Layout of piping system 

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... the authors’ knowledge, no general rule exists today which would express this amplitude condition, and it is suggested that some further research should be undertaken in this direction. Finally, it is still an open question whether vortex-shedding issues occur less often in low Mach-number regimes because the resonators are less efficient, or because the noise amplitude is lower. A more complex case of vortex shedding occurred recently in the cavity of an open gate valve in a power steam line (30). A pure tone at 460 Hz was observed for a flow associated to a Mach number equal to 0.182. Investigations showed that the noise was due to the cavity that houses the disk of the gate valve. According to literature, such a cavity noise should not generate a significant noise level at a Mach number below 0.2. However, this noise was amplified by coupling to an acoustic transverse mode of the pipe. What is more, the acoustic mode was coupled to a shell (lobar) mode of the structure, so that the noise was radiated far from the valve and became a source of disturbance for the nearby workers. Although it appears more complex than in the former cases, the physics of noise generation can here be fairly well modelled with a computer code based on non-linear Euler equations, because the shear layer development in the cavity and the acoustic resonance are non-viscous effects. The results of the computation are displayed in Figure 9 for one period of the phenomenon. On the right side of the figure, snapshots of the vorticity field in the cavity are shown: they highlight the vortex shedding mechanism in the cavity and the vortex interaction with the downstream corner. On the left side, snapshots of the pressure field in the duct are shown: the first transverse mode is excited and coupled with the cavity source radiation. Industrial investigations generally concern troubleshooting or they aim at the definition of rules and guidelines. In contrast to most academic research, many unchecked assumptions are often necessary during the investigation. Whether these assumptions are valid or not is a ‘non-scientific’ issue, which has nevertheless a strong influence on the quality of the results. As the two cases developed hereafter will illustrate, there is a need for simple and robust methods suited to industrial practice. A troubleshooting investigation can seldom be achieved according to the academic research standards of completeness and validation. When an expert engineer is summoned to solve a FSI case in an industrial plant, he/she is generally asked to fix it in a very short time, e.g., a few days for performing field tests and one more week for the final report including a proposed solution of the problem. Depending on the case study, the expertise can be successful or not, because FSI in practical situations is not fully understood today. As an illustration, one of the authors investigated recently a pure tone phenomenon at 12 Hz, which occurred in the water piping system sketched in Figure 10. The fluid is at rest except in the lower branch where the fluid flow varies from 1050 to 1200 m3/h. A pure tone at 12 Hz appears at the end of the closed branch, and at the end of the upper line when the left valve is open. Vortex shedding from the first T-junction is probable because its Strouhal number (based on the T-diameter and the flow velocity) would be close to 1 at the 12 Hz frequency, and one would expect an acoustic resonator to be involved in the assumed self-oscillation. However, the vibration still happens when the left valve is closed, which is in contradiction with the idea of an acoustic resonator, because the opening of the valve would change its natural frequency. The authors suspected after the tests a mechanical feedback, i.e. a vertical vibration of the T-piece due to a structural mode. The displacement of the T-piece could be enough to trigger the oscillation of the shear layer. However, as a modal analysis of the structure has not been performed, this explanation is only a wild guess. Due to plant constraints, no other tests could be performed, and the case is still unsolved. This is a typical case of an unexpected FSI effect, which requires time and academic research to be fully understood. Another industrial issue deals with the gap between design and reality. Most of the time, engineers expect a specification of a piping system based on design data to be accurate. As regards vibrations, this assumption is often incorrect: fixed points have finite stiffnesses, many supports do not block pipes due to their clearance, and the acoustic boundary conditions are everything but well-defined. From the experience of the authors, to accurately describe and model the low-frequency dynamic behaviour of industrial piping systems beyond the first natural modes appears hopeless. This conclusion is derived from significant efforts made in the past years. An illustration can be given by considering the piping system shown in Figure 11. It is a pump-to-pump water piping system made of stainless steel, with an outer diameter of 0.219 m, a thickness of 3.76 mm and a radius of curvature equal to 0.305 m. This piping system has the same design on several French nuclear plants. Vibration commissioning was required, so that data became available on five identical piping systems operating at the same hydraulic regime. The structural velocity spectra of the third elbow in the vertical direction are plotted in Figure 12. As can be seen, the similarity is poor, and only the range of the first natural frequencies and the average level can be held as meaningful. From a scientific point of view, the measurements are bad. Considered from an industrial point of view, these measurements are the best that can be made without expert analysis, including modal analysis and accurate control of the hydraulics of every individual piping system. Computer simulation can shed some light on this disagreement in results. In most piping systems, the vibrations from 2 Hz to some 500 Hz can be described using beam theory for the structure and plane wave acoustics for the fluid. The first modes of the pipe are generally mechanical, whereas the modes of higher order involve acoustics and FSI. As many academic papers proved it, beam theory is well suited to describe the behaviour of simple systems, provided that the boundary conditions are well defined. The difference of the frequency peaks in Figure 12 can be partly explained assuming that the stiffnesses of the supports of the pipes were different from one plant to the other. The differences can be reproduced by calculations, as shown in Figure 13, where the response of the pipe to a white noise pressure source is plotted for different elbow flexibilities and for different conditions of support flexibility. In practice, computer simulation can be used for control purposes, to obtain values of velocities and accelerations below which the structure is not exposed to fatigue failure. Defining the supports according to their function would in most cases lead to screening values of the maximum velocities or accelerations: the supports are usually designed as blocking the rotations, but the actual supports have finite stiffnesses which enhances the rotations. As a consequence, for a given stress in the pipe, the deflection with the actual support would be higher than the deflection with an ideal support. One issue would be to determine whether a structural dynamics code can be used for determining the fatigue criteria, or whether FSI effects necessitate fully-coupled calculations. It is yet the belief of two authors of the present paper that the deviation in the pipe parameters would generate more deviation in the dynamics of the pipes than FSI would ever do, whereas one of the authors strongly supports the opposite view. This paper presents FSI and FIV in liquid-conveying piping systems from an industrial point of view. It describes seven typical problems (in power plants) featuring excessive pipe vibration and/or fluid pulsation (including waterhammer). The underlying FSI mechanisms are explained and measured evidence is given. One mysterious problem shows the dilemma of the engineer: with a limited amount of data, he/she has to come to the right conclusion. Experience is what counts here, and it is of utmost importance that existing experience is being written down in textbooks like Refs (1, 2, 3, 4). Academia can help in the further development of knowledge and simulation tools, but it cannot take away the practical problem of lack of reliable (and accurate) data and information. Often the problem is simply too complex to handle, and one has to fall back on basic principles and simplified models. In this respect, there is a special need for guidelines and rules, preferably incorporated in international Codes and Standards. Financial support for part of this work was provided by the project WAHALoads (FIKS- CT-2000-00106) included in the 5 th Framework Programme and supported by the European Commission. The Surge-Net project is supported by funding under the European Commission’s Fifth Framework ‘Growth’ Programme via Thematic Network “Surge-Net” contract reference: G1RT-CT-2002-05069. The authors of this paper are solely responsible for the content and it does not represent the opinion of the Commission. The Commission is not responsible for any use that might be made of data ...