C OMSOL M ultiphysics™
V E R S I O N3.3
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COMSOL Multiphysics. Turbulence Modeling Minicourse.
© COPYRIGHT 1994–2006 by COMSOL AB. All rights reserved
Patent pending
The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or reproduced in any form without prior written consent from COMSOL AB.
COMSOL, COMSOL Multiphysics, and COMSOL Script are trademarks of COMSOL AB.
Other product or brand names are trademarks or registered trademarks of their respective holders. Version:September 2006 COMSOL 3.3
C O N T E N T S
2
Introduction
About T urbulence Equations  3
Wall Functions.  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    4
Residence Time in a T urbulent Reactor  5
Introduction  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    5
Key Instructive Elements .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    6
Modeling Strategy  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    6
The Reynolds Number.  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    7
Modeling the Flow Using Incompressible Navier-Stokes  .  .  .  .  .  .  .  .    8
Applying a Simple T urbulence Model  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  12
Parametric Study of the Eddy Viscosity  .  .  .  .  .  .  .  .  .  .  .  .  .  .  13
Stabilization T echniques  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  18
Mesh Convergence Analysis.  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  22
The k-ε T urbulence Model  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  23
Mass Transport of T racer Species: Convection and Diffusion  .  .  .  .  .  .  28
A Shell-and-Tube Heat Exchanger  36
Introduction  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  36
Model Definition .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  38
Results for the Flow/Heat Model.  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  41
Modeling in COMSOL Multiphysics .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  41
References  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  49
C O N T E N T S| i
ii |C O N T E N T S
T u r b u l e n c e M o d e l i n g M i n i c o u r s e
T U R B U L E N C E M O D E L I N G M I N I C O U R S E|1
Introduction
The concept of turbulence does not lend itself to a 1-page explanation. Actually,
scientists have not yet reached an agreement on what exactly turbulence is and the
definition keeps changing as we learn more about the phenomenon. Without being
too specific, turbulence can be said to be the chaotic motion that appears in a flow
when the fluid is moving fast or when an object moves with high speed through the
fluid.
When it comes to simulating turbulence, the problem is that the turbulent motions are
extremely small, often in the range between one micrometer and one millimeter.
Compare this to industrial applications where the domains of interest are typical of
order meters or even bigger, and it is easy to realize that there is no possibility to
resolve the turbulence.
The way to circumvent the severe resolution constraints is with turbulence modeling.
There are several approaches of which the so-called RANS methods are by far the most
common. COMSOL Multiphysics has implemented the standard k-ε model, which
describes the transport of the turbulent kinetic energy, k, and the rate of dissipation of
turbulent kinetic energy, ε.The use of the k-ε turbulence model reduces the resolution
requirements by up to a factor 100 in each space direction.
The flow field in itself is seldom the quantity of interest, but the primary problem is
more often, for example, the transport of some scalar quantity such as chemical species
or heat. This minicourse gives examples of how COMSOL Multiphysics can easily
provide a 2-way coupling between heat transfer and turbulence modeling, as well as
mass transfer and turbulence.
•  A first model describes a baffled water purification reactor in which we investigate
the flow properties from laminar to turbulent flow.
•  A second model shows how to model turbulent heat transfer in a shell-and-tube heat
exchanger.
These are merely clean-cut exercise examples. But your modeling will not end here—
you can couple simultaneous heat, mass, momentum transport, and other physics such
as magnetic and electric fields. You imagination is the only limit!
Enjoy your modeling!
The COMSOL Team
2|TU R B U L E N C E M O D E L I N G M I N I C O U R S E

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