Ecoulements Diphasiques Marc Massot Professor at Ecole Centrale Paris Laboratoire EM2C - UPR CNRS 288 - Ecole Centrale Paris Visiting Professor, Department of Mechanical Engineering, Center for Turbulence Research, Stanford University 2011-2012 Chairman of the Fédération de Mathématiques de l Ecole Centrale Paris FR CNRS 3487 1
Course information and Contact! Marc Massot marc.massot@ecp.fr! Mercredi 14h00 17h15 Mardi 8h00 11h15! Office Hours of M. Massot : Tel 1081 - Laboratoire EM2C Batiment Péclet Friday 11h30-13h! Lecture notes. Reference texts that can be downloaded: M. Massot, F. Laurent, S. de Chaisemartin, L. Fréret and D. Kah, Eulerian multi-fluid models : modeling and numerical methods. In Modelling and Computation of Nanoparticles in Fluid Flows", Lecture Series, von Karman Institute, Belgium, NATO RTO-EN-AVT-169 (2009) http://www.rto.nato.int/pubs/rdp.asp?rdp=rto-en-avt-169 D. Kah, Taking into account polydispersity for the modeling of liquid fuel injection in internal combustion engines, Ph.D. thesis, Ecole Centrale Paris, in English (2010) http://tel.archives-ouvertes.fr/tel-00618786/en/ O. Emre, Modélisation de la polydispersion des brouillards de gouttes sous l'effet des interactions two-way turbulentes pour l'injection directe à haute pression dans les moteurs, Ph.D. thesis, Ecole Centrale Paris, in English (2014) https://tel.archives-ouvertes.fr/tel-01089937 - Two-Phase Tutorial, Summer Program 2006 by Marcus Herrmann, Arizona State University, web site of SP http://ctr.stanford.edu/summerprogram/twophasetutorial.pdf - Vincent le Chenadec, A stable and conservative framework for detailed numerical simulation of primary atomization, Ph.D. Thesis, Stanford university 2012 - http://purl.stanford.edu/yg622ks5494 2 associated with further reading references.
Outline of last Lecture! Overview of some applications and typical multiphase flows! 1- Presentation of various applications and related issues at stake. What is a multiphase flow?! 2- Liquid fuel injection (Diesel) spray formation. A few exemples of up-to-date numerical simulations and their shortcomings in liquid jet injection due to scales to be resolved! 3- Spray dispersion, evaporation and combustion: just a piece of the puzzle and still lots of underlying assumptions: from fundamental modeling to HPC and industrial applications (aeronautical engines)! Conclusion and presentation of the topics of this course 3
Fuel injection - Internal combustion engines Multiphase flow involved Electric command system Fig: Dumouchel, Coria Fuel supply needle Longitudinal jet Bowl Piston Injection parameters " Injection pressure: 2000 bar " Injection velocity: 600 m.s -1 " Injection time : 2ms 4 4
Ecoulements Diphasiques Option 3A Energie / MAE Masters - ECP Experimental visualizations Source : IFP Energies nouvelles, France 5
Fundamental of atomization process Atomization process Injector Formation of a surface free flow Source F.X. Demoulin (CORIA- Rouen France) Primary Atomization Surface deformation Rupture Secondary Atomization Spray 6
Combustion chamber Source J. Reveillon (CORIA- Rouen France) Dispersion of droplets by turbulence Collisions, breakup/coalescence Secondary breakup 7
Combustion chamber Evaporation topology of the fuel mass fraction Preferential segregation Turbulent mixing Non-homogeneous mixture 8
Combustion chamber Combustion Partially premixed combustion Flame instabilities Spray/flame/wall interactions 9
A wide range of scales cm Liquid surface instabilities Turbulent Integral scale days Macro-mixing mm Ligaments µm Clusters of droplets Turbulent dissipation scale Thermodynamical processes Flame front Smallest droplet months years 10 Liquid-air interface
Ecoulements Diphasiques Option 3A Energie / MAE Masters - ECP In the first Lecture : overview of recent advances In the region where the liquid phase is dispersed (spray) there are two ways of describing the dynamics of the liquid phase through Lagrangian of Eulerian models with their dedicated numerical methods. Both approaches have advantages and drawbacks, which we will discuss further in the course. Applications in combustion have shown the necessity of taking into account the polydispersion of the spray (large size spectrum) in order to capture the physics and the right combustion dynamics. Both approaches have this capability either for - DNS (Direct Numerical Simulation) is it a true DNS? - LES (Large Eddy Simulation) for realistic applications Even if this is a rather mature field which has benefited from the scientific experience in the field of kinetic theory initiated by Maxwell and Boltzmann, there are still a lot of open problems, especially for LES. 11
In the first Lecture : overview of recent advances In the region where the liquid phase occupies a volume of the same order at the one of the gas (separated phase two-phase flows), a branch of the scientific community has developed powerful and efficient solvers in order to resolve the dynamics of such interfacial flows, using incompressible Navier-Stokes Equations in both gas and liquid. However, the accuracy of such solvers to fully resolve the generation of the polydisperse spray obtained after primary and secondary atomization for realistic Reynolds and Weber numbers is questionable, thus limiting their range of validity in the atomization process. 12
In the first Lecture : overview of recent advances In the region where the liquid phase occupies a volume of the same order at the one of the gas (separated phase two-phase flows), a branch of the scientific community has developed powerful and efficient solvers in order to resolve the dynamics of such interfacial flows, using incompressible Navier-Stokes Equations in both gas and liquid. This approach still stumbles on the fact that for a range of We and Re numbers not even close to the realistic values of Diesel injection, the range of spatial and temporal scales to be resolved are out of reach and it is impossible (and useful?) to resolve the whole atomization process down to the spray dynamics. 13
No unified model treating the whole jet consistantly - Incompressible flows - Level-Set / VOF / SPH - Non-Vaporizing - m to cm scales - Compressible or dilatable flows - Simple or complex chemistry - Disperse phase (Lagrangian or Eulerian) - Small spherical droplets - mm to µm scales 14 Different numerical methods, physical outcomes and communities!!! Junction stumbling block hot research topic - LES
Polydisperse spray modeling and simulation! Introduce the fundamental of polydisperse spray modeling underlying assumptions for the Williams Boltzmann equations at mesoscopic level parallel with Kinetic Theory of gases statistical description! Micro-Macro modeling and potential droplet models Thermodynamics and mesoscopic models Moment methods! Elements of numerical simulation dedicated to the particular structure of the resulting Eulerian system of conservation laws which resembles closely the compressible Euler gas dynamics equations. Homogenized two-fluid model and num. methods! Introduce the fundamental hierarchy of models as well as the various ways of averaging underlying assumptions for each type of model depending on equilibrium assumptions and physics to be described! Micro-Macro modeling and thermodynamics for such reduced-order models interface resolution potential - Rationale! Elements of numerical simulation dedicated to the particular structure of the resulting Eulerian system of equations which resembles the compressible Euler Navier-Stokes gas dynamics equations. Modeling of two-phase pipe flows 15
Ecoulements Diphasiques Option 3A Energie / MAE Masters - ECP I - Polydisperse spray modeling and simulation!introduce the fundamental of polydisperse spray modeling underlying assumptions for the Williams Boltzmann equations at mesoscopic level parallel with Kinetic Theory of gases statistical description!micro-macro modeling and potential droplet models Thermodynamics and mesoscopic models Moment methods KINETIC THEORY OF GASES Source of inspiration for Williams-Boltzmann equation F. Williams, Physics of Fluids (1958) 16
Spray counterflow diffusion flames Counterflow diffusion flame source: F. Lacas (EM2C Lab. - CNRS) 17 source: A. Gomez (Yale)
Spray counterflow diffusion flames Counterflow diffusion flame " 1D Poly-dispersed Spray Flames " Laminar: decoupling of drop-gas interaction from turbulence complication TEST CASE 18 " Droplet Description: " Polydisperse cloud " Vaporization " Heating " Slip " Gas description: " Complex chemistry " Detailed transport " Exchange terms
Spray counterflow diffusion flames Counterflow diffusion flame " 1D Poly-dispersed Spray Flames " Laminar: decoupling of drop-gas interaction from turbulence complication TEST CASE! intermediate in complexity between: single droplet burning studies and practical spray combustion systems! rich physical scenarios! can mimic many features present in practical flames 19 M. Massot, M. Kumar, A. Gomez, M.D. Smooke, Counterflow spray diffusion flames of heptane: computations and experiments, Proceedings of the 27th Symposium (International) on Combustion, Boulder, Colorado, U.S.A (1998) F. Laurent, V. Santoro, M. Noskov, A. Gomez, M.D. Smooke, M. Massot, Accurate treatment of size distribution effects in polydispersed spray diffusion flames: multi-fluid modeling, computations and experiments, Combustion Theory and Modelling 8, (2004), 385-412
Experimental setup " Experimental attention on " Flame flatness and stability " Uniform velocity conditions in the radial direction " Rapid and steady mixing of the droplets " Control on drop size " Technical " Ultrasonic nebulizer " N 2 " 3/1 Contraction " Water Cooling 20 " Measurements techniques " Phase Doppler Anemometer " Thermocouple
Counterflow spray diffusion flame: model Liquid Gas Statistical Transport Equation T, u, S Multi-fluid Eulerian description 1st order system Source terms dilute spray Navier-Stoker Equations Multi-component reacting flow Averaged source terms from the liquid Low Mach Number Approximation Isobaric flame equation 2nd order system Source terms 21
Counterflow diffusion flame: model Equations of the isobar flames : complex chemistry and detailed transport 22
Equations of the isobar flames : Counterflow spray diffusion flame Source terms: 23 With the distribution function of the spray
Kinetic Model The distribution function of the spray satisfying assumptions: " dilute spray: no droplet interaction " spherical droplets (We<<10) " uniform temperature inside rate of variation of the surface due to evaporation drag force applied to the droplet by the gas rate of variation of the temperature by heat transfer 24
I - Polydisperse spray modeling and simulation! Introduce the fundamental of polydisperse spray modeling underlying assumptions for the Williams Boltzmann equations at mesoscopic level parallel with Kinetic Theory of gases statistical description! Sedimentation of solid particles of sand in water with a large volume fraction of sand particles. The Williams-Boltzmann equation is not valid as the forces exerted on one particle are not localized in space.! Even in the case of a more dilute cloud of sand particles, the sedimentation velocity can deviated from the free fall velocity and be influenced by the particle volume fraction through two-particle interaction forces (See Batchelor JFM 1982) 25