Sometimes vibration problems develop because of changes in operating conditions. For example, pressurized water reactor (PWR) fuel failures occurred in the 1990s due to fretting wear between fuel rods and support grids. The problem was related to longer fuel residence time, which caused increased clearances between the rods and grids due to creep, and deregulation of fuel procurement. The latter allowed fuels from different suppliers at the same time in the reactor core. Differences in design caused slight differences in impedance resulting in increased cross flows and, thus, more flow‐induced vibration excitation. Changes in support grid design solved this problem.
Fig. 1-10 Schematic Drawing of CANDU‐PHW® Reactor (Pettigrew, 1978 / with permission of Atomic Energy of Canada Limited)
Vibration problems are not limited to material damage such as fatigue and fretting wear. For example, excessive vibration of control absorber guide tubes due to jet impingement could have caused a serious reactor control problem (see Fig. 1-11a). The problem was avoided by shielding the guide tube with a protective shroud, as shown in Fig. 1-11b.
Many other vibration problems have been encountered, such as fatigue failures of PWR core barrel tie rods and in‐core instrumentation nozzles, excessive acoustic noise due to control valve dynamics and mechanical damage resulting from acoustic resonance in gas heat exchangers. Although most vibration problems have very costly consequences, they are usually solved by simple design modifications or changes in operating conditions. After the fact, it is easy to see that most problems could have been avoided by proper understanding of flow‐induced vibration phenomena. Thus, it is important to understand flow‐induced vibration and damage mechanisms to prevent problems at the design stage and assist plant operators in predicting the life of components. It is hoped that this handbook will help in that direction.
Fig. 1-11 a) Control Absorber Guide Tube Vibration due to Jetting, b) Modification with Protective Shroud (Pettigrew, 1976 / with permission of Atomic Energy of Canada Limited).
1.3 Dynamics of Process System Components
1.3.1 Multi‐Span Heat Exchanger Tubes
From a mechanical dynamics point of view, heat exchanger and steam generator tubes are multi‐span beams clamped at the tubesheet and held at the baffle supports with varying degree of constraint (see Fig. 1-12). The degree of constraint depends on support geometry and, particularly, on tube‐to‐support clearance. Heat exchanger dynamics is inherently a non‐linear phenomenon since it depends largely on the interaction (impacting and sliding) between a particular tube and its supports. This non‐linearity is particularly important since it governs the evaluation of damping at the supports and the prediction of fretting‐wear damage to the tube.
Such analysis requires time domain non‐linear simulation of the tube dynamics in which the details of sliding‐friction, impact, viscous‐shear and squeeze‐film forces between tube and tube supports are modelled. Unfortunately, non‐linear simulations are difficult and some of the detailed information is lacking. Furthermore, the required non‐linear analysis is not yet in the form of a practical design tool. Some progress has been made in this area with the development of codes, such as VIBIC (Fisher et al, 1992), H3DMAP (Sauvé et al, 1987) and EPRI SG FW (Rao et al, 1988) to predict fretting wear of heat exchanger tubes.
In the future, we believe that all vibration analyses will consider non‐linear simulation of the dynamic interaction between tubes and supports and will include a fretting‐wear damage prediction. This kind of analysis is now done by specialists for very critical or very expensive components, such as nuclear steam generators. Fretting‐wear damage prediction is discussed in Chapter 12.
For the time being, quasi‐linear vibration analyses are used by the industry for most heat exchangers. Quasi‐linear analysis requires the formulation of tube‐to‐support dynamic interaction forces, such as damping, in terms of equivalent linear values. We have found this approach to be reasonable in practice for the prediction of overall tube vibration response and critical velocities for fluidelastic instability. Such analysis is adequate to eliminate most vibration problems. However, long‐term fretting‐wear damage and tube life can only be predicted in an approximate manner. Tube vibration measurements in real heat exchangers show generally good agreement between measured and predicted frequencies using the quasi‐linear approach.
Fig. 1-12 Multi‐Span Heat Exchanger Tube with N Spans and N‐1 Clearance Supports.
1.3.2 Other Nuclear and Process Components
Other process and nuclear system components, such as nuclear fuels, reactor internals, and piping systems, are often multi‐span beams with intermediate clearance‐type supports (e.g., piping supports, fuel bearing pads and support grids). Analysis of these components is similar to that of multi‐span heat exchanger tubes.
References
1 Au‐Yang, M.K., 2001, “Flow‐Induced Vibration of Power and Process Plant Components: A Practical Workbook,” ASME Press, New York, NY, USA.
2 Blevins, R. D., 1990, “Flow‐Induced Vibration,” 2nd Edition, Van Nostrand Reinhold Company, New York, NY, USA.
3 Chen, S. S, 1987, “Flow‐Induced Vibration of Circular Structures,” Hemisphere Publishing Corporation, New York, NY, USA.
4 Fisher, N. J., Ing, J. G., Pettigrew, M. J. and Rogers, R. J., 1992, “Tube‐to‐ Support Dynamic Interaction for a Multispan Steam Generator Tube,” Proceedings of ASME International Symposium on Flow‐Induced Vibration and Noise, Anaheim, California, November 8‐13, 2, pp. 301–316.
5 Kaneko, S., Nakamura, T., Inada, F., Kato, M., Ishihara, K., Nishihara, T., 2014, “Flow‐Induced Vibration,” 2nd Edition, Academic Press, Elsevier, London, UK.
6 Naudascher, E. and Rockwell, D., 1994, “Flow‐Induced Vibration: An Engineering Guide,” A.A. Balkma, Rotterdam, Netherlands.
7 Païdoussis, M. P., 1998, “Fluid‐Structure Interactions: Slender Structures and Axial Flow,” Vol. 1, Academic Press, Elsevier, London, UK.
8 Pettigrew, M. J., 1976, “Flow‐Induced Vibration of Nuclear Power Station Components,” 90thAnnual Congress of the Engineering