Transient cavitation in pipelines

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-The lowest pressure that can be attained will be equal to or somewhat less than the vapour pressure. Further expansion of the liquid only increases the vapour content, which phenomenon is known as cavitation of the liquid.

The examination of the phenomenon of water-hammer together with transient cavitation and gas release at low pressures is in an advanced state, but not yet complete, and some doubt still exists as to the possibly detrimental effects of both cavitation and released gases on the maximum pressures. Consequently, cavitation in pipelines is generally prevented by providing the pipeline with devices such as surge tanks and air chambers. Since the size and consequently the cost of these devices increase with the length of the pipeline, it is economically attractive to examine the possibility of omitting

a water-hammer device and permitting caviation. In long discharge lines, vapour pressure may result from a sudden pump failure, causing a negative pressure propagating downstream.

The possibility of pipeline rupture lays additional stress on the importance of examining transient cavitation in pipelines.

The propagation of the water-hammer waves caused by such rupture can also lead to vapour pressure in a part of the pipeline. This is of particular importance in the Netherlands, for instance, where pipelines often cross over dykes. Damage to that part of the pipeline in contact with the dyke would also damage the dyke.

The aim of the present study is to set up a one-dimensional mathematical model, which describes the transient flow in pipelines, taking into account the influence of cavitation and free gas. The flow will be conceived of as a three-phase flow of the liquid, its vapour and non-condensible gas. The wave attenuation following transient

cavitation observed by several authors, is explained taking into account the effect of gas diffusion towards individual bubbles. The possibility of shock waves is also considered. Although emphasis is placed on

application of the model to pump discharge lines transporting water, the model is also suited to other types of pipelines and liquids.

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-SUMMARY AND CONCLUSIONS

In this study transient cavitation, which is the formation of vapour voids by pressure waves in pipelines transporting liquids, is dealt with. Attention is devoted to the genesis of a region in which vapour pressure prevails, its nullification by pressure waves which have been reflected or generated at the ends of the pipeline, and the resulting pressure rise after cavitation. A mathmatical model describing the phenomena is developed. It distinguishes between regions of the pipeline with vapour pressure and regions with higher pressures. The transitions between both regions are continuous or practically discontinuous. In the

latter case shock waves occur.

The release of dissolved gas from the liquid and its influence on transient cavitation and wave propagation are included in the

mathematical model considered. Gas release seems to explain to a large extent the strong wave attenuation occurring after transient cavitation, which has frequently been observed. The calculation of the rate of gas release is based on a flow regime consisting of gas bubbles suspended in the liquid. The free gas is found to behave isothermally in many

cases of Civil Engineering practice in which the liquid is water. The vapour pressure of water can be assumed to be approximately constant. Regarding the rate of gas release at low pressures, it is demonstrated that both relative velocity of a bubble with repect to the liquid and radial motion of the bubble wall play a role.

The computational method developed is based on a simplification of the original mathematical model, which avoids explicit transitions from regions with vapour pressure to regions with higher pressures.

The method is versatile and yields results that compare well with experi-ments, although certain details of the phenomena are reproduced

inaccurately if column separation occurs. The experiments concern cavitating flow caused by the propagation of a negative pressure wave in the presence of a friction gradient, column separation, and wave propagation in bubble mixtures.

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-Including the effects of free gas in the theory ~s found to improve the agreement with experiments. Apart from wave attenuation, gas release causes a time shift in the phenomena. The quantitative prediction of the effects mentioned requires additional experimental data as to the number of bubbles and the relative bubble velocities.