Advanced Hydraulics is a course aimed at giving a deep knowledge on incompressible fluids motion and on their Mathematical modelling. The course is also aimed at developing the skills necessary to formulate and use basic numerical models for solving the most common mathematical models of applied Hydraulics: the method of characteristics and the finite difference method.
The course belongs to the master of Civil Engineering for the Protection from Natural Hazards, which is aimed at preparing a highly qualified Civil Engineer in the field of the protection of the territory and civil infrastructures from hydrogeological and seismic hazards.
In this framework, the course defines conceptual hydraulic models of increasing complexity, with particular reference to the most common ones: the 1D and 2D hydraulic model.
At the end of the course the student:
1) will own a deep knowledge of Fluid Mechanics;
2) will be able to formulate a model able to simulate a considered phenomenon, starting from the theories dealt during the course;
3) will be able to solve computationally the model using basic numerical methodologies;
4) will be able to interpret critically the results obtained from numerical models.
The course belongs to the master of Civil Engineering for the Protection from Natural Hazards, which is aimed at preparing a highly qualified Civil Engineer in the field of the protection of the territory and civil infrastructures from hydrogeological and seismic hazards.
In this framework, the course defines conceptual hydraulic models of increasing complexity, with particular reference to the most common ones: the 1D and 2D hydraulic model.
At the end of the course the student:
1) will own a deep knowledge of Fluid Mechanics;
2) will be able to formulate a model able to simulate a considered phenomenon, starting from the theories dealt during the course;
3) will be able to solve computationally the model using basic numerical methodologies;
4) will be able to interpret critically the results obtained from numerical models.
scheda docente
materiale didattico
1.1 The velocity field around a point: study of deformation in fluids
1.2 Vorticity: Helmholtz and Lord Kelvin theorems
1.3 Decomposition of the velocity field
2. Dynamics
2.1 Mass balance equation
2.2 Body and contact forces
2.3 Contact forces: dependence of effort on position
2.4 Momentum balance equation
2.5 Momentum balance equation
2.6 Energy balance equation
2.7 Constitutive relations and their application to the momentum and energy balance equations
2.8 Evolutionary equation of vorticity
3. Adimensional form of the equations of motion
3.1 Dimensionless form of the mass balance equation
3.2 Dimensionless form of the momentum balance equation
3.3 Dimensionless form of the energy balance equation
4. Motions with low Reynolds numbers (Re1)
6.1 Flow regimes: transition to turbulence due to hydrodynamic instability
6.2 Turbulence in incompressible fluids: Reynolds Average Navier Stokes Equations
6.3 Turbulence in incompressible fluids: Mean and turbulent kinetic energy balance
6.4 Turbulence in incompressible fluids: Spectrum of turbulent kinetic energy, Kolmogorov law
6.5 Turbulence in incompressible fluids: Uniform turbulent flow, logarithmic velocity profile and turbulent boundary layer
7. Ideal fluids
7.1 Equations of motion.
7.2 Motion around the cylinder
7.3 Motion around the semi-body
7.4 Gravity waves
8. One-dimensional hydraulic model
9. Non-stationary flow in pipes: the characteristic method and its applications
10. Non-stationary motion in free surface currents
11. Shallow Water equations
Programma
1. Kinematics1.1 The velocity field around a point: study of deformation in fluids
1.2 Vorticity: Helmholtz and Lord Kelvin theorems
1.3 Decomposition of the velocity field
2. Dynamics
2.1 Mass balance equation
2.2 Body and contact forces
2.3 Contact forces: dependence of effort on position
2.4 Momentum balance equation
2.5 Momentum balance equation
2.6 Energy balance equation
2.7 Constitutive relations and their application to the momentum and energy balance equations
2.8 Evolutionary equation of vorticity
3. Adimensional form of the equations of motion
3.1 Dimensionless form of the mass balance equation
3.2 Dimensionless form of the momentum balance equation
3.3 Dimensionless form of the energy balance equation
4. Motions with low Reynolds numbers (Re1)
6.1 Flow regimes: transition to turbulence due to hydrodynamic instability
6.2 Turbulence in incompressible fluids: Reynolds Average Navier Stokes Equations
6.3 Turbulence in incompressible fluids: Mean and turbulent kinetic energy balance
6.4 Turbulence in incompressible fluids: Spectrum of turbulent kinetic energy, Kolmogorov law
6.5 Turbulence in incompressible fluids: Uniform turbulent flow, logarithmic velocity profile and turbulent boundary layer
7. Ideal fluids
7.1 Equations of motion.
7.2 Motion around the cylinder
7.3 Motion around the semi-body
7.4 Gravity waves
8. One-dimensional hydraulic model
9. Non-stationary flow in pipes: the characteristic method and its applications
10. Non-stationary motion in free surface currents
11. Shallow Water equations
Testi Adottati
Lecture notes given by the teacher.Bibliografia Di Riferimento
1. AC Yunus, JM Cimbala, Fluid mechanics: fundamentals and applications, International Edition, McGraw Hill Publication, 2006 2. BR Munson, AP Rothmayer, TH Okiishi, WW Huebsch, Fundamentals of Fluid Mechanics, Wiley & Sons, 7th edition, 2012 3. BE Larock, RW Jeppson, GZ Watters, Hydraulics of pipeline systems, CRC press, 2000 4. MH Chaudry, Applied Hydraulic Transients, Springer, 2014 5. EB Wylie, VL Streeter, Hydraulics Transients, Mc Graw Hill, 1967 6. GK Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press, 1967 7. LD Landau, EM Lifshitz, Fluid Mechanics, Pergamon Press, 1987 8. SB Pope, Turbulent Flows, Cambridge University Press, 2000Modalità Erogazione
The course will be carried out in presence and simultaneously on the Teams platform. The lessons will be recorded. Attendance is recommended because four exercises will be carried out during the course, concerning: the analytical solution of viscous flows with low Reynolds number, the application of the method of characteristics to cases of unsteady pipe flow, the solution of the opena channel equations with the finite volume method and the simulation of a free surface flow with the Navier-Stokes equations. The exercises are not mandatory, but, if they are carried out and delivered on time, they will be an integral part of the evaluation during the exam.Modalità Frequenza
Attendance is optional but recommended.Modalità Valutazione
The exam can take place in two ways. a) If the course has been followed, the proposed exercises have been carried out and delivered on time, the exam consists of an oral test in which the following will be discussed: the fourth exercise, an exercise chosen by the student among the first three, a topic chosen by the student from those scheduled and a topic proposed by the teacher, chosen from those scheduled. b) If the proposed exercises have not been carried out in part or entirely, the exam consists of an oral test in which the following topics will be discussed: a topic chosen by the student from among those in the program and two topics proposed by the teacher chosen among those scheduled.
scheda docente
materiale didattico
Programma
Flow kinematics. Deformation. Vorticity. Decomposition of the flow field into a solenoidal and irrotational component. Dynamics. Mass, momentum and energy budget. Dimensionless form of the equations. Low Reynolds motions. Moderate Reynolds motions: boundary layer. High Reynolds motions: instability and transition to turbulence. Turbulence. Ideal flows and their applications. 1D scheme and its application in Hydraulics: pipe and open channel flows. The method of characteristics and finite differences for the integration of the motion equations. Applications to water hammer, dam-break and unsteady open channel flows. The 2D shallow water equations.Testi Adottati
Lecture notes written by the teacherBibliografia Di Riferimento
Bruce R. Munson, Donald F. Young, Theodore H. Okiishi, “Fundamentals of Fluid Mechanics”, John Wiley & sons; Yunus A. Cengel, John M. Cimbala, “Fluid Mechanics: Fundamentals and Applications” Mc Graw Hill.Modalità Erogazione
Lessons in presence and simultaneously on the Teams platform. The lessons will be recorded.Modalità Valutazione
Oral test with evaluation of the exercises and presentation of a topic of choice by the student and illustration of a topic proposed by the teacher. If the exercises have not been carried out, presentation of a topic of her choice by the student and illustration of two topics proposed by the teacher.