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

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STRUCTURE OF THE BUNDLED SOFTWARE

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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