Abstract
In this paper, the seven-equation two-fluid flow model is streamlined to a five-equation numerical calculation method. This method is applied to predict the wave attenuation of the cavitation jet. Compared with 9 different experimental schemes in two separate laboratories, it is found that the velocity flow characteristics are different from normal transient flow when the cavitation jet is formed in the pipeline. Such a difference in velocity flow characteristics will cause changes in the prediction deviation of pressure response time and amplitude. A numerical method for predicting the attenuation of pressure fluctuation with the cavitation jet is presented taken into account these flow characteristics. In this method, the unsteady friction model is opened after the jet wave transmits 3–5 cycles, and the cavitation jet wave attenuation is well simulated. This calculation method could provide a research basis for pipeline leakage, vibration, noise, and other fields that need accurate pressure signals.
Highlights
Water hammer with column separation in a pipeline system can cause cavitation jet [1,2,3]. e formation of the cavitation jet will cause a sharp rise in pressure, which has a serious impact on the safety of the pipeline system [4,5,6,7,8]
A typical two-fluid two-phase flow model under one-dimensional direction requires the solution of 7–9 equations [15,16,17,18,19,20,21,22,23]
Residual void of gas means that the volume of initial gas increases with the progress of time iteration. e principle of this phenomenon is that the initial calculation needs a certain amount of insoluble gas to satisfy the appeared second phase in the two-fluid model. e energy loss is not considered in the interaction between the two phases by the two-fluid model in theory. e expansion value of bubbles is often larger than the compression, which is expected to result in the void of gas gradually increasing with the advance of time
Summary
Water hammer with column separation in a pipeline system can cause cavitation jet [1,2,3]. e formation of the cavitation jet will cause a sharp rise in pressure, which has a serious impact on the safety of the pipeline system [4,5,6,7,8]. Ere are two main factors influencing the calculation accuracy of water hammer cavitation jet in the pipeline system: (1) residual void of gas and (2) wave attenuation. E residual void of gas will cause an obvious influence on the velocity of wave transmission It will continuously affect the wave, which will lead to obvious errors in the prediction of water hammer wave. E main problem of wave attenuation lies in the combination of unsteady friction model and cavitation jet calculation method. Erefore, it is an Mathematical Problems in Engineering urgent problem to predict the wave attenuation of the cavitation jet Another factor is the timeliness of the calculations. (1) e calculation method of velocity and pressure relaxation coefficient is rederived strictly through the interphase action mechanism of the seven-equation two-fluid model. (4) By setting the internal switch, the two-coefficient decay model was added into the five-equation calculation method. e calculation method of wave attenuation suitable for water jet cavitation was constructed
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