Fluid dynamics (2009/2010)

Course code
4S00258
Name of lecturers
Luigi Fraccarollo, Simone Zuccher
Coordinator
Luigi Fraccarollo
Number of ECTS credits allocated
6
Academic sector
MAT/07 - MATHEMATICAL PHYSICS
Language of instruction
Italian
Location
VERONA
Period
2nd Semester dal Mar 1, 2010 al Jun 15, 2010.

Lesson timetable

2nd Semester
Day Time Type Place Note
Monday 2:30 PM - 4:30 PM lesson Lecture Hall M  
Wednesday 2:30 PM - 4:30 PM lesson Lecture Hall M  
Friday 2:30 PM - 4:30 PM lesson Lecture Hall L  

Learning outcomes

The rheological nature of the fluids and the mathematical theoretical expressions of the conservation principles in the continuum mechanichs view and eulerian approach. Laminar flows, turbulent flows and the perfect fluid flows. Development and in depth analysis of: potential flows, uniform flows of non newtian fluids, laminar boundary layers, dispersion of passive tracers, viscous stability, turbulent flows analysis.

Syllabus

Fluids and solids in the view of continuum mechanics. The stress definition. Cauchy theorem. Fluid characterization in rheological terms. Pascal principle. Pressure definition. Comprimibility features in solids, liquids and gasses. Newtonian and non newtonian fluids.
The hydrostatic law and relevant pressure ditributions.
Lagrangian and Eulerian approaches to represent the physical principles. Lie derivative in time. Streamlines and trajectories, volumetric and mass discharges. The Reynolds theorem.
Mass conservation in global and indefinite forms.
The full costitutive law for the newtonina fluids.
Momentum conservation in global and indefinite forms. The Navier-Stokes equations for newtonian incompressible fluids and Euler equations.
Energy conservation in global and indefinite forms.
Euler equations in the streamline curvilinear system. Bernoulli theorem.
The case of irrotational flows. Joukowski theorem. Potential flows and the methods of fundamental solutions.
The analytical solution for uniform laminar flows in cylindrical pipes of Bingham fluids. Numerical representation of these flows in case of generic flow-section geometry.
Fick law and diffusion; dispersion of passive tracers in uniform Poiseuille flows.
Laminar boundary layer.
Prandtl theory. The Blasius self similar approach for the case of boundary layer over a plane and the corresponding numerical prediction by solving the two dimensional PDE Prandtl model for the evolving case or the one-dimensional ODE Blasius equation.
Fluid dynamic stability and transition phases.
Concepts and seminal Reynolds experiments. Orr-Sommerfeld equations for the stability analysis of shear flows. The Squire theorem. Non viscous stability by the Rayleigh criterium. Neutral curve in viscous and non viscous case.
Turbulence
Introduction. Need of a statistical approach. The Reynolds equations. Turbulent stresses and closure problem. Turbulent kinetic Energy.The wall turbulence. Hints to Large Eddy Simulation (LES) and Direct Numerical Symulation (DNS).

Assessment methods and criteria

The examination is oral. A few assigned exercises, developed and delivered by the students, become part of evaluation.