Turbulence Models and Numerical Solution of Turbulent Flow

Course guarantor:

Lecturer:

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Department of Technical Mathematics

Synopsis:

Basic characteristics of turbulent flow; governing equations; turbulent shear flow and thin shear flows; eddy viscosity turbulence models; Reynolds stress turbulence models; algebraic Reynolds stress models; low Reynolds number modifications; modelling transition to turbulence; numerical solution of averaged Navier-Stokes equations; examples of simulations.

Requirements:

Syllabus of lectures:

1. introduction to turbulent flow, mathematical and physical model, different approaches (DNS, LES, RANS)

2. mathematical properties of equations for RANS, LES, DNS. The role of convective and viscous term in turbulence; basic solution methods for incompressible flow.

3. basic governing equations; averaging; constitutive relations.

4. discretization methods from the point of view of turbulent simulations; numerical viscosity and dispersion; convection-diffusion model equation.

5. closures for averaged Navier-Stokes equations; Boussinesq hypothesis; algebraic models.

6. Basics of LES; filtering; algebraic turbulence models; discretization and boundarz conditions; data processing; examples.

7. one- and two-equation eddy viscosity models.

8. LES: continued.

9. low Re modifications; model with transport equation for eddy viscosity.

10. Solution of RANS equations; examples.

11. Reynolds stress turbulence models.

12. RANS simulations: channel flow and other examples.

13. algebraic Reynolds stress models; modelling laminar/turbulent transition

14. RANS simulations: continued

Syllabus of tutorials:

1. introduction to turbulent flow, mathematical and physical model, different approaches (DNS, LES, RANS)

2. mathematical properties of equations for RANS, LES, DNS. The role of convective and viscous term in turbulence; basic solution methods for incompressible flow.

3. basic governing equations; averaging; constitutive relations.

4. discretization methods from the point of view of turbulent simulations; numerical viscosity and dispersion; convection-diffusion model equation.

5. closures for averaged Navier-Stokes equations; Boussinesq hypothesis; algebraic models.

6. Basics of LES; filtering; algebraic turbulence models; discretization and boundarz conditions; data processing; examples.

7. one- and two-equation eddy viscosity models.

8. LES: continued.

9. low Re modifications; model with transport equation for eddy viscosity.

10. Solution of RANS equations; examples.

11. Reynolds stress turbulence models.

12. RANS simulations: channel flow and other examples.

13. algebraic Reynolds stress models; modelling laminar/turbulent transition

14. RANS simulations: continued

Study Objective:

Study materials:

Wilcox D.C.: Turbulence Modeling for CFD, La Canada, DCW Industries, 1993

Ferziger J.H., Peric M.: Computational Methods for Fluid Dynamics, Springer Berlin, 1996

Piquet J.: Turbulent Flows - Models and Physics, Springer Berlin, 1999

Pope S.B.: Turbulent Flows, Cambridge University Press, 2000

Příhoda J., Louda P. Matematické modelování turbulentního proudění, Nakladatelství ČVUT, Praha 2007

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: