ME-444 / 5 credits

Teacher: Gallaire François

Language: English

## Summary

Nondimensionalized Navier-Stokes equations result in a great variety of models (Stokes, Lubrification, Euler, Potential) depending on the Reynolds number. The concept of boundary layer enables us then to identify the different components of the hydrodynamic drag.

## Keywords

Waves, drag, lift, lubrication, boundary layer

## Required courses

Having followed an introductory class on Fluid dynamics is expected

## Recommended courses

Incompressible fluid dynamics

fluid flows

## Learning Outcomes

By the end of the course, the student must be able to:

• Explain in scientific terms the basic concepts of continuum mechanics (e.g. kinematics, dynamics, conservation equations, Eulerian/Lagrangian approach, stress and strain tensors, constitutive laws, linear elasticity, Newtonian fluid) and apply them to model and analytically resolve simple problems, AH42
• Link flow behaviour with non-dimensional parameters (e.g. Reynolds and Mach numbers), AH2
• Resolve analytically or numerically the potential flow around an airfoil, AH25
• Describe flow in simple geometries, such as over a flat plate, in a tube, or around a sphere or airfoil, AH11
• State the conserved quantities in a given flow and link them to a physical-mathematical description, AH16
• Define, describe and apply the basic flow equations, such as the Navier-Stokes equations, AH17
• Describe simplified governing equations, such as the Bernoulli or potential equations, their domain of validity and apply them in appropriate situations, AH19
• Obtain by an order of magnitude analysis, the simplified equations describing lubrication and boundary layers, AH22
• Describe in detail the physical phenomena associated with the interaction of a flow with a solid wall (as a function of its characteristics, e.g. roughness), AH5
• Describe in detail the physical phenomena associated with the interaction of a flow with a solid wall (as a function of its characteristics, e.g. roughness), AH5
• Apply by an order of magnitude analysis, the simplified equations describing lubrication and boundary layers, AH17
• Describe simplified governing equations, such as the Bernoulli or potential equations, their domain of validity and apply them in appropriate situations, AH15
• Define ,describe and apply the basic flow equations, such as the Navier-Stokes equations, AH14
• State the conserved quantities in a given flow and link them to a physical-mathematical description, AH13
• Describe flow in simple geometries, such as over a flat plate, in a tube, or around a sphere or airfoil, AH9
• Solve analytically or numerically the potential flow around an airfoil, AH19
• Explain in scientific terms the basic concepts of continuum mechanics (e.g. kinematics, dynamics, conservation equations, Eulerian/Lagrangian approach, stress and strain tensors, constitutive laws, linear elasticity, Newtonian fluid) and apply them to model and analytically resolve simple problems.
• Link flow behaviour with non-dimensional parameters (e.g. Reynolds and Mach numbers), AH2

## Transversal skills

• Summarize an article or a technical report.
• Continue to work through difficulties or initial failure to find optimal solutions.

## Teaching methods

Lectures and exercise sessions

## Assessment methods

written exam and two graded homeworks counting each for 10% of the final grade.

## Supervision

 Office hours No Assistants Yes Forum No

## Bibliography

Physical Hydrodynamics, Guyon, Hulin, Petit & Mitescu, Oxford,
2001.

## In the programs

• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Hydrodynamics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Hydrodynamics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Hydrodynamics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Hydrodynamics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Hydrodynamics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks

## Reference week

 Mo Tu We Th Fr 8-9 9-10 10-11 11-12 12-13 13-14 14-15 MEB331 15-16 16-17 MAA112MAA110 17-18 18-19 19-20 20-21 21-22

Monday, 14h - 16h: Lecture MEB331

Monday, 16h - 18h: Exercise, TP MAA112
MAA110