Czech

3

doc. Ing. Jiří Hájek, Ph.D.

Institute of Process Engineering

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 methods of the equations of fluid dynamics, used in commercial CFD codes.

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.

The course is taught through exercises which are focused on practical topics presented in lectures.

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

Participants may choose to finish the course either with a written test or with a technical report about their solution of a chosen computational problem using free student version of commercial software. The report must contain a description of the solved problem, summary of used methods and solution approach including boundary conditions, overview and analysis of results in graphical and alphanumerical form..

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).

Condition for obtaining course-unit credits is a regular participation at the lectures. (This means presence in at least two thirds of the lectures, i.e. 9 out of total 13).

Students have at their disposal a fully functional student version of commercial software, which opens up a possibility to acquire practical skills. These include mainly work with geometric model, creation of computational meshes and experience with user interface. Last but not least they will also improve their English.

Programme M2I-P: Mechanical Engineering, Master's
branch M-PRI: Process Engineering, compulsory-optional

39 hours, compulsory

doc. Ing. Jiří Hájek, Ph.D.

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