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.

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 fluiddynamic and thermal processes of multiphase systems take place, such as transportation pipelines, boilers, condensers, fluidized beds, etc.

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.

Subject 1. Introduction to Multiphase Flow.

Scope. Multiphase flow 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 4. Gas-Solid (Particle) Systems.

Classification of Gas-Solid Flows. Dynamics: gas-particle and particle-particle interactions, mass and momentum transport, convective heat transfer.

Case studies. Pneumatic conveying: flow regimes, classification of bulk solids, phase diagram, dilute versus dense phase conveying, saltation velocity, pressure drop in dilute and dense phase systems. Fluidized Beds: flow regimes, velocity and pressure, heat and mass transfer.

Subject 5. Liquid-Solid Systems.

Solidification and Melting. One-dimensional Stefan problem. Phase change with convection. Phase Change Materials for energy storage.

Case Studies. Freezing time of a liquid in a tube. Freezing in pipelines cooled by surrounding ambient air.

LABORATORY ACTIVITIES. Students will be involved in the experimental activities of the Multiphase Flow Laboratory at the Department of Energy, aiming at: major understanding of theoretical modelling through experimental validation; design and setup of suitable test sections; planning and execution of experimental runs, processing of empirical data. According to the availability of the facilities, attention will be turned to either liquid-liquid-gas adiabatic flows or forced convective boiling/condensation heat transfer.

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

5 ECTS course for Nuclear Engineering. The contents are limited to Subjects 1 to 3.

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.

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

1. 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;
2. final oral exam about the whole programme.

The homework has 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 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.

Chapters 5, 6, 7, 8

Chapters 1, 2, 3, 4, 5