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01RMFND

A.A. 2025/26

Course Language

Inglese

Degree programme(s)

Master of science-level of the Bologna process in Ingegneria Energetica E Nucleare - Torino

Course structure

Teaching | Hours |
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Lecturers

Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
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Context

SSD | CFU | Activities | Area context |
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ING-IND/19 | 6 | F - Altre attività (art. 10) | Altre conoscenze utili per l'inserimento nel mondo del lavoro |

2024/25

The course focuses on what is commonly called Computational Fluid Dynamics (CFD). The core of the course is devoted to the development and application of methods for the numerical solution of 1D and 2D/3D thermal-fluid dynamics problems, using the finite difference (1D) or the finite volume (2D/3D) approaches. Some emphasis is also put on the fundamental concepts of benchmark, verification and validation.

Thermal fluid dynamics is a fundamental discipline for the solution of energy problems. Unfortunately, the underlying Navier-Stokes equations cannot in general be solved analytically because of their nonlinearity and/or of the geometrical complexity of the domain. Therefore, the computer is needed. The present course focuses on what is commonly called Computational Fluid Dynamics (CFD), with the important addition of the thermal component (CtFD), and is aimed at investigating the solution on the computer of engineering-relevant heat transfer problems where convection is the major player. The core of the course is devoted to the development and application of methods for the numerical solution of 1D and 2D/3D thermal-fluid dynamics problems, using the finite difference or the finite volume approaches. Some emphasis is also put on the fundamental concepts of benchmark, verification and validation.

Through this course the student is expected to acquire a good knowledge of the above-mentioned methods, as well as the ability to perform simple CFD simulations using the commercial software STAR-CCM+. The student should also acquire a good knowledge of the procedure needed to confirm the quality/accuracy of the numerical solution of a given thermal-fluid dynamic model.

Through this course the student is expected to acquire a good knowledge of the above-mentioned methods, as well as the ability to perform CtFD simulations using the commercial software STAR-CCM+. The student should also acquire a good knowledge of the procedures needed to confirm the quality/accuracy of the numerical solution of a given thermal-fluid dynamic model. At the end of the course you should be ready to make good use of CtFD in your professional life -- a likely event.

As a minimum, the knowledge coming from traditional introductory courses in thermal fluid dynamics, e.g. from the course “Termofluidodinamica” in the Energy engineering BSc program at Politecnico di Torino, as well as in numerical analysis ("Calcolo numerico"), will be taken for granted. The former includes a basic knowledge of Navier-Stokes equations. The latter includes: basic numerical linear algebra (direct and iterative methods for the solution of large algebraic sets of equations), elementary methods for the numerical solution of nonlinear algebraic problems, numerical quadrature formulae, numerical integration of ordinary differential equations (initial value problems), together with some basic knowledge of MATLAB. As a reference for the students enrolled in the Energy and Nuclear engineering MSc program at Politecnico di Torino, the knowledge acquired in the course "Introduction to computational heat transfer" will be fully sufficient.

The knowledge coming from traditional introductory courses in thermal fluid dynamics, e.g. from the course “Termofluidodinamica” in the Energy engineering BSc program, as well as in numerical analysis ("Calcolo numerico"), will be taken for granted. The former includes a basic knowledge of Navier-Stokes equations. The latter includes: basic numerical linear algebra (direct and iterative methods for the solution of large algebraic sets of equations), elementary methods for the numerical solution of nonlinear algebraic problems, numerical quadrature formulae, numerical integration of ordinary differential equations (initial value problems). As a reference, the knowledge acquired in the course “Laboratorio Computazionale di Scambio Termico” (Energy engineering BSc program), will be sufficient.

1D scalar advection problems
- The method of characteristics
- Finite difference methods
- The CFL condition
- MATLAB application
1D scalar advection-conduction problems
- Boundary layers
- Finite-difference methods
- Upwind vs. centered approximations
- MATLAB application
2D scalar advection-conduction problems
- The finite volume method
- MATLAB application
The incompressible Navier-Stokes laminar problem
- Scalar vs. vector problems: co-located vs. staggered grids, coupled vs. segregated solution, pressure correction methods (SIMPLE, ...).
- Classical benchmarks: lid-driven cavity; buoyancy driven cavity: derivation of a numerical correlation for the Nusselt number.
- STAR-CCM+ application
Introduction to the numerical solution of turbulent flow and heat transfer problems
- Reynolds Averaged Navier-Stokes (RANS)
- Classical benchmark: turbulent flow and heat transfer in a circular pipe
- STAR-CCM+ application and validation against experimental (e.g. Blasius, Dittus-Boelter) correlations.

1D transient scalar advection problems
- The method of characteristics;
- Finite difference methods;
- The CFL condition.
1D steady-state scalar advection-conduction problems
- Boundary layers;
- Finite-difference methods;
- Upwind vs. centered approximations.
2D scalar advection-conduction problems
- The finite volume method.
The incompressible Navier-Stokes laminar problem
- Scalar vs. vector problems: co-located vs. staggered grids, coupled vs. segregated solution, pressure correction methods (SIMPLE, ...);
- Classical benchmarks: lid-driven cavity; buoyancy driven cavity: derivation of a numerical correlation for the Nusselt number.
Introduction to the numerical solution of turbulent flow and heat transfer problems
- Reynolds Averaged Navier-Stokes (RANS);
- Classical benchmark: backward-facing step; turbulent flow and heat transfer in a circular pipe.

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30 hours of computational lab are foreseen, where the students will individually work on PCs, using the abovementioned software (MATLAB and STAR-CCM+). Special emphasis will also be put on the issue of mesh generation.

30 hours of lectures are foreseen on the above-mentioned topics.
30 hours of computational laboratory are foreseen on the above-mentioned topics, where the students will individually work on PCs.

Selected chapters from:
- J. M. Cooper, "Introduction to Partial Differential Equations with MATLAB" (Birkhaeuser, 2000)
- R. Peyret, T.D. Taylor, Computational Methods for Fluid Flow (Springer, 1985)
- C. Hirsch, "Numerical Computation of Internal and External Flows", 2nd ed. (Butterworth-Heinemann, 2007)
- J. H. Ferziger, M. Peric, "Computational Methods for Fluid Dynamics", 3rd ed. (Springer, 2013)
- D.C. Wilcox, Turbulence modeling for CFD , 3rd edition (DCW industries, 2006)
- H. K. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method (Pearson Education, 2007)

Notes/slides provided by the lecturers.
Selected chapters from:
- J. M. Cooper, "Introduction to Partial Differential Equations with MATLAB" (Birkhaeuser, 2000)
- R. Peyret, T.D. Taylor, Computational Methods for Fluid Flow (Springer, 1985)
- C. Hirsch, "Numerical Computation of Internal and External Flows", 2nd ed. (Butterworth-Heinemann, 2007)
- J. H. Ferziger, M. Peric, "Computational Methods for Fluid Dynamics", 3rd ed. (Springer, 2013)
- D.C. Wilcox, Turbulence modeling for CFD , 3rd edition (DCW industries, 2006)
- H. K. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method (Pearson Education, 2007)

Slides; Esercitazioni di laboratorio;

Lecture slides; Lab exercises;

...
Students are grouped in small teams.
Each team works on a model CFD problem, starting in the second part of the semester, where it is asked to:
1) solve the problem, using STAR-CCM+ and MATLAB, and summarize the results in the form of suitable plots;
2) justify the choice of the methods used to find the solution;
3) discuss the quality/accuracy of the computed solution.
These three items are collected by the team in a short report (pdf file), to be discussed with the Teaching Assistant, who will individually evaluate the authors of the report.
The students with a report evaluation > 24/30 go to the oral, which is focussed on the theory part of the course and on the discussion of one of the scripts developed by them in the MATLAB applications during the course.
For the rest of the students, the report evaluation gives the final mark.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.

The exam consists of a group project on the computational laboratory and of an oral part focused on the theory presented during the lectures. The final mark is equal to the average between the two parts.
Group project:
Students are grouped in teams (pairs). Each team works on a CtFD Project, starting in the second part of the semester, where it is asked to:
– solve the problem, using STAR-CCM+, and summarize the results in the form of suitable plots;
– justify the choice of the methods used to find the solution;
– discuss the quality/accuracy of the computed solution.
These three items are collected by the team in a short report (PDF file). The Teaching Assistants will discuss with the team and then evaluate the individual contribution of the authors. The teams have two options:
• Produce one script (chosen by the team between two alternatives) + the Project report (computational laboratory mark up to 30L), OR
• Produce the Project report only (computational laboratory mark up to 27).

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.