Atomic Energy of Canada Limited EXPERIMENTAL STUDIES ON FLOW INDUCED VEBRATION TO SUPPORT STEAM GENERATOR DESIGN

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1 Atomic Energy of Canada Limited EXPERIMENTAL STUDIES ON FLOW INDUCED VEBRATION TO SUPPORT STEAM GENERATOR DESIGN PART I!: TUBE VIBRATION INDUCED BY LIQUID CROSS-FLOW IN THE ENTRANCE REGION OF A STEAM GENERATOR by M.j. PETTIGREW, J.L. PLATTEN and Y. SYLVESTRE Paper presented at the International Symposium on Vibration Problems in Industry, April 1973, Keswick, England. Chalk River Nuclear Laboratories Chalk River, Ontario May 1973 AECL-4515

2 EXPERIMENTAL STUDIES ON FLOW INDUCED VIBRATION TO SUPPORT STEAM GENERATOR DESIGN* PART II: TUBE VIBRATION INDUCED BY LIQUID CROSS-FLOW IN THE ENTRANCE REGION OF A STEAM GENERATOR M.J. Pettigrew J.L. Platten Y. Sylvestre SUMMARY At the entrance to the tube bundle of recirculating type steam generators, tube vibrations may be induced by cross-flow. The results of an experimental vibration study on a full size model of a 30 sector of the lower region of a steam generator under realistic flow conditions are reported. The vibration response of the tabes and in particular the nature of the flow-induced excitation forces are investiga ted.^t - Tube vibration amplitudes under normal operating Bruce steac generator flow conditions were generally less than in. Root Mean Square. Thus, no vibration problems are anticipated there. < The flow-induced excitation forces appear to be broad-band random in nature. The vibration response is directly related to a power of the flow velocity. O '",-' : Chalk River Nuclear Laboratories Chalk River, Ontario May 1973 AECL-4515 * Paper presented at the International Symposium on Vibration Problems in Industry, April 1973, Keswick, England.

3 Etudes expérimentales sur la vibration engendrée par l'écoulement pour faciliter la conception des générateurs de vapeur* Partie II: Vibration de tube engendrée par l'écoulement liquide transversal dans la région d'entrée d'un générateur de vapeur par M.J. Pettigrew J.L. Platten Y. Sylvestre Communication présentée au Symposium international sur les problèmes de vibration dans l'industrie avril 1973, Keswick, Angleterre. Résumé A l'entrée du faisceau de tubes des générateurs de vapeur de type recirculant, la vibration des tubes peut être engendrée par l'écoulement transversal. Les résultats d'une étude de vibration expérimentale effectuée sur un modèle grandeur nature d'un secteur de 30 de la région basse d'un générateur de vapeur, dans des conditions réalistes d'écoulement, sont présentés. La réponse S la vibration des tubes et en particulier la nature des forces d'excitation provoquées par l'écoulement, font l'objet d'une enquête. Les amplitudes de vibration des tubes dans les conditions normales de fonctionnement des générateurs de vapeur de Bruce ont été généralement inférieures à in., racine carré moyenne. Ainsi, aucun problême de vibration n'est anticipé pour la centrale de Bruce. Les forces d'excitation provoquées par l'écoulement semblent être de nature aléatoire à bande large. La réponse de la vibration est directement reliée â une puissance de la vitesse d'écoulement. L'Energie Atomique du Canada, Limitée Laboratoires Nucléaires de Chalk River Chalk River, Ontario Mai 1973 AECL-4515

4 PART I I: IHTROOnCTION TUBE VIBRATION INDUCED BY LIQUID CROSS-FLOW IN THE ENTRANCE REGION OF A STEAM GEHERATOI.. In recirculating type steam generators such as those used In the Bruce nuclear station, water at near saturation temperature flows by natural convection from the steam separator, down In the annulus between the tube bundle shroud and the outer shell, and to the bottom section of the tube bundle^1^. The water enters through ports In the shroud and flows radially In the tube bundle near the tubeaheet. The flow there Is to a large extent across the tubes. The design of the Bruce steaa generator was analysed from a flow-induced vibration point of vlew^l). Assuming that periodic wake shedding is the principal vibration excitation mechanism in liquid cross-flow, the analysis showed that tube resonance was possible at the entrance region if extreme values of the available data on periodic excitation frequencies were used. The scatter in the latter data is particularly large at the low pitch to diameter ratios of typical steam generator tube bundles. The tube response at resonance may be evaluated knowing the damping and the magnitude of the periodic wake shedding force which is usually expressed in terms of a fluctuating lift coefficient. However, data on fluctuating lift coefficients in tube bundle configurations are particularly scarce. Alternately the tubes may respond to random pressure fluctuations due to flow turbulence. This requires information on the nature of the random pressure fluctuations and their statistical properties such as their power spectral densities and spatial correlations. To the knowledge of the authors there is no available data on the latter for tube bundles. Whatever the excitation mechanisms, flow velocities and distribution must be known to forrulate flow-induced excitation forces. Flow calculations are very difficult to do with sufficient certainty in such a -complex three-dimensional flow path as the entrance region. Consequently we initiated an experimental investigation aimed particularly at making sure that the Bruce steam generators are free from vibration problems at the entrance region. Longer-term objectives are to study flow velocity distribution, excitation forces and tube bundle response in view of optimizing steam generator entrance geometry for minimum vibration. This note reports the results of vibration measurements on a full-size model of a 30 sector of the lower portion of the Bruce steam generator. The vibration response of the tubes and in particular the nature of the flow-induced excitation forces are investigated. The tube vibration amplitude under normal flow conditions was generally less than in. Root Mean Square (RMS). Thus no vibration problems are anticipated at the entrance region of the Bruce steam generators. The flow velocity measurements now in progress are not included

5 - 2 r. EXPERIMENTAL 2.1 Model Description and Test Conditions The model was designed to simulate realistically flow velocities and distribution in the tube bundle as well as the dynamic behaviour of the tibes. The model, shown on Figure 1, is a full size 30 sector of the lower portion of the Bruce steam generator. Thus one of the twelve entrance ports located around the circumference of the tube bundle shroud is reproduced. Approximately 700, in. O.D., in. wall, Type 304 stainless steel tubes were expanded at the tubesheet and supported by two broached plate type supports to simulate realistic boundary conditions. Details and dimensions of the model and of the broached plate supports are on Figure 4 and 6 respectively. It is Interesting to note that the two principal orientations of the triangular tube lattice are present in the 30 model. The flow is normal to the base of the triangular pitch on one side and parallel to It on the other. The model was designed for easy accessibility for flow velocity measurements and to accept different entrance port geometries for more general studies. Hater enters the model at the top, flows down in a simulated annulus of sufficient height for proper flow development and reaches the tube bundle through the entrance port at the bottom as shown on Figure 4. The water then flows up through the two broached support plates to form a free surface about one foot above the upper broached plate. channel to a sump. realistic weight simulation. From there it flows over a weir and in an open The tubes were generally filled with water for The model was connected to an ambient temperature (~90 F) low pressure recirculatlng test loop of nominal capacity of 1800 IGPM. This permitted testing at more than 150% of design flow. average flow velocity based on the entrance port area in the Bruce steam generator at 100% load is 1.47 ft/s^1. The Reynolds number R based on the tube diameter and the maximum gap velocity (calculated assuming that the flow enters the tube bundle only over the projected area of the entrance port, i.e: is 2 x 10* at 90 F compared to =14 x 10 4 The 1.47 x 0.8/( ) = 4.05 ft/a) for the steam generator under normal operating conditions. How this difference in Reynolds numbers affects the excitation forces is open to question. Chen^2) postulates from pressure drop coefficient measurements by other researchers that, for closely packed tube Lundles, the fluctuating lift coefficient Cj_ and the dlmensionless wake shedding frequency S (Strouhal number) do not vary much over the above Reynolds number range.

6 Instrumentation Eight weldable strain gauges (S.G.) were ik.o ir lied on five selected tubes to measure the dynamic strains induced by the tube vibration. So that strains would be induced for all the vibration modes, the gauges were attached close to the clamped end of the tubes (i.e: one inch from the tubesheet). installation are on Figure 2. gauges are shown on Figure 5. Details of the weldable strain gauge The location and orientation of the The gauges are either oriented radially or circumferentially to the tube bundle. This corresponds to the direction of the flow and the direction normal to the flow respectively assuming that the latter is mostly radial. The vibration response of the tube on which S.G. No. 7 and 8 were installed was also monitored with the biaxial accelerometer probe shown on Figure 3. Acceleration measurements were taken at a nunber of positions along the tube by traversing the probe inside it. Strain measurements were taken at the same time for comparison purposes. The tube was drained of water during this operation. Both accelerometer and strain gauge signals were recorded on magnetic tape. 2.3 Procedure and Data Analysis Dynamic strain measurements were taken at various average entrance port velocities from 0.76 to 2.24 ft/a. The acceleration measurements were taken along the length of one tube at 1.4 and 2.24 ft/s. " The signals were analysed with a 500 points real-time analyser and ensemble averager. The spectral analyses revealed two dominant narrow frequency bands indicating that the response of the tubes was of a narrow-band random nature with two predominant modes of vibration. Tfce lower frequency band was between 35 and 40 Hz, and the upper one between 60 and 70 Hz. For the acceleration signals measured with the tube empty the frequency bands were slightly higher as expected. That is Hz and Hz respectively. The upper frequency component was generally better defined than the lower one. Occasionally lower and much broader components were present (eg. 13, 20 Hz). Ho significant signal components were above 90 Hz. Selected frequency spectra are shown on Figure 7. The mean square values of the signals corresponding to each of the vibration modes were obtained by squaring and integrating the signals after filtering through a 48 db/octave bandpass filter. The filter was set for 10 to 45 Hz and 45 Hz to 80 Hz for the lower and upper mode respectively. For the acceleration signals the bandpass frequencies were 20 to 55 Hz and 55 to 90 Hz.

7 RESULTS AND DISCUSSION 3.1 Vibration Mode Analysis Normal modes and natural frequencies f are calculated to relate the measured dynamic strains e to the tube vibration amplitude y(x), the bending moment M Q at the tubesheet and the reaction R^ and R2 at the first and second tube support respectively. The tube boundary conditions are assumed to be clamped (C) at the tubesheet and free (F) or pinned (P) at the broached plate supports. The results are summarized in Table I below. TABLE I: Natural Frequencies and Dynamic Strain Relations Modes and Boundary Conditions f(h2) tlax y(x)/* H 2 0 [No H2O Tube Tub el ** X for Max y(x) Mo/ e *** B-l/ *** (lb.iil/ye) (lb/pe) (lb/ye) C-P-P l 8t 2 nd [40. 4jl [69. 8] D C-F-P l St 2 nd 3 rd [13 [43 [91 5] 8] 5] C-P-F l 8t 2 nd 3 rd [8 [54 [77 6] ] 8] C-F-F 2 nd 3 rd 4 th [19 3] 1 [54! [106] * ** *** Applies for both H2O andnc H2O Distance from tubesheet. Applies only : tor H2O in tube. in tube The lower mode natural frequency corresponds to either the 1st mode C-P-P or the 2 nd mode C-F-P whereas the upper node frequency to either the 2 nd mode C-P-P or the third mode C-P-F. The occasional lower frequencies mentioned earlier may be related to the mode C-F-P or the 2 nd mode C-F-F. Displacement amplitudes deduced from the acceleration measurements are plotted on Figure 8 with the amplitude deduced from the dynamic strain measurements (S.G. 7 & 8 only) for different assumed normal modes.

8 - 5 - For sinusoidal vibrations, displacement and acceleration are simply related by y(x)rms = 4ir 2 f2 y(z)rhs. This is not exact for ra-.iom vibration response. We have shown, however, using the analysis described in Section 4 to calculate both displacement and acceleration response to assumed random excitation forces, that th* above relation is approximately correct In this case. The accelerometer data appear to fit better the 2nd mode C-F-P (Figure 8b) than the 1st mode C-P-P (Figure 8c) at the lower frequency. At the higher frequency, sone of the accelerometer data fit better the 2nd mode C-P-P (Figure 8d) and other the 3*d mode C-F-F (Figure 8e). More likely a combination of these modes is excited. Comparing the magnitude of the vibration amplitudes to the tube-tc-tuoe support clearance (ie: In.), it is not surprising that the tube does not touch the support at times. Some of the high acceleration valuss at the support may be related to tube Impacting. Some of the discrepancy between the acceleration data and the strain gauge measurements may be attributed to the low acceleration levels, the low sensitivity of miniature accelerometers (ie; 1.5 p Cb/g) and the nature of such measurements (ie: probe displaced in tube, etc.). 3.2 Vibration Response The effect of flow velocity on the dynsmlc strains corresponding to the two dominant modes of vibration are shown on Figure 9. Corresponding maximum vibration amplitudes for the assumed vibration modes are also shown. proportional to the square of the velocity. For the lower mode, the dynamic strain Is There are no peaks in the curves to indicate the presence of wake shedding resonance at some flow velocity. The Strouhal Number based on 39.8 Hz and the entrance port velocity is 1.15 for 1.47 ft/s and 0.75 for 2.24 ft/s. Critical Strouhal number for p/d = 1.57 may be between 0.6 and 1.3 as taken from data collected from various sourcest 1^. Thus if wake shedding is an excitation mechanism here, resonance should have been expected unless a large portion of the flow is redistributed between the shroud and the tube bundle.' We shall know this when our flow velocity measurements are completed. The observed response indicates broad-band raauoa excitstics. This is not entirely surprising since the flow velocity distribution in the entrance port in unlikely to be uniform. would generate different wake shedding frequencies. Different velocitiss Also closepacked tube bundles encourage random turbulence rather than vortex formation^2). For the upper mode (Figure 9b) the response Is not quite directly related to a power of thi velocity. However, from a practical viewpoint, a velocity exponent of 2.6 fits the data adequately.

9 - 6 - Generally the outermost tubes vibrate most and the vibration amplitude is greater in the circumferential direction than the radial direction which is probably the prevailing flow direction. Vib.ation amplitudes, dynamic strains and support reactions are of the same order of magnitude for each mode. This ihows that higher mode vibration is just as likely to cause possible vibration fretting problems as the fundamental mode. The maximum vibration amplitude at 1.47 ft/s assuming the most likely modes of vibration is generally less than in.rms. 3.3 Damping Measurements The damping ratios t, obtained from logarithmic decrement results are and for the lower and upper frequency respectively. The logarithmic decrement data indicate that the damping is linear and that the corresponding viscous damping coefficient C is practically constant for the above frequencies. The coefficient C based on a lower frequency of 39.8 Hz is 8.4 x 10~ 4 lb-s/in. 4. RANDOM YIBRATIOH ANALYSIS We inferred in Section 3.2 that the excitation is of a broadband random nature. It may be shown with the assistance of References (3, 4, 5 and 6), that the mean square response y^(x) of a uni-dimenslonal continuous uniform structure to distributed random forces g(x,t) may be expressed by: S / (f) cos fe - s f (f) 6 L r r S S r 4 2 S 2 / H (f) H r s 167Tf * * J * r s o /A (x) <j> (x1 ) R(x,x',f) dx dx 1 df (1) a where: 1) the spatial correlation density function R(x,x',f) is defined by R(x,x\f) = 2 / C-o Jj / g( x,t) gcx'.t+t) dt e" j(2irf)t dx (2) J I» I -a -T J 2) the frequency response function is i (3) is the damping ratio at the rth mo(je and 6 of H r (f). ia the argument

10 - 7-3) <t>r( x ) aid * s < x ) represent the normal mode of vibration of the structure for the r'h and s tn mode, and 4) x and x». are points on the structure and T is a difference in time t. For the above derivation we assume that the damping is small and that it does not introduce coupling between modes to justify modal analysis. The structures considered here are the tubes which are effectively beams supported at several points. The normal modes are found using a method similar to thet suggested by Darnley(^) assuming that the effects of shear and rotary inertia are negligible, that the mass distribution and flexural rigidity are constant along the length of the tube and that the supports may be described by a set of homogeneous boundary conditions. The natural modes are normalized so that I / (4) o where m is the mass per unit length and includes the added mass due tc the inertia of the fluid around the tube and the fluid Inside the tube when applicable. If the random force Is concentrated in one point, part of Equation (I) becomes I I llty (*) $ (x) R(x,x',f) dx dx 1 = $ r (x o ) t a (» o ) s (») O o o where S -. is simply force. the power spectral density function of the Using Equation (1) we may calculate the response of the tube knowing the spatial correlation density function of the distributed random forces. Conversely, knowing the response, we may obtain some knowledge of the random forces. However, since we have little information on the statistical properties of the distx^uuted random forces we assume: 1) that the power spectral density function is independent of location, ie: RCx.x'.f) = R* Cx.x 1 ) S (g) (6) 2) that the random forces g(x,t) are completely correlated and constant over the height of the entrance port and nil elsewhere: R'CS.X 1 ) = 1 fc- 0<x<17.5 is., and»' (x.x 1 ) - 0 (7) for x>17.5 in.

11 - 8-3) and that the power spectral density function S( g ) is constant for a given mode of vibration. This assumption is usually valid since the vibration response of a structure to broad-band excitation is quite insensitive to variation in power spectral density away from its natural frequencies. Taking into account the above assumptions,we deduced from the tube response the power spectral density of the random forces at the frequency corresponding to the lower and upper observed vibration modes. For the purpose of discussion, we used the response measured with S.G. No. 7 at the design entrance port velocity (from Figure 9a and b at V = 1.47 ft/s) assuming 2 nd mode C-F-P (39.8 Hz) and 2 nd mode C-P-P (63.5 Hz) for the lower and upper mode respectively. This yields the somewhat contentious power spectral density function of the random forces shown on Figure 10. The total vibration response for the four lower modes of vibration considering the first four spans of the Bruce steam generator was calculated using Equation (1) and using the above spectral density function. The design parameter used in the calculations are E = 29 x 10 6 psi, I = 1.76 x 10-3 in 4,-C = 8.4 x 10" 4 lb-s/in., pinned supports 35 in. apart and m = lbm/in. The RMS response is plotted as a function of the distance along the tube on Figure 11. It is interesting to note that it is considerably less than the maximum amplitude calculated assuming response at resonance in Reference (1) (ie: 0.36 x 10~ 3 in.rms VS 2.39 x 10" 3 in.). 5. CONCLUDING REMARKS The results of our experimental study on a full-size model of a sector of che entrance region of a steam generator under realistic flow conditions show that: 1) The flow-induced excitation forces are of a broad band random nature. There is no evidence of narrow-band excitation frequencies usually attributed to periodic wake shedding. 2) Fundamental and second mode vibration are excited. The response amplitudes for each mode are of the same order of magnitude. They are less than in.rms for the Bruce steam generator entrance velocity. Thus no vibration problems are anticipated there. The amplitude is directly related to a power of the velocity. 3) The damping appears to be viscous. The damping coefficient is near.y constant over the frequency range considered. 4) Acceleration measurements tend to indicate that the tube supports do not necessarily hold the tubes at all times. 5) Outermost tubes vibrate most.

12 - 9 - ACKNOWLEDGEMENT We are thankful to Messrs G.A.W. Hewitt and J.A. Aikin for their technical assistance. Babcock and Hllcox Canada Limited contributed the tubesheet and the broached plate supports. LIST OF SYMBOLS c Viscous damping coefficient d Tube diameter f Tube natural frequency g(x,t) Excitation force at x and time t H r (f) Frequency response function of the r tn node SL Structure length m Mass per unit length M Bending moment at the tubesheet R Rj,R 2 Reynolds number Reaction forces at supports R(x,x", f) S t, T Time V Spatial correlation density function Strouhal number: fd/v Flow velocity x, x' Location of points on the structure S, > Spectral density function of the excitation forces e Dynamic strain (pe = 10~ 6 in./in.) Damping ratio 9 Argument of H r (f) T Time difference $ (x) i tn normal mode REFERENCES (1) Schneider, W., Pettigrew, M.J. and Hodge, r.i., "Vibration Analysis in the Design of Steam Generating Equipment for the Bruce Nuclear Power Station", Paper No.523 to be presented at this conference. (2) Chen, Y.N., "Fluctuating Lift Forces of the Karman Vortex Streets on Single Circular Cylinders in Tube Bundles", Part III - Lift Forces in Tube Bundles, ASME Paper 71-Vibr-13. (3) Thomson, W.T., "Vibration Theory and Applications", Prentice- Hall, Englewood Cliffs, N.J., (4) Meirovitch, L., "Analytical Methods in Vibration", Macmillan Company, N.Y., (5) Cranuall, S.H. and Mark, W.D., "Random Vibration in Mechanical Systems", Academic Press, N.Y., 1963.

13 (6) Thomson, W.T. and Burton, H.V., "The Response of Mechanical Systems to Random Excitation", Journal of Applied Mechanics, Vol. 24, No. 2, June 1954, pp (7) Darnley, E.R., "The Transverse Vibration of Beams and the Whirling of Shafts Supported at Intermediate Points", Phil. Mag. 56, Vol. 41, No. 241, Jan

14 FIGURE 1: FULL-SCALE MODEL OF STEAM GENERATOR ENTRANCE REGION (ENTRANCE PORT RE- MOVED TO SHOW TUBE BUNDLE) FIGURE 2: DETAILS OF STRAIN GAUGE INSTALLATION. FIGURE 3: BIAXIAL ACCELEROMETER PROBE (0.4 in. D)

15 WEIR FIGURE 5: STRAIN GAUGE LOCATION. FIGURE 4: SKETCH OF MODEL OF STEAM GENERATOR ENTRANCE REGION K).525"D FIGURE 6: BROACHED HOLF.

16 a) S.G. No 1, FLOW: 1.40 ft/s H20 In TUBE, AVG. TIME: 1601 c) ACCELERATION NOflHAL TO FLOW, AT 21 in FROM TUBE5HEET, FLOW: 3.24 ft/s. NO HjO In TUBE AVG. TINE: 80s. FREQUENCY (Hz) FREQUENCY (Hi) 2.0 li) S.G. No 7, FLOW: 2.24 ft/i. MjO 1n TUBE, AVG. TIME: d) ACCELERATION IN FLOW DIRECTION, AT 21 In FROM TUBESHEET, FLOW: 2.24 ft/s, HO HjO In TUBE AVG. TIME: BOl. FREQUENCY (III) FREQUENCY (Hi) FIGURE 7a,b,c,d: SELECTED FREQUENCY SPECTRA (FILTER BANDWIDTH: 0.3 Hz at 3dB).

17 0«AMPLITUDE NORMAL TO FLOW (CORRESPONDING TO S.G. 7) 5 2 a) CLAHP-FREE-PIN 2nd MODE, 43.B Hi PORT FLOW VELOCITY ft/s OA 1.40 ft/s b) CLAHP-FREE-PIN 2nd MODE, 43.8 Hz 35 DISTA..vc (in) 4i AMPLITUDE IN FLOW DIRECTION (CORRESPONDING TO S.G. B) 'o 0 \ 2: 2 c) CLAHP-PIN-PIN 1st MODE, 40.4 Hz 35 DISTANCE (in) 70 a. «d) CLAHP-PIN-PIN 2nd HODE, 69.8 Hz 35 DISTANCE (in) e) r 1P-PIN-FREE 3rd HODE, 77.8 Hz. 35 FIGURE 8a,b,c,d,e: VIBRATION MODES: COMPARISON BETWEEN VIBRATING AMPLITUDE MEASURED WITH ACCELEROMETER (1e, AOA) AND AMPLITUDE DEDUCED FROM STRAIN GAUGE MEASUREMENTS ASSUMING VARIOUS MODES (Solid lines).

18 c I n Vilocity iiponini l.i. ( plituih n»" I 3 1,9 FLOW VILOCITT (ft/i) J l_ FLOM ' a) Lower Mode: Filter Bandwidth Hz. b) Higher Mode: Filter Bandwidth Hz. FIGURE 9: EFFECT O. r AVERAGE ENTRANCE PORT FLOW VELOCITY ON TUBE VIBRATION.

19 FIGURE 10: DEDUCED POWER SPECTRAL DENSITY FUNCTION OF THE RANDOM FORCES. CM FIGURE 11: TOTAL RMS VIBRATION RESPONSE TO RANDOM """ EXCITATION vs DISTANCE ALONG TUBE. " \ \ \ 0.10 f m % 40 I 80 FREQUENCY (Hz) 0 EXCITATION 35 C P 70 P 105 DISTANCE (in) 140 P P

20 Additional copies of this document may be obtained irom Scientific Document Distribution Offics Atomic Energy of Canada Limited Chalk River, Ontario, Canada KOJ 1J0 Prica - 50< per copy