AIMS AND LEARNING OUTCOMES

The intention is to provide the student with the cultural basis for the correct formulation of problems in which it is necessary to predict the motion of fluids and the forces it can exert on surfaces and bodies. At the end of the exam, the student will be able to make an informed and critical choice of the best model to use. Furthermore, he will be able to interpret correctly the results obtained, for example by using a numerical code that implements these models.

TEACHING METHODS

The teaching is divided into lectures held by the teacher, in which the theory will be exposed and exercises.

In the lectures, the theory  will be applied to different examples.
 
In the part devoted to  exercises, the student will carry out independently exercises proposed by the teacher. The exercises  will be corrected in the classroom by the teacher.

SYLLABUS/CONTENT

1. Kinematics. Eulerian and Lagrangian description, material derivative. Principle of mass conservation.
2. Dynamics. Tension and stress tensor. Momentum principle, momentum moment principle.
3. The constitutive relation for a Newtonian fluid, continuity and Navier Stokes  equations. Boundary conditions.Exact solutions of  Navier-Stokes equations. Unidirectional flows.
4.  Ideal fluid. The scheme of irrotational flow. D'Alembert paradox. Two-dimensional irrotational motions. Flow field generated by a cylinder translating with constant velocity.
5. Flow field and forces on bodies in motion in a fluid.  Drag and lift.  Lift of slender bodies:  the Kutta hypothesis. Added mass force. Induced drag. Morison equation.
7. Flow at high Reynolds numbers. Simplified equations of the boundary layer. Blasius solution. Von Karman integral equation. Boundary layer on flat plate in the  laminar and in the turbulent regime. Transition to turbulence in the boundary layer. Separation of the boundary layer and introduction to the  the control systems of the boundary layer.
8. Turbulent flows. Average speed and pressure, the Reynolds equations. The problem of closure and Boussinesq hypothesis. Near_wall turbulence.  Introduction to  two-equations turbulence  models

RECOMMENDED READING/BIBLIOGRAPHY

Teacher's notes (downloadable from AulaWeb)

Ronald Panton "Incompressible flow" Wiley and Sons

Pijush K. Kundu, Ira M. Cohen and David R. Dowling "Fluid Mechanics - fifth edition" Elsevier 2012

G. K. Batchelor "An introduction to fluid dynamics" Cambridge university  press