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Naykodi Ganesh Dnyaneshwar1,
Mathe Raviraj Vikas2, Arote Sameer Pandurang3

123Department of Mechanical Engineering, Jaihind College of
Engineering, Kuran,Pune

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Abstract— It is
essential to designing and preventing the failure of fuel pellet in operating
conditions to predicts the thermo-mechanical Performance of fuel pellet in
nuclear reactor. In this paper, the structural analysis taken for fuel elements
in operating parameters of nuclear reactor. For performing this analysis
firstly, the thermal analysis of fuel pellet is taken to get the unsteady
temperature distribution in the fuel pellet and after that these thermal loads
are utilized in the structural analysis.

By performing this analysis, the
displacement stress and strain values of fuel pellet are find out for gap
thickness in the cladding and pellet surface from structural analysis, it is
known that expansion due to thermal effectuations and it’s within limit.

For cladding and pellet, the governed
equations are considered and the physical and thermal properties are considered
while taking analysis the height of fuel element is greater than the outer
diameter of fuel element rod. So the axially temperature variation is not
considered within analysis so there is 1-d heat transfer equation formation.

So far for this analysis, a finite
element method is used, ANSYS is used to discretization as Computational
Domain. The combined analysis of fuel element is taken out for finding
temperature thermal expansions, heat fluxes generation and the stress-strain


Keywords— Cladding,
Nuclear Pellet, Ansys, PCI

I.      Introduction

The propagation of cracks due to
thermal gradients and loads are calculated using cohesive models that are in
Finite Element Method Software, the most common packages are avail in the
market are ANSYS and ABAQUS. The nuclear rod which are releases the energy to
generates the power by heat exchanging devices and also the turbines has
chances to fail due to many reasons and the most significant behaviour of fuel
pellet rod to thermal characteristics.

After passing the time fuel element get
swells and come with contact of cladding surface so it is essential part to
control and prevent the temperatures discrepancy in a nuclear fuel rod. So this
paper and analysis can be prescribed the results and to design nuclear fuel rod
so the transfer of heat in nuclear pellet is get optimized to minimizing
failure and in adequacy in nuclear fuel rod.

For the purpose of analysis, nuclear
fuel rod of the pressurized water reactor are considered for signifying of
temperature propagation and analysis determination. The pellet material is used
Uranium (UO2) and the cladding material is Zirconuim-4. At the beginning, the
helium gas is containing in the divergence of pellet and cladding. The main
function is to contend the temperature propagation from nuclear fuel element
rod using ansys software. Then varying the boundary condition and gap thickness
for analysis by computational data parameters. After lot of studies across the
world the different power plants encounter with cracking and swelling the
nuclear pellet in the outer surface and cladding, there are many reasons which
nuclear fuel elements cause’s failures between them. Pellet –cladding
correspondent is influences one which affects mainly due to thermal enhancement
of cladding and pellets. So there is requirement to figure out the temperature
distribution and divine the stresses, strain and displacements in the

II.    Review of literature

Researches and scientist perform
plentiful works on the nuclear fuel pellet element in the world. The most work
accomplished with temperature variation nuclear fuel element. In certain cases,
the mechanical and physical studies are carried out some researches. Very less
study done on stability analysis. A detailed study of work mentioned here. The
accurate expectancy of the nuclear fuel rod’s temperature in the core of light
water reactor is essential when the uncover and re-floods phases of must
accident together. The correct presumption of temperature of fuel rod needs.
Also heat conduction solution required in fuel rod.

In the work of M. Dostal and A. Krupkin
successfully implementation of 2D and 3D FEM calculations software and it got
influences on cladding behaviour is shown. The mutual impact of interaction
with cladding was quantified-both the distribution of stresses and strains in
the cladding as a function of pellet cracking and influenced on of contact on
the crack initiation and propagation. The sensitivity for pellet cladding
friction coefficient was also assessed. They plan to further use of these model
as a supplement to the commonly used 1.5D fuel performance codes and to
evaluate the impact of the fuel pellet cracking on the prediction of a fuel behaviour
under fast transient, such as reactivity initiated accidents.2

In the paper work of Fernando Pereira
and Jean salome, the temperature on the surfaces of the canister increased
during the first nine years, reaching a plateau at 35.5? between the tenth and twentieth
years after the geological disposal. The saturation as expected, considering
that the heat released by SF decays during the time. To better determine the behaviour
of temperature plateau, the present analysis might consider being also
performed by the Ansys steady state thermal technique in the future studies,
which would permit to start the transient thermal analysis with the system
components in a non-uniform initial temperature. This work will be extended to
include studies of geological disposal of VHTR – ( Th,TRU)O2 , VHTR – UO2 ,PWR
and  ADS (Th, TRU)O2 spent fuels. Further
studies will evaluate the SFP dimensions needs for each reactor and their spent
fuel composition, as well as, critically calculation.3

In this paper Su Chiang and Shu Faya
were work on the fuel pellet crack healing time is an important factor because
the as-fabricated fracture strength is fully recovered after the healing. Three
crack healing correlations. The correlations that include the stress acting on
the crack surfaces in contact are represented by full and dashed lines. These
two correlations yield quite similar results and 1 MN/m2 is a good estimate of
that stress. The result of the experiment performed by Lawrence described in
Section 5 showed an increase of 25% gap closure after 5 cycles of 20 h instead
of 1 cycle of 100 h. This increase is expected. But the 40% gap closure after
one cycle during 100 h is not well-understood. Swelling is not supposed to
occur after such a short period of time although the heat rate is quite high
(25 KW/ft). The sudden large pellet diameter increase is also noticed in low
power tests.4

In this paper Young-Doo Kwon and  Bo-Kyoung Shim were analysed the three types
of nuclear fuel using the developed package, which validated the proposed fuel
type to be feasible after the comparison of the results with the commercial
package ADINA in the case of using simple materials. The major findings are
summarized as follows:

1. The thermo-mechanical behaviour of
the annular pellet nuclear fuel is between the achieved performance of the
conventional solid and annular fuels.

2. The reduction ratios in the tensile
and compressive stresses of the pellet in the pseudo-optimal annular pellet
fuel (Case 2) were 55.3% and 55.5%,  respectively,
compared with those of the solid nuclear fuel.

3. The reduction ratio of the maximum
temperature of the pellet in the annular pellet fuel was 38.6% compared with
that of the solid nuclear fuel 4. The thermo-mechanical behaviour of the
annular pellet nuclear fuel was inferior to that of the annular fuel. However,
it was more reliable than the latter and spared us from fabrication problems.

As mentioned above, the proposed annular
pellet nuclear fuel can replace the conventional solid-type nuclear fuel to
achieve higher heat generation at the same reliability scale or to realize
better reliability within the same heat-generation regime. If further studies
are conducted on the precise fabrication of the annular nuclear fuel and on the
effort of reducing overheating, we believe that the end product will assume a
primary position as a future standard of nuclear fuels.6



III. Mathematical Modelling of Equations and Solutions

Nuclear reactor
core possessed with cylindrical fuel pellet element which contain fuel pellet
cladding and influenced gap. The purpose of this work will calculate the
temperature drop from the middle of the fuel pellet where occurrence of maximum
temperature to the surface of cladding in expression of the different physical
and thermal properties parameters of nuclear fuel element, while these fuel
pellet element geometry have possessed with thermal properties and physical
characteristics are conscious. Additionally we are considering the thermal
analysis of pressurized water reactor fuel element. The general sequence for
solution of ideal heat conduction equation.

A Problem Definition

                The nuclear fuel rod includes with uranium oxide
(UO2) pellets in the zircaloy-4 cladding tube and also a very small influenced
gap in between surfaces of the pellet and the inner surface of cladding. The
heat accomplished by a nuclear fission is carried through fuel rod with convection
to the enclosed coolant in a flow stream channel. A radial type heat conduction
model are utilized for calculating the heat flux of fuel and temperature
variation. The thermal power energy arsenal and also transport modelling with
following assumption.

B Basic Assumption

1)Heat transfer
in axially is negligent. This is prescribed because of much larger length of
fuel rod than its outer diameter. And also high thermal resistance interfering
by the fuel pellet.

2) While making
the analysis the active heat transfer process is conduction the convection
process due to gas flowing through the cracks occurred in the fuel pellet is
not considered. It is good pronouncement because of here not an amount of gas
nor the flowing speed reached the higher level required to transfigure
appreciably the temperature enclosure.

3) The
temperature enclosure in the nuclear fuel affects on strain, but it does not

4) The heat
transfer coefficient in the influenced gap which is extensively depends on the
width of gap. The temperature on the fuel surface and on the inner surface of
cladding, the inside gas pressure and average mean temperature is accomplished
by introducing a given time function.

5) By this same
path, the film heat transfer coefficient in between coolant and cladding
surface is also adjacent by the time function.

The temperature
differentiation procured separately in the fuel pellet and cladding are
obtained separately and independently. The adaptation reason for un-synthesized
description are following,

I. The computational time
appreciably minimized.

II. It allows using equal
sub programming in both fuel and cladding.

III. The thermal properties
of a fuel element rod are explained within a certain percentage of error. It
would be ostensible to find high accurate characterization. The temperature
variation in the fuel and cladding is resulting by a solve the set of transient
heat equation.



material: uranium oxide (UO2).
material: zircaloy-4.





outer radius


Clad inner radius



Constant Properties of Pellet










T Constant Properties of Cladding










of elasticity




co-efficient of Expansion


TECHNICAL Data for Gap


conductivity for gap Material



10 atm of He




transfer coefficient



 127 0C.


7.171087 mPa.


Governing Equations

The transient heat
conduction equation for pellet

Neglecting axial
conduction is given by:


Element types and meshing of geometry:

In the finite element
analysis, multiple type’s element are commonly used for different application
and purpose. In this analysis work, the element type is used as tetra-hedron
for the meshing element sized is selected for meshing the fuel element is
0.7mm. In addition, edge and surface refining is used for better result

1 Bounding Box: X= 9.512mm

Y= 9.512mm

Z= 9.8mm

2 Volume: 696.3 mm3 

3 Mass: 5.466e-003 Kg

4 Elements: 30220

5 Nodes: 180873

6 Analysis type: 3D


3-D meshing geometry of fuel rod


Apply boundary conditions and loads

For finding
temperature distribution and total heat flux from fuel element in the thermal
analysis, a heat transfer coefficient is 40000 W/m2.K and 127? applied on
surface of fuel element. Internal heat generation rate of 0.8W/mm3
is applied in the pellet. Heat generation process is neglected for cladding

Fig. 6 Steady state thermal Analysis boundary

Fig. 6 Structural Analysis boundary conditions


steady state heat conduction solution is proceed out to know the initial
temperature at a fuel pellet surface. Inner cladding area and outer surface
this data was latterly use in transient heat conduction analysis. The other
boundary condition of heat transfer heat conduction analysis.

The following figure shows
the computational domain data with applied boundary condition. In the
structural analysis to get the thermal stress, thermal expansion and thermal
strain of the fuel pellet and cladding. The temperature distribution is getting
from thermal analysis and this considered as a thermal load on throughout the
geometry of a fuel element, simultaneously the coolant pressure is providing to
the surface of element and finally within the influenced gap as an initial
pressured is supplied. 


IV. Results and Discussions

main aim to do this work is to accomplish the structural analysis of nuclear
pellet element in functioning conditions by taking thermal analysis. In the
study of nuclear reactor the sufficient cases were obtained that by passing
certain time. Internal to fuel elements are swelling that means, due to thermal
loads structural displacement takes place.

So, this phenomenon causes
serious problem while consideration of pellet section or cladding sections,
because of expansion in structural due to temperature differentiation and
pressure differentiation. It might be found in some cause to adequacy to
failure of fuel pellet and this cause very serious problem which we known very
well. There is contingency of various kind of failure in fuel pellet element,
most of them PCI (pellet-cladding-interaction).so it is imperative.

So from this workout to
analyze thermal and the mechanical performance of fuel element.


A.   Divination
of Temperature for analysis

thermal analysis is proceed for knowing the non-uniform temperatures in the
fuel pellet element.

Fig. 6 Steady state thermal Analysis (Temperature)


the following figure this is clearly shows the result for 1 sec time, so it is
found that maximum temperature in the fuel pellet is 234.37 ? and selecting more time, it’s gradually increase
and at particular temperatures. In addition, resulting non-linear temperatures
and these are used in structural analysis as considering thermal load

Fig. 6 Total Heat Flux Distribution


B. the
Result of synthesized Analysis

this analysis, the structural and thermal analysis are synthesized to known the
stress, strain and displacement at various sections of fuel pellet. The carried
thermal analysis is taken for structural analysis where all temperature
variation to getting different parameters which is because of temperature

Fig. 7 stress distribution in fuel element


coolant pressure with the gap pressure are assumed in this analysis as
structural boundary conditions and with temperature thermal boundary condition.
Figure 9 shows the thermal distension in the fuel pellet and cladding from
figure shows the maximum displacement occurrence at surface of fuel pellet and
between the cladding.

Strain distribution in fuel element


displacements of different sections of nuclear fuel rod


Stress, strain and thermal expansion due to thermal effects

following figure 7 and figure 8 shows the thermal stress and thermal strain in
fuel pellet element. From figure7 shows the maximum value of stress occurred in
near the fuel pellet surface and for the various gap thickness. It is observed
that stress variation is not considerably changes so much. For figure 8 shows
the maximum strain value obtain at centerline of fuel pellet, here in this
work, PCI not affected get for this considered design. In addition, it is
within allowable limit.

                The influence gap between fuel pellet surface and
cladding is within range and it does not affect fuel element geometry. The
expansion of fuel element geometry will not affect on the reactor system by
this design.


The divination of thermal and
mechanical observance is seen for requirement to avoidance of failure of the nuclear
fuel element rod. This paper concerned the synthesize analysis of
thermal-structural stress, strain and the thermal expansion of nuclear fuel
pellet element. At the functioning parameter of nuclear power, plant there is
most certainty to failure the fuel element pellet. The inadequacy occurs in the
fuel element pellet because of various problem encountered in reactor. Amongst
them pellet-cladding-interaction (PCI) is predominating one.

this paper, the pressurized water reactor fuel pellet element is assumed and
these are made up of uranium oxide (UO2) and covered with zircaloy-4 cladding.
The influence between cladding and pellet surface is at the beginning filled
with helium gas by attempting this experiment, what kind of thermal
differentiation occurs in fuel element and by maintaining the pressure
differentiation between influence and coolant. From taking this analysis, it is
known that through the pellet-cladding expanding due to thermal variations, but
this are maintaining within safe zone. Also developed stress in the fuel
elements are within permissible limit.


We wish to express our heartfelt
thanks to all the contributing authors. My special thanks to our guide Prof. V.
R. Navale and Prof. Mankar, HOD, Jaihind College of Engineering, Kuran for
having given me an opportunity to prove my worth. Also thanks to all mechanical
engineering staffs Jaihind College of Engineering, Kuran, Pune credit goes to a
great measure to our friends for their help and encouragement. We would also to
express our gratitude to the authors and publishers of textbook, magazines, journals
and websites from where We have collected the materials and information from
this report.



M. Dostal, A Krupkin, “3D modelling of VVER fuel
pellet cracking during power ramp”

Fernando Pereira, Jean Salome., “Thermal
Analsys of spent Nuclear fuels Repository”, 5th international
ATELANTE Conference on nuclear chemistry for sustainable fuel cycles, Procedia
Chemistry 21 (2016) 386-393

Su Chaing shu Faya,”A Survey on Fuel Pellet
Cracking and Healing Phenomena in Reactor Operation.” INFORMA CAO IPEN-9

Marchal, N.,
Campos, C., Garnier, C. Finite element simulation of pellet cladding
interaction in nuclear fuel rodes, computational material Science vol. 45 page
821-826, 2009

Young-Doo Kwon and  Bo-Kyoung Shim,”Thermo-Mechanical Analysis of
Annular Pellet Nuclear Fuel and Its Comparison with Solid and Annular Nuclear
Fuel Types” International Journal of Applied Engineering Research ISSN
0973-4562 Volume 11, Number 21 (2016) pp.10543-1055.


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