an analysis and comparison of natural frequency analysis

8/4/2019 An Analysis and Comparison of Natural Frequency Analysis

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International Journal of Engineering & Technology IJET Vol: 9 No: 9 - 201 -

1936091 IJET-IJENS @ International Journals of Engineering and Sciences IJENS

Abstract Reactor components including fuel assemblies

and heat exchanger tubes are beam-type structures with

natural or forced boundary conditions or mixed type

boundary conditions. It is difficult to model such systems

accurately as it consists of both thermal fluid flow behavior

and structure of hollow fuel rods. An attempt is made to de- couple the problem into thermal fluid flow and structures.

First, a vibration analysis of the fuel rod is carried out

resulting in the form of natural frequencies and

corresponding mode shapes. Then, three-dimensional

transient thermal fluid flow transport equations are solved

across a hollow cylinder with specified boundary conditions.

This gives a transient temperature profile or the vorticity of

flow around the fuel rod in the form of fluctuating force

having a certain frequency. A comparison is made between

the fluctuating force frequency of the coolant fluid and the

hollow rod natural frequency; a phenomenon called lock-in

is obtained in both directions, resulting in much larger

amplitude of resonance vibration of the rod. The natural frequencies of the fuel rod for a 300 Mwe PWR Nuclear

Power Plant are calculated and compared with numerically

calculated Turbulence Induced Vibration (TIV) fluctuating

force frequencies. The present paper is very useful to

evaluate the fuel rod vibration with various boundary

conditions. An important result is obtained for the variation

in the vorticity along the axis; it is found that in the range 0-

700 mm, the vorticity is in the range 0-5 Hz i.e. it approaches

the first-mode natural frequency. A similar trend is seen

towards the end of the flow channel when the vorticity is 25

Hz corresponding to the third mode of natural frequency.

Further numerical investigation is needed with variable

coolant velocity and temperature.

Index Terms Computational Fluid Dynamics, Finite ElementMethod, Modal Analysis, Pressurized Water Reactor.

1 Dr. Tasneem M. Shah is a Professor at Air University, Islamabad,

Pakistan ; ph: 0092(300)5269610; fax: 0092(51)9260158; e-mail:

dr.tasneem@ mail.au.edu.pk.

Dr. Zafar Ullah Koreshi is a Professor at Air University, Islamabad,

Pakistan ; e-mail: zafar@ mail.au.edu.pk.

Engr. Sadaf Siddiq is an Assistant Professor at Air University, Islamabad,

Pakistan ; e-mail: sadaf@ mail.au.edu.pk.

I. INTRODUCTIONHE well-known problem of fuel degradation and potential

damage to instrumentation or fuel rods [1-3] in Pressurized

Water Reactors (PWRs) is investigated by studying the flow

field in the core of a 300 MWe reactor. Of the various flowinduced vibration mechanisms we have focused on turbulence

induced vibration as it is the prime excitation source in axial

flow and can lead to fretting wear damage in the core

internals.

The flow-field analysis is centered on the vorticity as it is

important to investigate how close it is from the natural

frequencies. In the first part, a modal analysis is carried out

resulting in natural frequencies of the cylinder. In the second

part, hydrodynamic analysis is carried out which gives the

vorticities (TIV). The objective is to compare the frequencies

to get the lock-in (resonance) conditions. An empirical

approach for cross-flow induced vibrations has been taken by

Khushnood et al [5] while Kang et al [6] has carried out asimilar analysis for a 55 bundle.

This work is useful for understanding the vulnerable domains

in a coolant flow channel in a PWR which has yet to undergo

detailed theoretical analysis.

We consider the fuel as a single body, and neglect the

cladding or internal structure of a rod. The coolant flow

channel is modeled as shown in Fig. 1. Due to symmetry, we

have considered one-fourth of the flow channel as shown in

Fig. 2.

An analysis and comparison of tube natural

frequency modes with fluctuating force

frequency from thermal cross-flow fluid in

300 MWE PWR

Tasneem M. Shah, Zafar U. Koreshi, Sadaf Siddiq1

T


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Fig. 1. Coolant flow domain between 4-Fuel Rods

Fig. 2. One-fourth of Fluid Domain for Computation

II. FEMMODALANALYSISOFFUELRODThe modal analysis of the bundle of fuel rod is carried out

by the standard finite element package ANSYS [7]. To find

frequency and mode shape, we have considered a single fuel

rod supported by the baffle plates. The rod is modeled by 8-

node SHELL63 element. For building 1 FE model of a rod,

14,800 elements are needed (Fig. 3). For the boundary

condition of the FE analysis, both ends of the rod are fixed.

Material properties for the components of the rod for a typical

300 Mwe PWR used here for the reference values in the

present analysis are listed in Table (1).

A. Finite Element Analysis Results:Natural frequencies obtained from the FE analysis for a rod

clamped at both ends are obtained by solving appropriate

second order differential equations using ANSYS for

calculating mode shapes and frequencies together with

material properties given in Table 1. Obtained frequencies are

summarized in Table (2), and corresponding mode shapes are

depicted in Figs. (4-6). Fig. 4 shows the first mode appeared

with a frequency 5 (Hz). Figs. (5-6) show the second and third

modes with corresponding frequencies 13 and 27 (Hz). Since

the present analysis is done for lock-in condition at the bottom

baffle plate so we are only interested in the first mode of the

clamped rod (5 Hz).

Fig. 3. Elements in FE Model

Fig. 4. First Mode Shape of Single Fuel Rod


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Fig. 5. Second Mode Shape of Single Fuel Rod

Fig. 6. Third Mode Shape of Single Fuel Rod

TABLE 1

GEOMETRY AND MATERIAL PROPERTIES OF FUEL ROD

S# Quantity Units Description Value

1 Diameter (mm) Fuel rod 10.0

2 Height (mm) Fuel Rod 3210.0

3 Thickness (mm) Fuel Rod 0.78

4 Density 3/cmg Fuel Rod 12.4

5 E 2/mN Young Modulus111088.1

6 - Poisson Ration 0.29

TABLE 2

NATURAL FREQUENCY AND MODE SHAPES OF SINGLE FUEL ROD

S. No. Frequency (Hz) Mode Shape

1 5 Fig. 1

2 13 Fig. 2

3 27 Fig. 3

III. FLUIDFLOWANALYSISA. Final Stage

The 3-D hydrodynamic model is solved on single fuel rod

supported at the bottom baffle plate where the inlet velocity,

temperature and pressure are specified given in Table (2). The

velocities and temperature are calculated by the code and

vorticites are obtained using velocity-vorticity relations [9].

TABLE 3

INPUT PARAMETERS FOR FLOW ANALYSIS

S# Quantity Units Description Value

1 3/mkg Water Density 1000.0

2in

V m/s Velocity atEntrance

8.0

3 P bar Pressure 155.0

4sT

K Temperature at

fuel rod surface

618

5inT

K Inlet

Temperature

561

6outT

K Outlet

Temperature

575

B. GOVERNING EQUATIONS:The conservation of mass, momentum and energy in three

dimensions for a turbulent, incompressible, Newtonian fluid

are given by [9]:

)2(][][

)()(

)1(,0

wuvu

uuwvu

zu

zyu

y

xu

xxp

zu

yu

xu

zw

yv

xu

+

+=+++

=++

)5(][

][][)(

)4(][][

)()(

)3(][][

)()(

z

T

z

zT

yxT

xzT

yT

xT

p

zw

zyw

y

xw

xz

p

zw

yw

xw

zv

zyv

y

xv

xy

p

zv

yv

xv

k

kkwvuC

wwwv

wuwvu

vwvv

vuwvu

+

+=++

+

+=+++

+

+=+++

where wvu ,, are mean velocities and wvu ,, are turbulent

fluctuations. A Mac-type staggered grid system is used to

locate the flow variables. The velocities are stored on the cell

faces and the pressure and temperature are stored at the cell

centers. Due to the staggering of the mesh three different

types of control volume are required for the momentum

equations and the continuity equation in the interior region,

with straightforward modifications near the boundaries. A

detailed description is given in [10].


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These equations are solved using standard 3-D Fluent [8]

hydrodynamic code using Finite Volume method. 0.81 Million

fluid elements with hexahedral unstructured mesh are taken in

the computational domain Fig. (2). Results for velocity,

vorticity and temperatures are obtained and depicted in Figs.

(6-13).

No slip boundary conditions for velocities on the solid surface

are given whereas temperature is kept constant. Symmetric

conditions for all variables are used on other boundaries.

Fig. 6. Velocity Contours on Cross-Sectional Area at z=1600 mm

Fig. 7. Vorticity Contours on Cross-Sectional Area at z=1600 mm

Fig. 8. Temperature Contours on Cross-Sectional Area at z=1600 mm

Fig. 9. Velocity Across Radial Direction

Fig. 10. Vorticity across Radial Direction


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Fig. 11. Temperature across Radial Direction

Fig. 12. Vorticity along Axial Direction

Fig. 13. Velocity along Axial Direction

IV. RESULTS AND DISCUSSIONSThe modal analysis of a single rod were carried out and the

results are given for natural frequencies for first, second and

third modes which are in the range of 5 to 27 Hz. [Table (3)].

The hydrodynamics analysis was performed and results were

obtained for vorticity (TIV) along the fuel rod. From Fig. 12,

it is observed that vorticity at axial distance 0-700 mm from

the bottom of fuel rod is in the range of 0-5 Hz which

increased exponentially from 5-60 Hz up to 1200 (mm) and

then suddenly is fallen to 25 Hz at the middle of the rod (1500

mm). From here onward along the rod, it remained 25 Hz till

the top of the rod (3210 mm).

These results have shown that lock-in (resonance) condition

has occurred at both ends of the fuel rod which may be

damaged the assembly at the bottom baffle plate in the power

reactor. To avoid such accident, the coolant velocity may be

reduced or controlled by some phenomena not to occur lock-

in condition. Further numerical investigations will be carried

out by varying coolant flow conditions to avoid lock-in

condition.

V. CONCLUSIONA comparison was done between fluctuating frequency

of the coolant fluid flow and the hollow rod material

frequency of a typical 300 Mwe PWR under operation.

This has been observed that the resonance (lock-in)

condition occurred at both ends of the fuel rod resulting

damage the assembly at the bottom baffle plate in the

power reactor. Numerical experiments have shown that

these phenomena could be controlled by lowering the

coolant flow rate (velocity). Further numerical

investigations will be carried out by considering the flow

rate of the coolant through pressure difference

REFERENCES

[1] El-Wakil, M.M. , Powerplant Technology, McGraw-Hill Inc. 1984[2] Kazimi, M . S, , High Performance Fuel Design for Next Generation

PWRs: Final Report Center for Advanced Nuclear Energy Systems

(CANES), MIT-NFC- PR-082. 2006.

[3] King, S. J., Young, M. Y., Seel, D. D, Conner, M. E., Lu, R. Y.andParamonov, D. V., Flow Induced Vibration and Fretting Wear in

PWR, International Conference on Nuclear Engineering, American

Society of Mechanical Engineering. 2002

[4] Mian, Z., and Nayyar, A. H., 1999, Pakistans Chashma NuclearPower Plant, A preliminary study of some safety issues and estimates of

the consequences of a severeaccident, Sustainable Development Policy

Institute,Monograph Series # 11.

[5] S. Khushnood, Z.M.Khan, M.A.Malik, Z.U.Koreshi and M.A.Khan,2003, Cross-Flow Induced Vibrations in Tube Bundles: A Review,

Proc. of the Eleventh International Conference on Nuclear Engineering,

(ICONE-11-36261), April 20-23, 2003, Tokyo, Japan.

[6] Kang, H. S., Choi, M. H., Yoon, K. H., Song, K. N. and Jung, Y. H.2004, A Vibration Analysis and Test of a 55 Rod Bundle,ICONE-12

Arlington, Virginia, April 25-29.

[7] ANSYS 10.0 Inc. Pittsburg, USA[8] Fluent 6.1 Inc, Lebanon, New Hampshire, USA[9] Fletcher, C. A., Computational Techniques for Fluid Dynamics,

Springer Verlag. 1986.

[10] S. Sivaloganathan and G. J. Shaw, A multigrid method for Recirculatingflows.Inter. J. Num. Methods for Fluids, 8:417-440. 1988.

an analysis and comparison of natural frequency analysis

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