant over all
other flow phenomena. That is why successful modeling of turbulence greatly
increases the quality of numericalsimulations.
All analytical and semi-analytical solutions to simple flow cases were already known
by the end of 1940s. On the other hand there are still many open questions on
modeling turbulence and properties of turbulence it-self. No universal turbulence
model exists yet.
Further more the price tag for our ignorance is immense. That makes the area of CFD
modeling also extremelyeconomically attractive.

2

GENERAL REMARKS

2.1 Ideal turbulence model
Solving CFD problem usually consists of four main components: geometry and grid
generation, setting-up a physical model, solving it and post-processing the computed
data. The way geometry and grid are generated, the set problem is computed and the
way acquired data is presented is very well known. Precise theory is...