FlerfasstrÃ¶mning - teori, modellering och numeriska metoder

**Valid from:** Autumn 2021**Decided by:** Anders Gustafsson / FUN**Date of establishment:** 2021-02-23

**Division:** Energy Sciences**Course type:** Course given jointly for second and third cycle**The course is also given at second-cycle level with course code:** MVKP20**Teaching language:** English

The aim of this course is to provide an introduction to multiphase flows concerning basic theoretical knowledge and the design of multiphase models and their applicability. Also, to provide knowledge on the numerical methods used for simulating flows with more than one phase. Furthermore, the intention is to provide skills in the analysis of multiphase flows. This knowledge should be sufficient to understand the background of multiphase models and the ability to choose an appropriate model for a given flow case.

*Knowledge and Understanding*

For a passing grade the doctoral student must

- be able to describe different types of multiphase flow from a physical perspective
- be able to describe interaction mechanisms between the phases
- be able to explain some of the important and basic terms of the subject
- be able to describe how the character of the multiphase flow is reflected in the modelling and in the choice of numerical method

*Competences and Skills*

For a passing grade the doctoral 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 multiphase model, and also to compare with alternative methods.
- be able to scrutinise and from given criteria estimate the credibility of results from multiphase flow simulations.

*Judgement and Approach*

For a passing grade the doctoral 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 of a multiphase flow situation, concerning choice of models and numerical methods, as well as simulation results

The course contains the basic theory for multiphase flows, how such flows may be classified and how that in turn is reflected in the modelling. The theoretical part contains description of the various kinds of multiphase flows occurring in industrial applications, such as sprays, particle clouds, free surface flows etc. Forces on and interaction among particles, bubbles and droplets are discussed as well as the influence of surface tension and virtual mass. The modelling part contains the most common types of multiphase flow models, including models for dispersed flow (e.g. Lagrangian particle tracking, and discrete element modelling) as well as Eulerian continuum models and interface models. The physical background, applicability and effects of the different models are discussed. The mathematical description is also treated, averaging of the governing equations, and derivation of the extra equations needed. The numerical methods are discussed with emphasis on what is needed beyond the methods for single phase flows. Computer laboratory exercises and project work will be performed in commercial or open CFD software.

- Tu, J., Yeoh & G.H.: Computational techniques for multiphase flows. 2019. ISBN 9780081024539.
- Yadigaroglu & Hewitt, G.: Introduction to multiphase flow basic concepts - Applications and modelling. 2018. ISBN 9783319587172.

**Types of instruction:** Lectures, exercises, project

**Examination formats:** Written exam, written assignments, seminars given by participants**Grading scale:** Failed, pass**Examiner:**

**Admission requirements:** FMA435 Calculus in Several Variables OR FMA430 Calculus in Several Variables OR FMAB35 Calculus in Several Variables OR FMAB30 Calculus in Several Variables.
FMA420 Linear Algebra OR FMAB20 Linear Algebra.
MMVF10 Fluid Mechanics OR VVRN35 Hydromechanics OR VVRF10 Fluid Mechanics OR KETF01 Transport Phenomena, Basic Course OR MMVF01 Thermodynamics and Fluid Mechanics OR MMVF15 Fluid Mechanics.

**Course coordinator:** Christer Fureby `<christer.fureby@energy.lth.se>`**Web page:** www.energy.lth.se