The highly turbulent flows of dense fluids through singularities of piping systems dynamically excite the structure by means of an unsteady pressure field issued at the flow and transferred to the pipe walls. The flow-induced excitation is broadband and most significant in the low-frequency range, which makes it dangerous to thin-walled structures and may eventually lead to rupture by fatigue. Although some attention has been payed to the wall pressure measurements on several points around the elbow conveying dense fluids [1, 2], few studies have analyzed the relationship between the velocity field and the resulting pressure distribution on the elbow flow. The present study proposes an analysis of the correlation found between pressure and velocity in the elbow flow, in view of low-order modeling of the flow-structure interaction phenomenon.

Although turbulent unsteady flows seem to behave randomly, some order in the chaos may be encountered under the form of organized fluid motion, where coherent structures are defined as a mass of fluid presenting phase-correlated vorticity over its extension [3, 4]. These large-scale motions generally contain most of the kinetic energy of the flow, allowing for the simpler reconstitution of the dynamic system by means of low-order modeling. Finally, from reduced-order models of the flow, information on the dynamic load applied by the fluid on the structure may be extracted. Techniques based on the decomposition of the flow field provide an orthogonal base of flow modes as a function of their contribution to the total kinetic energy of the system [5]. This can be done with a sufficiently high number of uncorrelated realizations of the local velocity field, a technique known as Snapshot-POD [6]. Moreover, a technique known as extended POD (e-POD, [7]) can be used to evaluate the correlation between these organized flow motions and the resulting pressure field.

A previously validated Large-eddy simulation (LES) of water flowing at Reynolds number 5.6 x 10^5 through a 90° elbow was used to provide a series of realizations of the velocity and pressure fields. Snapshot-POD is applied to the velocity field in order to evaluate the coherent structures issued on the elbow, such as a separation on the intrados, the resulting vortices shed and convected downstream and the Dean vortices typically found in the elbow flow. Coupled pressure and velocity modes are issued from the application of the e-POD on the flow downstream of the elbow. Finally, a discussion on the viability of the low-order modeling of the flow-structure interaction phenomenon around the elbow is proposed.

References

[1] T. Nakamura, T. Shiraishi, Y. Ishitani, H. Watakabe, H. Sago, T. Fujii, A. Yamaguchi and M. Konomura, Flow-Induced Vibration of a Large-Diameter Elbow Piping Based on Random Force Measurement Caused by Conveying Fluid: Visualization Test Results, American Society of Mechanical Engineers, 2005.

[2] S. Ebara, Y. Aoya, T. Sato, H. Hashizume, Y. Kazuhisa, K. Aizawa and H. Yamano, "Pressure Fluctuation Characteristics of Complex Turbulent Flow in a Single Elbow With Small Curvature Radius for a Sodium-Cooled Fast Reactor," Journal of Fluids Engineering, 2010.

[3] B. J. Cantwell, "Organized motion in turbulent flow," Annual review of fluid mechanics, 1981.

[4] A. F. Hussain, "Coherent structures and turbulence," Journal of Fluid Mechanics, 1986.

[5] J. L. Lumley, "The structure of inhomogeneous turbulent flows," Atmospheric turbulence and radio wave propagation, 1967.

[6] L. Sirovich, "Turbulence and the dynamics of coherent structures. Part I: Coherent structures," Quarterly of applied mathematics, 1987.

[7] J. Borée, "Extended proper orthogonal decomposition: a tool to analyse correlated events in turbulent flows," Experiments in Fluids, 2003.