OVERVIEW

• The main objective of the course is to give the students a thorough knowledge of turbulence modeling in CFD.
• During the course, we cover the theoretical background of RANS models and scale-resolving simulations (DES and LES).
• We also address accuracy and reliability of CFD turbulent simulations, as well as discretization techniques, solution strategies, and best standard practices when conducting CFD simulations.

AIMS AND CONTENT

LEARNING OUTCOMES

The aim of the course is to allow  students  to acquire a critical view of numerical strategies for the modelling of turbulence (both developed and in transition), both of  RANS type and of LES type. The expected result is a consequent  mature use of such numerical strategies, based on the awareness that simulations are not the real thing  but a sophisticated  modeling of it and, as such, susceptible to errors, sometimes relevant.

AIMS AND LEARNING OUTCOMES

• The course's main objective is to give the students a thorough knowledge of turbulence modeling in CFD.
• During this course, we also address accuracy and reliability of CFD turbulent simulations, as well as discretization techniques, solution strategies, and best standard practices when conducting CFD simulations.
• We also conduct hands-on sessions to help students develop essential skills to perform CFD simulation from scratch. That is, geometry generation, mesh generation, case setup, solution monitoring, post-processing, and assessing the results.
• At the end of the course, the student should be able to critically assess the influence of turbulence models on the outcome of CFD simulations, independently of the software used.

PREREQUISITES

• Basic knowledge of Fluid Mechanics.
• Basic knowledge of numerical methods.

TEACHING METHODS

• The course is based on 60 hours of frontal lectures.
• 50% of the hours are dedicated to theory and the other 50% are dedicted to hands on sessions.  
• The program is divided between lectures and guided tutorials.
• The course is graded in the base of continuous homework and a final project.
• Instructors can be contacted by the students for questions and clarifications during office hours.

SYLLABUS/CONTENT

The program is divided between lectures and guided tutorials. At least one lecture will be delivered on every topic, and to reinforce the knowledge acquired, we will conduct numerical simulations or analyze data using modern software and applications.

1. Transition to turbulence in shear flows.

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

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

4. Practical turbulence estimates.

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

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.

7. Statistical description of turbulence. Descriptive statistics. Joint statistics. One-point correlation. Two-point correlations. Time series. Turbulent kinetic energy spectrum. Power spectrum.

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

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

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

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

RECOMMENDED READING/BIBLIOGRAPHY

• D. Wilcox. Turbulence Modeling for CFD. DCW Industries Inc., 2010.
• S. Pope. Turbulent Flows. Cambridge University Press, 2000.
• P. Bernard. Turbulent Fluid Flow. Wiley, 2019.
• M. T. Landahl and E. Mollo-Christensen. Turbulence and Random Processes in Fluid Mechanics. Cambridge University Press, 1992.
• H. Tennekes and J. L. Lumley. A First Course in Turbulence. MIT Press, 1972.
• P.J. Schmid e D.S. Henningson, Stability and Transition in Shear Flows, Springer, 2001.
• U. Frisch, Turbulence, Cambridge Univ. Press. 1995.

TEACHERS AND EXAM BOARD

Exam Board

JOEL ENRIQUE GUERRERO RIVAS (President)

ALESSANDRO BOTTARO

LESSONS

Class schedule

TURBULENCE AND CFD MODELS

EXAMS

EXAM DESCRIPTION

• The final evaluation will consist of a CFD project where the student must put into practice all the knowledge acquired. The case to be developed must be agreed upon between the examiner and the student.

ASSESSMENT METHODS

• The course will be graded based on continuous assignments and a final project.
• A written report and a short presentation are expected at the end of the final project.
• Based on the examiner's feedback, the student will have a one-time opportunity to improve his/her report.

Exam schedule

FURTHER INFORMATION

For the hands-on sessions, students should bring her/his computer with all the software installed. All the software to be used is free and can be downloaded at the links provided.