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SMASH 2005-2008
Simulation, Modeling and Analysis of Heterogeneous Systems
INRIA – Provence University – CNRS
Richard Saurel
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Outline
• Team members
b) Main research interests
c) Some examples
d) Main results
e) Prospects
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SMASH Team composition (2005-2008)Leader: Richard Saurel, Professor
Marseilles groupProfessors = 3 (Éric Daniel, Sergey Gavrilyuk, Richard Saurel)Associate professors = 2 (Olivier Le Métayer, Jacques Massoni)CR INRIA = 1 (Marie-Hélène Lallemand)PhD Students = 11Post Doc = 4 (3 CNES, 1 AMN)
Sophia Antipolis groupDR INRIA = 1,5 (Hervé Guillard, Alain Dervieux 50%)PhD Students = 5 Post-doc = 1 (CEA + European support)Engineer = 3 (1 ANR, 1 ACI, 1 INRIA)Project Assistant: 0.2 (Montserrat Argente)
Total: 31,7 persons
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SMASH evolutions
• Olivier Le Metayer has been hired as Associate Professor by the Provence University (Polytech) in 2005 and has joined our team in Marseilles
• Sergey Gavrilyuk, Professor at Cezanne University in Marseilles has joined our team in 2005 (external collaborator before).
• Marie-Hélène Lallemand, CR1 has left the Roquencourt INRIA center near Paris to join our group in Marseilles
• Richard Saurel became scientific leader of SMASH in 2008, following a recommendation of INRIA direction.
• Hervé Guillard and Alain Dervieux have created a new team (PUMAS: plasmas, MHD) located at Sophia Antipolis and Nice University. They have left the SMASH team-project in 2009.
SMASH is now located in Marseilles only
Summary: +2 (Marseilles) – 2 (Sophia) = 0
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Environment
SMASH
UMR CNRS 6595 IUSTI = lab with 8 groups
INRIA Sophia Antipolis
Polytech Marseilles
Engineering Department
Provence University
RS2N
Private company created in 2004
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Responsibilities
• Eric Daniel is director of the Master Multiphase Flows, Energetic and Combustion: 20 students / year
• Richard Saurel is director of the Doctoral School in Engineering Sciences of Marseilles : 200 PhD students, 5 CNRS units = 300 researchers
• Richard Saurel is scientific leader of the RS2N company = 300 K€/year, 6 consulting experts
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In construction
• Eric Daniel is creating a ‘Specialization year’ at Polytech Marseilles in the area of industrial and natural risks
• Richard Saurel is working on the creation of a Multiphysics Department at Polytech Marseilles
orientation of the SMASH group to multiphysics modeling
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RS2N-SMASH customers- DGA: multiphase flows, explosions, detonations
(2005-2012, 2 M€)
- CNES + SNECMA: multiphase flows in cryogenic space launchers engines (Ariane V) (2008-2013, 1.5 M€)
- CEA/DAM: inertial confined fusion + shock waves propagation in foams
- AIRBUS: compressible flows in heterogeneous media
- Idaho National Laboratory (USA): DNS of the boiling crisis
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Main scientific interests
(i) Building of theoretical models for multiphase non-equilibrium mixtures and fronts/interfaces:- material interfaces, capillary fluids, phase transition fronts, cavitation;
- multi-velocities and multi-temperatures mixtures; - detonations in heterogeneous explosives, powders compaction;- solid–fluid interfaces with extreme solid deformations. Multiphase theory of DIFFUSE INTERFACES
Our models are always hyperbolic important for waves dynamics and numerical resolution Some equations are non-conservative difficulties for numerical resolution
(ii) Building of numerical schemes for hyperbolic systems 30% of our scientific activity. 8 publications in JCP in 4 years.The aim is to solve the same equations everywhere with the same numerical scheme: in pure materials and at interfaces, without Ghost Fluid or Front Tracking or Interface Reconstruction…
(iii) Analysis and reference solutions- Shock relations for multiphase mixtures with stiff mechanical relaxation- Hydrodynamic instabilities (KH, ICF)
iv) // computations - CHYMERE 3D // multiphase and multiphysics platform, with 4 models and 4 solvers
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How to compute the pressure in this artificial mixture zone?
The equations of state are discontinuous with restricted
domain of validity.
G
L
L
G
Mixture cells
Diffuse interfaces
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Our approach: Consider mixture cells as physical multiphase mixtures
εαε −<< 1k
Interface condition = equal normal velocities and equal pressures
Bubbles expansion/contraction and drag between phases impose mechanical equilibrium at each point of the diffuse interface
equal pressures and velocities on both sides of the interface
Saurel and Abgrall, JCP, 1999
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Asymptotic analogue: Kapila et al., 2001, reduced model
xu
cc
)cc(x
ut
2
222
1
211
112211
∂∂
αρ
+α
ρρ−ρ
=∂
∂α+
∂∂α
0x
ut
1111 =∂
ρ∂α+
∂ρ∂α
0x
)P²u(tu =∂
+ρ∂+∂∂ρ
0x
)PE(utE =∂
+ρ∂+∂∂ρ
0x
ut
2222 =∂
ρ∂α+
∂ρ∂α
Volume fraction equation = differential form of the pressure equilibrium condition
In the presence of shocks, this model needs appropriate closure relations
Saurel et al., Shock Waves, 2007
Mass
Momentum
Energy
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Example: hypervelocity impact of a solid projectile on a solid tank filled with liquid
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=
∇∇⊗∇−∇−++
∇++
∂
+∇
+∂
=
∇∇⊗∇−∇−⊗++
∂∂
=+∂∂
=ρ+∂
∂
=+
−−∇+
∂∂
0u.Y
YYIYσuP))²u
21
ρ
Yσρ(e(div
t
)²u21
ρ
Yσρ(e
0Y
YYIYσuuρIPdiv
tuρ
0)udiv(ρtρ
0)uYdiv(t
ρY
0div(u)
α
cρ
α
cρ
)cρc(ρα.u
tα
2
222
1
211
1122
Extension to capillary effects (Perigaud and Saurel, JCP, 2005)
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Falling droplet
Qualitative Quantitative (IUSTI experiments)
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Phase transition at interfaces (Saurel et al., JFM, 2008)
( ) ( )
( ) ( )122222
121111
ggudivt
ggudivt
−ρν−=ρα+∂
ρα∂
−ρν=ρα+∂
ρα∂
2
222
1
211
2
2
1
1
12
2
222
1
211
2
22
1
21
12
2
222
1
211
211
222
11
cc)TT(H
cc
cc
)gg()u(divcc
)cc()(grad.u
tα
ρ+
αρ
αΓ
+αΓ
−+
αρ
+α
ρα
+α
−ρν+
αρ
+α
ρρ−ρ
=α+∂
∂α
Mechanical relaxation volume variations heat exchanges
related to mass transfer
( )
( ) 0)upE(divtE
0)p(graduudivtu
=+ρ+∂ρ∂
=+⊗ρ+∂ρ∂
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The spinodal zone problem is solved !
02 <c
Hyperbolicity is preserved in the spinodal zone: the connection of the two isentropes is modeled as a kinetic path
• ≠ of the Van der Waals model
Mass transfer is modeled as a thermodynamic path:
ill posed model
Mixture
Mixture
Critical isotherm
Critical isotherm
cstes =1
cstes =2
022 <
∂∂−=
=ctesv
pvc
liquid
liquid
vapor
vapor
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Example: underwater missile
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Cavitation around an underwater missile @ 800 km/h
2 different interfaces are present:
- liquid-vapor with phase transition
- combustion products – vapor (simple contact)
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Validation against similar experiments (DGA facility)
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Computations in lines, experiments in grey area
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Detonations in heterogeneous condensed explosives –VNIEEF, Sarov, experimentVNIEEF, Sarov, experiment
Air
Explosive + Aluminium particles
Explosive
PMMA
LifIron
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- partition of the internal energies among the phases during shock propagation,
- convergence to the multiphase ZND detonation structure,
are guaranteed, for the first time !
Petitpas et al., Shock Waves, 2009
Simulations with the same model !
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Solid – fluid coupling
•A compressible hyper elastic flow model has been built (Gavrilyuk, Favrie, Saurel, JCP, 2008)
•It has been inserted in the multiphase formulation of diffuse interfaces (Favrie, Gavrilyuk and Saurel, JCP, 2009) and solved with a general hyperbolic solver for diffuse interfaces (Saurel, Petitpas and Berry, JCP, 2009).
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Example: 2D impact
solid0.2m
0.2m
0.1m
0.6m
A solid projectile impacts a metal plate
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Fluid limit copper/copper
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Example with softer materials
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Summary
• The multiphase theory of diffuse interfaces is able to deal with a wide range of physical situations
• Generalization to extra physics is in progress
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Main results (2005-2008)• Modeling compressible capillary fluids. JCP, 2005
2) Rankine – Hugoniot relations for multiphase mixtures with stiff mechanical relaxation (Shock Waves, 2007) and link with the Kapila et al., 2001 model.
3) Convergent method for shock propagation in multiphase mixtures. Partition of the internal energies among the various phases. JCP, 2007
4) Restoring velocity non equilibrium effects (drift) in the Kapila model. JCP, 2007
5) Modeling phase transition at interfaces. JFM, 2008
6) Modeling solid – fluid interfaces. JCP 2008, 2009
7) General hyperbolic solver for diffuse interfaces. JCP, 2009
8) Generalized Chapman-Jouguet conditions for detonations in heterogeneous explosives. Shock Waves, 2009
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Future work (2009-2012)• Extend this approach to extra physics: plastic transition in
metals, powder compaction, hot spot formation in explosives
• Couple capillary effects, phase transition, heat diffusion in a unique formulation to perform DNS of boiling flows, droplet evaporation. Critical heat fluxes in nuclear reactors.
• Complete drift effects modeling in the mechanical equilibrium model.
• Develop a generalized formulation: elastic, plastic, fluid, capillarity, phase transition, drift, compaction… All these effects are present simultaneously in situations involved in defense applications towards a general formulation and code. Collaboration with prof. S.K. Godunov.
• Regarding models for flows in total disequilibrium we plan to achieve the formulation from dense to dilute two phase flows, on the basis of the Discrete Equations Method (Abgrall and Saurel, JCP, 2003)
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Main competitorsAcademic level:• Lawrence Berkeley National Lab: P. Colella group
• Stony Brook Univ.: J. Glimm group
Engineering level:• CEA/DAM: competition +collaboration• Fluid Gravity Eng. (UK): competition + collaboration
SMASH level is perhaps higher regarding modeling. Our formulations are able to deal with many physical effects. They are also much simpler to implement.
SMASH level is lower regarding high performance computing.
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Distinctions and visibility
• Alain Dervieux, Marcel Dassault Prize of the Academy of Sciences 2006,
• Richard Saurel– Science and Defense Prize 2006, given by Minister Hervé
Morin in December 2007– member of the University Institute of France (2002-2007)
• Olivier Le Metayer, ‘P.Y Herve Prize’ 2007 of the French Pyrotechnic Association,
• 3 associate editors in international journals
• At least 5 invited conferences per year in international workshops and symposia.
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Publications (2005-2009)• JCP : 8• JFM : 4• Shock Waves : 4• Other CFD journals : 11• Other fluid mechanics journals: 9• Applied Mathematics journals: 11• Total: 48• Total per year: 12• Total per permanent per year: 1.6
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Thank you for your attention