2023-2024 / AERO0004-1

Turbulent Flows


26h Th, 26h Pr, 40h Proj.

Nombre de crédits

 Master : ingénieur civil en aérospatiale, à finalité spécialisée en "turbomachinery aeromechanics (THRUST)"5 crédits 
 Master : ingénieur civil en aérospatiale, à finalité5 crédits 
 Master : ingénieur civil physicien, à finalité5 crédits 


Vincent Terrapon

Langue(s) de l'unité d'enseignement

Langue anglaise

Organisation et évaluation

Enseignement au premier quadrimestre, examen en janvier


Horaire en ligne

Unités d'enseignement prérequises et corequises

Les unités prérequises ou corequises sont présentées au sein de chaque programme

Contenus de l'unité d'enseignement

In contrast to laminar flows, turbulence is characterized by chaotic, random and swirling fluid motions. Such a complex flow is typically observed when inertial forces are much larger than viscous forces, which can be measured by the dimensionless Reynolds number. As the vast majority of flows observed in nature or present in engineering applications are characterized by a large Reynolds number, laminar flows are more the exception than the rule. 

Because of the prevalence and complexity of such flows, turbulence represents one of the major challenges in science and engineering. 

This course is an introduction into turbulence in incompressible flows. Its objective is to present the main characteristics of turbulent flows and how they differentiate themselves from laminar flows, to describe the different methods of analysis used to treat turbulent flows, and to introduce numerical approaches and models that are frequently used in practice.

The course is divided into two parts. The first part explains the main features and properties of turbulent flows through dimensional analysis, physical intuition and statistical methods. In particular, following topics are covered:

  • Difference between molecular and turbulent diffusion (mixing length, gradient-diffusion assumption, eddy viscosity)
  • Statistical representation of turbulence (Reynolds-averaged equations; probability theory, mean, variance and correlations; Reynolds-stress and closure problem)
  • Scales in turbulent flows and their relation to the physics (energy cascade; Kolmogorov scaling)
  • Dynamics of turbulence (kinetic energy; vorticity)
  • Applications to canonical flows (free-shear flows; wall-bounded flows)
  • Spectral analysis of turbulence
  • Coherent structures in wall turbulence

The second part of the course will focus on models and numerical approaches that are used in practice to simulate turbulent flows:

  • DNS - Direct numerical simulations
  • RANS - Reynolds-Averaged Navier-Stokes simulations (algebraic models, two-equation models, Reynolds-stress models)
  • LES - Large-eddy simulations (filtering, eddy viscosity)
  • DES - Detached-eddy simulations
The second part will heavily rely on properties and tools derived in the first part.

Acquis d'apprentissage (objectifs d'apprentissage) de l'unité d'enseignement

At the end of the course, the students should be able to:

  • Know the major properties of turbulent flows, their physical origins and their consequences
  • Identify the relevant scales in specific configurations using dimensional analysis
  • Use statistical tools to derive average equations, and to characterize and quantify turbulent flows
  • Understand the role of the nonlinear terms in stability, energy transfer between scales and closure problem
  • Understand the specificities of free shear flows and wall-bounded flows
  • Use wall units and inner scaling
  • Describe the major structures observed in wall-bounded flows and explain their dynamics
  • Derive the energy cascade, Kolmogorov scaling and the logarithmic law
  • Understand the major differences between DNS, LES and RANS, and apply these numerical approaches to concrete situations
  • Understand the hypotheses, assumptions and simplifications in RANS models
  • Know the differences between different RANS models, and their strengths and shortcomings
  • Read and understand the classical literature on turbulence and more complex turbulence models
This course contributes to the learning outcomes I.1, I.2, II.1, II.2, II.3, III.1, III.2, IV.1, IV.3, VI.1, VI.2, VII.2, VII.3, VII.4, VII.5 of the MSc in aerospace engineering.

Savoirs et compétences prérequis

To efficiently follow this course, it is preferable to have some basic knowledge in fluid mechanics (viscous flows, dimensional analysis, ...), in statistical theory (probability, correlation, ...), and in basic mathematics (Fourier transform, tensor algebra, ...). Additionally, familiarity with a CFD solver (e.g., OpenFOAM, Fluent, CFX, Star-CCM) and some CFD background are useful for the final project.

Activités d'apprentissage prévues et méthodes d'enseignement

The course is divided into ~10 lectures that take place each Friday morning. Each lecture lasts about 2 1/2 hours and covers the different theoretical topics mentionned above. 

Learning activities also include five homework (during the first five weeks of the quadrimester) to be solved individually at home and to be uploaded on gradescope. These homework are evaluated and count towards the final grade. Their objective is to ensure a continuous learning of the subject, to consolidate the material seen in class, to allow a self-evaluation for the students, and to help the instructors in identifying the difficulties encounted by the students. 

Finally, a small project at the end of the course gives the students the opportunity to apply different RANS models in real CFD simulations. The project thus requires to use OpenFOAM, SU2 or another similar CFD solver. It is evaluated based on a written report and an oral presentation.

A detailed calendar of the course and important deadlines will be presented during the first lecture et distributed electronically to all registered students.

Mode d'enseignement (présentiel, à distance, hybride)

Cours donné exclusivement en présentiel

Explications complémentaires:

The course is given in class face-to-face. 
Exercises and project are done individually and independently by the students. The solutions of the problem sets must be uploaded by the deadline on gradescope.

Lectures recommandées ou obligatoires et notes de cours

The course material (lecture slides, problem sets, ...) are posted each week on the course website: www.mtfc.uliege.be/Turbulence .

Additionally, students are highly encouraged to acquire one of the following two textbooks:

  • "Statistical Theory and Modeling for Turbulent Flows", P.A. Durbin and B.A. Pettersson Reif, 2nd edition

  • "Turbulence: An introduction for scientists and engineers", P.A. Davidson, Oxford University Press, 2nd edition

Other useful reading material and reference manuals include:

  • "Turbulent Flows", S.B. Pope
  • "A First Course in Turbulence", H. Tennekes and J.L. Lumley
  • "Turbulence Modeling for CFD", D.C. Wilcox
  • "Statistical Fluid Mechanics - Mechanics of Turbulence", A.S. Monin and A.M. Yaglom
A copy of the different books can be consulted at the library.

Modalités d'évaluation et critères

Travail à rendre - rapport

Evaluation continue

Explications complémentaires:

The final grade for the course is based on

  • Homework exercises: 30%
  • Project (written report and oral presentation): 70%
A detailed personal feedback on the project report and oral presentation is also provided to all students.


Remarques organisationnelles et modifications principales apportées au cours

The course is taught in English. 

Lectures take place each Friday morning. Organizational aspects and important deadlines are communicated during the first lecture.

There is no major change with respect to previous year.


Students are encouraged to actively interact with the instructor, also outside of the lectures. It is recommended to set up an appointment first. 
Students are expected to follow a few basic rules when communicating by email: 

  • Indicate as subject "AERO0004: ...".
  • Only use ULg addresses (xxx@student.uliege.be).
  • Follow the elementary rules of politeness.
Prof. Vincent E. TERRAPON; MTFC Research Group; B52, 0/415; +32(0)4 366 9268; vincent.terrapon@uliege.be; https://www.mtfc.uliege.be

Association d'un ou plusieurs MOOCs