Turbulence and wind energy

Credits : 2 ECTS

Duration : 21 hours

Semester : S9

Persons in charge:

Emmanuel Plaut, professor


Michaël Hölling, associate researcher at ForWind, universität Oldenburg (with Erasmus+ support)


Keywords: deterministic models, stochastic models

Prerequisites: fluid dynamics elementary course

Objective: learn advanced turbulence modeling, with a focus on 1/ CFD 2/ Wind energy systems, that always operate under turbulent conditions.

Program and contents:

  1. Reynolds Averaged Navier-Stokes (RANS) approach and models

    We study turbulence modelling for computational fluid dynamics (CFD) by focusing on the RANS approach and models. The RANS approach is indeed closely linked to the statistical theory of turbulence, which is quite relevant. The RANS approach is basically interesting to characterize and gain some understanding on turbulence phenomena. Finally, RANS models are still, today, the preferred choice for engineering studies. After a brief discussion of Reynolds stress equations and  models, the focus is on eddy-viscosity 2-equations models, namely, the kε and k –  ω models.

    Using a problem-based learning approach, studies of the Direct Numerical Simulations (DNS) database of Lee & Moser (2015) will be performed with Matlab.

  2. Stochastic models, especially, in the context of wind energy

    This second part of the module is focused on the wind energy sciences. Knowing that the wind in the atmospheric boundary layer is always turbulent, the small scale statistics of turbulent flows is reviewed, with a focus on the intermittency phenomena and extreme events like `wind gusts'. The principles of wind energy conversion and the aerodynamics of wind turbines are also presented. The International Electrotechnical Commission (IEC) standards to evaluate power curves and annual energy production of a given wind turbine is introduced. The limitations of this approach are discussed and more accurate stochastic approaches are introduced, which lead for instance to the notion of `Langevin power curves'.

    The students will use the statistical computing software R to study various `turbulence experimental databases'.

Please check the web page of this module on http://emmanuelplaut.perso.univ-lorraine.fr/twe : it sketches the planning of this module, gives instructions and files, etc...



Description and operational vocabulary


Hybrid RANS - LES methods. Be aware of current research in the domain of CFD of turbulent flows


The RANS approach - the LES approach - Strengths and weaknesses of each approach

The notion of intermittency and extreme events


The RANS approach - the LES approach


The RANS approach - the LES approach

Analyze a velocity time series: be able to extract mean and standard deviation values, a PDF of the velocity and of the velocity increments, etc...

Analyze a wind time series: construct the IEC power curve



Choose a good approach - model to solve numerically a given turbulent flow problem


  • Written test
  • Continuous assessment
  • Oral presentation
  • Project
  • Written report