Water hammer with column separation: A historical review

Bergant, Anton; Simpson, Amanda; Tijsseling, AS Arris

doi:10.1016/j.jfluidstructs.2005.08.008

Cited by 328 publications

(167 citation statements)

References 111 publications

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“…3), consistent with the theoretical prediction, establishing that the alternative cavitation number Ca is a reasonable criterion for the onset of acceleration-induced cavitation. The alternative cavitation number can potentially be used as a criterion for brain injury caused by impact-induced cavitation (5,6), prediction of water hammer (4), and potentially applied to the development of safety devices (e.g., helmet design). (3,24).…”

Section: Discussionmentioning

confidence: 99%

Cavitation onset caused by acceleration

Pan

Kiyama

Tagawa

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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Striking the top of a liquid-filled bottle can shatter the bottom. An intuitive interpretation of this event might label an impulsive force as the culprit in this fracturing phenomenon. However, highspeed photography reveals the formation and collapse of tiny bubbles near the bottom before fracture. This observation indicates that the damaging phenomenon of cavitation is at fault. Cavitation is well known for causing damage in various applications including pipes and ship propellers, making accurate prediction of cavitation onset vital in several industries. However, the conventional cavitation number as a function of velocity incorrectly predicts the cavitation onset caused by acceleration. This unexplained discrepancy leads to the derivation of an alternative dimensionless term from the equation of motion, predicting cavitation as a function of acceleration and fluid depth rather than velocity. Two independent research groups in different countries have tested this theory; separate series of experiments confirm that an alternative cavitation number, presented in this paper, defines the universal criteria for the onset of acceleration-induced cavitation. . More commonly, sudden valve closing inside of a water pipe can cause a loud hammering sound due to the collapse of cavitation, resulting in damage on the inner walls (4). The effects of blast and impact that cause traumatic brain injury from cavitation have also been investigated (5, 6). To avoid cavitation-induced damage (7-9), it is crucial to predict the onset of cavitation.Cavitation onset in a high-speed flow [e.g., flow around propellers and in pumps (10)] can be characterized using a variant of the Euler number known as the cavitation number (11,12). The cavitation number is typically of the formwhere pr is the reference pressure, pv is the liquid vapor pressure, ρ is the liquid density, and v is the local velocity (13-16). This cavitation number is a ratio of the pressure difference to the pressure drop due to the fluid momentum. The large momentum of the fluid dominates when C 1, inducing cavitation. However, when C 1, the pressure at all locations is above the threshold for bubble formation, making cavitation unlikely. Practically, several advanced coefficients have been proposed to estimate cavitation inception for various geometries (16).However, the conventional cavitation number (C ) could incorrectly predict the cavitation onset in a liquid accelerated in a short amount of time. For example, the cavitation event that breaks the bottle in Fig. 1A has a maximum velocity of v ≈ 2 m/s, which yields the cavitation number C ∼ O(10 2 ). For the falling tube case in Fig. 1B a similar calculation leads to C ∼ O(10 2 ) (Table S1), whereas the conventional cavitation number requires C 1 (16). Thus, a new cavitation number is required to define the physics of cavitation onset.In the past, researchers have conducted similar experiments with a bullet-piston device to predict the tensile strength of a liquid, including pure water (17). They reported that the ...

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Section: Discussionmentioning

confidence: 99%

Cavitation onset caused by acceleration

Pan

Kiyama

Tagawa

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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“…Proper modelling of flows of liquids under pressure in such systems remains a significant challenge. Among the key issues widely discussed in new publications on the subject, special emphasis is placed on the correct modelling: of the time-varying hydraulic resistance (Vardy and Brown, 2003;Zarzycki et al, 2011;Reddy et al, 2012), cavitation (Zarzycki and Urbanowicz, 2006;Lewandowski, 2009, 2012;Bergant et al, 2006;Karadžić et al, 2014;Soares et al, 2015), the interaction between the liquid and walls of the conduit Henclik, 2015;Zanganeh et al, 2015), the viscoelastic phenomenon that occurs during the flow in a piping made of engineering polymers (Weinerowska-Bords, 2015; Soares et al, 2012; Keramat et al, 2013;Pezzinga et al, 2014;Urbanowicz et al, 2016). Taking into account all of the above phenomena while simulating unsteady flows has seemed impossible until recently.…”

Section: Introductionmentioning

confidence: 99%

Analytical expressions for effective weighting functions used during simulations of water hammer

Urbanowicz

2017

jtam

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For some time, work has been underway aimed at significant simplification of the modelling of hydraulic resistance occurring in the water hammer while maintaining an acceptable error. This type of resistance is modelled using a convolution integral, among others, from local acceleration of a liquid and a certain weighting function. The recently completed work shows that during efficient calculations of the convolution integral, the effective weighting function used does not have to be characterised by large convergence with a classical function (according to Zielke during laminar flow and to Vardy-Brown during turbulent flow). However, it must be a sum of at least two or three exponential expressions so that the final results of the simulation could be considered as satisfactory. In this work, it has been decided to present certain analytical formulas using which it will be possible to determine the coefficients of simplified effective weighting functions in a simple direct way.

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“…These waves may have very steep fronts when generated by, for example, the closure of lightly damped check valves [1] or the collapse of liquid column separations [2]. Steep-fronted waves are prone to excite the structural system and as a result make individual pipes move.…”

Section: Introductionmentioning

confidence: 99%