TURBULENCE  THEORY AND MODELLING MVK140

Higher education credits: 7,5. Grading scale: TH. Level: A (Second level). Language of instruction: The course will be given in English on demand. Optional for: F4, F4fs, M4, M4fs, Pi4. Course coordinator: Docent Johan Revstedt, Johan.Revstedt@vok.lth.se, Energivetenskaper. Prerequisites: MMV021/MMV211 Fluid Mechanics. Recommended prerequisits: FMA062 Applied Mathematics. Assessment: Examination is individual as well as based on group work. The compulsory home works and laboratory exercises are reported in writing, group-wise. The project assignment is reported both in writing and orally at a seminar, where all group members shall participate actively. The course ends with an individual oral exam. To pass it is required that all compulsory parts, i.e. home works laboratory exercises, project assignment and oral exam are approved. The grade is based on the oral exam. Further information: The course is based on lectures, exercises, laboratory exercises and group work in the form of home work and a smaller project assignment. The course will be given in English on demand. Home page: http://www.vok.lth.se.

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 Kolmogorovs 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 Kolmogorovs 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