Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2021/2022
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Docente Inzoli Fabio
Cfu 10.00 Tipo insegnamento Corso Integrato

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento

Obiettivi dell'insegnamento

Multiphase flow and heat transfer have a wide range of applications in nearly all aspects of engineering and science fields, particularly in energy engineering, mechanical engineering, chemical and petrochemical engineering and nuclear engineering. With the rapid development of the related technologies, research is growing very fast.

The course aims at providing an advanced knowledge of the fundamental physics of multiphase systems in order to develop tools for analysis and design of the most relevant energy technologies. Second goal is to provide the abilities to manage a commercial CFD code with awareness of the modelling problems involved. The case studies investigated are related to two phase flow with focus on application in nuclear field.

Risultati di apprendimento attesi

Attending the lectures will enable the student to:

  • Learn the fundamental quantities of a multiphase system and understand the relationships among them in order to achieve a thorough description of the system.
  • Learn to write the balance equations for mass, momentum and energy and understand the most common formulations useful to study the transport processes for multiphase systems.
  • Learn analysis and design methods for industrial apparatuses where fluid dynamic and thermal processes of multiphase systems take place, such as transportation pipelines, boilers, condensers, fluidized beds, etc.
  • Know the theoretical methodologies of analysis based on the numerical modelling of turbulent single-phase and two-phase flows and heat transfer with commercial computer codes
  • Set the numerical modelling with a CFD code through the setting of the boundary conditions and numerical techniques for solving the mathematical problem
  • Develop skills for the critical evaluation of results of CFD analysis

The above mentioned learning and understanding skills will be applied to the analysis of Case Studies including:

  • Calculation of pressure drop and pumping power for two-phase gas-liquid, liquid-liquid, solid-gas flows.
  • Calculation of the heat transfer coefficient for evaporating/condensing flows.
  • Thermal design of a variety of evaporators and condensers for both power and HVAC plants.
  • Basic design of fixed and fludized beds.
  • Performance evaluation of phase change materials for energy storage

To promote autonomy, during most of the exercise hours the students will be required to work independently or in team under the teacher's guidance.

The experimental laboratory aims at:

  • Learning to run an experimental facility in order to measure the pressure drop and the heat transfer coefficient for gas-liquid flows under a variety of experimental conditions.
  • Understanding the experimental results by means of suitable data processing.

The computer laboratory aims at:

  • Manage a commercial CFD code
  • Development capabilities to present numerical results and discuss their accuracy
  • Communicate through technical reports the results of the numerical simulation 

Argomenti trattati


Subject 1. Introduction to Multiphase Flow.

Scope. Multiphase ow notation. Flow patterns. Conservation of mass. Continuum equations for conservation of momentum. Averaging. Equations for conservation of energy.

Subject 2. Two-phase adiabatic flow.

Basic equations of two-phase flow. Homogeneous model. Separated flow model. Drift flux model. Empirical treatments. Extension to three-phase liquid-liquid-gas flows.

Case studies. Pressure loss evaluation in pipe flow and through enlargements, contractions, orifices, bends and valves.

Subject 3. Vapour-Liquid Systems.

Boiling heat transfer. Nucleation and bubble dynamics. Pool boiling. Critical Heat Flux. Convective boiling: flow regimes, onset of subcooled nucleate boiling, partial subcooled boiling, fully developed subcooled boiling, saturated forced convective boiling, dryout versus departure from nucleate boiling.

Case studies. Thermo-hydraulic design of Once-Through Boilers.

Condensation. Liquid formation and droplet growth. Film condensation on planar vertical and inclined surfaces, on horizontal and vertical tubes and tube bundles. Influence of the interfacial shear. Condensation within vertical and horizontal tubes. Drop-wise condensation.

Case studies. Thermo-hydraulic design of Steam Power Plant and Process Condensers.



Subject 1: CFD modelling in Nuclear engineering.

CFD as a tool for supporting product and process development applied to nuclear engineering design. The evaluation of the physical problem, the development of the mathematical modelling approach, the implementation of the model, the resolution and the evaluation of the results.

Subject 2: Problem Setting and solving

The geometrical modeling and discretization of the domain. The importance of the domain discretization using adequate mesh. The role of the solver. The numerical methods for solving the system of differential equations. The boundary conditions. The physics of turbulent flows and RANS models. Two phase flow modelling.

Subject 3: Post processing

The review of the results: qualitative and quantitative evaluation of the results. Comparison with available experimental and/or literature data. Sensitivity analysis on mesh size and critical review of the CFD model. The GCI.

Subject 4: Project managing

The CFD project cycle and the quality in CFD.


SEMINARS. Specialists coming from both research and industrial contexts will present the most recent advancements in multiphase flow physics and technologies.


The subjects of this course require a basic knowledge of Thermodynamics, Fluid Mechanics and Heat Transfer.

Attendance of the course of Heat and Mass Transfer is recommended, but not compulsory.

ANSYS provides free student products for work done in the classroom, such as homework. The products can be downloaded on web academic portal. ANSYS Student products can be installed on any supported MS Windows 64-bit machine. More information available on www.ansys.com

Modalità di valutazione

The evaluation carried out at the end of the course during the dedicated exam sessions is based on:

  • mandatory homework, which consists of writing a technical paper about the experimental activity or a review paper on selected subject collected from the main scientific databases;
  • mandatory CFD project work related to case study in nuclear plants with heat transfer and/or two-phase flow.
  • final oral exam about the whole programme.

The homework and the CFD project work have to be handed in at least a week before taking the oral exam.

Paper writing verifies the student's ability in collecting and analyzing the relevant literature in order to evaluate, compare and discuss his own achievements in the frame of the updated state of the art.

The CFD project work verifies the capability to applied proper methodology to solve the numerical models and to discuss, from engineering point of view, the obtained results.

The oral exam is intended to assess:

  • The degree of knowledge and understanding of the Subjects detailed in the Contents section.
  • The ability to address the Case Studies reported in the Contents section.
  • The discussion of Project works will be a public poster session format

Risorsa bibliografica obbligatoriaMiscellaneous teaching material https://beep.metid.polimi.it/
Risorsa bibliografica facoltativaGreg F. Naterer, Heat Transfer in Single and Multiphase Systems, Editore: CRC Press, Anno edizione: 2003, ISBN: 0-8493-1032-6 http://www.crcnetbase.com/isbn/9780849310324

Chapters 5, 6, 7, 8

Risorsa bibliografica facoltativaClayton T. Crowe, Multiphase Flow Handbook, Editore: CRC Taylor & Francis, Anno edizione: 2006, ISBN: 0-8493-1280-9 http://www.crcnetbase.com/isbn/9780849312809

Chapters 1, 2, 3, 4, 5

Risorsa bibliografica facoltativaH.K. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume, Editore: PEARSON PRENTICE HALL, Anno edizione: 2007, ISBN: 978-0-13-127498-3 https://www.pearson.com/us/higher-education/program/Versteeg-An-Introduction-to-Computational-Fluid-Dynamics-The-Finite-Volume-Method-2nd-Edition/PGM299497.html

Software utilizzato
Nessun software richiesto

Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Informatico
Laboratorio Sperimentale
Laboratorio Di Progetto
Totale 100:00 150:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese
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