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 Institute of Canada, Halifax, NS, Oct. 4‐8, (also Atomic Energy of Canada Report, AECL‐5852)
9 Pettigrew, M. J., and Campagna, A. O., 1979, “ Heat Exchanger Vibration: Comparison Between Operating Experiences and Vibration Analysis,” Proceedings of the International Conference on Practical Experiences with Flow‐Induced Vibrations, Karlsruhe, Germany, 1979 September, (also Atomic Energy of Canada Report, AECL‐6785).
10 Pettigrew, M. J., Sylvestre, Y. and Campagna, A. O., 1977, “Flow-Induced Vibration Analysis of Heat Exchanger and Steam Generator Designs,” 4th International Conference on Structural Mechanics in Reactor Technology, Paper No. F6/1+, San Francisco, California, Aug. 15‐19, (also Atomic Energy of Canada Report, AECL‐5826).
11 Pettigrew, M. J., Carlucci, L. N., Taylor, C. E. and Fisher, N. J., 1991, “Flow‐Induced Vibration and Related Technologies in Nuclear Components,” Nuclear Engineering and Design, 131, pp. 81–100.
12 Rao, M. S. M., Steininger, D. A., and Eisinger, F. L., 1988, “Numerical Simulation of Fluidelastic Vibration and Wear of Multispan Tubes with Clearances at Supports,” Proceedings of the ASME Symposium on Flow‐Induced Vibration and Noise‐1988: Vol. 5, Flow‐Induced Vibration in Heat‐Transfer Equipment, pp. 235–250.
13 Sauvé, R. G. and Teper, W. W., 1987, “Impact Simulation of Process Equipment Tubes and Support Plates‐A Numerical Algorithm”, Journal of Pressure Vessel Technology, 109, pp. 70–79.
Notes
1 1 CANDU‐BLW = Canada Deuterium Uranium – Boiling Light‐Water is a registered trademark of Atomic Energy of Canada Limited.
2 2 CANDU‐PHW = Canada Deuterium Uranium – Pressurized Heavy‐Water is a registered trademark of Atomic Energy of Canada Limited.
2 Flow‐Induced Vibration of Nuclear and Process Equipment: An Overview
Michel J. Pettigrew and Colette E. Taylor
2.1 Introduction
Failures due to excessive vibration must be avoided in process equipment, preferably at the design stage. Thus, a comprehensive flow‐induced vibration analysis is required before fabrication of process equipment, such as shell‐and‐tube heat exchangers. It must be shown that tube vibration levels are below allowable levels and that unacceptable resonances and fluidelastic instabilities are avoided.
The purpose of this chapter is to summarize our design guidelines for flow‐induced vibration in components operating in gas, liquid, and two‐phase flows. This overview
