The objective of this PhD Course is to provide an application-oriented yet theoretically rigorous overview of particle-laden flows, i.e., two-phase flows of solid particles within a carrier fluid (liquid or gas). These flows are encountered in many engineering fields, including but not limited to the mining industry, the oil & gas industry, and the hydraulic engineering. Students will learn how particle-laden flows can be characterized from a physical and engineering point of view, and they will be able to decide the most appropriate approach for handling these flows at the design level, including different techniques for the numerical simulation as well as the physical testing in laboratory setups. After discussing these aspects in a general framework, special attention will be paid to two phenomena of considerable industrial impact, namely, the liquid-solid transport in pipelines and the damage produced by the travelling solids on pipeline components and hydraulic equipment.

The course will be divided in two parts.

The first part will be given partly in the form of a MOOC, developed by the teachers in the context of a collaborative research project and available on the POLIMI-POK platform, and partly in the form of frontal lessons. The MOOC consists of 19 video-lessons organized into four weeks, dedicated to the following topics: fundamentals of particle-laden flows, simulations of particle-laden flows, transport of solids in pipeline systems, and solid particle erosion. For each of the first week of the MOOC: the teachers will introduce the topics of the video-lessons through a frontal lesson; the students will attend the video lessons and complement them with their own individual study; class activities including further deepening of the topics of the video lessons, document analysis, debate, project-based learning will be managed by the teachers.

The second part will be dedicated to laboratories prepared by the teachers. Particularly, in two laboratories the students will simulate the turbulent slurry flow in a horizontal pipe and the erosion produced by a slurry jet. The will start from numerical setups and mathematical models already developed by the teachers, and execute the simulations critically analyzing the results by answering specific questions. The last Laboratory will consist of a visit at the Hydraulic Laboratory of Politecnico di Milano, where two apparatus for slurry erosion testing are present. The students will be provided an overview of the functioning of the two apparatus and the experimental methodology and, depending on the availability of the equipment, might also try to execute a wet direct impact test under the guidance of the teachers.

Learning assessment will be based on:

• Attainment of the certificate released after attending the MOOC on the POLIMI-POK platform and completing the quizzes with 60% or more being corrected.
• Positive evaluation of the report in which a specific topic treated in the MOOC is analyzed in detail.
• Positive evaluation of a project developed by the students working single or in small groups (2-3 people), delivered in the form of oral presentation to the teachers and other students and of written summary report. The topic of the project and the followed methodology (e.g. conceptual/theoretical, numerical, or experimental) will be agreed with the teachers.

The detailed calendar as well as the (virtual or in-person class) will be defined at a later stage, depending on the COVD emergency, on the number of students, on the possibility to run experiments in the Hydraulic Laboratory.

Indicatively, there will be seven lessons, as follows

Lesson n° 1 (2 hours): Presentation of the course and introduction to the first slot (“week 1”) of lessons of MOOC “Particle-laden flows: theory and engineering applications”. Topic of “week 1”: fundamentals of particle-laden flows.

Lesson n° 2 (2 hours): Discussion of the first slot (“week 1”) of lessons of MOOC “Particle-laden flows: theory and engineering applications” and introduction to the second slot (“week 2”). Topic of “week 2”: simulation of particle-laden flows.

Lesson n° 3 (2 hours): Discussion of the second slot (“week 2”) of lessons of MOOC “Particle-laden flows: theory and engineering applications” and introduction to the third slot (“week 3”). Topic of “week 3”: “particle transport in slurry pipelines”.

Lesson n° 4 (2 hours): Discussion of the third slot (“week 3”) of lessons of MOOC “Particle-laden flows: theory and engineering applications” and introduction to the fourth slot (“week 4”). Topic of “week 3”: “solid particle erosion”.

Lesson n° 5 (4 hours): Discussion of the fourth slot (“week 4”) of lessons of MOOC “Particle-laden flows: theory and engineering applications”. Numerical laboratory on the sedimentation of a particle in a quiescent liquid.

Lesson n° 6 (4 hours): Numerical laboratory on the CFD modelling of turbulent liquid-solid flows in horizontal pipes.

Lesson n° 7 (4 hours): Experimental laboratory on wet direct impact tests for the characterization of impact erosion behavior of materials (depending on the availability of the lab).

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