# Naykodi the structural analysis. By performing this analysis, the

Naykodi Ganesh Dnyaneshwar1,

Mathe Raviraj Vikas2, Arote Sameer Pandurang3

123Department of Mechanical Engineering, Jaihind College of

Engineering, Kuran,Pune

Address

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

parameters..

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

pellet-cladding.

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

account.

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.

TABLE I

TECHNICAL DATA CONSIDERED FOR ANALYSIS

Pellet

material: uranium oxide (UO2).

Clad

material: zircaloy-4.

Gap

=Helium

Pellet

radius

4.782mm

Gap

thickness

0.193mm

Clad

outer radius

5.582mm

Clad inner radius

4.975mm

TABLE

III

Constant Properties of Pellet

Thermal

conductivity

29

W/M.K

Specific

heat

268J/Kg.k.

Density

11000kg/m3

Heat

generation

0.8

w/mm3

TABLE

IIIII

T Constant Properties of Cladding

Thermal

conductivity

13

W/m-k

Specific

heat

330J/Kg.k.

Density

6500kg/m3

Heat

generation

None

Modulus

of elasticity

0.99283e+011Pa

Poisson’s

ratio

0.33

Thermal

co-efficient of Expansion

20×10-6

TABLE IVII

TECHNICAL Data for Gap

Thermal

conductivity for gap Material

50w/m-k

Pressure

10 atm of He

TABLE VV

TECHNICAL DATA for Coolant

Heat

transfer coefficient

40000w/m2-k.

Temperature

127 0C.

Pressure

7.171087 mPa.

D.

Governing Equations

The transient heat

conduction equation for pellet

Neglecting axial

conduction is given by:

E.

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

purpose.

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

Fig.3

3-D meshing geometry of fuel rod

G.

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

material.

Fig. 6 Steady state thermal Analysis boundary

conditions

Fig. 6 Structural Analysis boundary conditions

Initially,

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

The

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

The

thermal analysis is proceed for knowing the non-uniform temperatures in the

fuel pellet element.

Fig. 6 Steady state thermal Analysis (Temperature)

From

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

conditions.

Fig. 6 Total Heat Flux Distribution

B. the

Result of synthesized Analysis

In

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

differentiation.

Fig. 7 stress distribution in fuel element

Applied

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.

Fig.8

Strain distribution in fuel element

Fig.9

displacements of different sections of nuclear fuel rod

C.

Stress, strain and thermal expansion due to thermal effects

The

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.

V.

Conclusions

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.

In

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.

Acknowledgment

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.

References

1

ANSYS.

2

M. Dostal, A Krupkin, “3D modelling of VVER fuel

pellet cracking during power ramp”

3

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

4

Su Chaing shu Faya,”A Survey on Fuel Pellet

Cracking and Healing Phenomena in Reactor Operation.” INFORMA CAO IPEN-9

OUTRBO/1981

5

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

6

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.