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4 FBR model
Nuclear Engineering and Design 240 (2010) 84–91
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Experimental investigation of weir instability in main vessel cooling system of 1/4 FBR model M. Thirumalai ∗ , M. Anandaraj, P. Anup Kumar, V. Prakash, C. Anandbabu, P. Kalyanasundaram, G. Vaidyanathan Fast Reactor Technology Group, Department of Atomic Energy, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu, India
a r t i c l e
i n f o
Article history: Received 29 April 2009 Received in revised form 9 October 2009 Accepted 15 October 2009
a b s t r a c t The 500 MWe Prototype Fast Breeder Reactor (PFBR) is under construction at Kalpakkam, India. The main vessel of this pool type reactor acts as the primary containment in the reactor assembly. In order to keep the main vessel temperature below creep range and to reduce high temperature embrittlement and also to ensure its healthiness for 40 years of reactor life, a small fraction of core flow (0.5 m3 /s) is sent through an annular space formed between the main vessel and a cylindrical baffle (primary thermal baffle) to cool the vessel. The sodium after cooling the main vessel overflows the primary baffle (weir shell) and falls into another concentric pool of sodium separated from the cold pool by the secondary thermal baffle and then returned to cold pool. The weir shell, where the overflow of liquid sodium takes place, is a thin shell prone to flow induced vibrations due to instability caused by sloshing and fluid–structure interaction. A similar vibration phenomenon was first observed during the commissioning of Super-Phenix reactor. In order to understand the phenomenon and provide necessary experimental back up to validate the analytical models, weir instability experiments were conducted in a 1:4 scale stainless steel (SS) model installed in a water loop. The experiments were conducted with flow rate and fall height as the varying parameters. The experimental results showed that the instability of the weir shell was caused due to fluid structure interaction. This paper discusses the details of the model, the modeling laws, similitude criteria adopted, analytical prediction, the experimental results and conclusion. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Prototype Fast Breeder Reactor (PFBR) is liquid metal sodium cooled pool type 500 MWe reactor currently under construction phase at Kalpakkam, India. The PFBR core is surrounded by thin axisymmetrical shells which separate sodium flow volumes and avoid thermal problems (Fig. 1). The shells are concentric thin walled structures (thickness– diameter ratio: t/D ∼ 1/650 and height–diameter ratio: h/d ∼ 1), each separated by thin annulus of liquid sodium (annulus gap–diameter ratio: w/D ∼ 1/100). These geometrical arrangements with interconnected liquid columns may respond to flow fluctuations which leads to vibration during reactor operation. Another special feature is the existence of free fluid surfaces which is the source of sloshing phenomenon. The main vessel of this pool type reactor carries about 2000 tonnes of weight and operates with reactor outlet temperature of 547 ◦ C. In order to keep the main vessel temperature below
∗ Corresponding author. Tel.: +91 044 27480500x22616; fax: +91 044 27480311. E-mail addresses: [email protected] (M. Thirumalai), [email protected] (V. Prakash). 0029-5493/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2009.10.012
creep range (<420 ◦ C) and to reduce high temperature embrittlement and to ensure its healthiness for 40 years of reactor life, a small fraction of core flow (0.5 m3 /s) is sent through an annular space formed between the main vessel and a cylindrical baffle (outer baffle) to cool the vessel. A part of the reactor sodium flow (≈5%) in the grid plate leaks out at the foot of the subassemblies through specially designed labyrinths collected in a chamber below and directed to the annular space indicated above, through 24 circumferentially spaced pipes (Fig. 2). Sodium then overflows the top of the primary thermal baffle (weir shell) and falls into the annular pool of sodium separated from the cold pool by the inner shell. The weir shell, where the overflow of liquid sodium takes place, is a thin shell prone to flow induced vibrations (Jalaldeen et al., 1991) due to liquid sloshing and fluid–structure interaction (FSI). This vibration phenomenon was first observed during the commissioning of French Super-Phenix reactor (Aita et al., 1986), which has a similar main vessel cooling arrangement. Weir instability studies were carried out earlier in house in a 1:16 scale model using aluminum and SS thermal baffles, simulating geometrically the design of PFBR. In the 1:16 scale aluminum baffle model, sloshing driven type of instability was observed (Jason Premnath et al., 1993) whereas in the 1:16 scale SS baffles model, no instability was observed. This could be
M. Thirumalai et al. / Nuclear Engineering and Design 240 (2010) 84–91
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Fig. 1. PFBR weir arrangement.
attributed to stainless steel baffles being quite rigid and this could have prevented the build-up of instability. The same observation was reported by Eguchi et al. (1991) for the same shell thickness, sloshing type of instability was observed when the end condition was changed from bolted support to elastic rubber attachment. Hence it is clear that stiffness of a baffle needs to be simulated properly. Moreover, many experiments were carried out world wide to understand the phenomenon using cylindrical tanks and baffles and only a few literatures are available related to pool type fast reactor by simulating all primary components inside the main vessel. In order to understand the phenomenon and also to provide necessary experimental back up to validate the analytical predictions, experiments were carried out on a 1/4 scale SS model installed in a water test loop. Experiments were conducted over a wide range of flow rates and fall heights to establish the instability chart, thereby to predict the safe operating zone. This paper discusses the details of the model, the modeling laws, similitude criteria adopted, analytical prediction, the experimental results and conclusion.
Fig. 3. Fluid elastic instability.
2. Excitation mechanisms The two important mechanisms identified for instability of the weir cooling system is sloshing and fluid elastic instability. These mechanisms are explained below. 2.1. Sloshing (Type I) Surface wave oscillation will be produced in a liquid filled container/tank when it is excited with an external force. In case of weir systems, the pressure pulsations due to the falling liquid over the free surface could be the source of excitation. When this exciting frequency coincides with system natural frequency, resonance like condition can occur which leads to very large surface liquid motion and vibration of the container. This is governed by the equation ω2 = n
g tan h D
nh D
where n is the constant dependent on mode shape; ω = sloshing natural frequency; h is the height of the tank; D is the characteristic length; (for cylindrical tank ‘D’ is the diameter of the tank). It is reported that, this kind of instability occurs in the system at very low flow rates and fall heights. 2.2. Fluid elastic instability (Type II)
Fig. 2. Weir cooling system.
If the weir shell is disturbed from its equilibrium position, it naturally vibrates with a particular wave number n. For the stable flow configuration, the vibration decays exponentially to zero. On the contrary, the shell vibrates with exponentially increasing amplitudes for the unstable system. If the dynamic fluid forces causing vibration are developed from the shell displacements, then the resulting unstable vibration is termed as fluid elastic instability. The fluid elastic instability which affects the weir shell is mainly due to the sloshing of the liquid free levels that is associated with the feeding and collection plenums. The mechanism is illustrated schematically in Fig. 3. If the kinetic energy imparted by the liquid falling from the weir crest and the free surface of the restitution
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Fig. 5. Weir arrangement in 1/4 model.
Fig. 4. 1/4 Reactor assembly model.
collector (collection plenum) is greater than the energy dissipated due to structural and fluid damping, then any perturbation introduced on the shell will develop to cause instability. In the weir flow configuration this situation arises under some critical combinations of flow rate and fall height. Let us assume that the weir shell (primary thermal baffle) is perturbed, due to the pressure pulsations caused by falling liquid over the free surface, to vibrate with one of the natural frequencies of wave number ‘n’; that is the shell moves radially inward and outward alternatively over the circumference. On those sectors corresponding to the feeding collectors where the shell moves outward the liquid is accelerated in the upward direction due to
the dynamic pressure developed on the outer surface of the weir shell. Hence the free level rises above the mean level, resulting in an increased over flow rate. At the same time, on the alternative sectors the liquid level falls below the mean level resulting in either decreased or no flow condition. If we look at the corresponding situations on the collection plenum, while the weir shell moves outward the free level falls below its mean level and the level rises when the weir moves inward. At any circumferential location, the level differences between the free surfaces of feeding and a collection plenum are the instantaneous fall height. The coolant passing through the feeding collector flows over the weir shell, falls along the weir over a distance ‘H’ called ‘fall height’ and reaches the free surface of the collection plenum after an interval ‘t’ called delay time. The delay time depends upon the over flow rate and associated fall height. Thus the flow rate, fall height and delay time have azimuthal and temporal variations. This is one important aspect responsible for the instability. For the given weir flow configuration, this situation arises under some critical combinations of flow rates and fall heights. It is reported that, this kind of instability will occur at higher flow rates and fall heights.
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3. Model description and modeling laws 3.1. Model description A 1:4 scale and 360◦ sector model of Prototype Fast Breeder Reactor (PFBR) assembly (Fig. 4) has been built for experimental determination of several thermal hydraulic and flow induced vibration phenomena pertaining to primary circuit of PFBR (Padmakumar et al., 2007). The model named SAMRAT, comprises all the primary components of PFBR reactor assembly viz. main vessel (MV), inner vessel (IV), thermal baffles, intermediate heat exchangers (IHXs), decay heat exchangers (DHXs), pumps, control plug (CP), core assembly, etc. and all the geometrical dimensions are reduced by a factor of 4 except the thickness of the thermal baffles. The model has 8 mm thick, 3212 mm ID and 3240 mm height stainless steel shell corresponding to the main vessel of PFBR. A 3.2 mm thick, 3154 mm ID and 1050 mm height stainless steel shell modeling the PFBR primary baffle (weir shell), is welded to the main
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vessel. Another SS shell modeling the PFBR secondary baffle is attached to the primary baffle. Fig. 5 depicts the partial plan view and geometrical details of the weir arrangement in the 1:4 scale model. Fig. 6 shows the flow path in the model for the experimental study. Water from a pump enters the upstream annulus through multiple entry points (24 nos) circumferentially and overflows the primary baffle and falls into the downstream annulus. This 24 entry points circumferentially over a main vessel was designed based on our earlier experiment carried out to confirm the uniformity of the flow over the main vessel and also to eliminate the sloshing and to minimize the gas entrainment problem in the reactor (Arasu et al., 1996). The water flow rate through the annulus is measured using pre-calibrated rotameters installed on individual feeding pipes of all 24 inlets. Water returns to the cold pool through multiple exit holes provided at the bottom of the secondary baffle. Model is isolated from pump and structure vibrations through the use of flexible rubber bellows and resilient mountings.
Fig. 6. Weir cooling flow path in model.
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M. Thirumalai et al. / Nuclear Engineering and Design 240 (2010) 84–91 Table 1 Free vibration analysis result.
3.2. Modeling laws In the vibration phenomenon under study, since there is a fluid flow with a moving free surface and vibration of a structure in a coupled mode, the forces that are dominant are gravity force, shell elastic force, fluid inertial force and the viscous force. Therefore Cauchy number (elastic/inertia), Froude number (inertia/gravity), frequency ratio and Reynolds number (inertia/viscous) need to be simulated if the results from the model are to be transposed to the reactor. Cauchy number, since the vibration is of bending mode, can be written as Cauchy number =
Et 3
Mode, n
Sloshing frequencies (Hz)
Weir structure natural frequencies (Hz)
1 2 3 4 5 6 7 8 9 10 11
0.283 0.504 0.626 0.732 0.848 0.942 1.024 1.101 1.173 1.242 1.305
6.966 3.021 2.035 2.212 3.045 3.941 4.473 5.141 5.622 6.524 6.973
L5 ω2 (1 − 2 )
ω2 L The Froude number = g where is the Poisson ratio; E is the Young’s modulus; t is the thickness of the vibrating member; L is the characteristic length; (diameter or height of weir shell); ω is the frequency of sloshing of the fluid; is the fluid density; g is the acceleration due to gravity. In the 1:4 scale model, the Cauchy and Froude number could be simulated by proper selection of material, baffle thickness and water as the test fluid. For simulation of Cauchy and Froude numbers, the thickness of the baffle for this model is selected as 3.2 mm, and nominal flow rate for the model is 52 m3 /h. Reynolds number (Re) is invariably distorted in small scale models; but it is not expected to have much influence on the results, because both the model and the prototype are in turbulent regime. Re for the prototype is 7.1 × 104 and for the model is 0.64 × 104 . Though dynamic similarity is maintained between the 1:4 scale model and the prototype, the structural natural frequencies are not scaled properly and hence the model results are not directly transposable to the reactor. The model results however, provide an insight into the
phenomenon and data for validating analytical prediction, thereby to predict analytically the instability regime of operation for the Prototype Fast Breeder Reactor. 4. Analytical prediction The free vibration analysis of main vessel weir shell system was carried out using INCA code (CASTEM-INCA, 1985). From the analysis the following sloshing frequencies and weir structure natural frequencies are obtained and tabulated in Table 1. 5. Instrument schematic and measurement setup For this experiment 34 number of strain gages were installed at various locations on the weir shell surface to measure circumferential and longitudinal strains (Fig. 7). Apart from this an accelerometer was also mounted on the weir shell for monitoring higher order frequency spectra and vibration. The strain gage output after filtering and conditioning was fed to a 256-channel PC based data acquisition system (DAS) in control room for monitoring
Fig. 7. Position of sensors. Note: All the sensors are mounted on the weir shell surface and all dimensions shown are sensor positions down from the weir shell top.
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Fig. 8. Instrumentation schematic.
the real-time signal. Simultaneously, the signals were connected to the 16-channel FFT analyser running PULSE Labshop 4.1 software for obtaining spectra of the signals. Parallelly, the signals were fed to a 2-channel FFT analyser for extracting probability density function (PDF) plots. During the instability build up, the filtered signals were fed to a digital oscilloscope for observing the real-time plots. The instrument schematic employed for the studies is as shown in Fig. 8. The water flow rate through the annulus is measured using precalibrated rotameters installed on individual feeding pipes. The fall height measurement was done using pressure transmitters connected to the bottom part of the annulus between the thermal baffles. Apart from this, manual measurements were also done to determine the fall height for each flow condition. 6. Results and discussion The experimental study was carried out for flows starting from 13 to 66 m3 /h, which corresponds to a range of 25–127% of nominal flow. For a particular flow, the fall height was varied from 0 to 40 cm in steps of 1 mm. At each fall height, sufficient time was allowed to see whether there was any build up of vibration in the primary baffle. Instability confirmed to have set in if there was a steady increase in the primary baffle vibration amplitude. For each flow, primary baffle vibrations were measured with strain gauges, mounted in circumferential and longitudinal directions and an accelerometer mounted at the top of the primary baffle. The data was acquired in real-time and analyzed in frequency and amplitude domains employing multi-channel analyzer. For each flow, the strain gauge and accelerometer readings were monitored. It was observed that the baffle system became unstable as the fall height approached 133 mm for flow rate of 30 m3 /h. Below 30 m3 /h the instability phenomenon is not observed for any fall height in the model. For higher flow rates (more than 30 m3 /h) the instability was observed at higher fall heights. Fig. 9a and b shows typical real-time plots of a strain gauge for nominal flow condition during stable and unstable operation of the weir system, respectively. From the spectrum in Fig. 10a and b, it can be inferred that, compared to random vibration signature during stable operation, a single predominant frequency with much higher amplitude of vibration was observed during instability. This single frequency resonance type of vibration could be observed in time signal also. Fig. 11a and b shows the variation in the PDF plot during stable and unstable operation conditions. This plot clearly explains the change over from random excitation during normal operation to a predominant sinusoidal one during instability. Spectra recorded during stable and unstable operation using strain gauges
Fig. 9. (a) Time signal: stable operation. (b) Time signal: unstable operation.
clearly indicate an increase in amplitude level of more than 30 times compared to stable condition. The presence of 4.41 Hz, as the predominant mode of frequency, which is very close to the analytically predicted value of 4.47 Hz, corresponding to one of the structural natural frequencies for the 1:4 scale model of PFBR. As per the analytical prediction, among many vibration modes of the shell, the vibration mode which has the lowest natural frequency corresponds to a circumferential mode wave number (n) lying in
Fig. 10. (a) Spectra: stable condition. (b) Spectra: unstable condition.
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Fig. 13. Instability spectra at 30 m3 /h flow.
Fig. 11. (a) PDF plot: stable condition. (b) PDF plot: unstable condition.
the range of 4–10 was expected. The observed frequency of 4.41 Hz corresponds to the circumferential mode wave number 7. This also confirms that the instability mechanism involved in the model is fluid–structure interaction. Analytical study also predicted a sloshing type of instability in the frequency range of 0.28–1.3 Hz (Table 1), which was however not observed in the experiment. Due to the system property of higher damping and higher stiffness due to real end condition, this particular mode might have been suppressed (4). Fig. 12 shows the time plot during instability build-up at the observed resonance frequency of 4.41 Hz, for nominal flow of 52 m3 /h at a fall height of 178 mm. This instability plot (time vs strain) shows the increase in strain level of more than 30 times compared to stable operation, which clearly demonstrates the consequences of unstable operation of the system (Aita and Gibert, 1986). It is observed that, during instability the flow over the weir was not continuous but it was interrupted type of flow and the liquid was splashing with sound above the top of the weir from the feeding and collection plenum due to the violent vibration of the thermal baffle. The frequency spectra observed for other two flows (30 and
Fig. 12. Instability buildup.
Fig. 14. Instability spectra at 66 m3 /h flow.
66 m3 /h) are given in Figs. 13 and 14. The small variation in the observed resonance frequency for different flow rates was due to the variation of added mass in the collection plenum and also due to the nature of the static liquid column acting on the weir because of the liquid level variation in the feeding and collection plenum. Based on the results obtained from the experimental investigation, the instability chart for 1:4 scale model of PFBR has been derived and is shown in Fig. 15. Damping coefficient for the SS baffles of this model estimated from the strain gauge spectra using half power method is 5% during instability. This confirms the conservativeness of damping value of
Fig. 15. Instability chart for 1/4 model.
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3. After the onset of instability, flow over the weir was intermittent and non-uniform. Water was splashing with sound above the top of the weir. Vibration of the weir shell increased much compared to stable weir operation. Also, the secondary thermal baffle and inner vessel were found vibrating with relatively large amplitudes. 4. An instability chart was established for 1/4 model of PFBR based on the experimental results. 5. Based on the experimental results, the analytical code was validated and the instability chart for PFBR weir cooling system for its selected range of flow and fall heights were analytically predicted and the weir system is found to be stable during its entire range of operation. Acknowledgement
Fig. 16. Instability chart for PFBR (analytical).
3–4% assumed during our analytical prediction. Based on the experimental results, the analytical code was validated and the instability chart for PFBR weir cooling system for its selected range of flow and fall heights were analytically predicted (Fig. 16) and the weir system is found to be stable during its entire range of operation. 7. Conclusion Experiment on 1:4 scale model with stainless steel baffles was conducted to study weir instability phenomenon. The following conclusions were arrived: 1. Fluid–structure interaction type of instability was observed. The observed frequency is very close to analytically predicted frequency of 4.47 Hz, for fluid–structure interaction phenomenon for the 1/4 scale model of PFBR. This predominant frequency of vibration observed in experiment, i.e. 4.41 Hz, which is one of the structural natural frequencies, confirms that the instability mechanism involved in the model is due to fluid–structure interaction. 2. This experiment has provided insight into the weir instability phenomenon and its governing aspects.
Authors are thankful to Shri. S.Jalaldeen, Head, Structural Mechanics Section of IGCAR for carrying out the analytical prediction and instability chart for this model. References Aita, S., Gibert, R.J., 1986. Fluid elastic instability in a flexible weir. In: Flow Induced Vibration, PVP, vol. 104. Aita, S., Tigeot, Y., Saclay, C.E.N., Bertaut, C., Serpantie, J.P., 1986. Fluid elastic instability analysis of a flexible weir: experimental observations. In: ASME PVP 1986 Conference, vol. 104, pp. 41–49. Arasu, K., Vaidyanathan, G., Kale, R.D., 1996. Gas entrainment studies on main vessel cooling model of PFBR. In: Proceedings of the 23rd National Conference on Fluid Mechanics and Fluid Power, Bhopal, India. CASTEM-INCA, 1985. A 2D Finite Element Code for Structural Analysis. CEN/DMT, Saclay, France. Eguchi, Y., Tanaka, N., et al., 1991. Flow induced vibration coupled with a thin cylindrical shell and coaxial annulus fluid”. In: Paper E12/4, SMiRT 11 Conference Proceedings, pp. 359–364. Jalaldeen, S., Balasubramanian, V., Chellapandi, P., Bhoje, S.B., 1991. Fluid-elastic instability analysis for PFBR main vessel cooling circuit. In: SMiRT 11, vol. E12/3, pp. 353–358. Jason Premnath, S.M., Thirumalai, M., Prabhakar, R., Kale, R.D., 1993. Experimental study of flow induced vibration of thermal baffles of PFBR. In: Paper E 10/4, SMiRT 12 Conference Proceedings, pp. 315–319. Padmakumar, G., Prakash, V., Banerjee, I., Thirumalai, M., Anandbabu, C., Prabhakar, R., Vaidyanathan, G., 2007. Comprehensive scale model for LMFBR reactor assembly thermal hydraulics. International Journal of Nuclear Energy Science and Technology 3 (November (4)), 325–344.
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Experimental investigation of weir instability in main vessel cooling system of 1/4 FBR model M. Thirumalai ∗ , M. Anandaraj, P. Anup Kumar, V. Prakash, C. Anandbabu, P. Kalyanasundaram, G. Vaidyanathan Fast Reactor Technology Group, Department of Atomic Energy, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu, India
a r t i c l e
i n f o
Article history: Received 29 April 2009 Received in revised form 9 October 2009 Accepted 15 October 2009
a b s t r a c t The 500 MWe Prototype Fast Breeder Reactor (PFBR) is under construction at Kalpakkam, India. The main vessel of this pool type reactor acts as the primary containment in the reactor assembly. In order to keep the main vessel temperature below creep range and to reduce high temperature embrittlement and also to ensure its healthiness for 40 years of reactor life, a small fraction of core flow (0.5 m3 /s) is sent through an annular space formed between the main vessel and a cylindrical baffle (primary thermal baffle) to cool the vessel. The sodium after cooling the main vessel overflows the primary baffle (weir shell) and falls into another concentric pool of sodium separated from the cold pool by the secondary thermal baffle and then returned to cold pool. The weir shell, where the overflow of liquid sodium takes place, is a thin shell prone to flow induced vibrations due to instability caused by sloshing and fluid–structure interaction. A similar vibration phenomenon was first observed during the commissioning of Super-Phenix reactor. In order to understand the phenomenon and provide necessary experimental back up to validate the analytical models, weir instability experiments were conducted in a 1:4 scale stainless steel (SS) model installed in a water loop. The experiments were conducted with flow rate and fall height as the varying parameters. The experimental results showed that the instability of the weir shell was caused due to fluid structure interaction. This paper discusses the details of the model, the modeling laws, similitude criteria adopted, analytical prediction, the experimental results and conclusion. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Prototype Fast Breeder Reactor (PFBR) is liquid metal sodium cooled pool type 500 MWe reactor currently under construction phase at Kalpakkam, India. The PFBR core is surrounded by thin axisymmetrical shells which separate sodium flow volumes and avoid thermal problems (Fig. 1). The shells are concentric thin walled structures (thickness– diameter ratio: t/D ∼ 1/650 and height–diameter ratio: h/d ∼ 1), each separated by thin annulus of liquid sodium (annulus gap–diameter ratio: w/D ∼ 1/100). These geometrical arrangements with interconnected liquid columns may respond to flow fluctuations which leads to vibration during reactor operation. Another special feature is the existence of free fluid surfaces which is the source of sloshing phenomenon. The main vessel of this pool type reactor carries about 2000 tonnes of weight and operates with reactor outlet temperature of 547 ◦ C. In order to keep the main vessel temperature below
∗ Corresponding author. Tel.: +91 044 27480500x22616; fax: +91 044 27480311. E-mail addresses: [email protected] (M. Thirumalai), [email protected] (V. Prakash). 0029-5493/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2009.10.012
creep range (<420 ◦ C) and to reduce high temperature embrittlement and to ensure its healthiness for 40 years of reactor life, a small fraction of core flow (0.5 m3 /s) is sent through an annular space formed between the main vessel and a cylindrical baffle (outer baffle) to cool the vessel. A part of the reactor sodium flow (≈5%) in the grid plate leaks out at the foot of the subassemblies through specially designed labyrinths collected in a chamber below and directed to the annular space indicated above, through 24 circumferentially spaced pipes (Fig. 2). Sodium then overflows the top of the primary thermal baffle (weir shell) and falls into the annular pool of sodium separated from the cold pool by the inner shell. The weir shell, where the overflow of liquid sodium takes place, is a thin shell prone to flow induced vibrations (Jalaldeen et al., 1991) due to liquid sloshing and fluid–structure interaction (FSI). This vibration phenomenon was first observed during the commissioning of French Super-Phenix reactor (Aita et al., 1986), which has a similar main vessel cooling arrangement. Weir instability studies were carried out earlier in house in a 1:16 scale model using aluminum and SS thermal baffles, simulating geometrically the design of PFBR. In the 1:16 scale aluminum baffle model, sloshing driven type of instability was observed (Jason Premnath et al., 1993) whereas in the 1:16 scale SS baffles model, no instability was observed. This could be
M. Thirumalai et al. / Nuclear Engineering and Design 240 (2010) 84–91
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Fig. 1. PFBR weir arrangement.
attributed to stainless steel baffles being quite rigid and this could have prevented the build-up of instability. The same observation was reported by Eguchi et al. (1991) for the same shell thickness, sloshing type of instability was observed when the end condition was changed from bolted support to elastic rubber attachment. Hence it is clear that stiffness of a baffle needs to be simulated properly. Moreover, many experiments were carried out world wide to understand the phenomenon using cylindrical tanks and baffles and only a few literatures are available related to pool type fast reactor by simulating all primary components inside the main vessel. In order to understand the phenomenon and also to provide necessary experimental back up to validate the analytical predictions, experiments were carried out on a 1/4 scale SS model installed in a water test loop. Experiments were conducted over a wide range of flow rates and fall heights to establish the instability chart, thereby to predict the safe operating zone. This paper discusses the details of the model, the modeling laws, similitude criteria adopted, analytical prediction, the experimental results and conclusion.
Fig. 3. Fluid elastic instability.
2. Excitation mechanisms The two important mechanisms identified for instability of the weir cooling system is sloshing and fluid elastic instability. These mechanisms are explained below. 2.1. Sloshing (Type I) Surface wave oscillation will be produced in a liquid filled container/tank when it is excited with an external force. In case of weir systems, the pressure pulsations due to the falling liquid over the free surface could be the source of excitation. When this exciting frequency coincides with system natural frequency, resonance like condition can occur which leads to very large surface liquid motion and vibration of the container. This is governed by the equation ω2 = n
g tan h D
nh D
where n is the constant dependent on mode shape; ω = sloshing natural frequency; h is the height of the tank; D is the characteristic length; (for cylindrical tank ‘D’ is the diameter of the tank). It is reported that, this kind of instability occurs in the system at very low flow rates and fall heights. 2.2. Fluid elastic instability (Type II)
Fig. 2. Weir cooling system.
If the weir shell is disturbed from its equilibrium position, it naturally vibrates with a particular wave number n. For the stable flow configuration, the vibration decays exponentially to zero. On the contrary, the shell vibrates with exponentially increasing amplitudes for the unstable system. If the dynamic fluid forces causing vibration are developed from the shell displacements, then the resulting unstable vibration is termed as fluid elastic instability. The fluid elastic instability which affects the weir shell is mainly due to the sloshing of the liquid free levels that is associated with the feeding and collection plenums. The mechanism is illustrated schematically in Fig. 3. If the kinetic energy imparted by the liquid falling from the weir crest and the free surface of the restitution
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Fig. 5. Weir arrangement in 1/4 model.
Fig. 4. 1/4 Reactor assembly model.
collector (collection plenum) is greater than the energy dissipated due to structural and fluid damping, then any perturbation introduced on the shell will develop to cause instability. In the weir flow configuration this situation arises under some critical combinations of flow rate and fall height. Let us assume that the weir shell (primary thermal baffle) is perturbed, due to the pressure pulsations caused by falling liquid over the free surface, to vibrate with one of the natural frequencies of wave number ‘n’; that is the shell moves radially inward and outward alternatively over the circumference. On those sectors corresponding to the feeding collectors where the shell moves outward the liquid is accelerated in the upward direction due to
the dynamic pressure developed on the outer surface of the weir shell. Hence the free level rises above the mean level, resulting in an increased over flow rate. At the same time, on the alternative sectors the liquid level falls below the mean level resulting in either decreased or no flow condition. If we look at the corresponding situations on the collection plenum, while the weir shell moves outward the free level falls below its mean level and the level rises when the weir moves inward. At any circumferential location, the level differences between the free surfaces of feeding and a collection plenum are the instantaneous fall height. The coolant passing through the feeding collector flows over the weir shell, falls along the weir over a distance ‘H’ called ‘fall height’ and reaches the free surface of the collection plenum after an interval ‘t’ called delay time. The delay time depends upon the over flow rate and associated fall height. Thus the flow rate, fall height and delay time have azimuthal and temporal variations. This is one important aspect responsible for the instability. For the given weir flow configuration, this situation arises under some critical combinations of flow rates and fall heights. It is reported that, this kind of instability will occur at higher flow rates and fall heights.
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3. Model description and modeling laws 3.1. Model description A 1:4 scale and 360◦ sector model of Prototype Fast Breeder Reactor (PFBR) assembly (Fig. 4) has been built for experimental determination of several thermal hydraulic and flow induced vibration phenomena pertaining to primary circuit of PFBR (Padmakumar et al., 2007). The model named SAMRAT, comprises all the primary components of PFBR reactor assembly viz. main vessel (MV), inner vessel (IV), thermal baffles, intermediate heat exchangers (IHXs), decay heat exchangers (DHXs), pumps, control plug (CP), core assembly, etc. and all the geometrical dimensions are reduced by a factor of 4 except the thickness of the thermal baffles. The model has 8 mm thick, 3212 mm ID and 3240 mm height stainless steel shell corresponding to the main vessel of PFBR. A 3.2 mm thick, 3154 mm ID and 1050 mm height stainless steel shell modeling the PFBR primary baffle (weir shell), is welded to the main
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vessel. Another SS shell modeling the PFBR secondary baffle is attached to the primary baffle. Fig. 5 depicts the partial plan view and geometrical details of the weir arrangement in the 1:4 scale model. Fig. 6 shows the flow path in the model for the experimental study. Water from a pump enters the upstream annulus through multiple entry points (24 nos) circumferentially and overflows the primary baffle and falls into the downstream annulus. This 24 entry points circumferentially over a main vessel was designed based on our earlier experiment carried out to confirm the uniformity of the flow over the main vessel and also to eliminate the sloshing and to minimize the gas entrainment problem in the reactor (Arasu et al., 1996). The water flow rate through the annulus is measured using pre-calibrated rotameters installed on individual feeding pipes of all 24 inlets. Water returns to the cold pool through multiple exit holes provided at the bottom of the secondary baffle. Model is isolated from pump and structure vibrations through the use of flexible rubber bellows and resilient mountings.
Fig. 6. Weir cooling flow path in model.
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M. Thirumalai et al. / Nuclear Engineering and Design 240 (2010) 84–91 Table 1 Free vibration analysis result.
3.2. Modeling laws In the vibration phenomenon under study, since there is a fluid flow with a moving free surface and vibration of a structure in a coupled mode, the forces that are dominant are gravity force, shell elastic force, fluid inertial force and the viscous force. Therefore Cauchy number (elastic/inertia), Froude number (inertia/gravity), frequency ratio and Reynolds number (inertia/viscous) need to be simulated if the results from the model are to be transposed to the reactor. Cauchy number, since the vibration is of bending mode, can be written as Cauchy number =
Et 3
Mode, n
Sloshing frequencies (Hz)
Weir structure natural frequencies (Hz)
1 2 3 4 5 6 7 8 9 10 11
0.283 0.504 0.626 0.732 0.848 0.942 1.024 1.101 1.173 1.242 1.305
6.966 3.021 2.035 2.212 3.045 3.941 4.473 5.141 5.622 6.524 6.973
L5 ω2 (1 − 2 )
ω2 L The Froude number = g where is the Poisson ratio; E is the Young’s modulus; t is the thickness of the vibrating member; L is the characteristic length; (diameter or height of weir shell); ω is the frequency of sloshing of the fluid; is the fluid density; g is the acceleration due to gravity. In the 1:4 scale model, the Cauchy and Froude number could be simulated by proper selection of material, baffle thickness and water as the test fluid. For simulation of Cauchy and Froude numbers, the thickness of the baffle for this model is selected as 3.2 mm, and nominal flow rate for the model is 52 m3 /h. Reynolds number (Re) is invariably distorted in small scale models; but it is not expected to have much influence on the results, because both the model and the prototype are in turbulent regime. Re for the prototype is 7.1 × 104 and for the model is 0.64 × 104 . Though dynamic similarity is maintained between the 1:4 scale model and the prototype, the structural natural frequencies are not scaled properly and hence the model results are not directly transposable to the reactor. The model results however, provide an insight into the
phenomenon and data for validating analytical prediction, thereby to predict analytically the instability regime of operation for the Prototype Fast Breeder Reactor. 4. Analytical prediction The free vibration analysis of main vessel weir shell system was carried out using INCA code (CASTEM-INCA, 1985). From the analysis the following sloshing frequencies and weir structure natural frequencies are obtained and tabulated in Table 1. 5. Instrument schematic and measurement setup For this experiment 34 number of strain gages were installed at various locations on the weir shell surface to measure circumferential and longitudinal strains (Fig. 7). Apart from this an accelerometer was also mounted on the weir shell for monitoring higher order frequency spectra and vibration. The strain gage output after filtering and conditioning was fed to a 256-channel PC based data acquisition system (DAS) in control room for monitoring
Fig. 7. Position of sensors. Note: All the sensors are mounted on the weir shell surface and all dimensions shown are sensor positions down from the weir shell top.
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Fig. 8. Instrumentation schematic.
the real-time signal. Simultaneously, the signals were connected to the 16-channel FFT analyser running PULSE Labshop 4.1 software for obtaining spectra of the signals. Parallelly, the signals were fed to a 2-channel FFT analyser for extracting probability density function (PDF) plots. During the instability build up, the filtered signals were fed to a digital oscilloscope for observing the real-time plots. The instrument schematic employed for the studies is as shown in Fig. 8. The water flow rate through the annulus is measured using precalibrated rotameters installed on individual feeding pipes. The fall height measurement was done using pressure transmitters connected to the bottom part of the annulus between the thermal baffles. Apart from this, manual measurements were also done to determine the fall height for each flow condition. 6. Results and discussion The experimental study was carried out for flows starting from 13 to 66 m3 /h, which corresponds to a range of 25–127% of nominal flow. For a particular flow, the fall height was varied from 0 to 40 cm in steps of 1 mm. At each fall height, sufficient time was allowed to see whether there was any build up of vibration in the primary baffle. Instability confirmed to have set in if there was a steady increase in the primary baffle vibration amplitude. For each flow, primary baffle vibrations were measured with strain gauges, mounted in circumferential and longitudinal directions and an accelerometer mounted at the top of the primary baffle. The data was acquired in real-time and analyzed in frequency and amplitude domains employing multi-channel analyzer. For each flow, the strain gauge and accelerometer readings were monitored. It was observed that the baffle system became unstable as the fall height approached 133 mm for flow rate of 30 m3 /h. Below 30 m3 /h the instability phenomenon is not observed for any fall height in the model. For higher flow rates (more than 30 m3 /h) the instability was observed at higher fall heights. Fig. 9a and b shows typical real-time plots of a strain gauge for nominal flow condition during stable and unstable operation of the weir system, respectively. From the spectrum in Fig. 10a and b, it can be inferred that, compared to random vibration signature during stable operation, a single predominant frequency with much higher amplitude of vibration was observed during instability. This single frequency resonance type of vibration could be observed in time signal also. Fig. 11a and b shows the variation in the PDF plot during stable and unstable operation conditions. This plot clearly explains the change over from random excitation during normal operation to a predominant sinusoidal one during instability. Spectra recorded during stable and unstable operation using strain gauges
Fig. 9. (a) Time signal: stable operation. (b) Time signal: unstable operation.
clearly indicate an increase in amplitude level of more than 30 times compared to stable condition. The presence of 4.41 Hz, as the predominant mode of frequency, which is very close to the analytically predicted value of 4.47 Hz, corresponding to one of the structural natural frequencies for the 1:4 scale model of PFBR. As per the analytical prediction, among many vibration modes of the shell, the vibration mode which has the lowest natural frequency corresponds to a circumferential mode wave number (n) lying in
Fig. 10. (a) Spectra: stable condition. (b) Spectra: unstable condition.
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Fig. 13. Instability spectra at 30 m3 /h flow.
Fig. 11. (a) PDF plot: stable condition. (b) PDF plot: unstable condition.
the range of 4–10 was expected. The observed frequency of 4.41 Hz corresponds to the circumferential mode wave number 7. This also confirms that the instability mechanism involved in the model is fluid–structure interaction. Analytical study also predicted a sloshing type of instability in the frequency range of 0.28–1.3 Hz (Table 1), which was however not observed in the experiment. Due to the system property of higher damping and higher stiffness due to real end condition, this particular mode might have been suppressed (4). Fig. 12 shows the time plot during instability build-up at the observed resonance frequency of 4.41 Hz, for nominal flow of 52 m3 /h at a fall height of 178 mm. This instability plot (time vs strain) shows the increase in strain level of more than 30 times compared to stable operation, which clearly demonstrates the consequences of unstable operation of the system (Aita and Gibert, 1986). It is observed that, during instability the flow over the weir was not continuous but it was interrupted type of flow and the liquid was splashing with sound above the top of the weir from the feeding and collection plenum due to the violent vibration of the thermal baffle. The frequency spectra observed for other two flows (30 and
Fig. 12. Instability buildup.
Fig. 14. Instability spectra at 66 m3 /h flow.
66 m3 /h) are given in Figs. 13 and 14. The small variation in the observed resonance frequency for different flow rates was due to the variation of added mass in the collection plenum and also due to the nature of the static liquid column acting on the weir because of the liquid level variation in the feeding and collection plenum. Based on the results obtained from the experimental investigation, the instability chart for 1:4 scale model of PFBR has been derived and is shown in Fig. 15. Damping coefficient for the SS baffles of this model estimated from the strain gauge spectra using half power method is 5% during instability. This confirms the conservativeness of damping value of
Fig. 15. Instability chart for 1/4 model.
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3. After the onset of instability, flow over the weir was intermittent and non-uniform. Water was splashing with sound above the top of the weir. Vibration of the weir shell increased much compared to stable weir operation. Also, the secondary thermal baffle and inner vessel were found vibrating with relatively large amplitudes. 4. An instability chart was established for 1/4 model of PFBR based on the experimental results. 5. Based on the experimental results, the analytical code was validated and the instability chart for PFBR weir cooling system for its selected range of flow and fall heights were analytically predicted and the weir system is found to be stable during its entire range of operation. Acknowledgement
Fig. 16. Instability chart for PFBR (analytical).
3–4% assumed during our analytical prediction. Based on the experimental results, the analytical code was validated and the instability chart for PFBR weir cooling system for its selected range of flow and fall heights were analytically predicted (Fig. 16) and the weir system is found to be stable during its entire range of operation. 7. Conclusion Experiment on 1:4 scale model with stainless steel baffles was conducted to study weir instability phenomenon. The following conclusions were arrived: 1. Fluid–structure interaction type of instability was observed. The observed frequency is very close to analytically predicted frequency of 4.47 Hz, for fluid–structure interaction phenomenon for the 1/4 scale model of PFBR. This predominant frequency of vibration observed in experiment, i.e. 4.41 Hz, which is one of the structural natural frequencies, confirms that the instability mechanism involved in the model is due to fluid–structure interaction. 2. This experiment has provided insight into the weir instability phenomenon and its governing aspects.
Authors are thankful to Shri. S.Jalaldeen, Head, Structural Mechanics Section of IGCAR for carrying out the analytical prediction and instability chart for this model. References Aita, S., Gibert, R.J., 1986. Fluid elastic instability in a flexible weir. In: Flow Induced Vibration, PVP, vol. 104. Aita, S., Tigeot, Y., Saclay, C.E.N., Bertaut, C., Serpantie, J.P., 1986. Fluid elastic instability analysis of a flexible weir: experimental observations. In: ASME PVP 1986 Conference, vol. 104, pp. 41–49. Arasu, K., Vaidyanathan, G., Kale, R.D., 1996. Gas entrainment studies on main vessel cooling model of PFBR. In: Proceedings of the 23rd National Conference on Fluid Mechanics and Fluid Power, Bhopal, India. CASTEM-INCA, 1985. A 2D Finite Element Code for Structural Analysis. CEN/DMT, Saclay, France. Eguchi, Y., Tanaka, N., et al., 1991. Flow induced vibration coupled with a thin cylindrical shell and coaxial annulus fluid”. In: Paper E12/4, SMiRT 11 Conference Proceedings, pp. 359–364. Jalaldeen, S., Balasubramanian, V., Chellapandi, P., Bhoje, S.B., 1991. Fluid-elastic instability analysis for PFBR main vessel cooling circuit. In: SMiRT 11, vol. E12/3, pp. 353–358. Jason Premnath, S.M., Thirumalai, M., Prabhakar, R., Kale, R.D., 1993. Experimental study of flow induced vibration of thermal baffles of PFBR. In: Paper E 10/4, SMiRT 12 Conference Proceedings, pp. 315–319. Padmakumar, G., Prakash, V., Banerjee, I., Thirumalai, M., Anandbabu, C., Prabhakar, R., Vaidyanathan, G., 2007. Comprehensive scale model for LMFBR reactor assembly thermal hydraulics. International Journal of Nuclear Energy Science and Technology 3 (November (4)), 325–344.