


Politecnico di Torino  
Academic Year 2016/17  
01NMFQD Advanced engineering thermodynamics/Numerical modelling 

Master of sciencelevel of the Bologna process in Mechanical Engineering  Torino 





Subject fundamentals
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. 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. 
Expected learning outcomes
The objective is to convey to the student indepth 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.
Additionally, the subject provides 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 of consistency, stability and convergence of numerical methods. The student is expected to learn how to use theoretical tools for studying heat transfer and energy balance of real systems, performing 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(r) 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. 
Prerequisites / Assumed knowledge
Thermodynamics and heat transfer basics.
Calculus, linear algebra and geometry basics. Basic knowledge of computer programming techniques and coding in compiled languages as Fortran or C. 
Contents
Concerning the first part, about advanced engineering thermodynamics, further details about the program are provided. There are essentially 5 chapters.
CLASSICAL MOLECULAR DYNAMICS and KINETIC THEORY. Introduction to classical molecular dynamics. Bond and nonbond 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. The distribution function dynamics. Linear relaxation towards the local equilibrium: Bhatnagar–Gross–Krook (BGK) model. Practical examples. CONTINUUM THERMOMECHANICS. 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 NavierStokesFourier 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 GuyStodola. Physical meaning of exergy. Efficiency according to the second principle. Examples of exergy analysis. Exergy diagrams. Thermodynamic diagrams. 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. 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 WeberFechner. Diagram of the normal acoustic response. Acoustic field, feeling and the intensity level, decibels. Isophon 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. Concerning the model of numerical modelling, the program of class lessons is provided below. General concepts about partial differential equations; boundary and initial conditions; properties of solutions. 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. Mathematical properties of consistency, stability and convergence of the numerical schemes. Modal analysis; the free vibration of a membrane; discretization of eigenvalue 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. Convectiondiffusion 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. 
Delivery modes
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 5 teams, as many as the number of applications. For each theme, they must provide (a) calculation of an offdesign 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. 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. 
Texts, readings, handouts and other learning resources
TEXTS, READINGS, HANDOUTS AND OTHER LEARNING RESOURCES
 P. Asinari, E. Chiavazzo, An Introduction to Multiscale Modeling with Applications, Società Editrice Esculapio, Bologna 2013.  M. Calì, P. Gregorio, "Termodinamica" Esculapio, Bologna 1997.  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.  Claudio Canuto, "Numerical Models and Methods", notes of the lectures with exercises, available online on the "Portale della Didattica".  Alfio Quarteroni, "Numerical Models for Differential Problems", Springer 2007 
Assessment and grading criteria
The exam consists of a written part and an oral part. The written part consists in a) solving a few exercises on the main topics treated in the module of Numerical Modelling, and b) answering some multiplechoice questions, by means of MATLAB. In forming the writtenpart mark, the teacher will take into account the possible, noncompulsory preparation of a computational project during the semester, developed by a small group of students on one of the topics discussed in the module of Applied Engineering Thermodynamics.
The oral examination is based on the detailed discussion of the topics proposed during the lessons of the module of applied engineering thermodynamics and the projects developed in the same module. An optional report about one of the laboratory of applied thermodynamics may ensure a maximum +2 bonus in the final examination score. The final mark is the average between the marks obtained in the written part and oral part. 
