Joel Guerrero's homepage

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. Review of some additional turbulence models. Algebraic models - The mixture length model. The K-Omega SST model. Wall resolving K-Epsilon model. Non-linear eddy viscosity models.

Part 7. On the closure coefficients. Galilean invariance. URANS and RANS.

Appendix 1. More turbulence models.

Appendix 2. Incomplete list of turbulence models and references.

Appendix 3. Budgets discussion.

Appendix 4. Incomplete list of turbulence databases.

Appendix 5. Examples of homogeneous and isotropic turbulence.

Appendix 6. Summary chart of incompressible flow turbulence models.

Video lectures

All the recorded lectures are available at the Teams channel - 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

References

P. Chou. On Velocity Correlations and the Solutions of the Equations of Turbulent Fluctuation.

D. Wilcox. The remarkable ability of turbulence model equations to describe transition.

D. Wilcox. Comparison of Two-Equation Turbulence Models for Boundary Layers with Pressure Gradient. AIAA Journal Vol. 31, No. 8, 1993.

C. Speziale, R. Abid, E. Anderson. Critical Evaluation of Two-Equation Models for Near-Wall Turbulence. AIAA Journal Vol. 30, No. 2, 1992.

V. Patel, W. Rodi, G. Scheuerer. Turbulence Models for Near-Wall and Low Reynolds Number Flows: A Review. AIAA Journal Vol. 23, No. 9, 1985.

P. Bernard. Limitations of the Near-Wall k-e Turbulence Model. AIAA Journal Vol. 24, No. 4, 1986.

P. Durbin. Some Recent Developments in Turbulence Closure Modeling. Annual Review of Fluid Mechanics Vol. 50:77-103.

C. Argyropoulosa, N. Markatos. Recent advances on the numerical modelling of turbulent flows. Volume 39, Issue 2, 15 January 2015, Pages 693-732.

S. Pope. A more general effective-viscosity hypothesis. Journal of Fluid Mechanics, 72(2), 331-340, 1975.

H. Kutkan, J. Guerrero. "Turbulent Premixed Flame Modeling Using the Algebraic Flame Surface Wrinkling Model: A Comparative Study between OpenFOAM and Ansys Fluent". Fluids 2021, 6(12), 462; https://doi.org/10.3390/fluids6120462.

U. Ahmed, D. Apsley, T.Stallard, P. Stansby, I. Afgan. Turbulent length scales and budgets of Reynolds stress-transport for open-channel flows; friction Reynolds numbers Re = 150, 400 and 1020. Journal of Hydraulic Research, Volume 59(1), 2021. Pages 36-50. https://www.tandfonline.com/doi/full/10.1080/00221686.2020.1729265

Lecture 7

Quantitative and qualitative post-processing of turbulent simulations. Data analysis and statistical tools used in turbulence modeling. Descriptive statistics. One-point and two-point correlations. Analysis of time series. Turbulent kinetic energy spectrum. Dealing with steady and unsteady simulations. Presenting results.

Turbulence and CFD Models

Lecture notes

On this page, you will find the lecture notes, supporting material, references, and links to the recorded theoretical sessions.

Course presentation

Course presentation - Preliminaries - Housekeeping issues.

Course material:

Lecture 1

Transition to turbulence in shear flows.

Course material:

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 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 4

Practical turbulence estimates.

Course material:

Lecture 5

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

Course material:

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 7

Course material:

Lecture 8

Beyond the Boussinesq hypothesis. Compressibility effects. Multiphase flows - Brief review of the VOF method for separated and dispersed flows. Effect of roughness on the law of the wall.

Course material:

Lecture 9

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

Course material:

Lecture 10

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

All the recorded lectures are available at the Teams channel - You need UNIGE credentials

Support material

Additional support material and a collection of best practices guidelines are available at the Teams channel.

Turbulence and CFD Models

Lecture notes

On this page, you will find the lecture notes, supporting material, references, and links to the recorded theoretical sessions.

Course presentation

Course presentation - Preliminaries - Housekeeping issues.

Course material:

Lecture 1

Transition to turbulence in shear flows.

Course material:

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 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 4

Practical turbulence estimates.

Course material:

Lecture 5

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

Course material:

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 7

Course material:

Lecture 8

Beyond the Boussinesq hypothesis. Compressibility effects. Multiphase flows - Brief review of the VOF method for separated and dispersed flows. Effect of roughness on the law of the wall.

Course material:

Lecture 9

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

Course material:

Lecture 10

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 All the recorded lectures are available at the Teams channel - You need UNIGE credentials Support material Additional support material and a collection of best practices guidelines are available at the Teams channel.

Video lectures

All the recorded lectures are available at the Teams channel - You need UNIGE credentials

Support material

Additional support material and a collection of best practices guidelines are available at the Teams channel.