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: [email protected]
