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Improvement of hydraulic flow analysis codefor APWR reactor internals
F.Kasahara, S.Nakura, T.Morii, and Y. Nakadai
Institute of Nuclear Safety (INS)Nuclear Power Engineering Corporation (NUPEC)
(PS) This study was performed under the sponsorship of METI
CFD Meeting Presentation Material in Aix en Provence, May 15-16, 2002
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CFD meeting presentation 1
Contents
1.Background and Objectives2.Results of the hydraulic flow characteristics
analysis of reactor internals3.Results of the dynamic pressure analysis of
downcomer4.Conclusion
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BackgroundSchedule of the project : Improvement of hydraulic flowanalysis code for APWR reactor internals
fiscal year 1996 1997 1998 1999 2000 2001 2002 2003i t em
ElectricTsuruga-3/4(APWR) Power Application� i� jNPPUtility plan forDevelopment
Coordination SafetyStart of operation : Council License
� ¤�¤2009 fiscal yearExpected)�i
Licensing schedule
Safety Review
Improve CFD(Computational Fluid Dynamics) codeSchedule of Project
Experiment
Design & roduce test facilityP
Investigation &Planning test facility
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In safety review, it is necessary for the regulatory body todevelop its own analysis codes in order to independentlyevaluate the safety analysis results done by applicant.
One of the most innovative design improvement of APWR is the neutronreflector which replaces the conventional baffle-former structure.
Concerns:
• Coolability of the neutron reflector by heating
• Fluid-structure interaction (FSI) caused by dynamic pressure fluctuation
Develop analysis codes to evaluate the concerns.
Verification of analysis code based on the results of hydraulic flow test using1/5 scale mode.
Objectives
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•••••Upper core plate
•••••••Lower core support plate
•••••Fuel assembly
•••••••
•••••••
••••
••••••
•••••
•••
•••••
••••
•••
•••••••
Flow pattern in APW R reactor vessel
Neutron reflector
Inlet nozzle
Core barrel
Reactor vessel
Outlet nozzle
main flow
by-pass flow
Lower core plate
Guide tube
Upper support column
Upper support plate
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Developing analysis codes
Developing analysis codes utilizing IMPACT code modules item code remark
1 Coolability of the neutron reflector by
heating CFD-1
CFD-1 should be parallel simulation code with Reynolds averaged numerical simulation method (k- model).
2 Flow-induced vibration by dynamic pressure fluctuation
CFD-2 +
Structure- vibration analysis
code (FELIOS)
CFD-2 should be parallel simulation code with Large Eddy Simulation method or dynamic numerical simulation method.
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CFD meeting presentation 9
Hydraulic flow analysis codes for APWR reactorinternals
• Hydraulic flow characteristics analysis of reactorinternals
Improvement of Reynolds averaged numerical simulation method (k-model) with unstructured grid• Dynamic pressure analysis of the downcomer Improvement of Large Eddy Simulation method with structured grid
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Objective of hydraulic flow characteristicsanalysis of reactor internals
To establish the numerical method to exactlycalculate flow distribution into the neutron reflector
Measurement items in this experiment• Flow distribution into the neutron reflector• Pressure distribution on the lower core plate• Pressure distribution of the lower plenum
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Calculation Conditions
Hydraulic flow characteristics analysis Analysis Case
Flow rate : 100 , Temperature : 150
Calculation Grid System Unstructured /or structured (BFC with Multi-block Methodl) Time Marching Method SIMPLE (Semi-Implicit Method-for Pressure-Linked Equation)
Turbulent Model k- model ( Reynolds averaged numerical simulation method)
Transient term Euler implicit Discretization
Convection term Donor-Cell method Density 917.0 [kg/m3]
Properties Viscosity 1.80 10-4 [Pa s] Inlet Constant : Vin=16.674 [m/s] Outlet Free out Boundary Condition Wall Log-Law
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Velocity distribution in the Reactor vessel
90°180°90° - 270° cross section
velocitym/s
18
0
Velocity
m/s
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0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 10 20 30 40
“± “ü E ”Ô †
”ñ \ ‘¢ Ši Žq
\ ‘¢ Ši Žq
ŽŽ Œ± Œ‹ ‰Ê�\‘¢Ši�q�i‚V‚V–œ�j
”ñ�\‘¢Ši�q�i‚U‚Q–œ�j
‰º•”˜F�S”ÂŒ`�ó�i��Œ±‘•’u�j
Flow distribution(Ratio to average)
••••••
Comparison between Calculation and Experiment
Structured grid
(770,000 meshes)
Unstructured grid
(620,000 meshes)
Unstructured
structured
experiment
Flow hole
Lower core plate
(test facility)Flow hole number
(Flow distribution into radial reflector)
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CFD meeting presentation 14
0.7
0.8
0.9
1
1.1
1.2
1.3
0 5 10 15 20 25 30 35 40
• • • • •
•••••••••••••
•
• • • •• • • •
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
0 5 10 15 20 25 30 35 40
• • • • • •••••••••••KPa•
• • • •
• • • •
Flow rate distribution into neutron reflector(ratio to average)
Pressure distribution on lower coreplate(deference from average kPa)
Comparison between Calculation and Experiment
Flow hole No.Flow hole No.
AnalysisExperiment
Analysis
Experiment
(Flow and pressure distribution at the entrance of neutron reflector)
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Experiment Calculation
Comparison between Calculation and Experiment
0�‹
180�‹
270�‹ 90�‹
270�‹
0�‹
90�‹
180�‹
[k Pa]
(Pressure distribution in the lower plenum:bottom surface of test vessel)
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Objective of dynamic pressure analysisof downcomer
Improve the code with LES to calculate adequately dynamicpressure by turbulent flow, selected in the 3-dimensional flowanalysis code which can simulate the model of flow passage.
To establish the numerical method tocalculate dynamic pressure induced byturbulent flow in downcomer.
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Measuring Points of Dynamic Pressure
Upper
Middle
Lower
50mm
Circumferential point
Axial point
Reference point compared with experiment
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Calculation Conditions
LES ( Analysis for optimized Cs value Analysis Case
Flow rate : 100 , Temperature : 150
Calculation Grid System BFC with Multi-block Method Time Marching Method SMAC ( Simplified Maker And Cell Method )
Turbulent Model LES (Smagorinsky eddy viscosity model : Cs=0.17 )
Transient term Euler Explicit Discretization Convection term QUICK Calculation of Time Interval 4.0 10-5 [s]
Density 917.0 [kg/m3] Properties
Viscosity 1.80 10-4 [Pa .s] Inlet Constant : Vin=16.674 [m/s] Outlet Sommerfeld Condition Boundary Condition Wall Log-Law
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Calculation Grid
Calculation grid both side of wall
(a) Core Barrel (b) Reactor Vessel
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Mean Velocity contour of downcomer
Calculation Results
(a) Core Barrel (b) Reactor Vessel
[m/s][m/s]
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Turbulent energy contour of downcomer
(a) Core Barrel (b) Reactor Vessel
m2/s2 m2/s2
Calculation Results
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Figure.4 Dynamic Pressure( 90 of downcomer see page 17 )
upper point middle point lower point
Calculate the dynamic pressure by turbulent flowto t = 0.6s. The data from t = 0.24s to t = 0.6s wasused in statistical analysis.
Calculation Results
- 50. 0
0. 0
50. 0
0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7
Š î� €̂ Ê’ u� ü• ûŒü‘ ŠŠ Ö̂ Ê’ u� ²• ûŒü‘ ŠŠ Ö̂ Ê’ u
ˆ³—
Í [k
Pa]
� �Š Ô [ s ]
- 50. 0
0. 0
50. 0
0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7
Š î� €̂ Ê’ u� ü• ûŒü‘ ŠŠ Ö̂ Ê’ u� ²• ûŒü‘ ŠŠ Ö̂ Ê’ u
ˆ³—
Í [k
Pa]
� �Š Ô [ s ]
- 50. 0
0. 0
50. 0
0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7
Š î� €̂ Ê’ u� ü• ûŒü‘ ŠŠ Ö̂ Ê’ u� ²• ûŒü‘ ŠŠ Ö̂ Ê’ u
ˆ³—
Í [k
Pa]
� �Š Ô [ s ]time [s] time [s] time [s]
time [s]
dyna
mic
pre
ssur
e [k
Pa]
dyna
mic
pre
ssur
e [k
Pa]
dyna
mic
pre
ssur
e [k
Pa]
dyna
mic
pre
ssur
e [k
Pa]reference pointcircumferential point
axial point
Experiment
reference pointcircumferential pointaxial point
reference pointcircumferential pointaxial point
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CFD meeting presentation 23
RMS Value of Dynamic Pressure
( ) ( ) ( )fkfffPdffPpk
kkxx
f
f xxRMS∆⋅=∆⋅≅⋅= ∑∫
=
,~max
min
max
min
2( ) : C/E value
Calculation Results
1.6 1.45 0.9090 [deg]2.0 1.57 0.790 [deg]
Lower
1.8 2.50 1.3990 [deg]1.7 1.75 1.030 [deg]
Middle
5.0 6.49 1.30135 [deg]
5.011.75 2.3590 [deg]
4.9 6.20 1.2745 [deg]2.0 2.80 1.400 [deg]
Upper
ExperimentCalculationCircumferentialPositionAxial position
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CFD meeting presentation 24
( ) ( )( ){ }∑ ∆⋅⋅
=
kxx
xxRMSxx
ffC
fCpfS2
~
Definition : RMS Spectrum
is the magnitude of Fourier coefficientxxC
RMSp~ is RMS value
Spectrum Analysis
Sampling cycle is 8 10-5 [s]
The spectrum is the ensembleaverage of Fourier coefficientcalculated by 2048 samples perone section.
( )fkf ∆⋅=
Calculation Results
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CFD meeting presentation 25RMS Spectrum ( 90°of downcomer )
Upper point Middle point Lower point
Upper point Middle point Lower point
0. 0
2. 5
5. 0
0 100 200 300 400 500
RMS
spec
trum
[k
Pa*s
0.5 ]
f r equency [ Hz]
0. 0
2. 5
5. 0
0 100 200 300 400 500
RMS
spec
trum
[k
Pa*s
0.5 ]
f r equency [ Hz]
0. 0
2. 5
5. 0
0 100 200 300 400 500
RMS
spec
trum
[k
Pa*s
0.5 ]
f r equency [ Hz]
Calculation Results
0. 0
2. 5
5. 0
0 100 200 300 400 500
Š î� €̂ Ê’ u� ü• ûŒü‘ ŠŠ Ö̂ Ê’ u� ²• ûŒü‘ ŠŠ Ö̂ Ê’ u
‚q‚
l‚rƒ
Xƒyƒ
Nƒgƒ
‹ [k
Pa*s
0.5 ]
� ü” g� ” [ Hz]
0. 0
2. 5
5. 0
0 100 200 300 400 500
Š î� €̂ Ê’ u� ü• ûŒü‘ ŠŠ Ö̂ Ê’ u� ²• ûŒü‘ ŠŠ Ö̂ Ê’ u
‚q‚
l‚rƒ
Xƒyƒ
Nƒgƒ
‹ [k
Pa*s
0.5 ]
� ü” g� ” [ Hz]
0. 0
2. 5
5. 0
0 100 200 300 400 500
Š î� €̂ Ê’ u� ü• ûŒü‘ ŠŠ Ö̂ Ê’ u� ²• ûŒü‘ ŠŠ Ö̂ Ê’ u
‚q‚
l‚rƒ
Xƒyƒ
Nƒgƒ
‹ [k
Pa*s
0.5 ]
� ü” g� ” [ Hz]
reference pointcircumferential pointaxial point
RM
S sp
ectru
m [k
Pa×s
0.5 ]
Experiment
frequency [Hz] frequency [Hz] frequency [Hz]
RM
S sp
ectru
m [k
Pa×s
0.5 ]
RM
S sp
ectru
m [k
Pa×s
0.5 ]
reference pointcircumferential pointaxial point
reference pointcircumferential pointaxial point
Experiment Experiment
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CFD meeting presentation 26
Definition : Normalized Cross-Spectrum
( ) ( )( ) ( )fPfP
fPf
yyxx
xyxy ⋅
=Γ( )fPxy( ) ( )fPfP yyxx ,
is real part of cross spectrumis power spectrum
Normalized Cross-Spectrum Approximated by Turbulent Theory**
‡ @ Axial Correlation
( )
−⋅⋅= −
C
fCxy U
yxfef πΓΓ 2cos10
*
‡ A Circumferential Correlation
( ) fCxy ef 10* −⋅= ΓΓ
**Taylor s hypothesis of frozen turbulence
Uc : Convection velocity is calculated form the peak of the cross-relation coefficient. C1 is approximated by the method of least squares using the normalized cross-spectrum raging the frequency shown by thick line.
Calculation Results
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CFD meeting presentation 27
Normalized Cross Spectrum ( 90°of downcomer )
Calculation Results
- 1 . 0
- 0 . 5
0 . 0
0 . 5
1 . 0
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0
–³�
ŸŒ³‰
»ƒNƒ
�ƒXƒ
Xƒyƒ
Nƒgƒ
‹
[�
|]
� ü” g� ” [ Hz ]
- 1 . 0
- 0 . 5
0 . 0
0 . 5
1 . 0
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0
–³�
ŸŒ³‰
»ƒNƒ
�ƒXƒ
Xƒyƒ
Nƒgƒ
‹ [
�|]
� ü” g� ” [ Hz ]
- 1 . 0
- 0 . 5
0 . 0
0 . 5
1 . 0
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0
–³�
ŸŒ³‰
»ƒNƒ
�ƒXƒ
Xƒyƒ
Nƒgƒ
‹ [�
|]
� ü” g� ” [ Hz ]
Cal
cula
tion
Cro
ss sp
ectr
um [-
]
Cro
ss sp
ectr
um [-
]
Cro
ss sp
ectr
um [-
]
Frequency [Hz] Frequency [Hz] Frequency [Hz]
Exp
erim
ent
Cro
ss sp
ectr
um [-
]
Cro
ss sp
ectr
um [-
]
Cro
ss sp
ectr
um [-
]
Frequency [Hz]Frequency [Hz]Frequency [Hz]
Upper point Middle point Lower point
Upper point Middle point Lower point
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CFD meeting presentation 28
( ) ( )( ) ( )
00 ==⋅
=
ττττ
ττ
yyxx
xyxy
CC
CR ( )τxyC : cross-correlation function
: auto- correlation function( ) ( )ττ yyxx CC ,
Definition : Coefficient of Cross Correlation
Auto-Correlation Function Inverse-Fourier transform of power-spectrum
( ) ( ) dtefPC ftxxxx πτ 2−∞
∞−⋅= ∫
( ) ( ) dtefPC ftyyyy πτ 2−∞
∞−⋅= ∫
( ) ( ) dtefPC ftxyxy πτ 2−∞
∞−⋅= ∫
Cross-Correlation Function Inverse-Fourier transform of cross-spectrum
Calculation Results
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CFD meeting presentation 29
Convection velocity
Calculation Results
9.410.7890 [deg]
6.28.800 [deg]Lower
9.98.9390 [deg]
5.9 9.190 [deg]Middle
9.58135 [deg]
12.612.0090 [deg]
9.8245 [deg]
5.4 7.380 [deg]
Upper
ExperimentCalculationCircumferentialPositionAxialposition
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CFD meeting presentation 30
xy
yxΓ
−−=
lnλ
Definition : Correlation Length
xyΓ : Absolute normalized cross-spectrum approximated by turbulent theory
yx − : Distance between measuring point x to y (=50mm)
Calculation Results
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CFD meeting presentation 31
Correlation length ( 90 deg Axial direction)
Calculation Results
0. 0
300. 0
600. 0
0 100 200 300 400 500
‘ŠŠ
Ö’·
[mm]
� ü” g� ” [ Hz]
0. 0
300. 0
600. 0
0 100 200 300 400 500
‘ŠŠ
Ö’·
[mm]
� ü” g� ” [ Hz]
0. 0
300. 0
600. 0
0 100 200 300 400 500
‘ŠŠ
Ö’·
[mm]
� ü” g� ” [ Hz]
Cal
cula
tion
Frequency [Hz] Frequency [Hz] Frequency [Hz]
Exp
erim
ent
Cor
rela
tion
leng
th [m
m]
Cor
rela
tion
leng
th [m
m]
Cor
rela
tion
leng
th [m
m]
Frequency [Hz]Frequency [Hz]Frequency [Hz]
Cor
rela
tion
leng
th [m
m]
Cor
rela
tion
leng
th [m
m]
Cor
rela
tion
leng
th [m
m]
Upper point Middle point Lower point
Upper point Middle point Lower point
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CFD meeting presentation 32
0. 0
300. 0
600. 0
0 100 200 300 400 500
‘ŠŠ
Ö’·
[mm]
� ü” g� ” [ Hz]
0. 0
300. 0
600. 0
0 100 200 300 400 500
‘ŠŠ
Ö’·
[mm]
� ü” g� ” [ Hz]
0. 0
300. 0
600. 0
0 100 200 300 400 500
‘ŠŠ
Ö’·
[mm]
� ü” g� ” [ Hz]
Correlation length ( 90 deg Circumferential direction)
Calculation ResultsC
alcu
latio
n
Frequency [Hz] Frequency [Hz] Frequency [Hz]
Exp
erim
ent
Cor
rela
tion
leng
th [m
m]
Cor
rela
tion
leng
th [m
m]
Cor
rela
tion
leng
th [m
m]
Frequency [Hz]Frequency [Hz]Frequency [Hz]
Cor
rela
tion
leng
th [m
m]
Cor
rela
tion
leng
th [m
m]
Cor
rela
tion
leng
th [m
m]
Upper point Middle point Lower point
Upper point Middle point Lower point
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CFD meeting presentation 33
Conclusion• CFD-1 with unstructured grids, SIMPLE method and k- turbulent model show good agreement with the experiments
data.• Considering present CFD technique, CFD-2 with structure
grids ( BFC method) , SMAC method and LES turbulentmodel is the best combination for the analysis of dynamicpressure fluctuation.
• Basically,CFD-1 and CFD-2 are applicable to plantoperating condition. For better evaluation, it is planed toconfirm that the numerical method of 1/5 scaled model isrightly applied to a real scale simulation.
Conclusion
Improvement of hydraulic flow analysis code for APWR reactor internalsHydraulic flow analysis codes for APWR reactor internalsObjective of hydraulic flow characteristics analysis of reactor internalsVelocity distribution in the Reactor vesselObjective of dynamic pressure analysis of downcomerConclusion
close: