Transport phenomena and computational fluid dynamics (Computational fluid dynamics)

This course provides an introduction to the principles and applications of Computational Fluid Dynamics (CFD) with a focus on chemical engineering processes. Students will learn the fundamental mathematical models governing fluid flow, heat transfer, and mass transport, and how these models are discretized and solved using numerical methods. The course covers the formulation of governing equations, turbulence modeling, and multiphase flow simulation, emphasizing practical applications in chemical reactors, separation processes, and transport phenomena. Hands-on exercises using widely used CFD software allow students to develop skills in setting up, running, and interpreting simulations relevant to chemical engineering problems.

Transport phenomena and computational fluid dynamics (Transport phenomena)

This course introduces advanced concepts of molecular transport phenomena, which refer to the processes by which mass, momentum, and energy are transferred at the molecular level in a physical system. These phenomena arise due to molecular motion and interactions, and they form the basis of many macroscopic transport processes in fluids and solids. There are three primary types of molecular transport phenomena: 1. Momentum transport – also known as viscous flow or momentum diffusion. - Caused by molecular motion transmitting momentum from one part of a fluid to another. - Described by Newton’s law of viscosity, which relates shear stress to the velocity gradient in a fluid. 2. Mass transport – also called diffusion. - Refers to the movement of individual molecules from regions of high concentration to regions of low concentration. - Governed by Fick’s laws of diffusion. 3. Energy transport – or thermal conduction. - Involves the transfer of kinetic energy between molecules, resulting in heat flow from high to low temperature regions. - Described by Fourier’s law of heat conduction. Together, these transport mechanisms are described mathematically by partial differential equations derived from the conservation laws (mass, momentum, and energy), often forming the foundation of fluid mechanics, heat transfer, and mass transfer analyses in chemical engineering.

Transport phenomena and computational fluid dynamics (Computational fluid dynamics)

By the end of this course, students will be able to: 1. Explain the fundamental governing equations of fluid flow, heat, and mass transfer relevant to chemical engineering processes. 2. Understand the principles of numerical discretization methods such as finite volume, finite difference, and finite element methods. 3. Set up and solve basic CFD problems involving laminar and turbulent flows using commercial or open-source CFD software. 4. Interpret and analyze CFD simulation results critically, identifying key flow features and transport phenomena. 5. Apply turbulence models and multiphase flow models appropriate to chemical engineering applications. 6. Design and implement CFD simulations for chemical reactors, separation units, and other process equipment. 7. Communicate CFD modeling results effectively through written reports and presentations.

Transport phenomena and computational fluid dynamics (Transport phenomena)

By the end of the course, students will be able to: 1. Explain the molecular basis of momentum, mass, and energy transport in fluids and solids. 2. Derive and interpret the fundamental transport equations (Navier–Stokes, Fick’s law, Fourier’s law) from first principles using conservation laws. 3. Analyze and solve steady-state and transient transport problems involving single or coupled transport mechanisms in various geometries. 4. Apply scaling and dimensionless analysis (e.g., Reynolds, Prandtl, Schmidt numbers) to assess the relative importance of different transport phenomena in a given system. 5. Develop and implement analytical solutions to transport problems, including complex boundary conditions or source terms. 6. Interpret transport behavior in complex systems, such as non-Newtonian fluids, multicomponent diffusion, and interfacial transport. 7. Critically evaluate and compare models for molecular transport in engineering and scientific applications. 8. Use transport theory to inform the design and optimization of chemical, biological, or mechanical processes.

Transport phenomena and computational fluid dynamics (Computational fluid dynamics)

Students should have prior knowledge of: 1. Fluid Mechanics - Fundamentals of fluid statics and dynamics - Continuity, momentum, and energy conservation equations - Basic concepts of laminar and turbulent flow 2. Heat and Mass Transfer - Basic conduction, convection, and diffusion principles - Steady-state and transient heat/mass transfer 3. Mathematics - Ordinary and partial differential equations - Vector calculus - Basic numerical methods (finite difference or finite volume methods) 4. Programming or Computational Skills - Basic programming skills in languages such as MATLAB, Python, or C++ - Familiarity with numerical computing environments

Transport phenomena and computational fluid dynamics (Transport phenomena)

Students should have a solid understanding of the following subjects, typically acquired during a bachelor’s degree in chemical, mechanical, or biomedical engineering (or a related field): 1. Fluid Mechanics - Basic principles of fluid statics and dynamics - Bernoulli’s equation, laminar and turbulent flow - Navier–Stokes equations (basic formulation) 2. Heat and Mass Transfer -Fourier’s and Fick’s laws -Steady and unsteady conduction/diffusion -Convective transport and basic correlations 3. Thermodynamics - Thermodynamic properties of pure substances and mixtures - First and second laws of thermodynamics - Phase equilibria and chemical potential 4. Mathematics - Differential equations (ordinary and partial) - Vector calculus and linear algebra - Fourier and Laplace transforms (basic understanding)

Transport phenomena and computational fluid dynamics (Computational fluid dynamics)

1. Introduction to CFD - Overview of CFD in chemical engineering - Role and limitations of CFD simulations 2. Governing Equations of Fluid Flow - Conservation of mass, momentum, and energy - Navier–Stokes equations and assumptions 3. Mathematical Foundations and Numerical Methods - Discretization techniques: finite difference, finite volume, finite element - Grid generation and mesh quality - Spatial and time discretization, stability, boundedness, convergence, and accuracy 4. Boundary and Initial Conditions - Types of boundary conditions in CFD - Treatment of inlet, outlet, wall, and symmetry boundaries 5. Turbulence Modeling - Introduction to turbulence - Reynolds-averaged Navier–Stokes (RANS) equations - Common turbulence models: k-ε, k-ω, LES basics 6. Heat and Mass Transfer in CFD - Coupling of momentum, energy, and species transport - Simulation of reactive flows and chemical reactions 7. Practical CFD Simulations - Setting up CFD cases relevant to chemical engineering - Post-processing and interpreting results - Use of commercial and open-source CFD software (e.g., ANSYS Fluent, OpenFOAM) 8. Case Studies and Applications - CFD applications in reactors, separation units, and process optimization - Troubleshooting common CFD problems

Transport phenomena and computational fluid dynamics (Transport phenomena)

1. Introduction to Molecular Transport Phenomena - Scope and importance in engineering and science - Continuum vs. molecular description - Overview of momentum, heat, and mass transport 2. Mathematical Preliminaries - Tensor notation and index rules - Conservation laws in integral and differential form - Constitutive relations 3. Momentum Transport (Newtonian and Non-Newtonian Fluids) - Molecular basis of viscosity - Derivation of the Navier–Stokes equations - Unidirectional flows and exact solutions - Creeping flow and lubrication theory - Introduction to non-Newtonian transport behavior - Introduction to turbulence 4. Energy Transport (Heat Conduction and Convection) - Molecular interpretation of thermal conductivity - Fourier’s law and energy conservation - Steady and unsteady conduction in various geometries - Convective heat transfer and boundary layer theory - Turbulent energy transport - Radiation 5. Mass Transport (Diffusion and Convection) - Fick’s laws and molecular diffusion - Diffusion in gases, liquids, and solids with and without chemical reactions - Unsteady diffusion and similarity solutions - Convective mass transfer and mass transfer coefficients - Multicomponent diffusion and Maxwell–Stefan equations - Turbulent mass transport and turbulence chemistry interactions

Transport phenomena and computational fluid dynamics (Computational fluid dynamics)

Transport phenomena and computational fluid dynamics (Transport phenomena)

Transport phenomena and computational fluid dynamics (Computational fluid dynamics)

The course consists of lectures (40%), tutorials on Ansys CFD Fluent (10%) and practical sessions in the computer laboratory working on a specific project (50%).

Transport phenomena and computational fluid dynamics (Transport phenomena)

The course is divided between lectures (60%) and practical sessions with exercises solved at the blackboard (40%).

Transport phenomena and computational fluid dynamics (Computational fluid dynamics)

Andersson B, Andersson R, Håkansson L, Mortensen M, Sudiyo R, van Wachem B. Computational Fluid Dynamics for Engineers. Cambridge University Press; 2011; https://doi-org.ezproxy.biblio.polito.it/10.1017/CBO9781139093590

Transport phenomena and computational fluid dynamics (Transport phenomena)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2007). Transport Phenomena (Revised Second ed.). John Wiley & Sons.

Transport phenomena and computational fluid dynamics (Computational fluid dynamics)

Dispense; Libro di testo; Video lezioni tratte da anni precedenti;

Transport phenomena and computational fluid dynamics (Transport phenomena)

Dispense; Libro di testo; Esercizi risolti; Video lezioni tratte da anni precedenti;

Transport phenomena and computational fluid dynamics (Computational fluid dynamics)

Modalità di esame: Elaborato progettuale in gruppo;

Transport phenomena and computational fluid dynamics (Transport phenomena)

Modalità di esame: Prova scritta (in aula); Prova orale facoltativa; Elaborato scritto individuale;

Transport phenomena and computational fluid dynamics (Computational fluid dynamics)

Exam: Group project;

Transport phenomena and computational fluid dynamics (Transport phenomena)

Exam: Written test; Optional oral exam; Individual essay;

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Transport phenomena and computational fluid dynamics (Computational fluid dynamics)

At the beginning of the course, students are divided into groups of five and assigned a design project to be solved using CFD tools. Each group is guided throughout the semester in the development and implementation of their project, which involves applying the concepts and methods learned during the course to a realistic chemical engineering problem. At the end of the course, each group delivers a 30-minute PowerPoint presentation summarizing their work. The presentation is followed by a question-and-answer session, during which students are expected to discuss their results and demonstrate a solid understanding of both their specific project and the general CFD principles covered in the course. Despite group work, the final grade is assigned individually, based on individual performance.

Transport phenomena and computational fluid dynamics (Transport phenomena)

The exam consists of a mandatory written test with 3 exercises: one on momentum transport, one on energy transport and one on mass transport. This weights for 24 out of 30 scores. During the semester the students can take part to an eligible crowdgrading test. Three exercises are given to the students, which then upload them into a crowdgrader platform. The exercises are then graded anonymously by three other students, randomly selected by the platform. This weights 6 out of 30 scores. The students can then improve their grade with an eligible oral test covering all the topics of the course. During the oral test the students are asked to solve simple numerical problems or undergo theoretical derivations.

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.