Course detail

CFD Modelling I

FSI-K10Acad. year: 2010/2011

This course provides an introduction to numerical methods of analysing fluid flows (CFD – Computational Fluid Dynamics). It is the first part of a two-semester course on modelling using CFD methods. Students will be acquainted with theoretical basics of fluid dynamics (derivation and classification of the governing equations), with methods for transformation of these equations to numerical methods used in computer simulations (i.e. discretisation methods of partial differential equations), with modelling of turbulent flows and other selected physical phenomena, as well as with algorithms for numerical simulations.
Users of commercial CFD systems need to have good apprehension of how these programs work, in order to use them effectively. Understanding the basic governing equations and numerical methods of their solution is an important prerequisite of such effective usage. After completion of this course, students should have that knowledge.

Language of instruction

Czech

Number of ECTS credits

3

Mode of study

Not applicable.

Guarantor

doc. Ing. Jiří Hájek, Ph.D.

Department

Institute of Process Engineering (ÚPI)

Learning outcomes of the course unit

Students will understand the basics of mathematical description of fluid flow and the fundamentals of modelling of selected physical phenomena related to fluid flow. They will be capable of performing derivation of discretised equations and they will have an overview of numerical solution of the equations of fluid dynamics, used in commercial CFD codes.

Prerequisites

Participants are only required to be familiar with the content of general courses of Mathematics I to IV from the first and second year of their study at the Faculty of Mechanical Engineering.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

The course is optional and no marks are given. Participation in the course will be confirmed by granting a course-unit credit.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The course objective is to make students familiar with the basics of fluid dynamics, the principles of numerical solution of the governing equations of fluid dynamics and to provide a theoretical training required before entering the second part of the course (CFD modelling II).

Specification of controlled education, way of implementation and compensation for absences

Course-unit credits will be granted to students who have regularly participated at the lessons (regular participation means presence in at least two thirds of the lectures, i.e. 9 out of total 13).

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Anderson J.D. Computational Fluid Dynamics: The Basics with Applications. McGraw Hill, 1995
Patankar S.V. Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corporation, 1980
Versteeg, H.K., and Malalasekera, W. An introduction to computational fluid dynamics: The finite volume method. Longman Group Ltd., 1995

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme N2301-2 Master's

    branch M-PRI , 1 year of study, summer semester, compulsory-optional
    branch M-PRI , 1 year of study, summer semester, compulsory-optional

Type of course unit

 

Computer-assisted exercise

39 hod., compulsory

Teacher / Lecturer

doc. Ing. Jiří Hájek, Ph.D.

Syllabus

1st week: Introduction and motivation for study of the subject; 4 models for derivation of governing equations; substantial derivative
2nd week: Physical meaning of divergence of velocity vector; derivation of continuity equation – models A-C
3rd week: Derivation of continuity equation – model D; integral and differential forms of the governing equations; derivation of Navier-Stokes momentum equation
4th week: Derivation of energy equation in non-conservative form; energy equation for internal energy of the fluid
5th week: Energy equation for incompressible fluids; conservative form; closed system of the equations of fluid dynamics; generalised transport equation
6th week: Mathematical properties of partial differential equations (PDE) and their impact on CFD
7th week: Physical behaviour of different kinds of PDE; boundary and initial conditions
8th week: Turbulence and its modelling – what is turbulence, impact on flow equations, classification of turbulence models
9th week: Most popular turbulence models; turbulence near walls; introduction to finite volume method (FVM)
10th week: FVM for diffusion problems; application of FVM – example with 1D heat conduction with generalisation to 2D and 3D; central differencing
11th week: FVM for mixed convection-diffusion problems; example with 1D convection and diffusion and central differencing
12th week: Properties of discretisation schemes; upwind differencing, hybrid scheme, power-law scheme, quick scheme, higher order schemes
13th week: Solution algorithms for pressure-velocity coupling in steady flows; staggered grid; algorithms SIMPLE, PISO; unsteady problems