Teacher(s)
Language
English
> French-friendly
> French-friendly
Prerequisites
Mécanique des fluides et transferts 1 [lmeca1321] or equivalent
Main themes
- Compressible flows in ducts and nozzles
- Incompressible flows in porous media
- Potential flows
- Introduction to transition, turbulence, and CFD
- Introduction to geophysical and environmental flows
Learning outcomes
At the end of this learning unit, the student is able to : | |
| 1 | In view of the LO frame of reference of the "Master Mechanical Engineering", this course contributes to the development, acquisition and evaluation of the following learning outcomes: LO1.1, LO1.2, LO1.3 LO2.1, LO2.2, LO2.3, LO2.4, LO2.5 LO3.1, LO3.2 LO4.1, LO4.2, LO4.3, LO4.4 LO5.4, LO5.5, LO5.6 LO6.1, LO6.2 Specific learning outcomes of the course At the end of this learning unit, the student will be able to:
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Content
Complements on turbulence, and introduction to CFD
- Recall of previous material (from lmeca1321): Reynolds-Averaged Navier-Stokes (RANS) equations; also simplified for thin shear flows, such as boundary layers.
- Closure of the RANS equations using a turbulent viscosity model: two-equations closure models. Calibration of the model coefficients
- Hands-on session using a CFD solver, and best practice guidelines.
- Scales in turbulent flows. Simple case of decaying homogeneous isotropic turbulence (DHT) in a periodic box: energy spectrum (Kolmogorov) and spectrum models. Experimental approximation of DHIT in a wind/water tunnel.
- Time and space scales of variability.
- Reactive transport.
- Geohydrodynamic equations.
- Impact of Earth's rotation and stratification.
- Relevant case studies (e.g., contaminant dispersion, geostrophic equilibrium, Ekman boundary layer).
- Recall of the conservation equations for compressible flows (mass, momentum, energy). Conservation equation for the entropy.
- Link between isentropic flows at moderate Mach number and ideal incompressible flows.
- 1-D isentropic flow in a converging-diverging Laval nozzle (subsonic and supersonic cases), sonic conditions and maximum flow rate. Normal shock in a supersonic flow and jump relations. Operating modes of a nozzle.
- 1-D adiabatic flow in a duct with wall friction (Fanno flow).
- Basic singularities: point vortex, point source/sink, dipole.
- Obtention of flows using complex potentials.
- Flow past a circle: case without circulation and case with circulation (Magnus effect).
- Transformation of a circle into airfoils of various shapes (Joukowski transformation).
- Flow past airfoils of various shapes. Kutta-Joukowski condition.
- Blasius formula to compute the force acting on the body. Lift due to the circulation.
Teaching methods
There are lectures given in an auditorium, each of 2 hours. The student must also acquire some of the course content on his/her own (e.g., content that is a review of material covered in previous mandatory courses, mathematical developments not covered in class).
Sessions of practical exercices (TP) are also organised in class, each of 2 hours and with an assistant, to further develop/detail the concepts covered during the lectures, and to do applications. Some sessions are not organised in class.
There are also laboratory sessions led by an assistant: a laboratory on supersonic nozzle flow in groups of 5-6 sudents and with one group report, and a laboratory on introduction to CFD in groups of 3 students and with one report). There are also homeworks.
The use of generative AI tools such as ChatGPT, Consensus, Perplexity,... to produce parts of results or reports is not allowed.
Sessions of practical exercices (TP) are also organised in class, each of 2 hours and with an assistant, to further develop/detail the concepts covered during the lectures, and to do applications. Some sessions are not organised in class.
There are also laboratory sessions led by an assistant: a laboratory on supersonic nozzle flow in groups of 5-6 sudents and with one group report, and a laboratory on introduction to CFD in groups of 3 students and with one report). There are also homeworks.
The use of generative AI tools such as ChatGPT, Consensus, Perplexity,... to produce parts of results or reports is not allowed.
Evaluation methods
The laboratory session(s) and the homework correspond to work that is mandatory and that must be performed during the quadrimester; each within a well-defined time period and with a given deadline for the report, that is graded.
It is mandatory to participate physically in each laboratory session. No experimental laboratory report will be accepted with the name of a student who did not participate in the laboratory.
It is not possible to do, or even re-do, any of the work mentioned above outside of the time period that was defined for it within the quadrimester.
The final exam is a written exam, with questions that can cover all parts of the course (lectures, exercice and laboratory sessions, homework).
The calculation of the final grade obtained by the student for the course is a weighted sum of the grade obtained for the final written exam (for 75 %) and of the grade obtained for the work to be performed during the quadrimester (laboratories and homeworks, for 25 %). It is however required to obtain at least 8/20 at the exam for that rule to apply. If the grade obtained at the exam is below 8/20, the final grade for the course is the grade of the exam.
If the student does not obtain the credit for the class at the deliberation of June, the grade obtained for the work to be performed during the quadrimester remains acquired for the second session of August.
It is mandatory to participate physically in each laboratory session. No experimental laboratory report will be accepted with the name of a student who did not participate in the laboratory.
It is not possible to do, or even re-do, any of the work mentioned above outside of the time period that was defined for it within the quadrimester.
The final exam is a written exam, with questions that can cover all parts of the course (lectures, exercice and laboratory sessions, homework).
The calculation of the final grade obtained by the student for the course is a weighted sum of the grade obtained for the final written exam (for 75 %) and of the grade obtained for the work to be performed during the quadrimester (laboratories and homeworks, for 25 %). It is however required to obtain at least 8/20 at the exam for that rule to apply. If the grade obtained at the exam is below 8/20, the final grade for the course is the grade of the exam.
If the student does not obtain the credit for the class at the deliberation of June, the grade obtained for the work to be performed during the quadrimester remains acquired for the second session of August.
Online resources
Moodle site of the course
Bibliography
Non-exhaustive list:
G.K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press 1967 (reprinted paperback 1994).
F. M. White, Viscous Fluid Flow, second edition, Series in Mechanical Engineering, McGraw-Hill, Inc., 1991.
P. A. Thompson, Compressible Fluid Dynamics, advanced engineering series, Maple Press, 1984.
D.J. Tritton, Physical Fluid Dynamics, Van Nostrand Reinhold, UK, 1985.
P. G. Drazin, Introduction to Hydrodynamic Stability, Cambridge Texts in Applied Mathematics, Cambridge University Press, 2002
P. G. Drazin and W. H. Reid, Hydrodynamic Stability, Cambridge University Press, 1985.
S. B. Pope, Turbulent Flows, Cambridge University Press, 2000
M. Van Dyke, An Album of Fluid Motion, The Parabolic Press, 1982.
H. Burchard, Applied Turbulence Modelling in Marine Waters, Springer, 2002
B. Cushman-Roisin and J.-M. Beckers, Introduction to Geophysical Fluid Dynamics - Physical and Numerical Aspects, Elsevier, 2011 (2nd ed.)
H. B. Fisher et al., Mixing in Inland and Coastal Waters, Academic Press, 1979
P. Kundu et al., Fluid Mechanics, Elsevier, 2015 (6th ed.)
G.K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press 1967 (reprinted paperback 1994).
F. M. White, Viscous Fluid Flow, second edition, Series in Mechanical Engineering, McGraw-Hill, Inc., 1991.
P. A. Thompson, Compressible Fluid Dynamics, advanced engineering series, Maple Press, 1984.
D.J. Tritton, Physical Fluid Dynamics, Van Nostrand Reinhold, UK, 1985.
P. G. Drazin, Introduction to Hydrodynamic Stability, Cambridge Texts in Applied Mathematics, Cambridge University Press, 2002
P. G. Drazin and W. H. Reid, Hydrodynamic Stability, Cambridge University Press, 1985.
S. B. Pope, Turbulent Flows, Cambridge University Press, 2000
M. Van Dyke, An Album of Fluid Motion, The Parabolic Press, 1982.
H. Burchard, Applied Turbulence Modelling in Marine Waters, Springer, 2002
B. Cushman-Roisin and J.-M. Beckers, Introduction to Geophysical Fluid Dynamics - Physical and Numerical Aspects, Elsevier, 2011 (2nd ed.)
H. B. Fisher et al., Mixing in Inland and Coastal Waters, Academic Press, 1979
P. Kundu et al., Fluid Mechanics, Elsevier, 2015 (6th ed.)
Teaching materials
- G. Winckelmans, "Compressible flows", lecture notes (version 2022)
- G. Winckelmans, "2-D potential flows (incompressible and irrotational)", lecture notes (version 2023)
- G. Winckelmans and Y. Bartosiewicz, "Reynolds-averaged Navier-Stokes (RANS) equations for incompressible and turbulent flows ", slides (version 2021, as complement to the lecture notes of lmeca1321)
- E. Deleersnijder, 2021, "Modelling transport processes in geophysical and environmental flows" (slides, problems, appendices, animations)
- R. Debroeyer and G. Winckelmans, "RANS equations for compressible flows", lecture notes (version 2021)
- G. Winckelmans, "equations for incompressible flows, and general results for periodic or unbounded flows", lecture notes (version 2021)
- G. Winckelmans, "Decaying homogeneous isotropic turbulence (DHIT)", lecture notes (version 2021)
- G. Winckelmans, "calibration of 2 equations closures in RANS", lecture notes (version 2021)
Faculty or entity
