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VTT TECHNICAL RESEARCH CENTRE OF FINLAND LTD
Coupling Serpent and
OpenFOAM
2015 Serpent User Group Meeting, Knoxville, TN
Riku Tuominen, [email protected]
mailto:[email protected]
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Outline
Motivation for the coupled calculations
Previous studies
Multiphysics interface
Adaptive search mesh
Test case
OpenFOAM
Serpent model
Coupling
Convergence in the coupled calculation
Results
Future work
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Motivation for the coupled calculations
Thermal feedback
• Neutron flux distribution and temperature
distribution are connected
Two main negative feedback effects with
increasing temperature
• Neutron absorption is increased in the fuel
(Doppler effect)
• Moderator density is decreased leading to
hardened neutron spectrum and increased
leakage
http://visual.ly/nuclear-reactor-core-schematic
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Previous studies
The thermal hydraulics part of the coupled problem has been
solved with subchannel codes in the past
Previously Serpent has been coupled with the subchannel code
SUBCHANFLOW
Monte Carlo/CFD coupling is a relatively new research topic as
both methods require a lot of computational power
With CFD the fidelity of the temperature and density distributions
of the coolant is increased vastly
It is interesting to see how the added fidelity affects the results of
the coupled calculation
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Multiphysics interface in Serpent 2
Allows the modelling of materials with arbitrarily refined temperature
and density distributions supplied by an external solver
Supports several formats, one of which is based on the OpenFOAM
unstructured mesh format
The same format can also be used to pass the volumetric power
density to the external solver
From the user point of view easy to use as one can pass the
temperature/density/power distribution without modification from one
code to another
Features an adaptive search mesh to speed up the cell search routine
User defined with a considerable impact on calculation time
Geometry can also be defined based on the OF mesh but this
increases calculation times
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Adaptive search mesh
At each interaction point the corresponding OF cell has to be found to
get correct state point information
OF mesh can have millions of cells so looping over all the cells is not a
viable option
The search mesh is a cartesian mesh placed on top of the OF mesh
Each search mesh cell includes the OF cells inside it
The correct search mesh cell can be determined from the interaction
coordinates with simple arithmetic operations
Only the OF cells inside the search mesh cell has to be checked
Memory consumption is reduced by adaptivity
The search mesh is gradually refined in regions where the density of OF
cells is large
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OpenFOAM
free, open source C++ toolbox for continuum mechanics
problems, including CFD distributed by the OpenFOAM
Foundation
Includes a large library with many functionalities such as tensor
and field operations, discretization, mesh, solution to linear
equations, turbulence models etc.
Also over 80 ready made solvers, and tools for meshing and
pre- and post-processing
VTT is an official contributor to OpenFOAM
OpenFOAM 2.3.x was used in this work
The Navier-Stoke equations concerning fluid flow are solved
with finite-volume method in an unstructured mesh
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Test case
A mock-up of a 5x5 fuel assembly cooled with
water in a steady state condition at full power
Neutronics with Serpent (Power distribution)
Conjugated heat transfer calculation with
modified chtMultiRegionSimpleFOAM
(Temperature and density distributions)
Axially finite (h=3.6 m) and horizontally infinite
Mesh generated with snappyHexMesh
(2228224 cells in total)
Possible boiling effects are neglected
Fuel rod
Cladding Water
Gadoline rod
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OpenFOAM model (1/2)
Four regions: one fluid and three solid
Connected with new boundary condition based on
turbulentTemperatureCoupledBaffleMixed which
balances heat fluxes at both sides of boundary
Additional thermal resistance at the fuel-cladding
interface
Horizontal symmetry
Periodic inflow (𝑣ave = 3.6 m/s) and fixed water temperature (𝑇 = 561 K) at inlet
Fixed pressure at outlet 𝑝outlet = 15.51 MPa
k-𝜔 SST turbulence model with wall functions
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OpenFOAM model (2/2)
Material properties:
Water: libFluid thermophysical library(Joona Kurki, VTT, 2014) +
custom OpenFOAM thermo class
Fuel: Custom specific heat capacity and thermal conductivity
submodels based on well-known FRAPTRAN correlations,
constant density
Cladding: polynomialTransport for thermal conductivity , a custom
specific heat capacity submodel with linear interpolation from
tabulated values, constant density
A custom fvOptions source to import the volumetric heat source from
Serpent
CFD convergence was determined by monitoring energy balance in
the coolant
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Serpent model
Geometry defined with Serpent’s own geometry model
Separate interface files for each material region
Two types of fuel: UO2 and UO2 + Gd2O3
k-eigenvalue criticality source method
At each iteration of the coupling program 40 × 106 active neutron histories were simulated
Total power was set to 1.0368 MW
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Coupling
Simple coupling program to run Serpent and OF solver in turns
OF solver is restarted on each iteration
Serpent communicates with the coupling program using POSIX-
signals
Iteration is initialized by running a Serpent calculation with
uniform temperature and density distributions
The temperature/density/power distribution data is transferred
between the codes using OF field files
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Convergence in the coupled calculation
The stochastic nature of the Monte Carlo neutronics complicates
evaluation of convergence
Always some statistical uncertainty in the fission power distribution
To overcome this problem Serpent uses relaxation based on the
stochastic approximation scheme
Fission power distribution is relaxed according to
𝑃rel(𝑛+1)
= 𝑃rel(𝑛)−
𝑠𝑛+1 𝑠𝑖𝑛+1𝑖=1
𝛼(𝑃rel(𝑛)
- 𝑃(𝑛+1))
If 𝑠𝑖 =constant and 𝛼 = 1 then 𝑃rel(𝑛+1)
= (1 −1
𝑛+1)𝑃rel
(𝑛)−
1
𝑛+1 𝑃(𝑛+1)
In the present work the convergence was evaluated retrospectively
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Results
Coupled calculation was run for 60+1 iterations
Total calculation time ≈ 72 h on a node with two Eight-Core Intel
Xeon E5-2680 2.7 Ghz CPUs with 128 GB RAM memory
Main results are the high fidelity temperature and density
distributions for an independent Serpent calculation
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Results
Fluid temperature on plane 1. Fuel temperature on plane 2.
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Results: Collision density in the moderator
Reference 256 axial layers
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Results: Search mesh optimization
Memory usage Transport cycle time
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Results: Convergence and relaxation
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Results: Mesh based geometry
Test calculation with 109 active neutron histories
Run with both Serpent’s own geometry model and mesh based
geometry model
Transport cycle time: 774 min (mesh) vs. 610 (Serpent)
The increase is about 27 %
If possible the use of mesh based geometry should be avoided
to save computational time
The advantage of mesh based geometry is in the modelling of
highly irregular geometries which are cumbersome to define with
Serpent’s own geometry model
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Future work
Inclusion of boiling and condensation:
Option 1:
• Single-phase simulation with material properties of the water-
steam mixture provided by libFluid
• Effective wall heat transfer coefficient evaluated from boiling
correlations
• Assumes local thermal equilibrium and zero slip velocity.
Option 2:
• Two-phase simulation
• On-going work at VTT in co-operation with OpenFOAM
Foundation
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Future work
Add spacer grids to the geometry
Separate fuel behaviour solver (Some initial testing has been
done with FINIX)
Modelling of a case where comparison with experimental data is
possible
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Thank you! Questions?
Ideas?
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