Multi-layer lid

of storage

cask

Tight storage

cask

Storage

container lid

Metal

protection

shell

Outlet

vent

channel

Inlet vent

channel

Concrete

container

DEFINITION OF TIME-DEPENDED EQUIVALENT HEAT

CONDUCTIVITY OF THE STORAGE CASK WITH

SPENT NUCLEAR FUEL BY SOLVING THE INVERSE PROBLEM

Svitlana Alyokhina,

PhD., senior scientific researcher

A. M. Pidgorny Institute For Mechanical Engineering Problems

of the National Academy of Sciences of Ukraine

ABSTRACTThe equivalent heat conductivity of the storage cask, which is used on Zaporizhska NPP, is

determined. The calculations for different time of storage with change of spent fuel assemblies heat

generation rate in the course of time were carried out.

THE METHODOLOGY

Definition method of the equivalent heat conductivity is based on decision of inverse

heat conduction problem (IHCP). Unlike the cases, when classical IHCP are used for

definition of the composite solid body heat conductivity, it is necessary to consider this

task in the conjugated formulation and solve the inverse conjugated task of heat

transfer due to presence of unsteady medium (helium, air).

For solving of IHCP was used the fitting method. The fitting method implies a

subjectively-based selection of a heat characteristic sought for in the IHCP, and

subsequent solution of the direct heat conduction problem. In solving the direct

problem, one defines the temperature pattern, including the temperature in the

measurement point (reference point), which now is a function of the chosen sought for

characteristic. Further, using the given and measured temperature, the discrepancy

value is found and compared with a preset value ε ≥ β. Should the discrepancy value

exceed ε, the sought for characteristic value is changed, and the direct problem is

solved again. After this, the found discrepancy value is compared with number ε, and

so forth, until a reasonable solution (to satisfy the condition of ε) is derived.

PROBLEM DEFINITION

Container’s structure

INTRODUCTION

Cask structure

The Dry Spent Nuclear Fuel Storage Facility(after finished the first stage of construction)

4973

4320

1664

1715Load-bearing lidProtective lid

(first layer)

Drain-pipe

А - А

Guide tube

Cask case

Neutron shield

AA

Spent fuel

assembly

Place for spent

fuel assembly

Helium zone

Helium zone

Helium zone

COMPUTATIONAL EXPERIMENTResearch of thermal processes in container with SNF was carried out by the

solution of the conjugate problems of heat exchange. The problem was considered in

quasi-steady formulation.

The mathematical model viewed stationary process of thermal physics includes the

following equations:

– continuity;

– motion of viscous fluid;

– energy;

– heat conductivity.

At identical external thermal influence, two problems are considered. In the first of

them the detailed geometrical model is used. In second one the simplified geometrical

model is considered. It assumes that the object of investigation is replaced on a

homogeneous isotropic body with heat conductivity λe. The determination of λe is

carried out using repeated solving of a problem with simplified geometrical model by

adjustment for the purpose of minimization mean-square residual between temperature

values, which received after problems decision with the detailed and the simplified

geometrical models:

( )min)( 1

2

→

−

=∑

=

N

TTN

i

s

i

d

i

eλσ

N – number of so called reference points in which the temperature deviation is

considered;

Tid

– temperature in the i-th reference point, which was obtained from solution with the

detailed geometrical model of the investigation object;

Tis

– temperature in the i-th reference point, which was obtained from solution with the

simplified geometrical model.

INVESTIGATIONS RESULTS

Helium

Head

Tail

Fuel

Outlet

channel

SteelConcrete

Air

SFA

xz

x

y

1

2

3

4

5

6

8

10

12

14

16

18

20

22

24

7

9

11

13

15

17

19

21

23

Cask caseNarrow channel

Wide channel

Guiding tubes

Detailed geometrical model

z

x

x

y

Simplified geometrical model

The spent nuclear fuel stored on the open area on

nuclear power plant territory. The Dry Spent Nuclear

Fuel Storage Facility (DSNFSF) it is designed for

storage of 350 containers within 50 years.

The structure of Ukrainian nuclear power industry includes four nuclear power plants.

Today fifteen nuclear plant units operate in Ukraine, therefore the problem of handling

with the spent nuclear fuel (SNF) is very important for Ukraine. Zaporizhska Nuclear

Power Plant (ZNPP) produce 134.4 tons of SNF every year alone. That is almost half of all

SNF in Ukraine. For the solving the problem of handling with SNF the technology of

interim dry storage has been chosen in Ukraine. It was realized on ZNPP.

The one of important problem during the dry storage of spent fuel is ensuring of the safe

thermal conditions. For complex object as the SNF storage, it is impossible to solve this

problem without mathematical simulation. In this case the detailed consideration of

structure of all elements of modeled object is not always rational. Some of them can be

presented as the simplified geometrical models with equivalent thermal physics properties.

This simplifies calculations appreciably.

The differential equation system is supplemented with the major equations of state for

closure. For that the ideal gas law is acceptable in investigated problem. The standard k-

ε turbulent flow model is used for the prediction of the turbulent component of

coefficients in equations. This model consists of two differential equations: for the

turbulent kinetic power k and velocity of its dissipation ε.

The mathematical model is supplemented with the equation which describes radiative

thermal exchange between outside surface of cask and inner surface of container and

also between outside surface of guiding tubes and inner surface of storage cask.

3.4

3.5

3.6

3.7

3.8

3.9

0 5 10 15 20 25 30 35

λe Вт/м*К

duration of storage,

year

SOLUTION STRATEGY

CONCLUSIONS

The results can be used in modelling of thermal state of group containers.

On the basis of the solution of conjugated inverse heat transfer problem, the procedure of

determination of equivalent heat conductivity of tight cluster basket was developed. It

allows to replace the basket by homogeneous isotropic body in the simplified

mathematical model.

The investigations of influence of quantity and arrangement of reference points on the

variation of λe were carried out too. For example, for cask at first year of storage, if

reference point at the lid and bottom of cask are excluded from the calculation by

equation (1), the λe value within the accuracy of 0.1 W/(m·K) remain unchangeable. The

same is observed if the reference points only at assemblies axes and guide tubes are

considered. When the guide tubes are excluded from calculation the information about

essential irregularity of temperature field in the cask is lost, as the temperature in

reference points at guide tubes is less on 20-50°С from the temperature in the reference

points at the center of assemblies at the same altitude.

Table 1. The values of temperature for detailed and simplified geometrical models for first year of storage

–5.20251.76246.56135

–25.49143.37117.8895

–6.23222.52216.2975

21.99122.78144.7739

12.30209.54221.8435

–16.58163.62147.0432

20.71113.63134.349

11.17192.55203.725

–14.24153.68139.442

Simplified geometrical model

(λe) = 3,9 W/(m·К)

Detailed

geometrical

model

Difference of

temperatures at using

detailed and

simplified geometrical

models, °С

Temperature, °С

No.

reference

point

–5.20251.76246.56135

–25.49143.37117.8895

–6.23222.52216.2975

21.99122.78144.7739

12.30209.54221.8435

–16.58163.62147.0432

20.71113.63134.349

11.17192.55203.725

–14.24153.68139.442

Simplified geometrical model

(λe) = 3,9 W/(m·К)

Detailed

geometrical

model

Difference of

temperatures at using

detailed and

simplified geometrical

models, °С

Temperature, °С

No.

reference

point

Contacts:st. Dm. Pozharsky 2/10, Kharkiv, UA-61046, Ukraine

Tel. +380(572)942794

E mail: alyokhina@ipmach.kharkov.ua