Specific Intended Learning Outcomes

Week 1

Week 1: List of videos and their intended learning outcomes

Video title	Intended learning outcomes
Introduction to multi-phase and particle-laden flows	Classify multi - and two-phase flows. Recall and apply the concepts of volume fraction and density of mixture. Illustrate and manage the extension to polydisperse mixtures.
Characterization of the dispersed phase	Understand the key components of a sieve analysis. Manage the concepts of particle size distribution. Evaluate whether a particle mixture can be modeled as monodisperse. Explain how to characterize particle shape. Define the concept of packing volume fraction.
The particle response time and the particle Stokes number	Define the particle response time and the particle Stokes number. Derive the expression of the particle response time for 1D Stokes flow. Explain the concept of particle Stokes number in turbulent flow. Discuss the implications for particle motion.
Coupling regimes and turbulence modulation	List and describe the coupling regimes. Illustrate and apply the Elgobashi map. Explain the concept of turbulence modulation.
The particle equation of motion	Classify the forces acting on a particle in a particle-laden flow. Define the drag force and characterize the drag coefficient. Explain the concept of unhindered fluid velocity. Discuss the effect of particle shape on the drag coefficient. List the different types of fluid–particle forces. Outline the models for particle–particle and particle–wall collisions.

Week 2

Week 2: List of videos and their intended learning outcomes

Video title	Intended learning outcomes
Overview of the modelling approaches (part 1)	List the main investigation approaches in fluid mechanics and explain their pros and cons. Illustrate the concept of synergistic problem solving. Highlight the greater challenges faced when dealing with particle-laden flows. Explain the basic idea and discuss pros and cons of Eulerian-Eulerian and Eulerian-Lagrangian modelling.
Overview of the modelling approaches (part 2)	Propose the best modelling approach for a given problem. Discuss Eulerian-Eulerian and Eulerian-Lagrangian modelling in the light of the coupling regime. Classify the modelling approaches in relation with the treatment of turbulence.
DNS-based Eulerian-Lagrangian models (part 1)	Discuss the implications of resolving all turbulence scales. Master the Navier-Stokes equations for single-phase flow.
DNS-based Eulerian-Lagrangian models (part 2)	Explain the basic idea of fully resolved and point-particle DNS-based Eulerian-Lagrangian models and discuss the implications on particle size.
RANS-based Eulerian-Lagrangian models (part 1)	Understand the concept of Reynolds-averaging and master the RANS/U-RANS for single-phase flow. Explain the basic idea of point-particle RANS-based Eulerian-Lagrangian models.
RANS-based Eulerian-Lagrangian models (part 2)	Illustrate the parcel approach. Explain how the drag force is modeled in RANS-based Eulerian-Lagrangian models with point-particle approximation.
Eulerian-Eulerian modelling: equations and closures	Outline the nature of the conservation equations in the Eulerian-Eulerian models. List the different types of coupling in the Eulerian-Eulerian models. Characterize the interfacial momentum transfer term in Eulerian-Eulerian models. Recognize and classify the constitutive equations of Eulerian-Eulerian models.
Eulerian-Eulerian modelling: turbulent flows and average methods	Discuss the implications of resolving the instantaneous Eulerian-Eulerian equations for turbulent flows. Explain the basic idea of the double-average approach. Assess the implications of the choice of the second average operator. Describe the origin of phase diffusion fluxes and turbulent dispersion force. Identify the main challenges of Eulerian-Eulerian modelling of turbulent particle-laden flows.

Week 3

List of videos and their intended learning outcomes

Video title	Intended learning outcomes
Slurry flows in pipes: technical parameters and flow regimes (part 1)	Define what a slurry is. Know and use the formulas for the flow rate of mixture and average velocity of slurry flow. Define the Specific Energy Consumption (SEC). List the main parameters affecting the friction losses.
Slurry flows in pipes: technical parameters and flow regimes (part 2)	Define and discuss the pipe characteristic curve. Define the deposition limit velocity and list the parameters affecting this variable. Define in-situ and delivered concentrations, and explain the difference between the two. Classify and discuss the different flow regimes of slurry flow in horizontal pipes.
Slurry flows in pipes: predictive models for settling slurries (part 1)	List the modeling approaches for slurry pipe flows. List the major predicted quantities. Illustrate the concept of Relative Solids Effect (RSE) for the evaluation of the frictional losses. Draw the typical characteristic curve of pseudo-homogeneous flow, heterogeneous flow, partially stratified and fully stratified flow and identify the physical mechanisms contributing to the frictional losses.
Slurry flows in pipes: predictive models for settling slurries (part 2)	Explain the basic idea of the equivalent liquid model. Identify the parameters affecting the frictional losses in heterogeneous flow. Explain the basic idea of layered models. Recognize the challenges related with polydisperse slurries.
Slurry flows in pipes: experimental testing	Illustrate pros and cons of laboratory and field testing of slurry pipe flows. List the key measurements in slurry pipe flows. Mention and discuss commonly used instruments to measure the slurry discharge, the solids concentration, and the local distribution of solids within the pipe.
Slurry flows in pipes: numerical modelling	Discuss strengths and limitations of Computational Fluid Dynamics as a tool for handling slurry pipe flows, refining the evaluation referring to the specific modelling approaches (Eulerian-Eulerian vs Eulerian-Lagrangian). Identify the main flow parameters that Eulerian-Eulerian models can provide. Explain the main features of the β-σ model.

Week 4

Week 4: List of videos and their intended learning outcomes

Video title	Intended learning outcomes
Key parameters affecting solid particle erosion	Classify the different types of erosion. Explain the effect of particle impact angle on the impact erosion of brittle and ductile targets. Identify the material- and particle-related parameters affecting impact erosion. Identify the particle-related parameters affecting impact erosion. Describe direct and indirect effects of particle size and shape on impact erosion. Discuss the effect of impact velocity on impact erosion. Illustrate the effect of solid loading and explain the screening effect. Illustrate the effect of time and discuss the feasibility of steady-state erosion approximation.
The direct impact test	Describe the direct impact test. Identify the control and output variables in a direct impact test. Characterize dry and wet direct impact tests from the fluid dynamic point of view. Justify the different erosion behaviors observed in dry and wet direct impact tests. Derive the expression for the Integral Erosion Ratio in dry and wet direct impact tests.
Numerical modelling of solid particle erosion (part 1)	Illustrate the standard methodology for CFD-based erosion prediction. List the main assumptions of this methodology. List the main output erosion-related variables and explain how they are obtained. Define what an erosion model is.
Numerical modelling of solid particle erosion (part 2)	Classify erosion models based on their origin. Explain how empirical erosion models can be obtained from a dry direct impact test. Cite a widely used erosion model.
Frontiers in erosion modelling	List the main limitations of the standard methodology for CFD-based erosion prediction. Explain the quasi-static approach to model unsteady-state erosion. Illustrate the motivation behind the mixed Eulerian-Eulerian / Eulerian-Lagrangian approach. Understand the critical issues related with point-particle approximation and mention a possible strategy to overcome them. Mention possible strategies to overcome the inaccuracies inherent in the use of empirical erosion models taken from the literature.