Turbulence and CFD Models

Lecture notes

In this page you will find the lecture notes, supporting material, references, and recorded sessions.

Course presentation

Course presentation - Preliminaries - Housekeeping issues.

Course material:

Course syllabus

Syllabus

Lecture notes

Continuous world and numerical world

Some examples

Presentation of DNS simulation of a periodic channel

Video lectures

Lecture 1 - You need UNIGE credentials

Lecture 1

Transition to turbulence in shear flows.

Course material:

Lecture notes

Transition to turbulence in shear flows

Video lectures

Lecture 1 - You need UNIGE credentials

Lecture 2 - You need UNIGE credentials

Lecture 3 - You need UNIGE credentials

Lecture 4 - You need UNIGE credentials

Support material

Additional support material is available at the Teams channel.

Lecture 2

CFD and turbulence modeling. Introduction to turbulence. Turbulence, does it matter? The nature of turbulence. Wall bounded flows and free shear flows.

Course material:

Lecture notes

The turbulent world around us. Turbulence, does it matter? Introduction to turbulence modeling. Wall bounded flows and shear flows

Video lectures

Lecture - You need UNIGE credentials

Lecture 3

Length scales in turbulent flows. From Kolmogorov scales to Taylor microscales, to integral scales. Energy cascade. Law of the wall. Near wall treatment.

Course material:

Lecture notes

Turbulence modeling and scales of turbulence. From Kolmogorov scales to Taylor microscales, to integral scales. Energy spectrum and energy cascade. Integral length scale and grid length scale. Turbulence near the wall - Law of the wall. A glimpse to a turbulence model

Video lectures

Lecture - You need UNIGE credentials

Python notebooks

Notebook 1 - Plotting the law of the wall

Data to be used with Notebook 1

Lecture 4

Practical turbulence estimates.

Course material:

Lecture notes

Practical turbulence estimates

Video lectures

Lecture - You need UNIGE credentials

Python notebooks

Notebook 1 - Compute turbulence estimates

Notebook 2 - Compute turbulence estimates of a demo case using Fluent reference values

Notebook 3 - Can the Kolmogorov eddies become smaller that the viscous sublayer length?

Lecture 5

Governing equations. Reynolds averaging. The Boussinesq hypothesis. The gradient diffusion hypothesis. Reynolds-averaged Navier-Stokes equations (RANS).

Course material:

Lecture notes

Part 1. Governing equations of fluid dynamics.

Part 2. RANS equations – Reynolds averaging.

Part 3. The Boussinesq hypothesis. The gradient diffusion hypothesis.

Part 4. Sample turbulence models.

Part 5. Quick review of solution methods for the governing equations of fluid dynamics.

Part 6. What is Ansys Fluent? – Executive summary.

Appendix 1. Navier-Stokes equations from the general transport equation.

Video lectures

Lecture 1 - Parts 1, 2, 3, 4 - You need UNIGE credentials

Lecture 2 - Parts 5, 6 - You need UNIGE credentials

Lecture 6

Closure problem. Algebraic models. One equation models. Two equation models. Reynolds stress models (RSM). Unsteady RANS simulations (URANS). Wall modeling and wall resolving simulations.

Course material:

Lecture notes

Part 1. The closure problem. Exact and solvable equations. Derivation of the Reynolds stress transport equation and turbulent kinetic energy equation. Another touch to the closure problem.

Part 2-1. Revisiting the Reynolds stress transport equation and the turbulent kinetic energy equation. Revisiting the closure problem.

Part 2-2. Two equations models - The k-epsilon model and the k-omega model. One equation models - The Spalart-Allmaras model.

Part 3-1. The Reynolds stress model. Budgets of turbulence kinetic energy, dissipation rate, and Reynolds stress.

Part 3-2. Transition models - Review of the Gamma-Re-Theta and intermittency models.

Part 4. Near wall treatment.

Part 5. RANS models deficiencies, palliatives, and corrections.

Part 6. On the closure coefficients. Galilean invariance. URANS and RANS.

Part 7. Review of some additional turbulence models. Algebraic models - The mixture length model. The K-Omega SST model. Wall resolving K-Epsilon model

Appendix 1. Incomplete list of turbulence models and references.

Video lectures

Midterm 1 - Q&A - You need UNIGE credentials

Lecture 1 - Part 1 - You need UNIGE credentials

Lecture 2 - Parts 2-1, 2-2 3-1 - You need UNIGE credentials

Lecture 3 - Part 4-1 - You need UNIGE credentials

Lecture 4 - Parts 3-2, 5-1 - You need UNIGE credentials

Lecture 5 - Parts 6-1, 7-1 - You need UNIGE credentials

Python notebooks

Notebook 1 - Plot of profiles of the mean turbulent quantities - Plot of turbulent budgets

Data to be used with Notebook 1

Lecture 7

Recap of Reynolds decomposition and time averaging. Statistical description of turbulence. Descriptive statistics. Joint statistics. One-point correlation. Two-point correlations. Time series. Turbulent kinetic energy spectrum. Power spectrum.

Course material:

Lecture notes

Recap of Reynolds decomposition and time averaging. Data analysis and statistical tools used turbulence modeling.

Video lectures

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Lecture 8

Post-processing turbulent simulations. Quantitative and qualitative post-processing. Dealing with steady and unsteady simulations.

Course material:

Lecture notes

Post-processing and analysis of turbulent simulations.

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Lecture 9

Beyond the Boussinesq hypothesis, compressibility effects and multiphase flows. Effect of roughness on the law of the wall.

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Lecture notes

Additional topics. Favre averaging. RANS models corrections. Wall functions for heat transfer. Wall functions – Additional observations. Surface roughness. Non-linear eddy viscosity models.

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Lecture 10

Scale-resolving simulations (SRS). DES, LES, DNS. Wall modeling and wall resolving simulations in SRS.

Course material:

Lecture notes

Part 1. SRS simulations. LES theoretical background and general remarks. Filtered Navier-Stokes equations.

Part 2. Subgrid-scale models for LES. DES models. A few mesh resolution guidelines and rough estimates for LES/DES simulations. Final remarks on LES/DES turbulence models.

Appendix 1. LES equations - Extended derivation.

Video lectures

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References

A. Leonard. "Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows". Advances in Geophysics, Vol. 18, Part A, pp. 237-248, 1975.

M. Germano. "Turbulence: the filtering approach". J. Fluid Mech., Vol. 238, pp. 325-336, 1992.

J. Smagorinsky. "General circulation experiments with the primitive equations: I. The basic experiment". Monthly Weather Review, 91(3), pp. 99-164, 1963.

J. Deardoff. "A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers". J. Fluid Mech., Vol. 41, pp. 453-480, 1970.

R. Clark, J. Ferziger, W. Reynolds. "Evaluation of subgrid-scale models using an accurately simulated turbulent flow". J. Fluid Mech., 91(1), pp. 1-16, 1979.

F. Nicoud, F. Ducros . "Subgrid-scale stress modelling based on the square of the velocity gradient tensor". Flow, Turbulence and Combustion, 62 (3), pp.183-200, 1999.

D. K. Lilly. "A proposed modification of the Germano subgrid‐scale closure method". Physics of Fluids A: Fluid Dynamics 4, 633, 1992.

M. Germano, U. Piomelli, P. Moin, W. Cabot . "A dynamic subgrid‐scale eddy viscosity model". Physics of Fluids A: Fluid Dynamics 3, 1760, 1991.

S. Pope "Ten questions concerning the large-eddy simulation of turbulent flows". New Journal of Physics 6, 35, 2004.

Lecture 11

Best practices in CFD and turbulence modeling. Numerical considerations. Validation and verification. Mesh dependency studies. Accuracy and reliability of turbulent simulations.

Course material:

Video lectures

Support material

email: joel.guerrero@unige.it