Modelling complex fluid-structure interaction problems with. EUROPLEXUS fast dynamic software. P. Galon (CEA). V. Faucher (CEA). F. Casadeï (JRC/IPSC).
Modelling complex fluid-structure interaction problems with EUROPLEXUS fast dynamic software P. Galon (CEA) V. Faucher (CEA) F. Casadeï (JRC/IPSC) S. Potapov (EDF R&D)
WCCM8 - ECCOMAS 2008 - Venice, Italy
June 30 - July 5
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Outline
- Nuclear safety Context - Latest developments implementation (finite volume Method for general equations of state on moving mesh) - Validation examples : - Mara 2 experiment (hypothetical core disruptive accident) - Detonation in presence of a wall - HDR (LOCA simulation : 1D-EF/3D-VF coupling) - Conclusion
WCCM8 - ECCOMAS 2008 - Venice, Italy
June 30 - July 5
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Nuclear Safety Context - Difficulties Analyzing the consequences of reference accidents : – – –
Loss Of primary Coolant Accident (LOCA) hypothetical core disruptive accident (HCDA) in fast Breeder Reactor steam explosion F.E.M Vulnerability : Air blast, explosions loading
F.V.M
Difficulties with F.E.M: - simulation of strong shocks is only accurate when using conservative methods - In some circumstances F.E.M discretization needs very fine mesh to accurately models flow field - Check-boarding phenomenon is more important with F.E.M (pressure oscillations) => development of a more general Finite Volume Method in the Europlexus software (complex
EOS, multi-constituent, multi-phase flow … on moving mesh). F.E.M (no convergence)
F.V.M (1000 cells)
F.V.M (10000 cells)
F.E.M mesh discretization near nozzle
Strong shock : PL/PR = 100000 WCCM8 - ECCOMAS 2008 - Venice, Italy
June 30 - July 5
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Finite Volume - Spatial Discretization (moving mesh) We use the conservation law for a general vector quantity U. We can therefore write the integral form of the governing equations as :
The time derivative of the conservative variable can be cast in the form :
where : The surface integral on the right-hand side of equation (1) is approximated by a sum of the fluxes crossing the face. We suppose that the flux is constant along each individual face (sufficient for a second order scheme) :
In Europlexus, the time derivative of the conservative variables U explicit Euler scheme (for first order scheme):
WCCM8 - ECCOMAS 2008 - Venice, Italy
June 30 - July 5
use
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Finite Volume - Spatial Discretization (moving mesh) thus : : volumes at time t and t + ∆t : conservatives variable at t and t + ∆t To satisfy the geometric Conservation Law (GCL) an intermediate frame is used to compute the fluxes :
• Flux can be compute in Europlexus using flux difference splitting scheme (Zha-Bilgen & Zha-Bilgen modified, Advection Upstream Splitting (AUSM+) : M.S Liou, Low Diffusion Flux Splitting Scheme (LDFSS-2) : J.R Edwards or more robust approximate Riemann solvers Rusanov (or Local Lax Friedrichs), DWC (Dominant Wave Capturing : M.G Edwards), HLLE (Harten – Lax - Van Leer modified), HLLC (Toro), exact Riemann solver for perfect gas.
WCCM8 - ECCOMAS 2008 - Venice, Italy
June 30 - July 5
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Extension to second order • Aim : first order scheme are too diffusive for many problems involving complexes geometries. Therefore more accurate methods are require for this flows. In FSI problems the structure impose the time steps and the solution compute with first order methods are stable but not accurate enough. • Solution reconstruction : for each face, the left and right states associated are built using centered gradients of neighbor cells :
L
R
I J
WCCM8 - ECCOMAS 2008 - Venice, Italy
June 30 - July 5
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Second order : Evaluation of Gradients - Limitation Green Gauss approach : the gradient of each conservatives scalar flow variable is approximated as : Reconstruction is achieved components by components for each conservative flow variables. The integration surface is the envelope of the control volume. We estimate conservative variable at the face center by : Reduce gradients High order spatial discretization require the use of non linear limiter functions to prevent spurious solutions in regions of high gradients (shocks, contact discontinuities …). Maxima (minima) in the flow field must be nonincreasing (non decreasing) and no new local extrema must be created. The purpose of limiters is to reduce the gradient used to reconstruct left and right state at any faces of the mesh. Limiters implemented in Europlexus : – Barth and Jespersen limiter – Dubois k-limiter Limiting occurs in the reconstruction of the left and right state :
WCCM8 - ECCOMAS 2008 - Venice, Italy
June 30 - July 5
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Extension to second order in time More robust computations can be achieved with the second order MUSCLHancock scheme. Two steps are necessary :
1. Data reconstruction : 1. Evolution : For each cell I, the extrapolate data at the face center IJ is advanced in time: With:
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June 30 - July 5
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hypothetical core disruptive accident (HCDA) – MARA 2 experiment In fast breeder reactor (LMFBR) it is assumed that the core of the nuclear reactor has melted partially and the interaction with liquid sodium has created high pressure bubble in the core. The experimental test MARA 2 simulates the explosive phenomenon in a flexible vessel. Explosive charge : initial conditions (computation) density ρ = 1350 kg/m3 Cp/Cv γ = 1.24 Initial Pressure P = 6.25 kbar
WCCM8 - ECCOMAS 2008 - Venice, Italy
June 30 - July 5
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hypothetical core disruptive accident (HCDA) – MARA 2 experiment
iso-density
Plastic strain in the vessel
WCCM8 - ECCOMAS 2008 - Venice, Italy
iso-surface density June 30 - July 5
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Detonation in presence of a wall
152,02 cm
Sensor Ref. A. Alia et M. Souli. High explosive simulation using multi-material formulations. Applied Thermal Engineering 26(2006), 10321042.
Wall
Simulation of a spherical high explosive C4 charge (radius 3.23 cm, weight 227 g). JWL equation of state is use in the entire computational domain:
- 862571 explosive)
WCCM8 - ECCOMAS 2008 - Venice, Italy
Finite
volumes
June 30 - July 5
(3038
in
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the
Detonation in presence of a wall
Animation
Pressure
2 ms
3.5 ms
WCCM8 - ECCOMAS 2008 - Venice, Italy
June 30 - July 5
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Lost Of Cooling Accident (LOCA) GV1
GV4
GV2
GV 3
Pipeline model PP1
PP2
Boucle 1 Boucle 2
Boucle 4 Boucle 3 PP4
Cuve PP3
Pipeline model Geometry of a 4-loop PWR
Pipe model of the reactor
Mixed pipeline / 3D model
Breaks location 1D/3D Fluid-Structure link
WCCM8 - ECCOMAS 2008 - Venice, Italy
June 30 - July 5
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HDR - Experiment Superheated Steam Reactor (KFA/ISR, Germany, 1980)
Finite Volume (3D) Finite Volume 1D/3D link (3D) element
Blowdown nozzle
Core barrel
Finite Element (1D)
Downcomer Pressure vessel
Blowdown nozzle: L = 1.37 m A = 0.0314 m2
Mass ring
Lower plenum
Core barrel: H = 7.57 m R = 1.32 m t = 0.023 m Mass ring: M = 13500 kg
First tests perform with unstructured FV using rigid structures to validate : - 1D (FEM) / 3D(FVM) links - two phase flow model for FV
WCCM8 - ECCOMAS 2008 - Venice, Italy
June 30 - July 5
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HDR - Experiment Superheated Steam Reactor (KFA/ISR, Germany, 1980)
WCCM8 - ECCOMAS 2008 - Venice, Italy
June 30 - July 5
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Conclusion The use of Finite Volume methods allows realistic prediction of phenomena Characterizing the consequences of reference accidents like LOCA, taking into account Fluid Structure Interaction (FSI) Strong shocks are much well resolves in problems involving explosion Check-boarding phenomenon is less important using V.F.M The possibility of linking 3D Finite volume and 1D finite element for pipeline systems allows the simulation of a full PWR primary loop with a coarser mesh and a less restrictive CFL condition highly distorted mesh involve more diffusive results and amelioration will be investigate in the Future
WCCM8 - ECCOMAS 2008 - Venice, Italy
June 30 - July 5
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