B6364 - Fluid Dynamics

Learning outcomes

The course aims at providing the students with the fundamental basic concepts for the description of the motion of fluids around a vessel (hull and sail plan) as well as an estimate of the forces exerted on it. At the end of the course the student will have the ability to understand the fluid dynamic phenomena associated with the motion of a vessel and to prepare models for the resolution of problems of application interest for Nautical Engineering.

Course contents

1. INTRODUCTION Characterization of fluids and their motion - Liquids and gases - The continuum hypothesis - The fluid particle and its properties - Thermodynamic, kinematic and transport properties - Deformation of a particle - The incompressibility hypothesis - Recalls of kinematics – Kinematic lines – Helmoltz theorems

2. THE EQUATIONS OF MOTION General aspects - The balance of mass, momentum and energy - Integral and differential formulation - The constitutive equations - Additional equations - Boundary conditions - General discussion on the complete equations - Non-linearity - Notes on the analytical and numerical equations – Simplified models

3. THE STATICS OF FLUIDS Stevino's law – Variation of pressure as a function of depth – Pascal's principle – Buoyancy and center of buoyancy – Notes on the stability of an immersed body

4. INCOMPRESSIBLE MOTION Incompressible motion equation – Irrotational motion – Bernoulli's theorem and its applications – Solutions of potential motion

5. ORIGIN AND DYNAMICS OF VORTICITY Origin of vorticity – Equation of the dynamics of vorticity – The vortex stretching term - The boundary layer – Physical parameters of the boundary layer - Trend of a boundary layer as a function of the pressure gradient – The separation of the boundary layer – Recirculation bubbles - The wake

6. TRANSITION AND TURBULENCE Laminar and turbulent motion – Reynolds' experience – The transition – Physical parameters in the transition – Outline on the methodologies for studying the transition – Transition scenarios – Turbulence – Fundamental characteristics – Statistical description of turbulence – Reynolds Averaged equations 7. AERODYNAMIC/HYDRODYNAMIC FORCES Definition of aerodynamic and bluff bodies - Shape and classification of airfoils - Lift generation mechanism - Distribution of pressures on the airfoils and their performance - High angle of attack behavior and stalling of airfoils - Numerical evaluation of lift on airfoils – Application of the potential method – The flow around the cylinder - Notes on conformal mapping - Theory of thin airfoils - Panel methods for airfoils – Numerical evaluation of drag on airfoils – Friction drag - Flat plate at zero incidence - Notes on integral methods - Form drag - Notes on the drag of bluff bodies - Energetic interpretation of drag – Drag of a cylinder - Lift and drag control systems - Flaps - Velocity and vorticity field in a wing of finite span - The wake and the induced drag - Numerical evaluation of the lift on wings of finite span – Lifting line Theory - Panel methods - Effects of the presence of the sweep - Numerical evaluation of the drag on wings of finite span - Notes on three-dimensional boundary layers 8. WAVES Wave equation – Physical parameters of waves – Formulation and solution of the problem – Physical characteristics of sea waves – Pressure distribution – Trajectories and streamlines – Approximation for deep and shallow water – Group velocity and dispersive waves – Non-linear effects – Hydraulic jump – Notes on the effects of stratification – Notes on anomalous waves

Readings/Bibliography

Elements of Fluid Dynamics – G. Buresti – Imperial College Press

ISBN 1848168896, 9781848168893

Fluid Mechanics, Edition 7, - Pijush K. Kundu, Ira M. Cohen, David R Dowling, Ph.D. and Jesse Capecelatro, Ph.D. - ISBN:9780128198070

Lecture notes provided by the Docent

Teaching methods

Lectures and frontal exercises held by the teacher. During the course, seminars could be organized held by highly qualified personnel and regarding technological aspects of fluid dynamics for nautical applications. The topics of the seminars held will form an integral part of the program and may be subject to verification during the exam.

Assessment methods

The assessment will take place through an oral examination during which the student must demonstrate sufficient mastery of the topics covered in class and the ability to synthesize the knowledge acquired. The exam consists of three distinct phases, during which the student will be asked to discuss three different topics, posed by one or more members of the examination board.

 The student must demonstrate adequate preparation in each of the requested topics. The final grade will be assigned by the board based on the overall level of preparation demonstrated. The exam is held in two rounds. However, students must be present at the roll call, which will take place at the beginning of the first round.

Final Grade Scale:

18–19: Evident gaps in a significant number of topics covered in the course; analytical ability emerges only with the help of the instructor; overall correct use of language.

20–24: Preparation on a limited number of topics covered in the course; independent analytical ability limited to purely procedural issues; correct use of language.

25–29: Preparation on a broad range of topics covered in the course; ability to perform analysis and synthesis; good command of specific terminology.

30–30 cum laude: Preparation on all topics covered in the course; full autonomy in the analysis and synthesis of problems related to fluid dynamics applied to naval engineering; excellent command of specific terminology.

Teaching tools

Electronic whiteboard and power point presentations.

Office hours

See the website of Alessandro Talamelli