PORTALE DELLA DIDATTICA

PORTALE DELLA DIDATTICA

PORTALE DELLA DIDATTICA

Elenco notifiche



Advanced engineering thermodynamics/Numerical modelling

01NMFQD

A.A. 2023/24

2023/24

Advanced engineering thermodynamics/Numerical modelling (Advanced topics of Engineering Thermodynamics)

The subject consists of two parts: the first one discusses some advanced topics in the field of engineering thermodynamics, the second one discusses the use of numerical methods for solving engineering problems. In particular, the modeling and numerical methods are applied to meaningful test cases relevant for engineering thermodynamics. The module of Advanced Engineering Thermodynamics is designed to complete the student's preparation in the field of engineering thermodynamics, whose basics were provided in previous subjects. This teaching module completes the theoretical background required by the design of devices with regards to the specific problems involving heat transfer. In particular, the subject discusses the thermal performance of energy components and mechanical systems and it provides some basic concepts about numerical fluid dynamics, including modeling of heat transfer systems. Finally, the basic concepts of environmental acoustics and lighting are provided in order to characterize the interaction of the devices with the end users.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

The module of Numerical Modelling is intended to provide the tools for the systematic and critical study of the main numerical models involving partial derivatives and used in various fields of engineering, which can be solved by appropriate numerical discretization methods. In particular, the module aims to provide the essential features for evaluating a numerical method in terms of the quality and the reliability of the numerical solution. Some test cases will be discussed in the field of advanced engineering thermodynamics.

Advanced engineering thermodynamics/Numerical modelling (Advanced topics of Engineering Thermodynamics)

The objective is to convey to the student in-depth knowledge of thermomechanical continuous media, thermodynamics and fluid dynamics, with particular emphasis on the concept of exergy, and, as regards the interaction with the end user, the basic elements of environmental acoustics and lighting. The student is expected to learn how to use theoretical tools for studying heat transfer and energy balance of real systems, performing energy and exergy analysis of complex real systems (including using appropriate mathematical models) and managing complex energy conversion systems. Another objective is to convey to the student the ability to understand the regulations about environmental acoustics and lighting and to perform basic design calculations.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

The student should acquire the basic knowledge about the discretization methods for initial and boundary value problems involving elliptic, parabolic and hyperbolic partial differential equations (PDEs). Some emphasis is put on the basic mathematical properties (such as consistency, stability and convergence) of numerical methods. Students should become able to transform numerical models into systems of algebraic equations, and to solve these systems. The student is expected to learn how to use theoretical tools for studying heat transfer and energy balance of real systems, performing energy and energy analysis of complex real systems (including using appropriate mathematical models) and managing complex energy conversion systems. Another objective is to convey to the student the ability to understand the regulations about environmental acoustics and lighting and to perform basic design calculations. Finally, the student is expected to learn the ability to implement in the MATLAB software, or similar ones, some numerical models that describe engineering problems (particularly those relevant to engineering thermodynamics) and to relate their performances to the theoretical context. The student should also develop the ability of applying the numerical tools to the simulation of the behaviour of simple yet significant problems in applied thermodynamics.

Advanced engineering thermodynamics/Numerical modelling (Advanced topics of Engineering Thermodynamics)

Thermodynamics and heat transfer basics.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

Thermodynamics and heat transfer basics. Calculus, linear algebra and geometry basics. Basic knowledge of computer programming techniques and coding in programming languages as C, C++, MATLAB o Python.

Advanced engineering thermodynamics/Numerical modelling (Advanced topics of Engineering Thermodynamics)

Concerning the first part, about advanced engineering thermodynamics, further details about the program are provided. There are essentially 5 chapters. CLASSICAL MOLECULAR DYNAMICS. Introduction to classical molecular dynamics. Bond and non-bond interactions. Force fields. Elementary numerical schemes (Verlet integration). Elementary statistical ensembles: Thermostats and barostats. Practical examples. Large systems approaching the local equilibrium: Maxwellian distribution function. Practical examples. CONTINUUM THERMO-MECHANICS. Deduction of the equation of mass and momentum conservation by both kinetic local equilibrium and by elementary control volume. Deduction of the wave equation. Small deviations from the conditions of local equilibrium. Phenomenological relations in Navier-Stokes-Fourier equations: Stress tensor and thermal flux. Generalization of the results obtained by the ideal gas to other types of fluids. Dimensionless equations. Meaning of dimensionless numbers. Incompressible limit. Equation for kinetic energy and enthalpy. First principle of thermodynamics. Generalization of entropy for continuous body. Generalization of Gibbs’s correlation. The second principle of thermodynamics for a continuous body. Work, heat and the thermodynamics of irreversible processes. THERMAL DESIGN. Deduction of the integral equations for closed systems and open systems. Technical formulation of integral equations. Physical meaning of irreversibility. Correct calculation of irreversibility by practical formulas. Turbulence and turbulent flows. Characteristic scales of the phenomenon, deduction of the equations for the average quantities and the closure problem. Artificial viscosity induced by turbulence and modeling. Exergy balance in a reversible system. Exergy and internal exergy for an ideal gas. The theorem of Guy-Stodola. Physical meaning of exergy. Efficiency according to the second principle. Examples of exergy analysis. Exergy diagrams. Thermodynamic diagrams. ACOUSTICS. Deduction of the wave equation. Introduction, elastic, plane, longitudinal and progressive waves. Propagation speed of elastic waves; sound speed of air. Mechanical power transported by sound wave, wave intensity, resistance and effective pressure. Acoustic intensity and acoustic feeling: Law of Weber-Fechner. Diagram of the normal acoustic response. Acoustic field, feeling and the intensity level, decibels. Iso-phon curves. Frequency bands, level of pressure, interpolating weight curve A. Interaction between elastic waves and materials, factors of reflection, transmission, absorption, apparent absorption. Effect of frequency. Apparent absorption factor of several walls. Acoustics in open environments. Open field. Sound tail. Acoustic energy balance and reverberation, reverberation time by conventional formula of Sabine. Sound insulation; sound proofing; plain wall and law of mass and frequency; case study for a pipe. LIGHTING. Deduction of the radiative transfer equation (RTE) from kinetic theory. The light, electromagnetic radiation, main features, diffuse radiation. Visual perception and photometric system. Definition of physical units of measured quantities. Point source. Light intensity. Indicator of emission. Light flux emitted from a point source with a given indicator of emission. The first formula of Lambert. Linear source, linear luminance, and lighting calculations on surface. Surface source, luminance, and lighting calculation on a surface. The second law of Lambert. Lambert emitter. Efficiency of a light bulb.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

Concerning the model of numerical modelling, the program of class lessons is provided below. INTRODUCTORY PART. General concepts about partial differential equations; boundary and initial conditions; properties of solutions. Basic concepts of numerical methods. STEADY-STATE PROBLEMS. Elliptic problems; the steady diffusion and the membrane equilibrium examples; discretization by centered finite differences; variational formulation; discretization by finite elements. Implementation of Dirichlet, Neumann and Robin boundary conditions. Reduction of the discrete problem to an algebraic problem; properties of the corresponding matrices; techniques for solving large systems of algebraic equations. Mathematical properties of consistency, stability and convergence of the numerical schemes. Modal analysis; the free vibration of a membrane; discretization of eigenvalue problems. TIME-DEPENDENT PROBLEMS. Formulation and discretization of evolutionary problems; parabolic and hyperbolic equations; the heat equation, the wave equation; mass lumping; time advancing techniques; asymptotic stability and choice of the time step; rate of convergence in space and time. Convection-diffusion problems; mesh Peclet number; centered versus upwind discretizations. Conservation and balance laws; characteristics; integral formulation; discretization by finite volumes; cell averages and numerical fluxes; review of the main classical methods; relation with finite differences; Courant number and CFL condition; numerical diffusion and dispersion; stability and convergence.

Advanced engineering thermodynamics/Numerical modelling (Advanced topics of Engineering Thermodynamics)

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

Advanced engineering thermodynamics/Numerical modelling (Advanced topics of Engineering Thermodynamics)

In addition to lessons, the following activities are provided. Concerning the first part of applied engineering thermodynamics, students are expected to develop a project. Students are divided into teams, each of them focusing on a different application. For each theme, they must provide (a) calculation of an off-design condition, (b) exergetic analysis and (c) all the technical details related to the design performed. To develop the project, specific notes are made available on the “Portale della Didattica”. In addition, some lectures are focused on the presentation of the guidelines for the project developments and practical examples. Concerning the part on applied acoustics, a practical application in class is developed, aiming at the evaluation of acoustic behavior of the room. In particular, three different analyses are performed: evaluation of the acoustic field, measurement of the reverberation time and measurements of the acoustic pressure.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

Concerning the part on numerical modeling, the following exercises and laboratory activity is developed: Mesh generation; construction of mass and stiffness matrices in various situations; iterative solution of large algebraic systems with sparse matrices; computation of the equilibrium configuration of several physical problems; analysis of the behavior of the spatial discretization error. Implementation of eigenvalue problems and modal analysis. Implementation of time advancing techniques; investigation on the stability of the schemes and the behavior of the temporal error; computation of the evolution of the temperature of a conducting body, and of the propagation of waves in an elastic body. Implementation of numerical schemes for scalar conservation laws and experimental investigation on their behavior.

Advanced engineering thermodynamics/Numerical modelling (Advanced topics of Engineering Thermodynamics)

- P. Asinari, E. Chiavazzo, An Introduction to Multiscale Modeling with Applications, Società Editrice Esculapio, Bologna 2013. - M. Calì, P. Gregorio, "Termodinamica" Esculapio, Bologna 1997. - A. Bejan, "Advanced Engineering Thermodynamic" John Wiley & Sons 1997. - G. Guglielmini, C. Pisoni, Introduzione alla trasmissione del calore, Casa Editrice Ambrosiana, 2002. - G. Comini, G. Cortella, Fondamenti di trasmissione del calore, Servizi Grafici Editoriali, 2001. - C. Canuto, "Metodi e Modelli Numerici ", note delle lezioni con esercizi, disponibile online sul Portale della Didattica. - A. Quarteroni, "Numerical Models for Differential Problems", Springer 2014.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

- C. Canuto, "Metodi e Modelli Numerici ", note delle lezioni con esercizi, disponibile online sul Portale della Didattica. - A. Quarteroni, "Numerical Models for Differential Problems", Springer 2014.

Advanced engineering thermodynamics/Numerical modelling (Advanced topics of Engineering Thermodynamics)

Lecture slides; Lecture notes; Exercise with solutions ; Video lectures (previous years); Self-assessment tools;

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

Advanced engineering thermodynamics/Numerical modelling (Advanced topics of Engineering Thermodynamics)

Exam: Written test; Compulsory oral exam; Group project;

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

Exam: Computer lab-based test; Written test; Group project;

Advanced engineering thermodynamics/Numerical modelling (Advanced topics of Engineering Thermodynamics)

The exam consists of a part related to the advanced engineering thermodynamics module and a part related to the numerical modeling module. The final evaluation of the exam is determined by the arithmetic average (rounded up) of the two partial scores obtained in the two modules. Regarding the advanced engineering thermodynamics module, the in-person exam follows the procedure described below: • In a equipped classroom at the university, each student will be given an online test on their computer via the Exam platform. The test may contain a maximum of 15 open-ended and/or multiple-choice questions that will focus on the fundamental aspects of the course, aiming to verify that the student has correctly grasped the theoretical foundations of continuum thermo-mechanics, thermodynamics, heat transfer, applied acoustics, and applied lighting covered in lectures and exercises. During this first part, the use of any teaching material or electronic support outside of the computer used for the exam is not allowed. The maximum time available to complete this part will be at least 40 minutes. The final score for this part will be a maximum of 15 points, always rounding up when necessary. It is necessary to achieve a minimum score of 5 points in this part to proceed to the subsequent oral evaluation. • Subsequently, a second part follows, where the student must demonstrate active participation in the group exercises and the related implementation of the application project by answering a second question from the teacher orally. In this way, through the analysis of a real system, it is verified that the student has acquired the knowledge of using thermal study tools, energy analysis, and exergy analysis of complex energy transformation systems. Alternatively, at the teacher's discretion, this second question may concern the exercise part on applied acoustics. The second question lasts approximately 30 minutes, and it is allowed to consult one's own group report. The maximum score for this part can be up to 18 points. • Each project group must submit the group project report and the report on applied acoustics at least one week before the exam date. The submission must be done through the Teaching Portal by uploading a single PDF file (containing both reports) in the "Elaborati" section. Only one representative per group is allowed to upload the file, making sure to include the names, surnames, and student ID numbers of each group member on the first page of the report. The final score for AET module will be calculated for each student by summing the score of the online test and the second part. The maximum score for this module will be 30 (possibly "cum laude" if the total score exceeds 30). The AET module is considered passed if the achieved score is at least 18, and both group reports have been submitted. For the overall calculation of the grade for both modules (i.e., AET and NM), a grade of 30 "cum laude" in each module is considered equivalent to 31 points.

Advanced engineering thermodynamics/Numerical modelling (Numerical modelling)

With regards to the module on Numerical Modeling, the evaluation procedure is based on the following tests: a) solving some exercises on the main topics covered in the module (available time: 60 minutes), b) answering a series of multiple-choice questions with the help of MATLAB using the Exam platform (available time: 45 minutes). No educational material is allowed in these tests. The mark of the written part will also take into account c) the optional preparation of a computational project during the semester, carried out by small groups of students on a numerical topic related to the group project developed in the advanced engineering thermodynamics module, and evaluated on the basis of the individual contribution. Tests a) and b) have a relative weight of 2/3 and 1/3, and overall they allow the student to obtain up to 28 points, whereas the computational project allows the student to obtain a higher mark than 28, including the laude. The mark of the written part will be communicated to students through the Portale della Didattica, together with the indication of when and where they can meet the teacher and check the results of their tests. Consistently with the expected learning outcomes, the written part of the exam aims to ensure the achievement of the following objectives: 1. In-depth knowledge of the main methods to numerically discretise a mathematical model and to translate it into a system of algebraic equations. This is accomplished by test a). 2. Ability to implement in MATLAB the numerical models presented in class. This is mainly established through test b), but also through test c). 3. Ability to apply the numerical tools to the simulation of the behaviour of physical problems of simple thermodynamic interest. This is establishes through test c).

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.
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