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MULTIFACTORIAL MODELS FOR HEAT CONDUCTION AND HIGH-TECH WAYS TO PROTECT FISSION MATERIALS. Saenko A.V. Obninsk State Technical University for Nuclear Power Engineering, Obninsk, Russia. MULTIPLE FACTOR ANALYSIS OF THE MODEL OF THE SPHERICALLY -SYMMETRIC DEVICE WITH FUEL ELEMENT. - PowerPoint PPT Presentation
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MULTIFACTORIAL MODELS FOR HEAT CONDUCTION AND HIGH-TECH WAYS TO
PROTECT FISSION MATERIALS
Saenko A.V.
Obninsk State Technical University for Nuclear Power Engineering, Obninsk, Russia
2
Model Considered factorsBM
Basic The standard model of stationary heat conduction
MHRModel with heat
resistance
Calculation of contact heat resistance between shells
RNMRestricted non-
linear model
Calculation of dependence of thermal conductivity from the temperature in IV shell
CNMComplete non-linear model
Calculation of dependence of thermal conductivity from the temperature in all shells
CNRComplete non-
linear model with heat
resistance
Calculation of dependence of thermal conductivity from the temperature in all shells and contact heat resistance
MRBModel with
radiation on external
boundary
Calculation of radiation on external boundary
MRFModel with
radiation in FE
Calculation of radiation in shell between spherical fuel element and reflector
MEIModel with
external influence
Calculation external influence as a Al-rods for cooling device
Structure of the bundled software and geometric configuration for three technology of device
MULTIPLE FACTOR ANALYSIS OF THE MODEL OF THE SPHERICALLY-SYMMETRIC DEVICE WITH FUEL ELEMENT
3
11
2
1 6)( Crru
1 1( ) 0u r Heat conduction equation for heat-generating sphere:
Solution of equation:
Heat conduction equations for shells:
rCCru i
ii1)(
LINEAR MODELS (BM, MHR, MRB, MRF, MEI)
NON-LINEAR MODELS(RNM, CNM, CNR)
0))(( 11 rugraddiv
( ) 0i iu r Solutions of equations:
411
21
221
11
11 3189
31)( rSrrk
rkru
( ( )) 0i idiv grad u r
iiiiiii
ii CrSrrk
rkru
221)( 222
Boundary conditions:
05 5)( Tru rr
5 55 5 0 5( ) ( )r r r r ru r h T u r
ii rrirri ruru )()( 1
5 5 5
4 45 5 0 5 0 5( ) ( ) ( )r r r r r r ru r h T u r T u r
Continuity conditions: 1 1( ) ( )
i ii r i r r i r i r ru r u r
1 1 1
4 41 * 2 2 * 2 1 ** *( ) ( ) ( ) * ( )r r r r r r r ru r u r u r u r
iiii kru )(i const
4
VISUALIZATION OF THE SOLUTIONThe temperature profiles (content of 238Pu 5.5%)
The dot-line are the temperature profiles for BM. Profiles for «High Technology» is low for 50 оС
CNM
CNR MRF
MHR
5
The model of device with rodsEffective heat conductivity coefficient
for IV shell:
34,4 ii
εi is defined for every parts as:
ii
ii SnS
Sn
,4
THE MODEL WITH EXTERNAL INFLUENCE
Low Technology
The temperature profiles (content of 238Pu 5.5%)
n=20
6
Correction for the content of 238Pu (in %)
«Low Technology» «High Technology» «Medium Technology»
MHR -4.6 -7.4 -4.1RNM -4.5 -5.5 -5.7CNM -9.2 -12.1 -8.6CNR -13.7 -19.2 -12.7MRF -9.3 -17.4 -11.6MEI +31.9 +76.5 +52.1
THE ADVICE TO CHANGE THE CONTENT OF 238Pu
7
STRUCTURE OF THE BUNDLED SOFTWARE
8
1. The bundled software was created for estimate thermal field in
spherically symmetric device with fuel element.
2. Temperature profiles were obtained for 8 models for two types of
the boundary problem and three technologies.
3. Correction for the content of 238Pu were calculated.
CONCLUSION