Menù principale
B027567 - MATHEMATICAL MODELS OF FLUID DYNAMICS
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Teaching Methods
Further information
Type of Assessment
Course program
Academic Year 2021-22
Coorte 2021 - Second Cycle Degree in Mechanical Engineering
Course year
First year - First Semester
Belonging Department
Industrial Engineering (DIEF)
Course Type
Single education field course
Scientific Area
MAT/07 - MATHEMATICAL PHYSICS
Credits
6
Teaching Hours
48
Teaching Term
13/09/2021 ⇒ 17/12/2021
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Mutuality
Course teached as:
B027567 - MODELLI MATEMATICI PER LA FLUIDODINAMICA
Second Cycle Degree in MECHANICAL ENGINEERING
Curriculum MODELLI PER L'INGEGNERIA INDUSTRIALE
B027567 - MODELLI MATEMATICI PER LA FLUIDODINAMICA
Second Cycle Degree in MECHANICAL ENGINEERING
Curriculum MODELLI PER L'INGEGNERIA INDUSTRIALE
Teaching Language
ITALIAN
Course Content
Incompressible gasdynamics
Compressible gasdynamics
Newtonian fluids
Turbulence (hints).
Compressible gasdynamics
Newtonian fluids
Turbulence (hints).
Suggested readings (Search our library's catalogue)
1) Moodle learning platform: Lectures Note.
2) A.J. Chorin, J. E. Marsden: A mathematical introduction to fluid mechancs, Springer, 1980.
3) C. Trusdell, K.R. Rajagopal: An introduction to fluid mechanics, Birkhauser, 2000.
2) A.J. Chorin, J. E. Marsden: A mathematical introduction to fluid mechancs, Springer, 1980.
3) C. Trusdell, K.R. Rajagopal: An introduction to fluid mechanics, Birkhauser, 2000.
Learning Objectives
CA3: Applying knowledge and understanding related to the choice and application of appropriate analytical and modelling methods, based on mathematical and numerical analysis, in order to better simulate the behavior of components and plants in order to predict and improve their performance.
CA10: Applying advanced knowledge and understanding to operate effectively, individually and as members of a group, having a clear understanding of the context of engineering problems and of the interdisciplinary implications that characterize mechanical engineering.
CA12: Applying adequate knowledge and understanding to understand English texts.
CC2: In-depth knowledge and understanding of the theoretical-scientific aspects of mathematics and other basic sciences. To be able to use this knowledge to interpret and describe complex and/or interdisciplinary engineering problems.
CA10: Applying advanced knowledge and understanding to operate effectively, individually and as members of a group, having a clear understanding of the context of engineering problems and of the interdisciplinary implications that characterize mechanical engineering.
CA12: Applying adequate knowledge and understanding to understand English texts.
CC2: In-depth knowledge and understanding of the theoretical-scientific aspects of mathematics and other basic sciences. To be able to use this knowledge to interpret and describe complex and/or interdisciplinary engineering problems.
Teaching Methods
Lectures: Presentation of the theory described in the course program, with teacher-student direct interaction, to ensure a full understanding of the subject.
Further information
Office hours Prof. Farina, by prior appointmentDipartimento di Matematica e Informatica "Ulisse Dini"
Viale Morgagni, 67/a
50134 - Firenze (FI)
Tel: 055 2751435
E-Mail: angiolo.farina@ unifi.it
Viale Morgagni, 67/a
50134 - Firenze (FI)
Tel: 055 2751435
E-Mail: angiolo.farina@ unifi.it
Type of Assessment
Final oral examination. A number of questions are posed. The oral examination is designed to evaluate the degree of understanding of the theory presented in the course. In the assessment, special attention is paid to communication skills, critical thinking and appropriate use of mathematical language.
Course program
INCOMPRESSIBLE GASDYNAMICS
• Ideal and incompressible fluids and their dynamics• Vorticity• Bernulli theorems, Lagrange-Thompson• Contour conditions• Stream function and potential function• External flow and aerodynamic action• D'Alambert's Paradox• Kutta-Joukowski's theorem• Conformal transformations• Plate, circle arch and generic Jukoswski profile.
COMPRESSIBLE GASDYNAMICS
• Thermodynamics of perfect fluids.• Sound speed, Mach number, fluid compressibility.• Sound waves.• Supersonic flows around thin profiles.• Characteristics lines.• Riemann Invariants• Prandtl-Meyer flows• Shock waves• Wave flat discontinuity finished. Rankine-Hugoniot Relations.• Uniqueness and condition of entropy.
NEWTONIAN FLUIDS
• Dynamics of incompressible Newtonian fluids• Equations by Navier-Stokes• Vorticity in Newtonian Fluids• Reynolds Number, laminar and turbulent regime• Some laminar flows: Hagen-Poiseuille and Couette• Laminar boundary layer• Exact solutions for flat plate• Laminar separation
TURBOLENCE (hints)
• Ideal and incompressible fluids and their dynamics• Vorticity• Bernulli theorems, Lagrange-Thompson• Contour conditions• Stream function and potential function• External flow and aerodynamic action• D'Alambert's Paradox• Kutta-Joukowski's theorem• Conformal transformations• Plate, circle arch and generic Jukoswski profile.
COMPRESSIBLE GASDYNAMICS
• Thermodynamics of perfect fluids.• Sound speed, Mach number, fluid compressibility.• Sound waves.• Supersonic flows around thin profiles.• Characteristics lines.• Riemann Invariants• Prandtl-Meyer flows• Shock waves• Wave flat discontinuity finished. Rankine-Hugoniot Relations.• Uniqueness and condition of entropy.
NEWTONIAN FLUIDS
• Dynamics of incompressible Newtonian fluids• Equations by Navier-Stokes• Vorticity in Newtonian Fluids• Reynolds Number, laminar and turbulent regime• Some laminar flows: Hagen-Poiseuille and Couette• Laminar boundary layer• Exact solutions for flat plate• Laminar separation
TURBOLENCE (hints)