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
The RELAP5Mod3.2.2 code has been developed for the analyses of light water reactor coolant systems during
transients and postulated accidents. Code RELAP5Mod3.2.2 code is based on a nonhomogeneous
and nonequilibrium model for the twophase system that is solved by a fast, partially implicit numerical scheme to
permit economical calculation of system transients. The code includes many generic component models from
which general systems can be simulated. The component models include pumps, valves, pipes, heat releasing or
absorbing structures, reactor point kinetics, electric heaters, jet pumps, turbines, separators, accumulators,
and control system components. In addition, special process models are included for effects such as form
loss, flow at an abrupt area change, branching, choked flow, boron tracking, and noncondensable gas transport.
Code RELAP5 also includes a model for calculating the thermal conductivity, based on the composition of gas in
the gap. The RELAP5 dynamic gap conductance model defines an effective gap conductivity based on a
simplified deformation model generated from FRAP- T6.4.11-1 The model employs three assumptions as
follows: a the fuel-to-cladding radiation heat transfer, which only contributes significantly to the gap
conductivity under the conditions of cladding ballooning, is neglected unless the cladding deformation model is
activated, b the minimum gap size is limited such that the maximum effective gap conductivity is about the
same order as that of metals; c the direct contact of the fuel pellet and the cladding is not explicitly considered
[1]. The gap conductance through the gas is inversely proportional to the size of the gap. Since the longitudinal
axis of the fuel pellets is usually offset from the longitudinal axis of the cladding, the width of the fuel-
cladding gap varies with circumferential position. This variation causes the conductance through the gas in the
fuel-cladding gap to vary with circumferential position. The circumferential variation of the conductance is taken
into account by dividing the gap into several equally long segments, as shown in Fig. 3. [1]. The conductance for
each segment is calculated and then an average conductance, hg, is computed in the FRAP-T6 model by
the equation. The RELAP5 code analyzes the heat transfer in the gap on the basis of the following
relationships and for the given position of fuel and cladding shown in Fig. 3. [1].
Heat transfer coefficient in the gap is solved by following relationship 6 for given gas composition in
the gap in RELAP5 code [1]:
1 2
1
1 3 2
N G
G n
F C
n
N t
, r
r g
g
λ α
=
= +
⋅ +
+ +
∑
6 The width of the fuel-cladding gap at any given
circumferential segment is calculated by the equation:
Fig. 3. Segmentation at the fuel-cladding gap
2 1
1
n G
o
n t
t t
N ⎡
− ⎤ ⎛
⎞ =
+ − +⎜ ⎟
⎢ ⎥
⎝ ⎠
⎣ ⎦
7 The value of t
n
in equation 7 is limited between zero and 2t
g
. The circumferential averaged width of the fuel cladding gap, t
g
, in equation 7 is determined by the expression:
G F
C
t t
u u
= − + 8 The radial displacements, u
F
and u
C
, are primarily due to thermal expansion. The radial displacement, of the
fuel pellet surface, u
F
, is calculated by the equation:
F TF
r S
u u
u u
= + + 9
The radial displacement of the inner surface of the cladding is calculated by the relationship:
C TC
CC e
u u
u u
= +
+ 10
IV. Computational Model
The input file contains data describing one hydraulic channel with one fuel rod with adequate flow of coolant
and one hydraulic channel with one fuel assembly 126 fuel rods with adequate flow of coolant through the
assembly. The hydraulic components are divided into 12 axial sections and the heat structures representing the
fuel rod are divided into 10 axial sections. The input file also contains data describing the geometry of the
hydraulic channel and also data describing the material properties of the fuel rod.
Heat transfer in the gap between fuel and cladding is specified as a constant, as it is normally used for safety
analyses or is initiated by a separate computational module for calculating the heat transfer in the gap by
RELAP5. To simplify calculations and accelerate the evaluation, the input file describes two fuel rods and two
fuel assemblies.
The model includes a hot channel of VVER 440 fuel assembly, which represents the most power-laden fuel
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
294 rod and the worst heat transfer. The fuel rod is divided
into 10 sections in the axial direction Fig. 4a. In the radial direction Fig. 4b, the fuel rod is divided into 9
sections = 10 nodes, 5 sections for fuel, 1 section for gap and 3 sections for cladding [2], [5], [6].
a b Figs. 4. a Axial and b radial division of the fuel rod
IV.1. Geometry of the Fuel Rod
The minimum, nominal and maximum geometry of the fuel rod was based on the fuel manufacturing
tolerances. Changes in geometry of the fuel rod are under consideration because at the beginning of the cycle, the
process of sintering the fuel pellets continues, it comes to densification and reduction of fuel pellet. With
increasing burn up, it comes to accumulation of gas fission products at the grain boundaries and to swelling.
As a result, the gap is being closed and the fuel gets into a direct contact with cladding. The geometry of the fuel
rod is shown in following tables.
TABLE I
B
OUNDARY
C
ONDITIONS
Coolant temperature at the core inlet 270°C
Absolute pressure of coolant at the core inlet 12,5MPa
Flow of coolant at the inlet to a hydraulic channel with fuel assembly
21,58 kgs Flow of coolant at the inlet to a hydraulic channel
with one fuel rod 0,172 kgs
TABLE II
V
ARIABLE
P
ARAMETRES
F
OR
C
ALCULATION
Width of the gap
Minimum 0,0650 mm
Nominal 0,0875 mm
Maximum 0,1100 mm
Conductivity in the gap
Minimum 0,350 WmK
Nominal determined by calculating the internal algorithm
of RELAP5 Maximum 2,625
WmK TABLE
III G
EOMETRY
O
F
T
HE
F
UEL
R
OD
O
F
T
HE
VVER 440
F
UEL
A
SSEMBLY
W
ITH
M
ANUFACTURING
T
OLERANCES
Diameter of fuel pellets 7,57-7,6 mm
Outer diameter of cladding 9,1 mm
Inner diameter of cladding 7,73+0,06 mm
Diameter of central hole 1,2+0,3 mm
TABLE IV
C
ALCULATED
P
ARAMETERS
F
OR
T
HE
F
UEL
R
OD
O
F
T
HE
VVER 440
F
UEL
A
SSEMBLY
Width of the gap 0,065-0,11 mm
Average gap width 0,0875 mm
Thickness of cladding 0,655-0,685 mm
Average cladding thickness 0,670 mm
TABLE V
M
INIMUM
G
EOMETRY
O
F
T
HE
F
UEL
R
OD
Minimum geometry of the fuel rod
Outer radius of fuel pellet [mm] 3,8000
Inner radius of cladding [mm] 3,8650
Outer radius of cladding [mm] 4,5500
Width of the gap [mm] 0,0650
TABLE VI
N
OMINAL
G
EOMETRY
O
F
T
HE
F
UEL
R
OD
Nominal geometry of the fuel rod
Outer radius of fuel pellet [mm] 3,7925
Inner radius of cladding [mm] 3,8800
Outer radius of cladding [mm] 4,5500
Width of the gap [mm] 0,0875
TABLE VII
M
AXIMUM
G
EOMETRY
O
F
T
HE
F
UEL
R
OD
Maximum geometry of the fuel rod
Outer radius of fuel pellet [mm] 3,7850
Inner radius of cladding [mm] 3,8950
Outer radius of cladding [mm] 4,5500
Width of the gap [mm] 0,1100
Table I and Table II are the basis for defining the minimum, nominal and maximum geometry of the fuel
rod of the VVER 440 fuel assembly [2].
Fig. 5. Nominal and maximum width of the gap
Fig. 6. Nominal and minimum width of the gap
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
295 IV.2.
Distribution of Fuel Rods The power of fuel rods in the whole active zone was
analyzed on the basis of a representative load core. Fuel rods were divided to groups depending on its power. Hot
rod is the fuel rod with a maximum power, which is not actually in the core, but it is considered in modeling. The
power of hot rod is 1,692 times higher than the power of average rod and it reaches 56,6 kW. Average rod is the
fuel rod in the core with an average power 1471,25 349 assemblies 126 rods = 33,46 kW. For the purpose of the
calculation following fuel rods were chosen [2].
TABLE VIII
D
ISTRIBUTION
O
F
F
UEL
R
ODS
F
OR
C
ALCULATING
The multiple of the average power
Power kW
Label
0,8 26,77 0,8AR 1
33,46 Average rod - AR
1,2 40,15 1,2AR 1,4 46,84 1,4AR
1,7 56,60
Hot rod - HR
Axial power distribution of hot and average rod is shown in Fig. 7. and Fig. 8.
Fig. 7. Axial power distribution of hot rod
Fig. 8. Axial power distribution of average rod
IV.3. Evaluation of Temperature Field of the Fuel Rod
Variable parameters in the calculation were the width of the gap and the conductivity of gas in the gap.
Those material parameters were analyzed, that can be put in the model of fuel rods in RELAP5.
The results of the calculations are series of temperature field diagrams for fuel rods with a various
power. The series of temperature field diagrams, which are
shown in Fig. 9., are processed for selected fuel rods according to the Table VIII [2], [5].
Fig. 9. Series of temperature field diagrams
The Fig. 10. shows, as an example, a temperature field diagram of hot rod with a nominal width of the gap and
nominal conductivity in the gap.
Fig. 10. Temperature field diagram of hot fuel rod with a nominal width of the gap and nominal conductivity of gas in the gap
The analysis showed that the 9th axial section is the most loaded and therefore the maximum temperatures
inside the fuel are achieved at the top of the fuel rod.
IV.4. Comparison of the Results of the Analyses
The following tables show the temperatures achieved in the 9th axial section of the hot and average fuel rod
with various combinations of the width of the gap and conductivity of the gas in the gap.
The Fig. 11. shows the temperature field in the 9th axial section of all fuel rods according to Table VI with
nominal width of the gap and nominal conductivity of the gas in the gap. The figure shows that the highest
temperatures inside the fuel are achieved in the hot fuel rod. For complexity of the analysis, the other fuel rods
and minimum values of temperature were also considered.
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
296 An example of the temperature field in the 9th section
of average fuel rod with nominal width of the gap and nominal conductivity of gas in the gap is showed in Fig.
12.
TABLE IX
T
EMPERATURE
I
N
T
HE
9
TH
A
XIAL
S
ECTION
O
F
T
HE
H
OT
A
ND
A
VERAGE
F
UEL
R
OD
W
ITH
N
OMINAL
C
ONDUCTIVITY
I
N
T
HE
G
AP
A
ND
V
ARIOUS
W
IDTH
O
F
T
HE
G
AP
TABLE X
T
EMPERATURE
I
N
T
HE
9
TH
A
XIAL
S
ECTION
O
F
T
HE
H
OT
A
ND
A
VERAGE
F
UEL
R
OD
W
ITH
N
OMINAL
W
IDTH
O
F
T
HE
G
AP
A
ND
V
ARIOUS
C
ONDUCTIVITY
I
N
T
HE
G
AP
Fig. 11. The temperature field in the 9th section of all analyzed fuel rods with nominal width of the gap and nominal conductivity in the gap
TABLE XI
T
EMPERATURE
I
N
T
HE
9
TH
A
XIAL
S
ECTION
O
F
F
UEL
R
ODS
W
ITH
N
OMINAL
W
IDTH
O
F
T
HE
G
AP
A
ND
N
OMINAL
C
ONDUCTIVITY
I
N
T
HE
G
AP
TABLE XII
T
EMPERATURE
D
IFFERENCES
I
N
T
HE
9
TH
A
XIAL
S
ECTION
O
F
F
UEL
R
OD
M
ATERIAL
W
ITH
N
OMINAL
W
IDTH
O
F
T
HE
G
AP
A
ND
N
OMINAL
C
ONDUCTIVITY
I
N
T
HE
G
AP
Fig. 12. The temperature field in the 9th section of average fuel rods with nominal width of the gap and nominal conductivity in the gap
V. Conclusion
