(Created 2010-07-25.)

TURBULENCE THEORY AND MODELLING | MVK140 |

**Aim**

The aim of this course is to provide basic theoretical knowledge on turbulence as well as the design of turbulence models and their applicability. Furthermore, the intention is to provide skills in the analysis of turbulent flows. This knowledge should be sufficient to understand the background of turbulence models and the ability to chose an appropriate turbulence model for a given flow case.

*Knowledge and understanding*

For a passing grade the student must

- be able to describe the physical mechanisms of the transition from laminar to turbulent flow for a simple flow case
- be able to explain Kolmogorovs theory, including the basic assumptions and the validity of the theory
- be able to, from a phenomenological perspective, assess if a flow is turbulent
- be able to explain some of the important and basic terms of the subject
- be able to describe the character of the turbulence in different flow situations with respect to the properties and development of the turbulence, and explain how the differences between these flow situations are reflected in the modelling

*Skills and abilities*

For a passing grade the student must

- be able to analyse a flow case and suggest a method for numerical simulation with respect to governing equations, possible simplifications and choice of turbulence model, and also to compare with alternative methods.
- be able to scrutinise and from given criteria estimate the credibility of results from turbulent flow simulations

*Judgement and approach*

For a passing grade the student must

- be able to actively participate in discussion of problems relevant for the subject
- be able to present, both orally and in writing, a technical report containing analyses and choice of turbulence model

**Contents**

The course contains the basic theory for turbulent flows, the transition from laminar to turbulent flows and the physical basis for different types of turbulence models. The turbulence theory part contains statistical and phenomenological description of turbulence Kolmogorovs hypotheses, and also wall bounded and free shear flows. Homogeneous and isotropic turbulence is discussed as well as anisotropy in different types of flow. The modelling part contains the most common types of turbulence models, i.e the ones based on the Reynolds averaged equations and Large Eddy Simulation. The physical background and effects of different models are discussed. The mathematical description is also treated, averaging of the governing equations, and derivation of the extra equations needed.

**Literature**

Pope, S.B., Turbulent Flows. Cambridge Univ. Press 2003. ISBN: 0-521-59886-9