Numerical simulation and modelling of transport phenomena

The main objective of this course is to introduce students to transport phenomena through an integrated approach to the transfer of energy, matter and quantity of motion in continuous media. It is intended that they understand the fundamental laws that govern these three phenomena, which are closely interrelated, and that they acquire the ability to formulate mathematical models that represent the essential aspects of real problems in chemical engineering processes. At the end of the course, students should be able to:

• Apply the laws governing the transfer of quantity of motion, energy and matter, interrelating these three phenomena.
• Formulate complex mathematical models representing real systems in both steady state and non-steady state.
• Develop simple analytical models to obtain the individual and global transport coefficients needed to s o l v e real problems.
• To understand the concept of numerical simulation and the scope of this tool for solving engineering problems.
• Understand the fundamentals of the finite element method.
• Numerically approach simplified models for which it is easy to obtain an analytical solution, as well as models of greater complexity for whose resolution the use of numerical simulation is essential.

1. Introduction to numerical simulation

1.1. Finite element method.
1.2. Introduction to Comsol Multiphysics software package
1.3. Analysis and interpretation of numerical simulation results.

2. Transit of movement quantity

2.1. Introduction to transport phenomena. Levels of description of transport phenomena. Nomenclature. Viscosity and mechanisms of transport of quantity of motion: Newton's law of viscosity. Generalization of Newton's law.
2.2. Microscopic level balances of quantity of motion in envelopes. Velocity distributions for one-dimensional flow in laminar regime in steady state. Boundary conditions.
2.3. Conservation equations in isothermal systems: Continuity equation. Equation of motion. Use of conservation e q u a t i o n s to solve problems.
2.4. Transport of quantity of movement in turbulent flow: Introduction to turbulent flow. Average conservation equations. Introduction to individual and global transport coefficients.
2.5. Numerical simulation of single-phase fluids in laminar regime in two and three dimensions.

3. Heat Transfer
3.1. Transport by conduction, thermal conductivity. Fourier's law. Variation equations for non-isothermal systems in steady state. Conduction with generation. Temperature distribution in solids.
3.2. Convective transport. Transport coefficients. Forced and free convection. Temperature distribution in laminar flow.
3.3. Energy equations.
3.4. Numerical simulation: heat transfer in solids; heat transfer in fluids.

4. Mass Transfer

4.1. Fundamentals and general concepts of mass transfer. Fick's law of diffusion. Velocities of species in diffusion. Continuity equations for different geometries. Most common boundary conditions.
4.2. Steady state molecular diffusion with chemical reaction. Heterogeneous chemical reaction. Homogeneous chemical reaction.
4.3. Numerical simulation: diffusion without convection; diffusion with convection; diffusion with chemical reaction.

BIBLIOGRAFÍA BÁSICA

• BIRD R.B STEWART W.E. AND LIGHTFOOT E.N, Transport Phenomena. 2ª ed. Revised, New York: John Wiley & Sons, 2007. ISBN: 978-0-470-11539-8. SINATURA ETSE: SOLICITADO EBOOK

• BIRD R.B STEWART W.E. Y. LIGHTFOOT E.N, Fenómenos de Transporte. Barcelona: Editorial Reverte, 2006 (y ediciones anteriores). ISBN 8429170502. SINATURA ETSE: A111 2 E, A111 2 F

• BIRD R.B. STEWART W.E. y LIGHTFOOT E.N. Transport Phenomena. 2ª ed. New York: John Wiley & Sons, 2007 (y ediciones anteriores). ISBN 0-471-41077-2. SINATURA ETSE: A111 1, 111 20

• COMSOL Multiphysics User’s Guide. Disponible en línea https://www.comsol.com/


BIBLIOGRAFÍA COMPLEMENTARIA

• WELTY J.R. WICKS, C. Fundamentos de transferencia de momento, calor y masa. 2ª ed México: Limusa, 1999. ISBN 968-18-5896-4. SINATURA ETSE: A111 3E

• RASMUSON, ANDERS ET AL. Mathematical Modeling in Chemical Engineering. Cambridge: Cambridge University Press, 2014. ISBN 978-1-107-04969-7. SINATURA ETSE: 010 37

• DOBRE, T.G., SANCHEZ MARCANO, J.G., Chemical Engineering: Modelling, Simulation and Similitude, Wiley-VCH, 2007. ISBN: 9783527306077

• FINLAYSON, B. A., Introduction to chemical engineering computing, USA, John Wiley & Sons, 2006. ISBN-10: 0-471-74062-4. SINATURA ETSE: A012 46.

• FINLAYSON, B. A., Introduction to chemical engineering computing, USA, John Wiley & Sons, 2006. ISBN-10: 0-471-74062-4. Disponible en línea:
https://ebookcentral-proquest-com.ezbusc.usc.gal/lib/buscsp/reader.acti…

• FINLAYSON, B. A. Introduction to Chemical Engineering Computing. Second edition. Wiley, 2014. SINATURA ETSE: A012 46 A

• REDDY, J. N. Introduction to the Finite Element Method, Fourth Edition /. 4th edition. New York, N.Y: McGraw-Hill Education, 2019. Disponible en línea:
https://www-accessengineeringlibrary-com.ezbusc.usc.gal/content/book/97…

• RICE, R. G., Do, D., Applied Mathematics and Modelling for Chemical Engineers, 2nd Ed., John Wiley & Sons, 2012. ISBN-10: 1118024729

Knowledge

(CN02) Acquire advanced knowledge and demonstrate, in a scientific and technological or highly specialized
research context, a detailed and grounded understanding of the theoretical and practical aspects and
methodology of work in one or more fields of study in Chemical Engineering.

Competition

(CP01) Apply knowledge of mathematics, physics, chemistry, biology, and other natural sciences, obtained
through study, experience, and practice, with critical reasoning to establish economically viable solutions to
technical problems.
(CP02) Conceptualize engineering models, apply innovative methods in problem solving and appropriate
computer applications, for the design, simulation, optimization and control of processes and
systems.
(CP03) Design products, processes, systems and services of the chemical industry, as well as the optimization of
others already developed, taking as a technological basis the different areas of chemical engineering, including
processes and transport phenomena, separation operations and engineering o f chemical, nuclear,
electrochemical and biochemical reactions.

Ability

(HD01) Have the ability to solve problems that are unfamiliar, incompletely defined, and have c omp e t i n g
specifications, considering possible solution methods, including the most innovative, selecting the most
appropriate, and be able to correct the i m p l e m e n t a t i o n , evaluating different design solutions.
(HD04) Search, process, analyze and synthesize, in a critical way, information from different sources for the
establishment of the corresponding conclusions.

The subject has been assigned 6 ECTS credits that will be developed over 12 hours of theoretical teaching, 16 hours of interactive seminar teaching and 24 hours of interactive computer classroom teaching and 1 hour of small group tutorials per student. The Virtual Campus (Moodle) will be used as a tool to provide information/announcements about the teaching activity throughout the course and complementary materials for the study of the subject.

Lectures will be used to develop a part of the syllabus. Before starting a topic, the teacher will describe the contents in a generic way, relating them to each other and to previous topics so that the students can appreciate the importance of the topic. At the end of the subject, a small balance of what has been seen will be made, emphasizing the aspects that may present more difficulties to the student.

The seminar classes will be basically dedicated to problem solving and case studies related to the theoretical concepts. Both in the expository and interactive classes, the aim will be to raise real issues and questions to arouse interest and clarify concepts. Different activities will be proposed throughout the development of the subject that will be associated with the delivery through the Virtual Campus of written documents or the realization of oral sessions (face-to-face or telematic), evaluable in both cases.

The computer classroom classes will have an eminently practical character but without losing sight of the basic fundamentals of the numerical methods used. For each of the examples considered, a brief description of the underlying real problem and the mathematical model used to approach it will be made, as well as the simplifications adopted to approach its numerical resolution. We will proceed to its resolution by means of the Comsol Multiphysics software package, carrying out a critical analysis of the results obtained, which will also allow validating the models.

A compulsory group work will consist of applying the microscopic balances of matter, energy and quantity of movement to a real industrial process and its simulation with the Comsol Multiphysics software. The work will be presented and defended in the group tutorial on the date officially marked in the calendar.

During all these activities, and given the eminently practical nature of the classes, students are expected to develop the competencies associated with the methodology used:

Lectures: CN02
Seminar classes: CN02, CP01, CP02, CP03, HD01
Computer classroom classes: CN02, CP01, CP02, CP03, HD01
Group work: CN02, CP01, CP02, CP02, CP03, HD01
Group Tutoring: HD04

The assessment of the subject consists of two parts: a final exam and a group work. Both the final exam and the group work will assess the competences acquired in Modelling with Transport Phenomena (MFT) and in Simulation with Numerical Methods (SMN) separately. In particular:

1. The final exam will consist of two parts: a theoretical-practical part corresponding to the MFT part and a practical part on computer corresponding to the SMN part.

2. The work will consist of applying the microscopic balances of matter, energy and quantity of movement to a chemical engineering process and its simulation using Comsol Multiphysics software. The work will be presented and defended in the group tutorial on the date officially marked in the timetable.

Grading of the subject:
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A minimum of 3 out of 10 will be required in the exam, as well as in the work and the tutorial of each of the parts (SMN and MFT) in order to pass the subject. Depending on whether or not this minimum is reached, two cases are distinguished:

- CASE A) If the minimum mentioned above is reached, the grades in each of the parts are calculated as:

CMFT = 0.7 * NE1 + 0.25 * NT1 + 0.05 * NET1
CSMN = 0.7 * NE2 + 0.25 * NT2 + 0.05 * NET2

where:

- CMFT: Rating corresponding to the transport phenomena modelling part,
- CSMN: Rating corresponding to the part of simulation with numerical methods,
- NE1/2: Grade of the written exam in the MFT/SMN part, NT1/2: Grade of the written exam in the MFT/SMN part
- NT1/2: Grade for the paper in the MFT/SMN part, NT1/2: Grade of the paper in the MFT/SMN part
- NET1/2: Grade obtained in the presentation of the paper in the MFT/SMN part.

In this case, the final grade of the subject is defined as follows:

If CMFT >= 4 and CSMN >= 4, then CF = ( CMFT + CSMN )/2 2.
2. Otherwise, CF= min(4, (CMFT+CSMN)/2).

If, as a result of this operation, CF >=5, the subject is considered passed and the grade CF obtained is assigned to the record.
Otherwise, if CF< 5, the subject is failed.

- CASE B) If the minimum of 3 out of 10 mentioned above is not reached, the final grade will be calculated as follows:

CF = Min(3, (CMFT+CSMN)/2).

In the event of failing the subject at the first opportunity, it may be made up at the second assessment opportunity. The student may sit the parts with a grade lower than 5. In order to pass the subject at the second opportunity, it is necessary to reach the minimums previously established in each part of the subject.

Repeating students:
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They will follow the same evaluation system as students enrolled for the first time.


Evaluation of activities and competences:
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Examination: CN02, CP01, CP02, CP03, HD01
Group work: CN02, CP01, CP02, CP03, HD01
Group tutoring: HD04


Fraudulent tests:
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For cases of fraudulent performance of exercises or tests, the provisions of the Regulations on the assessment of students' academic performance and the review of qualifications shall apply.

It is estimated a total of 150 hours (6 ECTS), which are divided between 58 classroom hours and 92 hours of autonomous work of the student. The distribution of classroom hours according to the type of activity will be as follows:

- Theoretical teaching: 12 h
- Interactive seminar teaching / technical visit: 16 h
- Interactive laboratory/computer classroom teaching: 24 h
- Small group tutoring: 1 h
- Examination and review: 5 h

Attendance and active participation in the classes of this subject.

The subject will be taught in Spanish. If necessary, doubts will be answered in English to foreign students.