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