Fluid-structure interaction in liquid-filled pipe systems: a review

Abstract

A review of literature on transient phenomena in liquid-filled pipe systems is presented . Waterhammer , cavitation , structural dynamics and fluid-structure interaction (FSI) are the subjects dealt with . The emphasis is on the history of FSI research in the time-domain . Waterhammer is the most probable cause for the transient vibration of liquid-filled pipe systems . When correctly modelling the liquid and pipe vibrations , FSI must be taken into account . The development of adequate mathematical models and their validation by physical experiments is surveyed . ÷ 1996 Academic Press Limited W HEN STARTING HIS RESEARCH ON FLUID-STRUCTURE interaction (FSI) in liquid-filled pipe systems in 1986 , the author found the literature survey by Wiggert (1986) very helpful . This paper is an extension of Wiggert’s survey . Its aim is twofold : (i) to be a starting-point for researchers new in the field and (ii) to be a state-of-the-art record of relevant contributions to the subject . The emphasis of the present review is on transient phenomena and , consequently , time-domain analyses . FSI is presented as an extension of conventional waterhammer theory , as in Skalak’s (1956) classical article . FSI , and some practical sources of excitation , are shown schematically in Figure 1 . Pipe systems experience severe dynamic forces during a waterhammer event . When these forces make the system move , significant FSI may occur , so that liquid and pipe systems cannot be treated separately in a theoretical analysis : interaction mechanisms have to be taken into account . In the majority of the analyses reviewed , the pipes are slender , thin-walled , straight , prismatic and of circular cross-section . The liquid and the pipe-wall material are assumed linearly elastic and cavitation is assumed not to occur . The theories developed are valid for long (compared to the pipe diameter) wavelength , acoustical (convective velocities neglected) phenomena . Important dimensionless parameters in FSI analyses are (i) the Poisson ratio , (ii) the ratio of pipe radius to pipe-wall thickness , (iii) the ratio of liquid mass density to pipe-wall mass density , and (iv) the ratio of liquid bulk modulus to pipe-wall Young’s modulus . When the hydraulic and structural mass and elasticity , and hence the propagation speeds of pressure and stress waves , are of the same order of magnitude , FSI is likely to be of importance , provided that the transient excitation is suf ficiently rapid . FSI is usually of no importance in gas-filled pipes because the mass density and elasticity (bulk) modulus of gases are negligible compared to those of solid pipes . A classification of one-dimensional FSI models according to their basic equations , written as a hyperbolic set of first-order partial dif ferential equations , is often made . The two-equation (one-mode) model refers to classical waterhammer theory , where the liquid pressure and velocity are the only two unknowns . The four-equation (two-mode)