To develop and rationalize principles of physical and mathematical modelling of turbulent flows and to understand the applications and limitations of standard turbulent models.

Student will gain knowledge in turbulence modelling and its application, and also understand the limitations of specific turbulent models in some types of turbulent flows.

Introduction to turbulence modelling and simulations. Direct numerical simulations of homogenous and inhomogenous turbulence. Turbulent viscosity. Turbulence models based on turbulent viscosity (RANS models). Algebraic models. Models based on turbulent kinetic energy. One-equation and two-equation models. Full stress closure. Redistribution tensor. Returning to isotropy models. Anisotropy of turbulent stress tensor. No-nlinear forms of return-to-isotropy model. Rapid distortion theory. Basic LRR-IP model. Advanced models for redistribution tensor. Wall effects. Fluctuating pressure and disipation of turbulent kinetic energy near the wall. Wall functions. Turbulent models based on elliptic relaxation. Algebraic models based on non-linear turbulent viscosity. Large eddy simulation (LES) approach. Filtering. Filtered equations of motions. Basic models in LES: Smagorinsky and dynamic Smagorisky models. Imlicit LES. Wall effects in LES.

Detailed discussion of themes from the lectures, with characteristic examples. Application of OpenFOAM software for calculation of characteristic turbulent flows like turbulent flow in channel and, backward facing step, etc.

Passed exam "Fluid Mechanics-D" and "Turbulent flows"

Computer classroom SimLab.

Total assigned hours: 65

New material: 40
Elaboration and examples (recapitulation): 10

Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 5
Review and grading of the project: 0
Test: 0
Test: 5
Final exam: 5

Activity during lectures: 0
Test/test: 30
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 30
Project: 0
Final exam: 40
Requirement for taking the exam (required number of points): 0

Pope, S.P. : Turbulent Flows, Cambridge University Press, 2013; Durbin P.A., Petterson Reif B.A.: Statistical Theory and Modeling for Turbulent Flows, Wiley, 2011; Wilcox, D.: Turbulence Modeling for CFD, DCW Industries Inc., 2006; Launder, B.E., Sandham N.D. (editors): Closure Strategies for Turbulent and Transitional Flows, Cambridge University Press, 2002