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Computing turbulent deflagrations
(for nuclear safety studies)
J.-C. Latche
Institut de Radioprotection et de Surete Nucleaire (IRSN)
CALIF3S: https://gforge.irsn.fr/gf/project/isis
Outline
1 Motivations
2 Evaluating the consequences of a deflagration in a local
3 Scope & main features of the P2REMICS computer code
Outline - p.2
Core melting accidents
- 1/ 1
Schéma de la cuve du réacteur de
Three Mile Island
Schematic view of the core and bottom head after the TMI2 accident
Motivations - p.3
In nuclear safety, prefer numerical crash tests...
Motivations - p.4
Deflagration in a building: problem position
local 1(explosive
atmosphere)
corridorlocal 2
� Formation of an explosive atmosphere: stoechiometric H2/air mixture cloud located in theupper part of ”local 1”.
� Near the ceiling of local 1, the medium is congested (pipes).
� In case of a deflagration, what is the overpressure seen by ”local 2” ?
Evaluating the consequences of a deflagration in a local - p.5
Deflagration in a building: modelling
burnt zone
fresh zone
uf
uf
uf
ufuf
uf
Modelling of the deflagration:
� total irreversible chemical reaction occurring in a burnt zone extending at the velocity uf
(with respect to the fresh gases),
� uf depending on the local composition of the mixture, flow turbulence,. . .
� uf in a congested medium ?
Evaluating the consequences of a deflagration in a local - p.6
Validation matrix (deflagration)
self-acceleratedflames
s.1 Fh-ICT half-sphere
s.2 THAI experiments HD 7 and HD 15 : dry homogeneous atmosphere,initial temperature equal to 20◦C and 90◦C
Jetsj.1 EXJET-2: free (underexpanded) large scale jet
j.2 EXJET-4: (underexpanded) large scale jet in a congested medium
Flames accel-erated by ob-stacles
o.1 flame stabilized by a bluff body (Volvo test rig)
o.2 medium scale flame acceleration pipe
o.3 ENACCEF, homogeneous atmosphere, 0, 5 and 9 obstacles
o.4 ENACCEF, RUN 765: stratified dry atmosphere, ∂z yH2 ≤ 0, 9 ob-stacles
o.5 ENACCEF2, MITHYGENE project
V1.0 (november 2017), further version
⇒ uf ∈ [10 m/s, 40 m/s]
Evaluating the consequences of a deflagration in a local - p.7
Flame acceleration experiment: experimental setup
2 3 4 5 6 7 81
7.6 cm
7.6 cm3.15 cm
A
� Context:
I Accelerating flame in an obstructed square channel.
� Objective:
I Because of reactor building obstruction, P2REMICS must be able to simulate a flame accelerationdue to obstacles.
� Geometry [Johansen, Ciccarelli, 2009]:
I Closed combustion channel (length: 2.44 m),
I One optical module and three non optical ones (square section of 7.6 cm× 7.6 cm),
I 8 obstacles by module with a blockage ratio of 0.33.
� Configuration:
I Stoichiometric methane-air mixture,
I Ignition point located on the left of the facility (point A).
Evaluating the consequences of a deflagration in a local - p.8
Flame acceleration experiment: results
� Good approximation of the flame brush shape.
� Flame propagation slower than to the experimental one (inter-frame: 4 m/s instead of2.66 m/s):
I Turbulent flame speed correlations available in P2REMICS are designed for situations where theturbulence is fully developped.
Evaluating the consequences of a deflagration in a local - p.9
Deflagration in a building: results
Velocity in the plane z = 1.5m, a t = 68 ms et t = 80 ms. From blue to red, the velocity normvaries between 0 and 250 m/s; values greater than 250 m/s correspond to red zones.
Evaluating the consequences of a deflagration in a local - p.10
The model: a system of PDEs
Euler reactive equations:
∂t%+ div(%u) = 0,
∂t (%yi ) + div(%yiu) = ωi , i = 1, Ns
∂t (%u) + div(%u ⊗ u) + ∇p = 0,
∂t (%E) + divˆ(%E + p)u
˜= 0,
E =1
2|u |2 + e, e = es +
NsXi=1
∆hf ,iyi , p = (γ − 1) %es .
The reaction term reads:
ωi =ρu uf
δfζi νiWi ω, ω = min(yF , yO ) (G − 0.5)−,
with:∂t (ρG) + div(ρG u) + ρu uf |∇G| = 0.
Evaluating the consequences of a deflagration in a local - p.11
Numerical schemes: staggered space discretization and fractional stepalgorithms
LKσ = K |LK , pK , eK
σ
DK ,σ
DL,σσ′ǫ = σ|σ ′
(IRSN/I2M - AMU) Pres. orr. s heme for omp. rea tive �ows Toulouse, November 2017 1 / 1Scheme for Euler equations (time semi-discrete setting):
Prediction step:1
δt(%∗u − %∗∗u∗) + div(%∗u ⊗ u∗)−divτ (u) + ξ∇p∗ = 0.
Correction step:
˛˛˛˛
%∗
δt(u − u) + ∇p − ξ∇p∗ = 0,
1
δt(%− %∗) + div(%u) = 0,
1
δt(%e − %∗e∗) + div(%eu) + p divu = S ,
p = ℘(%, e) = (γ − 1) %e.
Evaluating the consequences of a deflagration in a local - p.12
The P2REMICS (CFD) computer code
� Scope : safety issues related to explosion hazards
I Handled usually as three linked (but uncoupled) phases . . .
1 - Release and dispersion of explosive gases, formation of apartially premixed explosive atmosphere,
2 - Chemical reaction (explosion) phase,
3 - Blast waves propagation and interaction with structures.
� Main related challenges :
I Release & dispersion : compressible or low Mach number flows,turbulent (scalar) mixing, wall-bounded turbulent flows, . . .
I Explosion : deflagration-detonation, flame front structure andturbulence coupling, detailed chemistry, . . .
I Blast waves : inviscid (Euler) wall-bounded flows, fluid-structureinteractions, . . .
Scope & main features of the P2REMICS computer code - p.13
Overview of physical modeling
� Flow modeling
I Incompressible flows
I Weakly compressible flows
(Low-Mach number approximation)
I Compressible flows (shock waves . . . )
� Turbulence modeling
I Reynolds-Average approach
(two-equation models)
I Hybrid methods
I Large eddy simulation
� Multi-species modeling
I Inert mixture of ideal gases (LMN)
I Wall condensation
� Premixed combustion modeling
I Geometrical description of the flame frontstructure (G-equation)
I Flame speed turbulence model
Scope & main features of the P2REMICS computer code - p.14
Some applications of interest
Incompressible flowVentilated room (CARDAMOME)
Compressible reacting flowFlame acceleration (ENACCEF)
Multi-species low-Mach number flowErosion of a stratification
Compressible flowBlast wave reflexion
Scope & main features of the P2REMICS computer code - p.15
Some applications of interest
Incompressible flowVentilated room (CARDAMOME)
Compressible reacting flowFlame acceleration (ENACCEF)
Multi-species low-Mach number flowErosion of a stratification
Flow induced by a fire with four sprinklers (only two are visisble)
Scope & main features of the P2REMICS computer code - p.16
Overview of numerics
� Space discretization
I Staggered structured and unstructureddiscretization
I Scalar variables at cell centers
I Velocity at faces (MAC scheme,Crouzeix-Raviart/Rannacher-Turek)
I Non-conforming local mesh refinement isallowed
� Time discretization
I Fractional step algorithm
I Solve in a segregated way for :
- energy
- species
- . . .
- pressure correction scheme formomentum and mass balance equations
� Available space schemes
I Scalars : upwind, hybrid, MUSCL
I Velocity : upwind, centered, QUICK
� Available time schemes
I Scalars : BDF1 & 2
I Velocity : BDF1 & 2, Crank-Nicolson
Scope & main features of the P2REMICS computer code - p.17
Overview of code structure
� Based on embedded software components library (C++)
PELICANS
Environment, Algebra, Geometry, ...
Fluid Flow Solver
CALIF S3
P REMICS2
Pre-processing- GAMBIT (FLUENT)- EMC2 (INRIA)- ...
Post-processing- PARAVIEW- OpenDx (IBM)- ...
Linear Algebra librairies- PETSc- MUMPS- ...
I Object-oriented programming
I Version control system (SVN)
I Non-regression tests
I Collaborative websites(https://gforge.irsn.fr/gf/project/)
- PELICANS : Plate-forme Evolutive de LIbrairies de Composants pour l’Analyse Numerique et Statistique
- CALIF3S : Components Adaptative Library For Fluid Flow Simulations
Scope & main features of the P2REMICS computer code - p.18