Mechanical Engineering

Part A. Turbulence The statistical approach to Turbulence: Averages, probability distributions and conditional probability distributions. The transport equation for probability distributions. Basic concepts in turbulence: Reynolds decomposition and the averaged Navier-Stokes equations. Mean field kinetic energy. Turbulent kinetic energy, production dissipation and transport. Turbulent wall bounded flows: Friction velocity, characteristic scales and the law of the wall. The overlap region and the friction law. Turbulent jets: Turbulent jet dynamics and the entrainment process. Momentum flux and the similarity law for the mean velocity profile. Small scale turbulence: The energy spectrum, spectral energy balance and the Kolmogorov law. Structure functions and the Kolmogorov equation. Part B. Combustion Statistical mechanics: Hamilton’s equations and the Liouville equation. The notion of ensemble in statistical mechanics, the microcanonical ensemble. Canonical ensemble, partition functions, free energy and energy equipartition. Thermodynamics: Perfect gases and mixtures. Internal energy, entropy, pressure, chemical potential. The enthalpy of a mixture. Transport process kinetics: Chemical potential and affinity. Constitutive relations for mass fluxes. Chemical kinetics: Reaction order and reaction rates. Arrhenius expression for the reaction speed. Reaction mechanisms. The Navier-Stokes equation for a reacting mixture: The equation for the mass of the species in a reacting mixture. Mass conservation for a mixture. Peculiar momentum and total momentum conservation. Energy conservation: total energy, internal energy, entropy, enthalpy and temperature equations. The low Mach number limit of the Navier-Stokes equations. Laminar flames: Premixed flames and the Zeldovich/Frank-Kamenetsii model. Jump relations across a thin combustion front. Non-premixed flames. Turbulent flames: Classification of turbulent premixed flames and the Borghi diagram. The flamed model and the turbulent reaction speed. Turbulent non-premixed flames.

Good knowledge of calculus and basic understanding of ordinary and partial differential equations. Good understanding of mechanics, basic physics, thermodynamics and elementary chemistry. Good knowledge of fluid dynamics.

Turbulence. Lecture notes. Combustion. Lecture notes. Turbulent Flows, Stephen B. Pope, Cabridge University Press Combustion Physics, Chung K. Law, Cambridge University Press Warnatz, Maas, Dibble. Combustion, Springer Peters. Turbulent Combustion, Cambridge University Press.

The corse is mainly taught through lessons delivered to the class. Almost one fourth of the course is spent by the student in laboratory classes where he/she learns basic elements for the numerical simulation of turbulent and reactive flows.

Although not mandatory, attendance to class lecture is warmly encouraged.

The final evaluation consists in a written exam to be completed in 3 hours followed by an oral discussion typically taking place the following day. The written exam consists of a series of open questions (typically four) concerning the different prats of the program illustrated during the lectures. Each answer is evaluated with a mark ranging from 1 to 10 and the final score is obtained by averaging the partial marks and rescaling in the range 1 to 30. The following oral discussion is focused on the answers given by the student in the written exam with additional questions concerning laboratory lectures and subjects autonomously elaborated by the student. The exam is illustrated and discussed with the students twice: in the introductory lecture of the course and at the end of the semester. The exam aims at evaluating knowledge and skills acquired by the student along the lines described in the “training goals” (obiettivi formativi). In particular: comprehension of concepts and analysis techniques illustrated in the class;

The corse is mainly taught through lessons delivered to the class. Almost one fourth of the course is spent by the student in laboratory classes where he/she learns basic elements for the numerical simulation of turbulent and reactive flows.

Part A. Turbulence The statistical approach to Turbulence: Averages, probability distributions and conditional probability distributions. The transport equation for probability distributions. Basic concepts in turbulence: Reynolds decomposition and the averaged Navier-Stokes equations. Mean field kinetic energy. Turbulent kinetic energy, production dissipation and transport. Turbulent wall bounded flows: Friction velocity, characteristic scales and the law of the wall. The overlap region and the friction law. Turbulent jets: Turbulent jet dynamics and the entrainment process. Momentum flux and the similarity law for the mean velocity profile. Small scale turbulence: The energy spectrum, spectral energy balance and the Kolmogorov law. Structure functions and the Kolmogorov equation. Part B. Combustion Statistical mechanics: Hamilton’s equations and the Liouville equation. The notion of ensemble in statistical mechanics, the microcanonical ensemble. Canonical ensemble, partition functions, free energy and energy equipartition. Thermodynamics: Perfect gases and mixtures. Internal energy, entropy, pressure, chemical potential. The enthalpy of a mixture. Transport process kinetics: Chemical potential and affinity. Constitutive relations for mass fluxes. Chemical kinetics: Reaction order and reaction rates. Arrhenius expression for the reaction speed. Reaction mechanisms. The Navier-Stokes equation for a reacting mixture: The equation for the mass of the species in a reacting mixture. Mass conservation for a mixture. Peculiar momentum and total momentum conservation. Energy conservation: total energy, internal energy, entropy, enthalpy and temperature equations. The low Mach number limit of the Navier-Stokes equations. Laminar flames: Premixed flames and the Zeldovich/Frank-Kamenetsii model. Jump relations across a thin combustion front. Non-premixed flames. Turbulent flames: Classification of turbulent premixed flames and the Borghi diagram. The flamed model and the turbulent reaction speed. Turbulent non-premixed flames.

Good knowledge of calculus and basic understanding of ordinary and partial differential equations. Good understanding of mechanics, basic physics, thermodynamics and elementary chemistry. Good knowledge of fluid dynamics.

Turbulence. Lecture notes. Combustion. Lecture notes. Turbulent Flows, Stephen B. Pope, Cabridge University Press Combustion Physics, Chung K. Law, Cambridge University Press Warnatz, Maas, Dibble. Combustion, Springer Peters. Turbulent Combustion, Cambridge University Press.

The corse is mainly taught through lessons delivered to the class. Almost one fourth of the course is spent by the student in laboratory classes where he/she learns basic elements for the numerical simulation of turbulent and reactive flows.

Although not mandatory, attendance to class lecture is warmly encouraged.

The final evaluation consists in a written exam to be completed in 3 hours followed by an oral discussion typically taking place the following day. The written exam consists of a series of open questions (typically four) concerning the different prats of the program illustrated during the lectures. Each answer is evaluated with a mark ranging from 1 to 10 and the final score is obtained by averaging the partial marks and rescaling in the range 1 to 30. The following oral discussion is focused on the answers given by the student in the written exam with additional questions concerning laboratory lectures and subjects autonomously elaborated by the student. The exam is illustrated and discussed with the students twice: in the introductory lecture of the course and at the end of the semester. The exam aims at evaluating knowledge and skills acquired by the student along the lines described in the “training goals” (obiettivi formativi). In particular: comprehension of concepts and analysis techniques illustrated in the class;

The corse is mainly taught through lessons delivered to the class. Almost one fourth of the course is spent by the student in laboratory classes where he/she learns basic elements for the numerical simulation of turbulent and reactive flows.

The course will be taught by Prof. Casciola and Prof. Giacomello. The following syllabus refers to part taught by Prof. Giacomello. Laminar shear flows: - parallel flows - boundary layer flows - Blasius solution - Falkner-Skan solution Stability of shear flows: - Reynolds-Orr equation - Linear inviscid analysis - Viscous linear stability - Non-linear stability Noise production in turbulence - wave equation - solutions to the wave equation - mass injection in a flow - Lighthill's analogy - acoustic energy equation - Integral representations - Kirkhhoff's formula - Fraunhofer approximation - Lighthill's theory of jet noise

Good knowledge of calculus and basic understanding of ordinary and partial differential equations. Good understanding of mechanics, basic physics, thermodynamics and elementary chemistry. Good knowledge of fluid dynamics.

Turbulence. Lecture notes. Combustion. Lecture notes.

The course is mainly taught through lessons delivered to the class.

optional

The final evaluation consists in a single written exam for both the parts taught by Prof. Casciola and by Prof. Giacomello. The exam is to be completed in 3 hours followed by an oral discussion typically taking place the following day. The written exam consists of a series of open questions (typically four) concerning the different parts of the program illustrated during the lectures. Each answer is evaluated with a mark ranging from 1 to 10 and the final score is obtained by averaging the partial marks and rescaling in the range 1 to 30. The following oral discussion is focused on the answers given by the student in the written exam with additional questions concerning laboratory lectures and subjects autonomously elaborated by the student. The exam is illustrated and discussed with the students twice: in the introductory lecture of the course and at the end of the semester. The exam aims at evaluating knowledge and skills acquired by the student along the lines described in the “training goals” (obiettivi formativi). In particular: a) comprehension of concepts and analysis techniques illustrated in the class; b) capability of autonomous learning; c) capability of critical assessment of problems in turbulent and/or combustion. d) communication skills and ability in synthesizing complex issues.

Schmid, P. J., & Henningson, D. S. (2012). Stability and Transition in Shear Flows (Vol. 142). Springer Science & Business Media. Rienstra, S.W. & Hirschberg, A. An Introduction to Acoustics. Eindhoven University of Technology

The course is mainly taught through lessons delivered to the class.

The course will be taught by Prof. Casciola and Prof. Giacomello. The following syllabus refers to part taught by Prof. Giacomello. Laminar shear flows: - parallel flows - boundary layer flows - Blasius solution - Falkner-Skan solution Stability of shear flows: - Reynolds-Orr equation - Linear inviscid analysis - Viscous linear stability - Non-linear stability Noise production in turbulence - wave equation - solutions to the wave equation - mass injection in a flow - Lighthill's analogy - acoustic energy equation - Integral representations - Kirkhhoff's formula - Fraunhofer approximation - Lighthill's theory of jet noise

Good knowledge of calculus and basic understanding of ordinary and partial differential equations. Good understanding of mechanics, basic physics, thermodynamics and elementary chemistry. Good knowledge of fluid dynamics.

Turbulence. Lecture notes. Combustion. Lecture notes.

The course is mainly taught through lessons delivered to the class.

optional

The final evaluation consists in a single written exam for both the parts taught by Prof. Casciola and by Prof. Giacomello. The exam is to be completed in 3 hours followed by an oral discussion typically taking place the following day. The written exam consists of a series of open questions (typically four) concerning the different parts of the program illustrated during the lectures. Each answer is evaluated with a mark ranging from 1 to 10 and the final score is obtained by averaging the partial marks and rescaling in the range 1 to 30. The following oral discussion is focused on the answers given by the student in the written exam with additional questions concerning laboratory lectures and subjects autonomously elaborated by the student. The exam is illustrated and discussed with the students twice: in the introductory lecture of the course and at the end of the semester. The exam aims at evaluating knowledge and skills acquired by the student along the lines described in the “training goals” (obiettivi formativi). In particular: a) comprehension of concepts and analysis techniques illustrated in the class; b) capability of autonomous learning; c) capability of critical assessment of problems in turbulent and/or combustion. d) communication skills and ability in synthesizing complex issues.

Schmid, P. J., & Henningson, D. S. (2012). Stability and Transition in Shear Flows (Vol. 142). Springer Science & Business Media. Rienstra, S.W. & Hirschberg, A. An Introduction to Acoustics. Eindhoven University of Technology

The course is mainly taught through lessons delivered to the class.