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3 courses to choose among master FME - Grenoble INP - Master MFE - FME Master

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3 courses to choose among master FME

3 courses to choose among :
- Two-phase flows
- Electro-Magneto-Hydro-Dynamics or Rheology
60 6
- Convective heat transfer
- Radiative transfers
- Thermodynamics of machines
- Project
60 6
- CFD for the design of energy systems
- Optimization for the design of energy systems
60 6
- Hydraulic machines and hydroelectricity
- Cavitation
60 6
- Fluid structures interactions
- Renewable marine energies
60 6
- External aerodynamics
- Combustion
60 6


Two-phase flows

Instructor: H. Djeridi

This course provides fundamental notions for understanding and modelling the dynamics of elementary particles (solids, bubbles, drops...) imbedded in complex flows of a continuous carrier phase. This course aims at delivering key ingredients exploited in modern simulation tools devoted to multiphase flows.

Detailed presentation
  • 0. Multiphase flow characteristics and principal applications, need for a multi-scale approach, presentation of the available strategies to cope with multiphase flow modelling.
  • I. Interface mechanical description: a) conservation, state and constitutive equations, b) surface rheology: general concepts (surface tension, surfactants, adsorption isotherm, adsorption kinetics, interfacial molecular transport) and surface rheology c) illustrations: drag on a contaminated inclusion (Marangoni effect) / rheology characterisation using capillary waves / adsorption kinetics by way of the Savart experiment
  • II. Inclusion dynamics: permanent and transient movement in an infinite medium (drag, deformation and trajectory instability, added mass, history force) / general equation for a small inclusion in a general flow field (BBOT equation) / Other forces: lift forces, wall interactions... / particule - turbulence interactions, dispersion / Connections with dispersed flow modelling illustrated on elementary systems
  • III. Coalescence, break-up and population balance equation: main mechanisms driving coalescence, break-up or agglomeration / introduction to population balance equation / examples
Key-words: interface, interface rheology, particle or inclusion dynamics, two-fluid model, dispersed two-phase flows

Skills: Understanding of the principal mechanisms occuring in dispersed two-phase flows, and how to model them.


Instructor: F. François (researcher, CEA/Grenoble)

The thermal-hydraulics lecture deals with the snag of two-phase flow modeling in presence of phase change. It is organized into four main parts describing successively the fundamental balance equations and how they are derived, some measuring techniques that are specifically used in the field of two-phase flows, some simple one-dimensional models, and the main regimes of heat transfer in boiling two-phase flows.
Detailed presentation: The subject of the lecture deals with the snag of two-phase flows modeling with a specific focus on boiling two-phase flows. It is divided into four main parts. The first-one is devoted to the drawing up of the fundamental balance equations (mass, momentum and energy) for each phase associated to the interface jump conditions (with or without phase-change). The second part concerns the problem of measurement in two-phase flows. Several measuring techniques are briefly introduced and their main specificities are discussed (optical probe, thermal anemometry, X-ray tomography...). In a third part, some simple one-dimensional models (homogenous, slip ratio, drift flux model...) are presented and their fundamental hypotheses are discussed. The main models of pressure losses in two-phase flows are also given. Finally, the last part is devoted to the boiling phenomena. Some reminders are made about thermodynamics. The main regimes of heat transfer in two-phase flows (from nucleate boiling to film boiling) are illustrated and some heat transfer correlations are given. A specific focus is made on the boiling crisis (departure from nucleate boiling) problem.

: Two-phase flow, Phase-change, Boiling, Balance equations, Measurement techniques



Instructor: L. Davoust, O. Doche
Transport equation for the magnetic field (convection and diffusion). Dynamo effect. Alfven waves and magneto-acoustics. DC and AC magnetic fields. Hartman flows. Flows in ducts, buoyancy-driven convection, external flows. Flow stability and turbulence in a magnetic field.


Instructor: L. Jossic (MCF G-INP, 24H)

Short presentation: We introduce the basic concepts of rheology: classification of types of flows and types of flow behavior. Emphasis is given to rheometry,especially on the methods of characterization based on controlled flows.
Detailed presentation:

  • Description of fluids behaviour :
    Solids and liquids
    Newtonian liquids, Elastic solids and viscoelastic materials
    Yield stress,
    Basic behaviour of polymer melts and solutions, suspensions, emulsions and gels.

  • Characterization methods of fluid materials :
    Shear rheometry: rotational rheometers, pressure-driven flows
    Elongational rheometry: simple extension, multiaxial extension, stagnation flows.
  • Analysis of rheometry experiments :
    Time-temperature superposition
    Interrelations between spectroscopy data, step-strain, creep...
    Spectrum calculation
  • Flows description :
    Stress and rate of deformation invariants
    Linear and non-Linear Viscoelasticity
    Introduction to implementation process modelisation: behaviour law, linear and non-linear domains, link with rheometry.

Key-words : Rheology, rheometry, constitutive laws, non-newtonian fluids
Pre-requisites : Participants are expected to have a solid background in fluid or continuum mechanics or in softmatter. No particular experience is required in the field of rheology


Convective heat transfer

Instructor: Y. Delannoy

Objective: to provide a thorough knowledge of transport phenomena for single-phase flows.

  • Introduction, concepts and governing equations: Transport of momentum and enthalpy, thermodynamic and constitutive relations, dissipation and entropy.
  • External (boundary-layer) laminar flows and forced convection: momentum and thermal boundary layers approximations, similarity transformation, integral equations and global integral scales, effects of pressure gradient, Falkner-Skan type boundary layers, nonsimilar boundary layers.
  • Internal laminar flows with heat transfer: fully developed duct flows, fully developed heat transfer, exact solutions.
  • Buoyancy-driven laminar flows: self similarity and integral equations, stratification, buoyancy driven flows combined with forced convection, condensation and change of phase.
  • Turbulence: wall turbulence, turbulent boundary layers and turbulent internal flows, one point closures, eddy viscosity and diffusivity, velocity and temperature distributions near the wall, turbulent free shear flows, jets, plumes and thermal wakes.
  • Mass transfer: basic notions, similarity with scalar transport, applications.


  • Convection Heat Transfer, A. BEJAN, J.Wiley, 1984
  • Convection Heat Transfer, V.S. ARPACI; P.S. LARSEN, Prentice-Hall 1984
  • Ecoulements avec échange de chaleur 1 et 2 , M. FAVRE-MARINET, S. TARDU, Hermès, 2008
  • Convective Heat Transfer, M. FAVRE-MARINET, S. TARDU, J. Wiley, 2009


Radiative transfers

Instructor: Y. Delannoy

  • Phenomenology, heat transfer modes, thermal resistances and their limits, radiation with or without participating media, natural and forced convection for internal / external flows, laminar or turbulent.
  • Radiometry / black body: radiometric quantities, radiative equilibrium and black body, Planck law.
  • Surface radiation: phenomenology, grey/lambertian surfaces, Snell's law, real surfaces, view factors
  • Participating media: radiative transfer equation, emission / absorption in gases, diffusion (Rayleigh/Mie)
  • Convection equations, models with turbulent viscosity, incompressible flows, Boussinesq approximation, boundary layer approximations
  • Scale analysis, application to those equations, dimensionless numbers and their use in transfer laws
  • Flat plate boundary layer, scale analysis, profiles (Blasius, log.law), transfer laws
  • Natural convection on a wall: scale analysis, transfer laws, case of horizontal walls
  • Forced convection in ducts: mixing temperature, entry length, fully developed flow, developed thermal solution for constant flux or temperature. Profiles and transfer in developed conditions
  • Natural convection phenomena in internal flows: thermosyphons, cavities, stratification, instability.

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Thermodynamics of machines

Instructor: J.-P Thibault

The course is mainly focused on the thermodynamics of heat-engines. The first part concerns idealized reversible and irreversible transformations and cycles. A special attention is adressed to the nature of the intrinsec irreversibilites of ideal gas and vapour cycles. Next, for each family of heat engine (gas-turbines, turbojets, internal combustion engines, steam-turbines) a brief overview is developped about the consequences of technological constraints on the effective limits of the real thermodynamic cycles. An energetic and exergetic analysis is then developed to identify performance criteria (first law and seceond law efficiencies, specific energy…) as well as possible improvement of the basic cycle.
  • Elements of thermodynamics : first & second law, thermodynamic state functions, reversible & irreversible processes.
  • Gas-turbines
  • Turbojet
  • Internal combustion engine
  • Steam-turbines
  • Frigorific engine


CFD for the design of energy systems

Instructors: G. Balarac

Contents: Method of weighted residuals; three main methods of spatial discretization:

  • I. Finite difference, upwind-centered schemes (upwind, QUICK), compact schemes
  • II. Structured-unstructured finite volume
  • III. Galerkin method applied to FEM; uncentered schemes (SUPG). Temporal patterns.
Convergence, stability and precision of numerical schemes. Calculation of incompressible flow equation for pressure, pressure correction or penalty.


Optimization for the design of energy systems

Instructor: B. Ramdane

Some selected optimization techniques are described in detail to develop an in-depth knowledge of the user-defined parameters upon which the engineer can play in order to maximize the performance of these techniques (faster convergence to a global optimum). Since the course is oriented towards engineering and not mathematical optimization the cost of the optimization process will be carefully analyzed and practicals means to reduce this cost by the use of surrogate models will be proposed and described. Selected optimization techniques will be applied to some multi-objective multi-parameter engineering problems and analysis tools such as parallel coordinates, self-organizing maps will be described and also applied. Techniques for robust design optimization will be finally reviewed in order to avoid selecting an over-sensitive optimal design. The lectures hours will systematically alternate with lab work sessions where real-life engineering optimization problems will be solved using the commercial software mode FRONTIER. Once skilled enough with the software, the students will apply it to the solution of a real-life optimal design problem on which they will write a full technical report.

Hydraulic machines and hydroelectricity

The courses are based on theoretical, experimental and numerical approaches to training engineering students to treat industrial key concepts of hydraulic machinery including turbines and hydraulic storage issues. The problems related to the coupling betwwen turbines and grid will also be presented. The participation of industrial partners will give a pragmatic view of the methods used, as well as will present the issues and the challenges.






Instructors: J-P. Franc (DR CNRS, 18H), D. Colomb

This course is intended to provide the state-of-the-art information on the development of cavitation in liquid flows and its various consequences. Lectures on the fundamentals of cavitation will be followed by a workshop during which the participants will have anopportunity to implement standard techniques for the computation of cavitating flows.
Detailed presentation: After a general introduction on cavitation, the physics of the microbubble as a cavitation nucleus will be presented with special emphasis on stability. The dynamics of a spherical bubble will then be explored by means of the classic Rayleigh-Plesset equation. Various additional effects such as the effect of liquid compressibility, heat transfer or noise radiation will be examined in details.
After the single bubble, bubbly flows will be studied with a special emphasis on the acoustics of dilute bubbly mixtures and the dynamics of a bubble cloud.
The course will continue with a presentation of the various types of attached cavities which are known to develop on blades of a hydraulic machine for instance. Partial sheet cavitation will be presented with special attention given to cloud cavitation and more generally to cavitation instabilities.
Other types of cavitation as travelling bubble cavitation, vortex cavitation, shear cavitation or supercavitation will also be presented. The consequences of cavitation such as cavitation erosion will be discussed.
During a specific workshop, each participant will be given the opportunity to compute a particular cavitating flow and the workshop will be concluded by a general presentation of all computational results and by a technical discussion of various issues of cavitation modelling.

Key-words: cavitation, bubble, two-phase flow

Pre-requisites: Participants are expected to have a background in thermodynamics and fluid mechanics but no particular expérience in the field of cavitation or two-phase flow.

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Fluid structures interactions & Renewable marine energies

Instructor : Brun Christophe, Garbuio Lauric, Maitre Thierry

Objectives : The main objectives of the module concerns firstly the understanding and calculation of wind and tidal turbines (aero-hydrodynamic design, performance and control of the rotor) and secondly the static and dynamic analysis of structures subjected to aero or hydrodynamics efforts (wind turbine blades or turbines, fairings, masts, anchors, barges floating wind etc ...).
A read thread, implemented over the life of the module allows aims at giving a general knowledge on new sources of energy that can be harnessed from the sea (offshore wind, tidal power, wave power, thermal, osmotic).

Course - TD in 3 parts that can be handled in parallel.

  • I. Lecture / discussion "red thread" on marine renewable energy : 2H
  • II. Design and control of a wind or marine turbine : 16H
    II.1 Betz Theory
    II.2 Aerodynamics of airfoils
    II.3 Rotor Design
    II.4 Aerodynamics and electrical control of the turbine
    II.5 Careening device design
  • III. Hydro-aeroelasticity : 18H
    III.1 Flightaerodynamics and material resistance
    III.2 Static aeroelasticity: profile divergence
    III.3 Dynamic aeroelasticity: floating of a standard profile
    III.4 Unsteady aerodynamics of a cylinder wake

2 practical works (4H each planned)

Operation of a wind turbine or tidal turbine and its control: starting, stoping, power optimization and limitation.
Aeroelastic behavior of the blades of a wind rotor with the use of strain gauges and force balance on models.
4 (NP) numerical project are planned (4H each)

These projects highlight the need to take into account the aerodynamic constraints and static and dynamic resistance of structures to achieve a realistic design of rotor. They therefore allow to aware students that a strong link exists between two "objects" addressed by the module: the fluid and structure.
  •     NP1: Design of a rotor, performance calculation and effort on the blades
  •     NP2: Annual electric production of a wind turbine or tidal turbine
  •     NP3: static and dynamic aeroelastic design of a wind turbine
  •     BE4: static and dynamic hydroelastic design of a tidal turbine
The NP1 allows to obtain efforts undergone by blades and then calculate their static and dynamic deformation (NP3 and NP4). The NP2 addresses variable speed aspects, pitch control and profitability of a park versus different sites.


External aerodynamics & Combustion

Instructor : Laurent Jossic / Applied aerodynamics : J.-D. Marion, Dassault Aviation

Objective : The course goes through all the basic concepts of aerodynamics for engineers, focusing on the external aerodynamics of aircraft.

Content : Aerodynamic forces. Aerodynamic characteristic of aircraft. Shockwaves. Transonic flows. Swept wing. Delta wing. Boundary layer. Hyperlift. Air intakes. Challenges of current warplanes. Aerodynamics outside aircraft.
Content: Mono-dimensional thermodynamical analysis. Flow analysis in the circumferential plane. Simplified radial equilibrium equation. Application test-case (studied in-depth during the laboratory (BE) session) : design of a stage of axial compressor.
The course of combustion presents the fundamental principles of combustion, with an application to aerospace propulsion


Master MFE - FME Master
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