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OpenFOAM Analysis of CANDU-6 Moderator Circulation
S. M. Chang*¶, H. T. Kim**, K. L. Jeong***
* Kunsan National University
** KAERI, ***NEXT foam
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Contents
- Objective of Research - 2-D and 3-D Models with Results - Benchmark: STERN Lab. Experiment - CANDU-6 Moderator Circulation
- Summary
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Objective of Research
3-D Analysis with CFD(Computational Fluid Dynamics code and consideration of its feasibility in the moderator system of heavy-water CANDU reactors: Calandria tank
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Introduction: Calandria Tubes
LOCA: Loss Of Coolant Accident CHF: Critical Heat Flux Codes: MODTRUC/MODTRUC_CLAS, CATHENA, CUPID
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Key Physics
Primary Physical Phenomena 1) Incompressible flow solver + turbulence model 2) Heat transfer: energy equation 3) Buoyancy term: source terms in N-S equation 4) Porous media: modeling of porosity, permeability 5) Heat source model: energy equation Boundary conditions No-slip (wall), adiabatic, inlet/outlet, ……
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Governing Equations
0 V
2
0 0p T Tt
VV V g V g
sp QTTt
TC
2 V
tk b M k
j k j
k kk P P Y S
t x x
V
2
1 3 2t
k b
j j
C P C P C St x x k k
V
2kCt 1 21.44, 1.92, 0.09, 1.0, 1.3kC C C
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Solvers
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OpenFOAM: Folder Structure
0
constant
system
*.msh
U, p, k, epsilon, R, nuTilda, nut
polyMesh
RASProperties transportProperties
controlDict decomposeParDict
fvSchemes fvSolution
… I/C, B/C
… Mesh info.
… Turb. model, Mat. property
… Solver ctrl, Num. coeff., Scheme, Tolerance, etc. 8
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blockMeshDict #include <stdio.h> #include <math.h> #define R (.03302/2.) #define L (.0714) #define Imax 28 #define Jmax 4 #define IMAX (Imax*3) #define JMAX (Jmax*3) #define Per ((IMAX+1)*(JMAX+1)) #define Nx 10 #define Ny 10 #define Width .2 // Width of Channel #define PI 3.14159265 // Circumference ratio main() { int i, j, k, is, js, nc, Nc; double x, y, z, Xc, Yc; FILE *out; out = fopen("blockMeshDict.dat", "wt"); // Header fprintf(out, "FoamFile \n{ \n version 2.0; \n format ascii; \n"); fprintf(out, " class dictionary; \n object blockMeshDict; \n} \n\n"); fprintf(out, "convertToMeters 1;\n\n"); // Vertices fprintf(out, "vertices \n( \n"); for(k=0; k<=1; k++) { if(k==0) z = 0.; if(k==1) z = Width; y = 0.; for(j=0; j<=JMAX; j++) { …………………………………………………………………………………….
FoamFile { version 2.0; format ascii; class dictionary; object blockMeshDict; } convertToMeters 1; vertices ( (0.000000 0.000000 0.000000) (0.024026 0.000000 0.000000) (0.047374 0.000000 0.000000) (0.071400 0.000000 0.000000) (0.095426 0.000000 0.000000) (0.118774 0.000000 0.000000) (0.142800 0.000000 0.000000) (0.166826 0.000000 0.000000) (0.190174 0.000000 0.000000)
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Alternative: Transform of Grids Transformation of FLUENT Grids: CFX (*.gtm) -> *.msh file -> fluentMeshToFoam
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Example 1: Single Cylinder
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Example 2: 2-D Computation
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Example 3: 3-D Computation Velocity
Pressure 13
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Benchmark: STERN Lab. Exp.
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Material Properties
Dia. of tube: 0.03302 m X = 2 m
Y = 0.02856 m Z = 0.2 m
Case Vm [ m/s]
Density [ kg/m3]
Viscosity [ kg/(m s)]
Red
1 0.054 992.25 0.000653 2,709
2 0.070 981.00 0.000440 5,153
3 0.103 971.60 0.000355 9,308
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Boundary Condition / Grids Inlet Boundary Condition: fix volume flow rate Turbulence Intensity: assume 5% 2
'2
1Vk
l
kC 5.175.0
Outlet Boundary Condition: const pressure Wall Boundary Condition: no slip
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Treatment of Porosity: Theory
,
j
i j
i j i i
i j
pu u u S
t x x x
N-S (Momentum) Equation:
Porosity
, ,
1
2i i j kk i j iS D u F u
Darcy-Forchheimer Equation:
21
2
pU c U
L K
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Correlation: Experiment
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cos 2
p PLCV
L p
Re Red
V d
0.1724.54RePLC
Staggered Array In-Line Array
CT Tubes
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Implementation: OpenFOAM
1 ( porous { coordinateSystem { e1 ( 1 0 0); e2 ( 0 1 0); } Darcy { d d[0 –2 0 0 0 0 0] (2.5e10 2.5e10 0) f f[0 –1 0 0 0 0 0] (700 700 0) } } )
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2
pU c U
L K
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3-D Grids System
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Comparison of Result
COMSOL Multiphysics
ANSYS-CFX
OpenFOAM
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Comparison of Results
Cause of error: 1) Turbulence Intensity:
- Intake Turbulence - Surface Roughness
2) 3-D Effect: - Axial Flow along the Cylinder Surface - Relaxation of Flow Instability
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Full 3-D CANDU-6 Grids
Total = 6.74 M Hexa = 5.11 M Pyramid = 0.013 M Tetra = 1.62 M 23
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Boundary/Initial Conditions
- Massflow rate at each inlet = 127.4 kg/s. (Total Massflow = 1,019 kg/s) - No-slip at the wall.
- Outlet pressure: fixed, & zero-gradient otherwise.
- Inlet temperature = 47.3 degC. - Adiabatic at the wall.
- Initially stationary & isothermal.
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Modeling of the Heat Source
Total Thermal Power = 100 MW Correction Factor for the Volume of Tube Bundle = 1.089
)(, zfrfQzrQ zrss
mzzzf
mrrrrrrf
z
r
0.30.31111.00.1
38.30.000256.003888.00995.001989.094588.0
2
432
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Implementation with OpenFOAM
File Name: fvOption
energySource1 { type scalarCodedSource; active true; selectionMode all; #{ … forAll(cc,cellI) { … //define the source terms } #}; }
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Turbulence Scale
At 935 s, y+ <80
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Temperature at the Inlet/Outlet
Stage 1
Stage 2 28
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Velocity Profiles
Cross-sectional
Axial 29
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Temperature Profiles
Cross-sectional
Axial 30
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Animations
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1) Computation with OpenFOAM: gives us a new horizon in potential. Simulation of CANDU-6 with open source codes may be possible with full scale in the near future.
2) Validation of STERN Lab. Exp. with OpenFOAM: - Cause of Error: turbulence intensity, surface
roughness, 3-D effect, and grid dependency, etc. 3) Simulation of Full-scale CANDU-6 Moderator: - Two-stage computation/pseudo-steady - Max. temperature: 89 degC
Summary and Conclusion
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Q & A
Thank you for your attention!
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