VTT TECHNICAL RESEARCH CENTRE OF FINLAND LTD

Coupling Serpent and

OpenFOAM

2015 Serpent User Group Meeting, Knoxville, TN

Riku Tuominen, riku.tuominen@vtt.fi

mailto:riku.tuominen@vtt.fi

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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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