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Dynamic qualification of complex structural components of nuclear power plants
Nuclear Engineering and Design 180 (1998) 147 – 154
Dynamic qualification of complex structural components of nuclear power plants R.I.K. Moorthy *, Jyoti K. Sinha Vibration Laboratory, Reactor engineering di6ision, Bhabha Atomic Research Centre, Mumbai 400 085, India Received 9 December 1996; received in revised form 5 August 1997; accepted 10 November 1997
Abstract The safety requirements and the lack of accessibility for any future repair, impose the design requirement that the integrity of reactor components of nuclear power plants be assured for the lifetime of the plant. To meet this design requirement it is essential to qualify the component, i.e. prove its capability to perform the design function for the design life. In performing its design function, the component is subjected to both static and dynamic loads. The qualification for static loads is rather simple and reliable, but qualification for dynamic loads is complex and often uncertain. This is because analytical tools are often inadequate for a realistic dynamic qualification and exact structurally simulated experimental models are almost always difficult to build. In such a situation, methods using tests on simple experimental set-ups supplemented by conservative analytical back-ups must be evolved. This paper highlights the intricacies involved in the conservative dynamic qualification of the complex components by considering the example of the moderator sparger tube. This component is a perforated tube submerged in water and excited by flow. For such a case, a completely analytical or a totally experimental qualification is not possible. This paper describes a procedure by which the required dynamic characteristics such as added mass, damping and fluid forces are generated from simple experiments and the component is qualified by analysis using these data. © 1998 Elsevier Science S.A. All rights reserved.
1. Introduction The structural components of a nuclear power reactor are subjected to both static and dynamic loads during its operation. Since the safety of a nuclear reactor is of utmost importance, it is essential to ensure, by design, the integrity of the components over the entire life of the reactor. Furthermore, the inaccessibility of these struc* Corresponding author. Tel.: + 91 22 5563060; fax: + 91 22 5560750; e-mail: [email protected]
tures for any repair at a future date makes it imperative to qualify the components. That is, each component is required to be proven to be capable of performing the design function for the design life of the plant. Such a qualification for static loads is rather simple and reliable, but the qualification for dynamic loads is complex and often uncertain. The dynamic qualifications for seismic loads are well defined (IAEA-50-SG-D15, 1992) and are usually applied to qualify the structural components. However, the procedures for the qualification of structural components for the
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R.I.K. Moorthy, J.K. Sinha / Nuclear Engineering and Design 180 (1998) 147–154
Fig. 1. Schematic view of moderator sparger tube.
service load conditions, though important, are not so well defined. In this paper, the authors highlight the intricacies involved in the conservative dynamic qualification of complex components. This is achieved using, as an example, the moderator sparger tube (a perforated tube submerged in water and excited by flow) proposed for use in some of the pressure tube type pressurized heavy water reactors. The feasibility of a purely analytical method of qualification for the component is investigated and the possibility of a totally experimental means of qualification is reviewed. Based on the limitations of both methods, a combination of tests and analysis was arrived at by which the component could be qualified conservatively.
2.1. The choice of example This particular component has been chosen as it appears deceptively simple. Functionally this could be considered as a pipe conveying fluid. In this case, the standard guidelines (ASME, O&M1990) could be used for qualification. However, features such as the perforations all over the length, excitation due to water flowing out through the perforations and the component being submerged in water, make the dynamic qualification very complicated. Therefore, this component which seems simple by design could reveal the intricacies involved in the dynamic qualification and has been chosen as the typical example.
2. Typical details of the moderator sparger tube The moderator sparger tube is designed to carry and distribute the moderator inside the reactor vessel (calandria). To achieve uniform distribution along the length, perforations of different sizes and pitch are made on the tube as shown in Fig. 1. There are three such sparger tubes suitably spaced in the cross-section of the reactor to ensure uniform volumetric distribution of the moderator. For usage in a nuclear context, the construction material selected for the sparger tube is zircaloy-2. The ends of the tube are rolled into the tube sheets of the calandria, effectively realizing a fixed–fixed end condition. The stainless extensions beyond the calandria carry the moderator to the sparger tube for distribution inside the vessel. During normal operation, the calandria is filled with moderator, i.e. the sparger tube is filled with and surrounded by, the moderator.
3. Feasible qualification methods and their applicability for the example chosen The components could be qualified either totally by analytical means, or by experiment. For a component to be qualified exclusively by analysis, it must be possible to reliably model the dynamics of the structure. In many cases this could be difficult; even with a good model of the structure, the damping could be uncertain and must be decided conservatively. In addition to the dynamic characteristics of the structure, the excitation during its operation needs to be defined completely, which is often difficult for reactor components. For the specific example under consideration, a purely analytical method of qualification is not possible, due to: 1. Uncertainty in the dynamic characteristics of the structure such as
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149
Fig. 2. Schematic representation of mock-up test facility.
1.1. Added hydro-dynamic mass of a perforated tube in water. 1.2. Damping for the perforated tube—both structural and fluid induced. 2. Absence of any analytical definition of excitation for perforated tubes distributing water over its length. Therefore, as in the case of the sparger tube, an experimental approach must often be resorted to. For experimental qualification, it would be ideal to carry out the same on the actual reactor as all the design features are fully incorporated, along with any constructional deviations. However, this is obviously not possible at the design stage and at best could be used only for re-confirmation later. A structurally simulated mock-up is therefore required to highlight the dynamic characteristics adequately. In addition, for estimating the operational excitation characteristics, the mock-up must also include, as in the example chosen, flow considerations. However, an experimental set-up of the component simulating the actual conditions expected in service is often difficult to build. Considering our example of the sparger tube, it is necessary to model both structural and fluid dynamic effects, as well as the coupling between them. With the difficulties associated with scaling, a full scale mock-up may become the only reliable option.
Even with a full scale mock-up, exact structural simulation is not practicable, since the support stiffness provided by the tube sheet at either end is over 8000 times the bending stiffness of the tube and is too large to be achieved in a laboratory model. Therefore, it is essential to make a critical assessment and arrive at the simplest acceptable model from which the required information can be extracted. For the example of the sparger tube under consideration, the minimum requirement of any laboratory model is its usefulness to reliably extract the information regarding added hydro-dynamic mass, the damping and the excitation. Based on a critical assessment, a full size mock-up having a quarter segment of calandria with provision for rated flow, as shown in Fig. 2, has been used. No attempt to simulate the support stiffnesses at the ends was made for the reasons mentioned earlier. The outer tank has been sized to ensure that no wall effects (Chen, 1974; Krajcinovic, 1974; Blevins, 1979) act on the sparger tube. In the actual reactor condition, the sparger tube is surrounded by calandria tubes. Since the gap between the tubes is sufficiently larger than a tube radius, the fluid coupling (Chen, 1975a,b; Blevins, 1979) due to the presence of neighbouring calandria tubes may not be significant. However, in order not to leave out any effect of coupling,
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the calandria tube was also included in the mockup. The information in relation to dynamic characteristics and excitation extracted from this mockup could be used for analytical extrapolation to actual plant conditions. The maximum alternating stress induced (including the stress concentration factor to account for the perforation) due to the rated flow through the sparger tube could be estimated from the analysis and compared with the endurance limit of zircaloy-2 material to qualify the component. The following Sections 4–6 describe the procedure and the results.
4. Dynamic characterization of the components The first step towards qualification is the extraction of the modal properties. For this, an experimental modal analysis must be carried out. This modal analysis was carried out on the full scale mock-up by the impulse – response method (Braun, 1986; Ewins, 1986). In the modal test, an impulse was given at one location of the tube and the acceleration response was obtained from many locations along the entire length of the tube. The excitation of the impulse was maintained at a level just sufficient to obtain a measurable response in all the instrumented locations. The experimental data thus obtained have been analyzed using a built-in modal analysis programme available in the dual channel analyzer HP 5423A. The modal data — natural frequencies, mode shapes and modal damping — have been extracted by sin-
Fig. 3. Experimental transfer function (inertance) of sparger tube in air.
gle degree of freedom circle curve fit on the experimentally obtained transfer functions (inertance) The modal test was conducted with the tank simulating calandria empty (i.e. sparger tube in air) as well as when filled with water. The requirements and the information obtained through these tests are discussed below.
4.1. Test in air In the actual reactor, the sparger tube is rolled into thick tube sheets. These are much stiffer than the minimum stiffness required to approach a fixed–fixed end condition, but in the laboratory model, it is not feasible to build such stiff endsupports and this was not attempted. To estimate the actual support condition in the mock-up, a modal test in air was carried out when the vessel was empty, i.e. sparger tube in air. A typical transfer function (inertance) is shown in Fig. 3
Table 1 Mock-up condition reactor Mode
Mock-up condition
Reactor condition
In air
First Second Third a
In water
Experimental Analytical (Hz) (Hz)
Damping (%)
Experimental Analytical (Hz) (Hz)
Damping (%)
Analytical (Hz)
Dampinga (%)
17.24 46.56 103.9
2.730 0.668 0.496
12.65 37.12 64.04
3.660 1.960 1.200
12.91 36.30 69.73
3.660 1.960 1.200
18.93 50.61 101.3
Assumed to be the same as in the mock-up (Section 5).
12.13 32.33 62.34
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Fig. 4. Mode shapes of moderator sparger tube in air: (a) experimental; (b) analytical.
and the natural frequencies identified by the test are listed in Table 1. The experimentally-obtained mode shapes are shown in Fig. 4A, where it can be observed that the ends of the sparger tube deflect not too insignificantly in all the modes. This is to be expected when the end supports are flexible. To estimate the support stiffness, a finite element (FE) model of the mock-up assembly (shown in Fig. 4B) was constructed (Cook et al., 1989; Clough and Penzien, 1993). It consists of simple beam elements (two degrees of freedom at
each node) for the sparger tube with end restraints represented by spring elements of the translational stiffness, K1 and rotational stiffness, K2. The structures extending outside the calandria have also been modelled, as shown in the figure. To notionally account for the inertial and stiffness effects of the perforations, a thickness equivalent to the volume of holes was removed uniformly from the inner diameter of the tube. The values of K1 and K2 for the mock-up were arrived at by trial and error, such that the natural frequencies of the analytical model compared with those ex-
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perimentally observed. Table 1 also lists the analytical natural frequencies for comparison with the experimental values and Fig. 4 shows the mode-shapes.
4.2. Test in water As is explained above, the moderator sparger tube has many unique design features. It is a long thin tube with perforations of varying hole sizes and pitch. No formulation is available to estimate the added mass coefficient and damping for such complex components. To obtain reliable values of the added mass and damping for this particular case, the modal properties were extracted when the sparger tube was immersed in water. For this, the quarter segment of the calandria surrounding this sparger tube was filled with water and the impulse–response test repeated. Table 1 also lists the experimental natural frequencies of the component in water.
4.2.1. Estimation of added mass For the estimation of added mass, the increase in mass required to be added in the FE model, derived in Section 4.1 above, to obtain the experimentally observed natural frequencies was estimated. However, the analytical model of the mock-up required one more effect to be incorporated into it before this estimate could be carried out. It can be observed from the constructional detail of the mock-up that when the vessel is filled with water, there is hydrostatic pressure on the end-plates. The axial tension in the sparger tube due to this hydrostatic pressure is sufficiently significant to cause geometrical stiffening. Hence, in the above FE model, an additional stiffness due to this axial tension (Clough and Penzien, 1993) was also incorporated. The analytically obtained natural frequencies using the new stiffness matrix and the added mass, equal to 1.6 times the mass of water contained in the sparger tube, are also included in Table 1. It can be seen that the analytical model matches the experimental one reasonably well. It is possible to refine the analytical model further to bring the frequencies closer, but for the present
objective of presenting the qualification method, such a refinement is not important.
4.2.2. Estimation of damping The modal damping of the structure for different modes was obtained using single degree of freedom curve fit on the experimentally obtained frequency response function (Ewins, 1986). These damping values are included in Table 1. One interesting observation that can be made from the table is that the damping in the first mode both in air and in water is significantly larger than that for higher modes. This shows that the damping is not proportional to stiffness, as is often assumed in analysis. Similar observations of higher damping in the first mode are well known in the case of an unperforated pipe (Blevins, 1990; Ware, 1991). 5. The complete analytical model of the component in service From the results of the tests and analysis outlined in Section 4, it is possible to construct a complete dynamic model of the mock-up, as shown in Fig. 4. In order to obtain the model for the actual reactor conditions, the spring stiffnesses, K1 (equal to 1.6 × 106 kg m − 1 in the mock-up) and K2 (equal to 1.0× 10 kg-m rad. − 1 in the mock-up) must be replaced by values corresponding to the supports provided by the tube sheets. As described earlier in Section 4.1, these tube sheet supports approach fixed–fixed conditions. So the values of K1 and K2 are increased in the FE model untill the natural frequencies approach values closer to those representing fixed– fixed conditions. The minimum spring stiffnesses required to realize these frequencies were estimated to be 5.0× 108 kg m − 1 and 5.0× 107 kg-m rad. − 1, respectively. The natural frequencies corresponding to these conditions are given in Table 1. As can be seen from Table 1, the difference in the natural frequencies of the tube for mock-up as well as reactor conditions is small. However, considering the thrust of the paper on the procedure evolved for the dynamic qualification, digression on the various reasons for these differences and their quantitative effects are not considered.
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Since testing the sparger tube under actual reactor conditions is impossible at the design stage, the damping values can be assumed to be the same as those obtained for the mock-up (Table 1). Such an assumption is conservative, as the modal test was carried out with a small excitation (Stevenson, 1980; Ibaner et al., 1981).
6. Estimation of excitation and dynamic stress in the component For qualifying the reactor component, it is necessary to ensure that the stress levels induced (including stress concentration factors) are well within the endurance limits of the material. Since the mock-up was not an exact structural simulation of the component in reactor, the response measured from the mock-up could not be used directly for this assessment. One approach could be to measure the flow induced excitations which could be applied directly on the FE model. The component sparger tube is subjected to distributed dynamic load along the entire span due to the fluid it conveys into the calandria. Since it is difficult to measure the load distribution along the entire length of the span, another alternative, as explained below, has been adopted. The power spectral density (PSD) of the fluid flow induced excitation is broad-band and is expected to remain grossly unaltered for both the mock-up and the actual reactor. The sparger tube, in response to this excitation, vibrates with significant amplitudes at its natural frequencies. Therefore, instead of attempting to measure the force distribution along the length, the modal responses could be measured, which could be used to reach a conservative estimate of alternating stress in the actual structure and the fatigue life of the component. It is assumed that the same modal response as seen in the mock-up occurs in the reactor—a conservative assumption, as can be seen from the following argument. The PSD of the excitation generally decreases with frequency (Blevins, 1990). Since the natural frequencies of the sparger tube under the actual reactor conditions are higher, the excitation at these frequencies would be lower in the reactor. Consequently, for the same damping
153
the response would also be lower than that measured on the mock-up. Thus, the assumption of the same response in the reactor would give a conservative assessment. However, the quantification of factor of conservatism is not taken up here. Fig. 5 shows the vibration spectrum of the sparger tube due to the excitation caused by the design flow through the tube of the mock-up. The response in the first beam mode is indicated by the cursor in the figure. The modal response in the modes higher than the first beam mode is seen to be insignificant. It can also be seen from the figure that due to the structural configuration of the mock-up, high deflection occurs at a frequency lower than the first beam mode frequency of the sparger tube. This low frequency response below the first mode is not possible in the reactor due to the end support of high stiffness. For estimating the maximum alternating stress on the sparger tube in the reactor, the uniformly distributed load on a fixed–fixed beam which could cause the same static deflection as the vibration amplitude at the first beam mode of the mock-up has been estimated and applied. The maximum alternating stress has been found to be in the order of 0.1% of the endurance limit of zircaloy-2. Considering the perforation in the tube, the stress concentration factor (SCF) must be accounted for (a conservative SCF was assumed based on a literature survey). SCFs are generally
Fig. 5. Sparger tube response at rated flow-measured PSD.
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available for tension. During bending, some portion—upper or lower depending on curvature— would be under tension. Considering the developed portion of the tensile region as a perforated plate, a conservative estimate of SCF was made (Slot, 1972). The maximum alternating stress including SCF was compared with the endurance limit of zircaloy-2 to assess the acceptability of design.
7. Conclusion Components subjected to dynamic loads require an elaborate qualification procedure. Analytical methods may not always be possible due to limitations in the present state of the art. Production of an exact structural model is also often difficult, as the actual stiffnesses seen in a reactor cannot always be built into them. In this paper, the authors have evolved the procedure for dynamic qualification through the example of a component. The component chosen had features which did not permit the qualification by analysis or by test alone. A combined experimental and analytical method was adopted exploiting the strengths of both analytical and experimental techniques for reliable conservative qualification of the component. Those parameters difficult to define analytically were generated by tests conducted on a simple structural model of the component. An analytical method using these generated test data was then used to obtain the maximum alternating stress, which was found to be well within the endurance limit of the construction material, thus qualifying the component.
Acknowledgements The authors acknowledge the support provided
.
by the staff of the Vibration Laboratory, RED, BARC in carrying-out the different measurements.
References ASME Code on Operation and Maintenance of Nuclear Power Plants, 1990. Requirement for pre-operational and initial start-up vibration testing of Nuclear Power Plant Piping System, Part-3. ASME/ANSI-O&M. Blevins, R.D., 1979. Formulas For Natural Frequency and Mode shape. Van Nostrand Reinhold, New York. Blevins, R.D., 1990. Flow Induced Vibration, 2nd edn. Van Nostrand Reinhold, New York. Braun, S., 1986. Mechanical Signature Analysis — Theory and Applications. Academic Press, London. Chen, S.S., 1974. Dynamic of a rod-shell system conveying fluid. Nucl. Eng. Des. 30, 223 – 233. Chen, S.S., 1975a. Dynamic responses of two parallel circular cylinders in a liquid. J. Press. Vessel Technol. 97, 78–83. Chen, S.S., 1975b. Vibration of nuclear fuel bundles. Nucl. Eng. Des. 35, 399 – 422. Clough, R.W., Penzien, J., 1993. Dynamics of Structures, 2nd edn. McGraw-Hill, New York. Cook, R.D., Malkus, D.S., Plesha, M.E., 1989. Concept and Applications of Finite Element Analysis. Wiley, New York. Ewins, D.J., 1986. Modal testing — Theory and Practice. Research Studies Press, England. IAEA Safety Series No. 50-SG-D15, 1992. Seismic Design and Qualification for Nuclear Power Plants Safety, IAEA, Vienna. Ibaner, P., et al., 1981. Methods and benefits of experimental structural dynamics evaluation of NPPs. Nucl. Eng. Des. 64, 1 – 32. Krajcinovic, D., 1974. Vibration of two co-axial cylindrical shells containing fluid. Nucl. Eng. Des. 30, 242 – 248. Slot, T., 1972. Stress Analysis of Thick Perforated Plates. Technomic Publishing, CT, USA. Stevenson, J.D., 1980. Structural damping values as a function of dynamic response and deformation levels. Nucl. Eng. Des. 60, 211 – 237. Ware, A.G., 1991. The history of allowable damping values for US nuclear plant piping. J. Press. Vessel Technol. 113, 284 – 290.
Dynamic qualification of complex structural components of nuclear power plants R.I.K. Moorthy *, Jyoti K. Sinha Vibration Laboratory, Reactor engineering di6ision, Bhabha Atomic Research Centre, Mumbai 400 085, India Received 9 December 1996; received in revised form 5 August 1997; accepted 10 November 1997
Abstract The safety requirements and the lack of accessibility for any future repair, impose the design requirement that the integrity of reactor components of nuclear power plants be assured for the lifetime of the plant. To meet this design requirement it is essential to qualify the component, i.e. prove its capability to perform the design function for the design life. In performing its design function, the component is subjected to both static and dynamic loads. The qualification for static loads is rather simple and reliable, but qualification for dynamic loads is complex and often uncertain. This is because analytical tools are often inadequate for a realistic dynamic qualification and exact structurally simulated experimental models are almost always difficult to build. In such a situation, methods using tests on simple experimental set-ups supplemented by conservative analytical back-ups must be evolved. This paper highlights the intricacies involved in the conservative dynamic qualification of the complex components by considering the example of the moderator sparger tube. This component is a perforated tube submerged in water and excited by flow. For such a case, a completely analytical or a totally experimental qualification is not possible. This paper describes a procedure by which the required dynamic characteristics such as added mass, damping and fluid forces are generated from simple experiments and the component is qualified by analysis using these data. © 1998 Elsevier Science S.A. All rights reserved.
1. Introduction The structural components of a nuclear power reactor are subjected to both static and dynamic loads during its operation. Since the safety of a nuclear reactor is of utmost importance, it is essential to ensure, by design, the integrity of the components over the entire life of the reactor. Furthermore, the inaccessibility of these struc* Corresponding author. Tel.: + 91 22 5563060; fax: + 91 22 5560750; e-mail: [email protected]
tures for any repair at a future date makes it imperative to qualify the components. That is, each component is required to be proven to be capable of performing the design function for the design life of the plant. Such a qualification for static loads is rather simple and reliable, but the qualification for dynamic loads is complex and often uncertain. The dynamic qualifications for seismic loads are well defined (IAEA-50-SG-D15, 1992) and are usually applied to qualify the structural components. However, the procedures for the qualification of structural components for the
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Fig. 1. Schematic view of moderator sparger tube.
service load conditions, though important, are not so well defined. In this paper, the authors highlight the intricacies involved in the conservative dynamic qualification of complex components. This is achieved using, as an example, the moderator sparger tube (a perforated tube submerged in water and excited by flow) proposed for use in some of the pressure tube type pressurized heavy water reactors. The feasibility of a purely analytical method of qualification for the component is investigated and the possibility of a totally experimental means of qualification is reviewed. Based on the limitations of both methods, a combination of tests and analysis was arrived at by which the component could be qualified conservatively.
2.1. The choice of example This particular component has been chosen as it appears deceptively simple. Functionally this could be considered as a pipe conveying fluid. In this case, the standard guidelines (ASME, O&M1990) could be used for qualification. However, features such as the perforations all over the length, excitation due to water flowing out through the perforations and the component being submerged in water, make the dynamic qualification very complicated. Therefore, this component which seems simple by design could reveal the intricacies involved in the dynamic qualification and has been chosen as the typical example.
2. Typical details of the moderator sparger tube The moderator sparger tube is designed to carry and distribute the moderator inside the reactor vessel (calandria). To achieve uniform distribution along the length, perforations of different sizes and pitch are made on the tube as shown in Fig. 1. There are three such sparger tubes suitably spaced in the cross-section of the reactor to ensure uniform volumetric distribution of the moderator. For usage in a nuclear context, the construction material selected for the sparger tube is zircaloy-2. The ends of the tube are rolled into the tube sheets of the calandria, effectively realizing a fixed–fixed end condition. The stainless extensions beyond the calandria carry the moderator to the sparger tube for distribution inside the vessel. During normal operation, the calandria is filled with moderator, i.e. the sparger tube is filled with and surrounded by, the moderator.
3. Feasible qualification methods and their applicability for the example chosen The components could be qualified either totally by analytical means, or by experiment. For a component to be qualified exclusively by analysis, it must be possible to reliably model the dynamics of the structure. In many cases this could be difficult; even with a good model of the structure, the damping could be uncertain and must be decided conservatively. In addition to the dynamic characteristics of the structure, the excitation during its operation needs to be defined completely, which is often difficult for reactor components. For the specific example under consideration, a purely analytical method of qualification is not possible, due to: 1. Uncertainty in the dynamic characteristics of the structure such as
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Fig. 2. Schematic representation of mock-up test facility.
1.1. Added hydro-dynamic mass of a perforated tube in water. 1.2. Damping for the perforated tube—both structural and fluid induced. 2. Absence of any analytical definition of excitation for perforated tubes distributing water over its length. Therefore, as in the case of the sparger tube, an experimental approach must often be resorted to. For experimental qualification, it would be ideal to carry out the same on the actual reactor as all the design features are fully incorporated, along with any constructional deviations. However, this is obviously not possible at the design stage and at best could be used only for re-confirmation later. A structurally simulated mock-up is therefore required to highlight the dynamic characteristics adequately. In addition, for estimating the operational excitation characteristics, the mock-up must also include, as in the example chosen, flow considerations. However, an experimental set-up of the component simulating the actual conditions expected in service is often difficult to build. Considering our example of the sparger tube, it is necessary to model both structural and fluid dynamic effects, as well as the coupling between them. With the difficulties associated with scaling, a full scale mock-up may become the only reliable option.
Even with a full scale mock-up, exact structural simulation is not practicable, since the support stiffness provided by the tube sheet at either end is over 8000 times the bending stiffness of the tube and is too large to be achieved in a laboratory model. Therefore, it is essential to make a critical assessment and arrive at the simplest acceptable model from which the required information can be extracted. For the example of the sparger tube under consideration, the minimum requirement of any laboratory model is its usefulness to reliably extract the information regarding added hydro-dynamic mass, the damping and the excitation. Based on a critical assessment, a full size mock-up having a quarter segment of calandria with provision for rated flow, as shown in Fig. 2, has been used. No attempt to simulate the support stiffnesses at the ends was made for the reasons mentioned earlier. The outer tank has been sized to ensure that no wall effects (Chen, 1974; Krajcinovic, 1974; Blevins, 1979) act on the sparger tube. In the actual reactor condition, the sparger tube is surrounded by calandria tubes. Since the gap between the tubes is sufficiently larger than a tube radius, the fluid coupling (Chen, 1975a,b; Blevins, 1979) due to the presence of neighbouring calandria tubes may not be significant. However, in order not to leave out any effect of coupling,
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the calandria tube was also included in the mockup. The information in relation to dynamic characteristics and excitation extracted from this mockup could be used for analytical extrapolation to actual plant conditions. The maximum alternating stress induced (including the stress concentration factor to account for the perforation) due to the rated flow through the sparger tube could be estimated from the analysis and compared with the endurance limit of zircaloy-2 material to qualify the component. The following Sections 4–6 describe the procedure and the results.
4. Dynamic characterization of the components The first step towards qualification is the extraction of the modal properties. For this, an experimental modal analysis must be carried out. This modal analysis was carried out on the full scale mock-up by the impulse – response method (Braun, 1986; Ewins, 1986). In the modal test, an impulse was given at one location of the tube and the acceleration response was obtained from many locations along the entire length of the tube. The excitation of the impulse was maintained at a level just sufficient to obtain a measurable response in all the instrumented locations. The experimental data thus obtained have been analyzed using a built-in modal analysis programme available in the dual channel analyzer HP 5423A. The modal data — natural frequencies, mode shapes and modal damping — have been extracted by sin-
Fig. 3. Experimental transfer function (inertance) of sparger tube in air.
gle degree of freedom circle curve fit on the experimentally obtained transfer functions (inertance) The modal test was conducted with the tank simulating calandria empty (i.e. sparger tube in air) as well as when filled with water. The requirements and the information obtained through these tests are discussed below.
4.1. Test in air In the actual reactor, the sparger tube is rolled into thick tube sheets. These are much stiffer than the minimum stiffness required to approach a fixed–fixed end condition, but in the laboratory model, it is not feasible to build such stiff endsupports and this was not attempted. To estimate the actual support condition in the mock-up, a modal test in air was carried out when the vessel was empty, i.e. sparger tube in air. A typical transfer function (inertance) is shown in Fig. 3
Table 1 Mock-up condition reactor Mode
Mock-up condition
Reactor condition
In air
First Second Third a
In water
Experimental Analytical (Hz) (Hz)
Damping (%)
Experimental Analytical (Hz) (Hz)
Damping (%)
Analytical (Hz)
Dampinga (%)
17.24 46.56 103.9
2.730 0.668 0.496
12.65 37.12 64.04
3.660 1.960 1.200
12.91 36.30 69.73
3.660 1.960 1.200
18.93 50.61 101.3
Assumed to be the same as in the mock-up (Section 5).
12.13 32.33 62.34
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Fig. 4. Mode shapes of moderator sparger tube in air: (a) experimental; (b) analytical.
and the natural frequencies identified by the test are listed in Table 1. The experimentally-obtained mode shapes are shown in Fig. 4A, where it can be observed that the ends of the sparger tube deflect not too insignificantly in all the modes. This is to be expected when the end supports are flexible. To estimate the support stiffness, a finite element (FE) model of the mock-up assembly (shown in Fig. 4B) was constructed (Cook et al., 1989; Clough and Penzien, 1993). It consists of simple beam elements (two degrees of freedom at
each node) for the sparger tube with end restraints represented by spring elements of the translational stiffness, K1 and rotational stiffness, K2. The structures extending outside the calandria have also been modelled, as shown in the figure. To notionally account for the inertial and stiffness effects of the perforations, a thickness equivalent to the volume of holes was removed uniformly from the inner diameter of the tube. The values of K1 and K2 for the mock-up were arrived at by trial and error, such that the natural frequencies of the analytical model compared with those ex-
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perimentally observed. Table 1 also lists the analytical natural frequencies for comparison with the experimental values and Fig. 4 shows the mode-shapes.
4.2. Test in water As is explained above, the moderator sparger tube has many unique design features. It is a long thin tube with perforations of varying hole sizes and pitch. No formulation is available to estimate the added mass coefficient and damping for such complex components. To obtain reliable values of the added mass and damping for this particular case, the modal properties were extracted when the sparger tube was immersed in water. For this, the quarter segment of the calandria surrounding this sparger tube was filled with water and the impulse–response test repeated. Table 1 also lists the experimental natural frequencies of the component in water.
4.2.1. Estimation of added mass For the estimation of added mass, the increase in mass required to be added in the FE model, derived in Section 4.1 above, to obtain the experimentally observed natural frequencies was estimated. However, the analytical model of the mock-up required one more effect to be incorporated into it before this estimate could be carried out. It can be observed from the constructional detail of the mock-up that when the vessel is filled with water, there is hydrostatic pressure on the end-plates. The axial tension in the sparger tube due to this hydrostatic pressure is sufficiently significant to cause geometrical stiffening. Hence, in the above FE model, an additional stiffness due to this axial tension (Clough and Penzien, 1993) was also incorporated. The analytically obtained natural frequencies using the new stiffness matrix and the added mass, equal to 1.6 times the mass of water contained in the sparger tube, are also included in Table 1. It can be seen that the analytical model matches the experimental one reasonably well. It is possible to refine the analytical model further to bring the frequencies closer, but for the present
objective of presenting the qualification method, such a refinement is not important.
4.2.2. Estimation of damping The modal damping of the structure for different modes was obtained using single degree of freedom curve fit on the experimentally obtained frequency response function (Ewins, 1986). These damping values are included in Table 1. One interesting observation that can be made from the table is that the damping in the first mode both in air and in water is significantly larger than that for higher modes. This shows that the damping is not proportional to stiffness, as is often assumed in analysis. Similar observations of higher damping in the first mode are well known in the case of an unperforated pipe (Blevins, 1990; Ware, 1991). 5. The complete analytical model of the component in service From the results of the tests and analysis outlined in Section 4, it is possible to construct a complete dynamic model of the mock-up, as shown in Fig. 4. In order to obtain the model for the actual reactor conditions, the spring stiffnesses, K1 (equal to 1.6 × 106 kg m − 1 in the mock-up) and K2 (equal to 1.0× 10 kg-m rad. − 1 in the mock-up) must be replaced by values corresponding to the supports provided by the tube sheets. As described earlier in Section 4.1, these tube sheet supports approach fixed–fixed conditions. So the values of K1 and K2 are increased in the FE model untill the natural frequencies approach values closer to those representing fixed– fixed conditions. The minimum spring stiffnesses required to realize these frequencies were estimated to be 5.0× 108 kg m − 1 and 5.0× 107 kg-m rad. − 1, respectively. The natural frequencies corresponding to these conditions are given in Table 1. As can be seen from Table 1, the difference in the natural frequencies of the tube for mock-up as well as reactor conditions is small. However, considering the thrust of the paper on the procedure evolved for the dynamic qualification, digression on the various reasons for these differences and their quantitative effects are not considered.
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Since testing the sparger tube under actual reactor conditions is impossible at the design stage, the damping values can be assumed to be the same as those obtained for the mock-up (Table 1). Such an assumption is conservative, as the modal test was carried out with a small excitation (Stevenson, 1980; Ibaner et al., 1981).
6. Estimation of excitation and dynamic stress in the component For qualifying the reactor component, it is necessary to ensure that the stress levels induced (including stress concentration factors) are well within the endurance limits of the material. Since the mock-up was not an exact structural simulation of the component in reactor, the response measured from the mock-up could not be used directly for this assessment. One approach could be to measure the flow induced excitations which could be applied directly on the FE model. The component sparger tube is subjected to distributed dynamic load along the entire span due to the fluid it conveys into the calandria. Since it is difficult to measure the load distribution along the entire length of the span, another alternative, as explained below, has been adopted. The power spectral density (PSD) of the fluid flow induced excitation is broad-band and is expected to remain grossly unaltered for both the mock-up and the actual reactor. The sparger tube, in response to this excitation, vibrates with significant amplitudes at its natural frequencies. Therefore, instead of attempting to measure the force distribution along the length, the modal responses could be measured, which could be used to reach a conservative estimate of alternating stress in the actual structure and the fatigue life of the component. It is assumed that the same modal response as seen in the mock-up occurs in the reactor—a conservative assumption, as can be seen from the following argument. The PSD of the excitation generally decreases with frequency (Blevins, 1990). Since the natural frequencies of the sparger tube under the actual reactor conditions are higher, the excitation at these frequencies would be lower in the reactor. Consequently, for the same damping
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the response would also be lower than that measured on the mock-up. Thus, the assumption of the same response in the reactor would give a conservative assessment. However, the quantification of factor of conservatism is not taken up here. Fig. 5 shows the vibration spectrum of the sparger tube due to the excitation caused by the design flow through the tube of the mock-up. The response in the first beam mode is indicated by the cursor in the figure. The modal response in the modes higher than the first beam mode is seen to be insignificant. It can also be seen from the figure that due to the structural configuration of the mock-up, high deflection occurs at a frequency lower than the first beam mode frequency of the sparger tube. This low frequency response below the first mode is not possible in the reactor due to the end support of high stiffness. For estimating the maximum alternating stress on the sparger tube in the reactor, the uniformly distributed load on a fixed–fixed beam which could cause the same static deflection as the vibration amplitude at the first beam mode of the mock-up has been estimated and applied. The maximum alternating stress has been found to be in the order of 0.1% of the endurance limit of zircaloy-2. Considering the perforation in the tube, the stress concentration factor (SCF) must be accounted for (a conservative SCF was assumed based on a literature survey). SCFs are generally
Fig. 5. Sparger tube response at rated flow-measured PSD.
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available for tension. During bending, some portion—upper or lower depending on curvature— would be under tension. Considering the developed portion of the tensile region as a perforated plate, a conservative estimate of SCF was made (Slot, 1972). The maximum alternating stress including SCF was compared with the endurance limit of zircaloy-2 to assess the acceptability of design.
7. Conclusion Components subjected to dynamic loads require an elaborate qualification procedure. Analytical methods may not always be possible due to limitations in the present state of the art. Production of an exact structural model is also often difficult, as the actual stiffnesses seen in a reactor cannot always be built into them. In this paper, the authors have evolved the procedure for dynamic qualification through the example of a component. The component chosen had features which did not permit the qualification by analysis or by test alone. A combined experimental and analytical method was adopted exploiting the strengths of both analytical and experimental techniques for reliable conservative qualification of the component. Those parameters difficult to define analytically were generated by tests conducted on a simple structural model of the component. An analytical method using these generated test data was then used to obtain the maximum alternating stress, which was found to be well within the endurance limit of the construction material, thus qualifying the component.
Acknowledgements The authors acknowledge the support provided
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by the staff of the Vibration Laboratory, RED, BARC in carrying-out the different measurements.
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