SMASH 2005-2008

Simulation, Modeling and Analysis of Heterogeneous Systems

INRIA – Provence University – CNRS

Richard Saurel

Outline

• Team members

b) Main research interests

c) Some examples

d) Main results

e) Prospects

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

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

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

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

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

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

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

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

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

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

Example: hypervelocity impact of a solid projectile on a solid tank filled with liquid

=

∇∇⊗∇−∇−++

∇++

∂

+∇

+∂

=

∇∇⊗∇−∇−⊗++

∂∂

=+∂∂

=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)

Falling droplet

Qualitative Quantitative (IUSTI experiments)

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∂

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

Example: underwater missile

Cavitation around an underwater missile @ 800 km/h

2 different interfaces are present:

- liquid-vapor with phase transition

- combustion products – vapor (simple contact)

Validation against similar experiments (DGA facility)

Computations in lines, experiments in grey area

Detonations in heterogeneous condensed explosives –VNIEEF, Sarov, experimentVNIEEF, Sarov, experiment

Air

Explosive + Aluminium particles

Explosive

PMMA

LifIron

- 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 !

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).

Example: 2D impact

solid0.2m

0.2m

0.1m

0.6m

A solid projectile impacts a metal plate

Fluid limit copper/copper

Example with softer materials

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

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

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)

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.

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.

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

Thank you for your attention