Special Issue on Heat Transfer, February 2011
Manuscript received and revised January 2011, accepted February 2011 Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved
291
Analysis of Temperature Field Inside the Fuel Rod of the VVER 440 Fuel Assembly
Miriama Sa čková
1,2
, Branislav Hatala
1
, Vladimír Ne čas
2
Abstract – The presented work is oriented to analysis of temperature field inside the fuel rod of the VVER 440 fuel assembly. The project is based on overview of physical phenomena, which
influence the thermal conductivity of the gap between fuel and cladding and temperature field inside the fuel rod. By analyzing the physical causes, the most important boundary conditions
were identified that determine fuel temperature values. The work analyses the temperature field inside the fuel rod in dependence on parameters, which have significant impact on the maximum
temperature inside the fuel. The work is focused on the evaluation of the impact of changes of analysed parameters on the maximum temperature inside the fuel. Copyright © 2011 Praise
Worthy Prize S.r.l. - All rights reserved. Keywords:
Fuel Rod, RELAP5, Temperature Field
Nomenclature
α Heat transfer coefficient
[Wm
2
K] α
G
Heat transfer coefficient in the gap [Wm
2
K] δ
G
Thickness of gap [mm]
δ
C
Thickness of cladding [mm]
λ
F
Thermal conductivity of fuel [WmK]
g
1
,g
2
Temperature jump distance terms for fuel andcladding
[-] q
F
´´´ Heat flux density
[Wm
3
] q
C
´´´ Heat flux density in coolant
[Wm
3
] n
Number of a circumferential segment
[-] N
Total number of circumferential segments 8
[-] r
F
Surface roughness of the fuel [m]
r
C
Surface roughness of the cladding [m]
R
F
Radius of fuel pellet [mm]
t
n
width of gap at the midpoint of the n-th circumferential segment
[m] t
G
Circumferentially averaged fuel- cladding gap width
[m] t
o
As-fabricated fuel-cladding gap width
[m] T
S0
Temperature inside the fuel [K]
T
S1
Temperature on the edge of the fuel
[K] T
S2
Temperature on the inner edge of cladding
[K] T
S3
Temperature on the outer edge of cladding
[K] T
ref
Reference coolant temperature [K]
u
F
Radial displacement of the fuel pellet surface
[m] u
C
Radial displacement of cladding inner surface
[m] u
TF
Radial displacement due to thermal expansion
[m] u
r
Radial displacement due to uniform fuel relocation
[m] u
S
Radial displacement due to fission gas induced fuel swelling and
densification [m]
u
TC
Radial displacement due to thermal expansion
[m] u
CC
Radial displacement due to cladding creepdown
[m] u
e
Radial displacement due to elastic deformation
[m]
I. Introduction
The safety analyses, which are usually carried out by using computer programs, are the mean to show
the reached level of nuclear safety of nuclear facility. The safety analysis evaluates the risk of operation of nuclear
facility and analyzes if safety requirements against the release of radioactive materials in the initiating events,
which occur or may occur in the whole range of operating conditions, are fulfilled.
The object of this work is focused on analysis of temperature field inside the fuel rod of the VVER 440
fuel assembly. The aim of this analysis was to present the isolated influence of the individual parameters on
temperatures inside the fuel, in the gap between fuel and cladding and inside the cladding of fuel rod. The analysis
includes changes of those parameters which could be put in a model of fuel rod by using the RELAP5 code [1].
The work contains creating a computational model of
Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
292 fuel rod of the VVER 440 fuel assembly for the RELAP5
calculation. The model was developed for analysis of temperature
distribution in the fuel rod with variable power distribution, burn up and with a possibility to analyze
changes of all parameters with significant impact on thermal conductivity in the gap. The model, which was
developed, is used for computational analysis of several cases, which cover the whole range of significant initial
and boundary conditions. The work analyses the temperature field inside the fuel rod in dependence on
parameters, which have significant impact on the maximum temperature inside the fuel.
The results of these computational analyses were processed in an appropriate form for presentation the
influence of the individual parameters on one hand and to illustrate reached limit values on the other [2].
II. Temperature Field inside the Fuel Rod
The investigated fuel rod contains 3 materials: a Fuel – UO
2
enriched 4,25
235
U, b Gap between fuel and cladding – Helium, and c Cladding – Zr +1Nb.
Fig. 1. Temperature field inside the fuel rod
The Fourier equation of heat transfer was applied to the calculation of the temperature field in the fuel rod.
Fourier differential equation of heat transfer - steady state [3]-[8]:
´´´ F
F
T q
λ
∇ ∇ +
=
1 Solution [3]:
2 1
4
´´´ F
S S
F F
q T
T R
λ
− =
2
2 1
2
2
´´´ F
G F
S S
F F
F
R q
T T
R ln R
δ λ
⎛ ⎞
+ −
= ⎜
⎟ ⎝
⎠
3
2 2
3
1 2
´´´ C
F S
S F
F F
G
q T
T R ln
R
δ λ
δ
⎛ ⎞
− =
+ ⎜
⎟ +
⎝ ⎠
4
2 3
2
´´´ ´´´
C F
F S
ref F
G C
q q R
T T
R
α α
δ δ
− =
= +
+
5 In operation, fuel properties are changed due to
elevated temperatures, production of fission products and deformations. If temperature of UO
2
fuel reaches temperature around 1700°C, it comes to change the
crystal structure of fuel. This creates a layer of crystal bar and fuel tends to the formation of radial cracks
cracking. In temperature range 1400-1700°C, it comes also to recrystallization of material. It can be expected
that during the operation of the reactor, three areas with different thermo-physical properties are formed. In the
central area of the fuel cell, where the temperature may reach more than 1700°C, at oxide fuel the mass transfer
occurs. This movement of cavities and pores of the fuel in the direction of temperature gradient leads to the
expansion of the central hole and increasing the fuel density. This phenomenon is called densification. The
gas fission products are released during burn up and get into the gap between fuel and cladding through the
cracks. As a result, the inner pressure under the cladding increases. With increasing burn up and depending on the
temperature inside the fuel, swelling occurs. This phenomenon is related to the accumulation of fission
products and the possibility of their diffusion in the fuel. Changes of fuel properties during the operation are
shown in Fig. 2.
The gap between fuel and cladding is filled with helium. In the process of burning up, the gap gradually
narrows, UO
2
gets into a direct contact with cladding and the contact pressure between fuel and cladding increases
with increasing burn up. Heat transfer in the gap has a complicated character. In terms of calculating the radial
temperature distribution in the gap, there are two processes. If the gas gap between fuel and cladding is
sufficiently large fresh fuel, it comes to heat transfer by conduction in the narrow gas gap. If the fuel is in contact
with cladding partially spent fuel, it is a case of heat conduction in gas and heat conduction at the interface of
two solids. At higher temperature, the heat transfer by radiation is applied [2], [7], [9]-[11].
Fig. 2. Changes of fuel properties during burn up
R
F
+ δ
G
+ δ
C
R
F
R
F
+ δ
G
δ
G
δ
C
T
S0
T
S1
T
S2
T
S3
α
T
ref
q
F
´´´
Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
293
III. RELAP5
