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Syllabus for

Academic year
MTF270 - Turbulence modeling  
Syllabus adopted 2019-02-21 by Head of Programme (or corresponding)
Owner: MPAME
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: Second-cycle
Major subject: Mechanical Engineering

Teaching language: English
Application code: 03119
Open for exchange students: Yes
Block schedule: C

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0102 Examination 7,5 c Grading: TH   7,5 c   02 Jun 2020 am J,  11 Oct 2019 pm M   18 Aug 2020 am J

In programs

MPAME APPLIED MECHANICS, MSC PROGR, Year 1 (compulsory elective)


Lars Davidson

  Go to Course Homepage


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

MTF072 Computational fluid dynamics (CFD) or Mechanics of Fluids or any
corresponding course


The object of the course is to give the students a thorough knowledge and understanding of modern,
advanced turbulence models for unsteady fluid flow simulations.

Learning outcomes (after completion of the course the student should be able to)

  • Describe different RANS turbulence models such as Reyonlds stess models, algebraic Reynolds stress models, k-els, k-omega, V2F, k-omega SST
  • Understand and outline the difference between LES, RANS, URANS, DES and hybrid LES-RANS
  • Derive the exact transport turbulence equations using tensor notation
  • Describe the modeling assumptions, using tensor notation, in turbulence models
  • Identify and interpret the different terms in the turbulence models presented in the course.
  • Describe the difference between resolved and modeled Reynolds stresses
  • Describe different approaches to handle the near-wall problem in LES
  • Describe the advantages of second-moment closures compared to eddy-viscosity models
  • Derive the V2F model
  • Reproduce the different spatial filtering approaches in LES
  • Derive the SGS models using tensor notation
  • Understand and describe the concept of modeled (for example SGS) dissipation between resolved and modeled scales
  • Describe the method how to prescribe unsteady, fluctuating inlet boundary conditions
  • Be able to carry out an simulation with a commercial CFD code


The development of computers and Computational Fluid Dynamics  (CFD)
has made the numerical simulation of complex fluid flow, combustion,
aero-acoustics and heat transfer problems possible. Turbulent flow in
three-dimensional, complex geometries -- unsteady or steady -- can be
dealt with. Presently CFD methods can replace, or complement, many
experimental methods; we can use a numerical wind tunnel instead of an
experimental one. 

Today, most CFD simulations are carried out with traditional RANS
(Reynolds-Averaged Navier-Stokes). In RANS, we split the flow variables
into one time-averaged (mean) part and one turbulent part. The latter is
modelled with a turbulence model such as k-eps or Reynolds Stress
Model. For many flows it is not appropriate to use RANS, since the
turbulent part can be very large and of the same order as the mean.
Examples are unsteady flow in general, wake flows or flows with large
separation. For this type of flows, it is more appropriate to use Large
Eddy Simulation (LES).  In order to extend LES to high Reynolds number
flows new methods have been developed. These are called DES (Detached
Eddy Simulation), URANS (Unsteady RANS) or Hybrid LES-RANS.  They are
all unsteady methods and they are a mixture of LES and RANS. In
aero-acoustics the noise is generated by turbulence. The best way to
accurately predict large-scale turbulence is to carry out an unsteady
simulation of the flow field (i.e. LES, DES, hybrid LES-RANS or URANS).
After that the noise is predicted separately in CAA (Computational

In LES, DES, URANS  and  Hybrid LES-RANS the large-scale part of the
turbulence is solved for by the discretized equations whereas
the small-scale turbulence is modeled. The definition of ''large-scale''
varies in the different methods. Furthermore, the limit between
''large-scale'' and ''small-scale' is often not well defined. Since
turbulence is three-dimensional and unsteady, it means that in all the
methods the simulations must always be carried out as 
three-dimensional, unsteady simulations.

We will address questions like:

  • How should I make my mesh?
  • why should I in LES use a non-dissipative discretization scheme?

  • is it necessary to used central differencing in DES and URANS?
  • what is the different between LES and unsteady RANS?
  •  what turbulence models can I use in DES and unsteady RANS?
  • to enhance numerical stability, can a turbulence model with high dissipation be used?
  • how do I prescribe inlet boundary conditions?
  • inlet boundary conditions: can I use steady inlet boundary conditions? which is best, synthesized turbulence or a pre-cursor DNS?

In the first project, we will learn how to interpretat results from
an unsteady simulation. We will also use a commercial CFD package to
evaluate different RANS turbulence models.

When doing LES-URANS/DES, you have to ask yourself similar questions as when doing measurements:

  • when is the flow fully developed so that I can start time-averaging?
  • for how long time do I need to time-average?
  • is it enough if I get accurate mean flow or do I also need accurate resolved turbulent stresses?
  • how do I estimate the quality of my LES or hybrid LES-RANS? Spectra?   2-point correlations? SGS dissipation?

most important drawback/bottleneck of LES is the requirement to use
very fine grid near walls. The grid must be fine in all directions, not
only the wall-normal direction. Much of the research on LES is today
focused in getting around this bottleneck. One approach is hybrid
LES-RANS. In this method  RANS is used near walls and LES is used in the
remaining part of the domain.

.For more information

.Lecturer's homepage



Two/three lectures per week will be given.

Two projects should be carried out by the students.

The students will be given data from a numerical simulation (LES or
DNS). The data will be two-dimensional, time-averaged velocity
(recirculating flow) and pressure fields, the Reynolds stresses. The
data will be analyzed. First we will study the velocity fields and find
out how large are the forces (per unit volume) due to pressure gradient,
turbulent Reynolds and viscous stresses. The forces ska balance the
acceleration term on the left-hand side.

Next we analyze the transport equations of the turbulent
stresses, u_iu_j. We identifiy regions of large production terms, which
should correspond to regions of large Reynolds stresses. Reynolds
stresses will be computed using the eddy-viscosity assumption, and these
will be compared to their exact counter-parts.

In the second part
of this assignment, the students will use a commercial CFD package to
compute flows using RANS. Different turbulence models will be evaluated.

The students will be given instantaneous three-dimensional data from a
DNS (Direct Numerical Simulation) of channel flow. From these data
various exact terms in the transport equations of turbulent quantities
(turbulent kinetic energy k or shear stress u'v', for example) will be
compared by the corresponding modeled terms. Different filtered
quantities relevant for LES will be computed such a SGS stresses,
dynamic Leonard stresses. Since the instantaneous fields are given in
the database, the students will also be given the opportunity to use FFT
to obtain spectra from two-point correlations, to create PDFs
(probability density function) etc.


The eBook can be downloaded from the course home page

Examination including compulsory elements

Written reports of exercises are one part of the examination. A written exam is the other part of the examination

Page manager Published: Thu 04 Feb 2021.