13. Vibration analysis

D.A. Jobson, Paper 13, BNES SMiR T Symposium

13.

361

Vibration analysis

D. A. J O B S O N , BSc(Eng), MIMechE, U K A E A , Risley

Reference has already been made to the papers presented at the second SMiRT Conference on dynamic analysis in connexion with fast reactor safety studies. There were, in addition, sessions devoted specifically to vibration aspects of structural dynamics, namely D3 on fuel, E4 on reactor components, and E5 on related fluid/gas dynamic effects. It should also be noted that a whole section of the conference was, in addition, given over to seismic analysis. More than 50 papers were presented on this subject but, as I was unable to attend these sessions, no specific reference will be made to them in this review. Session D3 opened with an analysis of flow induced movement of a fast reactor sub-assembly z, such as that shown in Fig. 1. This was a situation where the allowable amplitude of the random or resonant vibration was more likely to be governed by its effect on reactivity noise than by

Fig. 1. Sub-assembly for the prototype fast reactor at Dounreay

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mechanical considerations. The concepts of random vibration theory allowed the power spectral density of the response to be related to that of the excitation, assuming that the latter arose dynamically from fluctuations of the exit jet. The paper showed how the modal amplitudes of a cluster depended on the corresponding Strouhal number S, which was a measure of the ratio of the modal frequency N, normalized to the exit jet diameter D and corresponding flow velocity V: S = ND/V. This emerged as an important variable, together with such parameters as the effective modal mass and the damping, which together determined the root mean square values of the resonant and random amplitudes for a given fluid density and exit jet size (Fig. 2). Other papers in this section were concerned with parallel flow-induced fuel rod and bundle vibrations. Experiments, such as those reported by Ohlmer and Schwemmle,2 sup-

Fig. 2. Power spectral densities of excitation and modal response

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ported the concepts of response functions H2(to) to relate the power spectral density of the pressure fluctuations to movement (Figs 3 and 4). This work, carried out at the Euratom Joint Research Centre at Ispra,. showed, however, that H2(w) was sensitive to the bundle geometry. Experiments had also been carried out by Westinghouse Canada Ltd on CANDU type fuel bundles in a vertical flow tube. Forrest and Hancox 3 reported a dominant frequency response at 10 Hz, which corresponded to the fourth bending mode of the string. In their case there had also been an apparent coupling between the flow and structural excitations. This relative motion had, however, become small at velocities above 9 m/s. At a flow velocity of 13 m/s the relative motion between the flow tube and the fuel string was determined by the flow-borne excitation and the effect of the mechanically imposed excitation was then negligible. Mr Gittus has already referred to the work done at the Reactor Fuel Laboratory, Springfields, to establish rubbing, fatigue and wear criteria for CACR fuel columns (Fig. 5). Sansom and Jones 4 described how histograms had been extrapolated, assuming Gaussian or Rayleigh distributions, to derive probable lifetime maximum values for a complete core. When a resonant system was subjected to broad-band noise, those signals lying within the resonant frequency range were selectively amplified. As a result, the system vibrated predominantly at its natural frequency but with a continuously varying amplitude. Consequently the fatigue life of materials, when subjected to what has become known as narrow-band random vibration, had assumed some importance in applications of this kind. It has been found necessary, when considering the vibratory movements of fuel pins, to take these considerations into account in defining the limits for maximum acceptable strains in the reactor. A further U K contribution relevant to CAGRSwas that by Emsley and Bryant: It described the experimental pro-

Fig. 4. P S D of pressure difference fluctuations for different pitch widths

Fig. 5. Sectional view of Mk II

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gramme which has been carried out to develop and endorse on-power refuelling for the Hinkley B reactor. The evolution of the channel outlet geometry was traced (Fig. 6), and the role played by model and rig trials in this development was outlined. Fig. 7 shows the full-scale rig in diagrammatic form and gives an idea of the size of the latter, which provides for the 26 m fuel assemblies. These stringers were nosed in and out of a channel against a free flow of 90 kg/s having a density of 38.5 kg/m 3 and a velocity of 40 m/s. The final solution involved the use of a brush-type seal at the end of the fuel stringer. The latter engaged with a perforated conical tundish, and this arrangement has been proved by instrumented tests for repeated traverses. A wider ranging session was that concerned with reactor components (E4). The opening paper of this session, by Hitchings and Dance, 6 surveyed the methods of analysis which were currently available. It described how tbe equa-

D.A. Jobson, Paper 13, BNES SMiR T Symposium

363

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tions of motion for a lumped representation of a real system could be formulated in matrix terms by using stiffness methods, often based on the use of finite elements. Reference was made to the use of master and slave nodes, particularly to reduce computing times for finding mode shapes and frequencies. As an alternative to the use of modal methods, solutions to the original coupled equations could be marched out. It was pointed out that this approach had disadvantages, however, when an extensive amount of transient work had to be done. The basic ideas of random vibration were introduced and links were either shown or implied between the use of probabilistic and deterministic methods. A French contribution from Saclay by Tigeot et al. 7 reported on the work they had done in connexion with Phenix, which is similar in many respects to the U K prototype fast reactor at Dounreay. Their conclusions had turned out to be very similar to the British ones. In particular, the measured strains had proved, if anything, to be smaller than had been anticipated from model tests and analytical studies. The associated sequence of development work in connexion with the latter was described. Flow studies and model tests were carried out in conjunction with analysis work and the use of spectral methods. Subsequent structural stiffening was introduced and this was followed by a programme of full-scale measurements on the reactor internals. The latter included vibration scans and use had been made of the modal acquisition techniques developed by O N E R A . The vibration measurements made during construction had provided a background of knowledge for the subsequent survey which had been made with the sodium circulating pumps in operation. Measurements had been made of fluid pressure fluctuations as well as component accelerations. Difficulties were encountered in the interpretation of these data, mainly attributed to the background noise levels.

364

D.A. .lobson, Paper 13, BNLS SMiR T S)'nlposium

These problems had been aggravated by the a t t e n u a t i o n at low frequencies and the high operating temperature. T h e best results had been obtained f r o m the strain gauges, which h a d confirmed that the m e a s u r e d levels of vibration on all the major structural c o m p o n e n t s were quite acceptable, 1 microstrain having been the m a x i m u m measured. A contribution by Bastl 8 emphasized that one vital need in reactor operation was the detection of u n t o w a r d behaviour of a n y kind. It was pointed out that there was a wide range of potentially useful m e a s u r e m e n t s which could be m a d e for this purpose. These included the m o n i t o r i n g of c o m p o n e n t vibrations either directly, by displacement m e a s u r e m e n t s for example, or indirectly t h r o u g h the use of pressure or acoustic transducers. The systematic use o f correlation a n d power spectrum techniques provided a m e a n s by which such information could be sorted out. Cross-correlation of these with other quantities, such as neutron flux measurements, provided a potential m e a n s for relating cause to effect. It was maintained that m u c h valuable i n f o r m a t i o n had been, and could be, obtained from surveillance of a system in this way. It presupposed that those concerned h a d been given the o p p o r t u n i t y to obtain the necessary basic information a b o u t the system in the first place. Vibration m e a s u r e m e n t s made t h r o u g h the use of shaker tests could be of use for this purpose. Such techniques had proved valuable on the reactors at Sena a n d Trino. They had been used there to prove the adequacy of remedial work, the need for which was believed to have arisen from the pendular behaviour of the reactor vessel/core barrel structure. The effect of the latter could be seen from an analysis of the n e u t r o n flux signal. Similarly, special experiments performed in the E C O reactor had shown the influence of fuel rod oscillations on the n e u t r o n flux. In a subsequent session (E5) a French paper" described the work done following the troubles that had been encountered on the PWR at Chooz. T h e pendular etfect referred to in connexion with other PWRS in previous papers had led to fatigue of the thermal shield attachrnents, core barrel bolts and tie rods. These failures, which had arisen from flow-induced vibration, had given rise to difficult repair work on irradiated material. This had" taken two years a n d had cost several millions of francs. Saclay was now engaged on a p r o g r a m m e to simulate flow distributions in PWRS. It included flow visualization studies which had been carried out by replacing the central part of a reactor model by a plexiglass cylinder. A most interesting film obtained in this way showed the turbulent mixing effects and the associated vortices in the s u r r o u n d i n g annulus. The sources of excitation in the main circuits of the Safran loop were also characterized. The a p p a r a t u s consisted

essentially of a vessel with a d u m m y core and three connecting loops, to simulate on a m o d e l scale the m a j o r flow circuits in a PWR. M e a s u r e m e n t s had been m a d e of the vibration characteristics for various a r r a n g e m e n t s of the reactor internals. This p r o g r a m m e was c o n t i n u i n g a n d was ultimately a i m e d at a hydro-elastic evaluation from associated vibration a n d hydraulic tests. Reviewing the scope of the papers, it could be clearly seen that current trends are leading towards statistical descriptions a n d probabilistic assessments. T h e need for developm e n t s in these directions has arisen from the problems being encountered, which require a significant b r o a d e n i n g of what has traditionally been u n d e r s t o o d by the term ' v i b r a t i o n analysis'. Flow-induced vibration is not generally m o n o tonic in character; b r o a d - b a n d excitation requires the a d o p t i o n of spectral a n d correlation techniques. These trends were apparent, not only in the field of vibration analysis, but also in the associated areas of acoustic a n d seismic analysis. REFERENCES 1. JOBSON D. A. R e s p o n s e predictions for resonant a n d r a n d o m vibrations of fast reactor fuel sub-assemblies.

Second Int. Conf. Structural mechanics in reactor technology, Trends in structural mechanics, Berlin, 1973. Paper D3/I. 2. O~LMER E. a n d SCHWEMMLE R. Investigation on vibration behaviour a n d driving forces for fuel d e m e n t models in parallel flow. lbid, Paper D3/2. 3. FORREST C. F. a n d HANCOX W. T. The response of a reactor fuel string to flow a n d structurally transmitted excitation, lbid, Paper D3/8. 4. SANSOM K. A. a n d JONES P. M. The evaluation o f inreactor vibratory a n d impact m o v e m e n t s of civil AGR fuel elements. Ibid, Paper D3/10. 5. EMSLEY G. M. a n d BRYANT T. Co. Inhibition of vibration during on load charging of the AGR fuel stringer. Ibid, Paper D 3 / l l (see also Paper 514 of U K A E A / N P L International S y m p o s i u m on Vibration Problems in Industry, Keswick, 1973). 6. H1TCHINGS D. a n d DANCE S. H. R e s p o n s e of nuclear structural systems to transient a n d r a n d o m excitation, using both deterministic a n d probabilistic methods, lbid, Paper E4/I. 7. T[GEOT Y. et al. Vibrations des structures internes de r6acteurs c o m p a r a i s o n , exp6riences, calculs, lbid,-Paper E4/2. 8. BASTL W. Vibration measurements and analysis in nuclear power plants. Ibid, Paper E4/4. 9. ASSEDO R. et al. The Safran test l o o p - - m o d e l experimentation and analysis of flow induced vibrations of PWR reactor internals. Ibid, Paper E5/2.