KFKM994-16/G . REPORT

S.KISS, S. UPCSEI

LABORATORY EXPERIMENTS WITH IMPACTING FUEL RODS

Hungarian Academy of Sciences CENTRAL RESEARCH INSTITUTE FOR PHYSICS

B U D A P E S T

KFKM994-16/G REPORT

LABORATORY EXPERIMENTS WITH IMPACTING FUEL RODS

S. Kiss and S. LIPCSEI

Applied Reactor Physics Department KFKI Atomic Energy Research Institute

H I 525 Budapest, P. O. Box 49, Hungary

Presented at I MORN 25 Informal Meeting on Reactor Noise

Jubilee Anniversary

June 13 15, 1994 Raleigh, North Carolina

USA

LABORATORY EXPERIMENTS WITH IMPACTING FUEL RODS

S. Kiss and S. LIPCSEI

Applied Reactor Physics Department KFKI Atomic Energy Research Institute

H-I52S Budapest, P. O. Box 49, Hungary

Presented at IMORN-25 Informal Meeting on Reactor Noise

Jubilee Anniversary

June 13-15. 1994 Raleigh, North Carolina

USA

ABSTRACT

Vibration surveillance and diagnostics of fuel rods and fuel assemblies are important tasks in NPPs. They are so much the more difficult since the commonly used ar^cicromctcrs do not operate properly under the extreme conditions of the core of reactor. Therefore vibration (or impact) of fuel rods can only be detected indirectly from neutron noise or pressure fluctuation signals. Thus accurate knowledge of vibration phenomena and mcasurability is very important. Experimental results on models without limitcr give good coincidence with theoretical calculations. Spectra measured on impacting rod become smoother with increasing impacting level. Spectra of fuel rods have a wider range in impacting rate and higher level of smoothing than spectra of model rod have. The impacting rate strongly depends on mechanical properties of the rod. By the experiments, one can state that as for Fourier spectra the only thing caused by the impacts is the smoothening. This, however, has the very remarkable consequence, that disappearance of certain peaks does not always reflect a decrease in the vibration amplitude, but can also mean the opposite case — a vibration increased to such an extent that the rod is impacting on its surroundings. Thus there is a higher chance to give faulty diagnosis by Fourier spectra only. Consequently investigation of fuel rod vibration requires increased caution.

KEYWORDS

Fuel rod vibration; impact; laboratory measurement.

INTRODUCTION

Vibration surveillance and diagnostics of fuel rods and fuel assemblies are important tasks in NPPs. They are so much the more difficult since the commonly used accelerometers do not operate properly under the extreme conditions of the core of reactor. Therefore vibration (or impact) of fuel rods can only be detected

2

indirectly from neutron noise or pressure fluctuation signals. Thus accurate knowledge of vibration phenomena and measurability is very important.

In our previous papers (Lipcsei et. a/., 1992 and 1994) fuel rod vibrations were investigated in simplified models which can be reproduced in laboratory environment. This practice is still more convenient in case of such complicated phenomenon as the impact of fuel rods or BWR instrumentation tubes (sec eg. Laggiard et. al.t 1992).

The rue! rod under investigation is placed in a narrow gap thus impacts can already develop during weak vibration.

Measurements were completed on a fuel rod model equipped with a limiter to investigate the appearance of impacts in vibration spectra.

EQUIPMENT FOR THE MEASUREMENTS

Measurements were carried out on the equipment described by Lipcsei et. al. (1992), supplemented with a limiter (Fig. I). The ends of the fuel rod were fastened with pin connections to the basement at bottom and !r> a vibration exciter at top. The signals of acccleromctcrs of type B&K 4375 mounted on the rod were connected to a Fourier analyser type ONO SOKKI CF-920. The vibration exciter was driven by the white noise output of the analyser.

MMF l.V 103 amplifier

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Pig. 1. Measurement equipment.

The parameters listed in Fig. 1 were set to the following values: rod length, L = 1357 mm; detectors distance from the limiter, /rf =50 mm; position of the exciter, /, the latter was changed between 665 and 913 mm with 50 mm step.

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A simple circuit was used to measure the impacting rate (Fig. 2). Time history (/(/) is the characteristic function of the amplitude function of the rod at the limiter. It is equal to zero while impacting, and

t/„ otherwise. Impacting rate — which is the time of contact between rod and limiter relative to the *• + ** entire period — can easily be read from the Amplitude Probability Density function of U(t).

ВАК 4375 •ccelerometer

ВАК 4375

Fig. 2. Circuit diagram to measure impacting rate.

EXPECTATIONS FROM THEORETICAL MODELS

First let us investigate the two extreme cases. If the gap between the rod and the limiter is large enough (a), there is no impact. Then eigenfrequencies and eigenfunctions previously found by Lipcsei et. al. (1992) develop and spectra shown in the same paper can be measured (see Fig. 3).

»•»К V *»

Flg. 3. Eigenfunctions and APSD of the fuel rod without limiter. When the limiter is placed very close to the rod (b) (in case of limiters at both sides of the rod) no movement allowed by the limiter, thus limiters act like a pin connection. In this case (Fig. 4) eigenfrequencies and eigenfunctions can easily be calculated.

In terms of dimensions in Fig. 1 Ц=1, L^^L-l. Use of two coordinate systems results simpler equations while substituting into the boundary conditions. Eigenfunctions for the first and second parts of the rod are (as described by Lipcsei et. al (1992)):

4

L>

zT TT ъ X

Fig. 4. Dimensions and coordinate systems in calculation.

->

Ф,(х) = asin(ß,,x)+ *cos(ß„x) + csinh(ßBx) + </cosh(ß,,x), <&,(*,)=Í siniß.Xj)+/cos(ß„x2)+ g sinh(ß,,x2)+Acoshfoxj),

respectively, where ß / = {2itf„ ) 2 — . The terms a.b,...,h are restricted by the boundary conditions: IE (1) Ф,(0)=0, (2) Ф;|О)=О, О) Ф,(А)=О, (4) Ф ; ( 1 , ) = Ф ' 2 Ю ,

(5) Ф ; ^ ) = Ф 2 ' И , ) ,

(6) Ф 2 К ) = О . (7) Ф2(0)=0, (8) Ф,'(о) = 0.

This homogeneous linear equation system has a nontrivial solution if the determinant of the system is equal to zero.

s inn ig ) sin(fcA) 0 0 cosh(ß,i,) cosiß^) -coshiß,^) - c o s f o l j . sinh(ß,i,) -MM sinh(ß„0 -siniß^)

0 0 sinhiß,!,) MtA) This latter equation gives the possible values of ß„ (which in turn contain the eigenfrequencies /„) and then the eigenfunctions can be written in final form:

The eigenfrequencies resulting írom ß„ are presented in Fig. 5.

Let us investigate in more depth the special case — = 0.5, that is when the limiter is placed at the middle of

the rod. This position has a specific role since it has the longest distance from the pin connections, thus — assuming a homogeneous density of mass — this point of the rod is expected to have the largest vibrational

= 0

5

amplitudes. Consequently in a closed space (e.g. in a tube) this is the most likely point to impact. Investigating the eigenfrequencies and the respective eigenfunctions one can observe an interesting behaviour. Eigenfrequencies and eigenfunctions of odd order are the same as the ones in case a half long rod with pin connections at its both ends. While eigenfrequencies and eigenfunctions of even order correspond to the ones of the similar half long rod but one end of which is built in (Fig. 6). This interesting similarity

results from symmetry. Similar correspondence can also be found at other special cases (e.g. — = - , - etc.). L 3 4

20 40 60 80 100 120 140 160 180 200 nBQUBnQf

Fig. S. Eigenfrequencies depending on the position of the limiter.

In more realistic cases impacts can also occur at other positions. These cases can generally be described by non-linear models and frequently exhibit chaotic behaviour (see e.g. Moon et. a!., 1983).

В

Fig. 6. The first five eigenfunctions of rod with pin connection at middle (A) and analogies with half long rod (B: pin connections at both ends, C: one end is built in)

Looking at the process from another viewpoint, one argues that it is a mixture of the two extreme cases described above. Thus between two impacts the forces are the same as in case (a) (pin connection at both ends), and during the contacts between die rod and the limiter the situation correspond to case (b) (additional pin connection at middle). One would expect that both types of peaks shall appear in the spectra. This is, however, not the case because an important moment is neglected. Case (a) and (b) are steady states, but in case of impacts duration of each case is so short that transients has increased role. Thus spectra measured on impacting rod has distortion compared to the sum spectrum of the two above cases.

6

EXPERIMENTAL RESULTS

In the measurements two accclerometers were mounted on the rod near the limiter, one in each direction from the impacting point to the ends of the rod. This gives a more definite identification of the nodes of the eigenfunctions.

In the majority of measurements symmetrical pairs of limiters were used. Some measurements have been carried out with a single limiter positioned on one side of the rod. This alteration had no significant effect on spectra.

Most of the measurements wee performed on a fuel rod model made from solid aluminium (Figs. 7-11). For the sake of comparison spectra as presented in Fig. 12 were measured on a real fuel rod. It is known that the stiffness of the model rod is larger, the mass per unit length is smaller than for a fuel rod. These differences cause higher eigenfrcquencies in case of model rods. Inner damping of the fuel rods is larger because of the fuel pellets, thus peaks of spectra measured on the model rod are more significant.

Rod without Limiter

Theory and measu-ements on fuel rod without limiter were described in detail by Lipcsei et. ál. (1992). in case of pin connection at both sides eigenfrcquencies relative to the first one coincide with the series of squares of integer numbers (Table 1), whereas eigenfunctions arc the same as the ones of string vibration (half periods of sinuses, see Fig. 3 and column В of Fig. 6).

A'~ " ' " " Л A'~ " ' " " Л & A &

1. 1 4 2. 4 6.24 3. 9 16 4. 16 20.26 5. 25 36

Table 1 . Relative eigenfrequencies with different constraints.

Fig. 7 shows the APSDs measured by the two accelerometers and coherence and phase between the signals of the accelerometers. It is apparent that the positions of the sinks follow the trend given by the theoretical model. Characteristic sink structure can be seen on the spectra This depends mainly on detector positions (see Lipcsei el. al. (1994) for details). Detector positions were set according to the cases with iimiter at the middle of the rod.

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7

Limiter Extremely Near to the Rod: Pin Connection

a) Pin Connection at Middle. This case means — = 0.5 in the above calculations. The first five

eigcnfrequencics (normalised to the first one of the rod without limiter) can be found in Table!. Eigenfunctions are shown in Fig. 6. Fig. 8 shows APSDs, coherence and phase functions of this measurement. Again the spectra follow the trend predicted by the theoretical model.

»•Í w » » « l . . i t / l w » l i N*.«l< 1199*.IS. II, I R«« vib-«tl . i , / n . u i , к» « | | 11994.IS. <•. > Um. *.9C/ 2V В:К/ 2У 9.ÍU» SJ/K 00««. U IttHi e (1С/ ÍV ГЧС/ 11 S.MJN JJ/JI CURL I.

'9.»*«« Fig. 8. Measured spectra with limiter at middle.

b) Pin connection at positions different from middle. Eigenfrcquencics of general cases can be read from Fig. 5. The measured spectra confirmed our expectations: cigcnfrcqucncies arc according to the previously calculated values. Spectra in Fig. 11 were measured with a limiter placed at 20 cm from middle. Spectra of the last row are completed with limiter extremely near to the rod (that is with pin connection).

Measurements with Impacts

Experiments were completed with different levels of impacting (gap between the rod and the limiter was changed) to observe transition between the spectra of the two extreme cases of limiter clearance. I.evel of impacting was set by a subjective mode by the level of impacting sound. Impacting rate of the model rod — measured by the circuit in Fig. 2 — was definitely lower than the rate with fuel rod at the same sound level. In Fig. 9 a typical part of time history U(i) (measured by circuit in Fig. 2) is shown.

ПЧЕ Ч LIN MaX'C Fig. 9. A typical part of the characteristic function of impacting rod.

Fig. 10 contains APSDs, coherence and phase functions measured on a model rod with medium level impacting.

It is interesting to see the smearing of peaks: peaks corresponding to case (a) vanished, while peaks of case (b) have not appeared yet. Peaks at 40 and 155 Hz are exceptions. These are eigenfrequencies of both cases, which comes from the special position of limiter. This result corresponds to the expectation, that the limiter has no effect on eigenfrequencies when one node coincides with the limiter position. Thus the longer the

8

distance of the limiter from nodes of an etgenfunction, the higher the suppressing effect on a given eigenfrequency.

«•4 » i k t t l . * * . / I « . » » ) , N».aM H M 4 . M . I I . I R.4 . i b . t l l x i « / l « . « » l . • ! • . * ( • 11994 • ) I I I ТМИ. Й:ЧС/ 2» B:«C/ 2» S.»W S 2 / Í Í OOflL I t JWM. Q.PC/ W в:«С/ « ».111« M/S2 01WL It

Fig. 10. Measured spectra with limiter at middle, medium level impacting (impacting rate is 8 %)

In Fig. 11 series of spectra is shown which were measured with limiter position 20 cm from middle. The first row contains spectra of rod without limitcr, and the spectra of the last row was completed with limiter placed near the rod.

Fig. 11. Measured spectra with limiter position 20 cm from middle (first row: without limrter, 2-5 row: increasing impacting rate (4-18 %), last row: limiter contacting with rod).

In real fuel rods fuel pellets cause higher internal friction, thus peaks of spectra are less significant than peaks of model rod. This effect is especially remarkable in spectra of impacting (Fig. 12).

9

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Fig. 12. APSDs measured on a real fuel rod (without limiter, with medium level of impacting (47 %), and with limiter near to rod, respectively).

CONCLUSIONS

Experimental results on models without limiter give good coincidence with theoretical calculations. Spectra measured on impacting rod became smoother with increasing impacting level. Spectra of fuel rods have a wider range in impacting rate and higher level of smoothing than model have (middle spectrum of Fig. 12 is almost flat, for example). The impacting rate strongly depends on mechanical properties of the rod.

By these experiments, one can state that as for Fourier spectra the only thing caused by the impacts is the smoothening. This, however, has the very remarkable consequence, that disappearance of certain peaks does not always reflect a decrease in the vibration amplitude, but can also mean the opposite case — a vibration increased to such an extent that the rod is impacting on its surroundings. Thus there is a higher chance to give faulty diagnosis by Fourier spectra only. Consequently investigation of fuel rod vibration requires increased caution.

ACKNOWLEDGEMENT

This work was supported by OTKA grant no. 1845 and OMFB grant no. 91-97-42-0344.

REFERENCES

LAOOIARD, E., J. RUNKEL and D. STEOFMAN (1992). Study of the vibration and impacting of an instrument tube in a BWR. IMORN-23, Nyköplng, Sweden.

LIPCSEI, S., S. KISS and G. PóR (1992). On the eigenfrequencies of fuel rod vibration in NPPs. Progr. Nucl. Energy, Ц, No I, 11-24.

LIPCSEI, S., S. KISS and G. PÓR (1994). Effect of detector size and position on measured vibration spectra of string.* and rods. Progr. Nucl, £«rgy, & No 2,91-102.

MOON, F. C. and S. W. SHAW (1983). Chaotic vibrations of a beam with non-linear boundary conditions. Int. J. Non-Linear Mechanics, lfl, No. 6,465-467.

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Title and classification of the issues published in this year:

KFKI-1994-1/G J. Végh, M. Bodnár, L, Bürger, M. Tanyi, FSefcsik: Development and testing of a prototype N T information system based on the G2 expert system shell

KFKI-1994-Z/N G. Németh, L. Böröczky: Efficient texture analysis: Advanced methods, applications

KFKI-1994-3/M Z. Katona, Т. Nemes, E. Szentgyörgyi: Development of intelligent real-time I/O boards using TMS320C25 digital signal processor.

KFKI-1994-4/J,K K. Berci, L. Misáros: Recent advances in the organic chemistry of astatine

KFKI-1994-5/G Z. Mzer, L. Szabados: Overview of LOBI Data Base for W E R Purposes

KFKI-1994-6/G M. Dús, Z. Hóier, A. Takács: Implementation of CATHARE Code VI.IE

KFKI-1994-7/G Makai M., Temesvári E.: Atomerőművekben alkamazott számítási- és in-core kiértékelési mód­szerek ellenőrzésének gyakorlata

KFKM994-8/B N. Fáy, Á. Holba, B. Lukács. More Redshifts írom the Abell Catalogue I: the Brightness-Redshift Relation

KFKM994-9/M-N J. Bogdany, G. Vesztergombi: WORKSHOP ON PARALLEL PROCESSING Technology and Applications

KFKI-1994-10/A J. Balog, Т. Hauer: Polynomial Form Factors in 0(3) Nonlinear o-Model

KFKI-1994-I1/C Sz. Bérezi, B. Lukács: May Icy Meteorites Lie on Antarctica?

KFK1-1994-12/G A. Rácz. S.Kiss: Methodotogical examination of UAR based change detection

KFKI-1994-13/C Sz. Bérezi, BLukács: On Possible Spheruliie Sources

KFKI-1994-14/B e.Z^itóci.Onthe7iOTPoimofÜiea>emkalPotenial

KFKM994-15/B /. Horváth, В. Lukács: All stationary vacuum solutions with geodesic shearfree eigenrays

KFKI'1994-léVG S. Kiss, S. Lipcsei: Laboratory experiments with impacting fuel rods

Kiadja a Központi Fizikai Kutató Intézet Felelős kiadó: Szegő Károly Szakmai lektor: Lux Iván Nyelvi lektor: Lux Iván Példányszám: 143 Készült a PROSPERITÁS Kft.nyomdaűzemóben Budapest, 1994. októberber hó