Different families of the Discrete Vapour Cavity Model (DVCM) are developed, including the frictionless, steady and quasi-steady friction models. A relaxation-dissipation approach is proposed to ...improve the timing of pressure pulses predicted by the classic DVCM. In this approach, a friction correction factor is introduced into the steady/quasi-steady friction term to reduce the local value of the dissipation term in regions facing with cavitation. The proposed approach is completely consistent with the classical water-hammer framework. The importance of the steady/quasi-steady friction term is investigated by comparing numerical results of different DVCMs with the experimental data for various cavitation problems. Based on a frictionless study, it is shown that there exists an unrealistic attenuation in pressure pulses of the classic DVCM. For problems with high-intensity cavitation, it is shown that the frictionless, steady and quasi-steady friction models generally produce different results, especially in terms of the pressure pulses timing. Within the range described in the manuscript, the timing of the classic DVCM pressure pulses can generally be improved by applying the proposed relaxation-dissipation approach on the steady/quasi-steady friction term.
•Different types of Discrete Vapour Cavity Model were developed based on the friction terms.•A new steady/quasi-steady acceleration-relaxation approach was introduced.•The proposed approach is completely consistent with water-hammer framework.•For high-intensity cavitation, improved pressure pulses were predicted.
Accurate and rapid prediction of the pipeline water hammer process is beneficial to the design and operation of the pipeline system. This paper proposed an accurate and efficient wave tracking method ...(EWTM) for the numerical simulation of water hammer in pipeline system. The proposed EWTM was developed based on the unsteady friction model and a new implementation scheme, which is combined with the Lagrangian scheme and the Eulerian scheme. The wave propagation equations of reservoir, valve and discrete vapor cavity model (DVCM) were also derived. To evaluate the performance of the EWTM, the single-phase water hammer and the two-phase water hammer were calculated with the EWTM and compared with the method of characteristic (MOC) and the experimental data. The evaluation result shows that EWTM has the same calculation accuracy as MOC, and the proposed EWTM method is over 90% more efficient than the MOC, which addresses the accuracy and efficiency limitations of the conventional wave tracking method (WTM).This paper provides a new idea on the improvement of simulation procedures and efficiency, which can be used for rapid calculation of transient flow in complex pipelines and for fault diagnosis which requires the highest numerical simulation accuracy.
Discrete multiple-cavity models coupled with quasi-two-dimensional (quasi-2D) friction models are effective solutions to simulating transient cavitation pipe flows. The simulation accuracy of such ...models hinges upon the understanding of key parameters of the models, which remains elusive so far. To address such an open issue, this paper employs the discrete vapor cavity model (DVCM) and the discrete gas cavity model (DGCM), combined with the quasi-2D friction model, with a particular focus on revealing the sensitivity of these models to the key parameters such as grid number and weighting parameters. Based on the quantitative analysis and pressure fluctuation history, a method is developed to evaluate the accuracy of numerical results. Results show that the inclusion of the quasi-2D friction model improves the accuracy of predicting time of cavity formation and collapse; however, it does not affect the selection of grid number. Meanwhile, numerical results are sensitive to the weighting parameter of the viscous term in the quasi-2D friction model except for the case of low-intensity cavitation and its value of 1 is suggested for all cases. From the practical point of view, our finding is helpful to understand the feature of discrete multiple-cavity models and improve the simulating accuracy of transient cavitation pipe flows. HIGHLIGHTS For the two-dimensional discrete vapor cavity model (2D-DVCM) and the two-dimensional discrete gas cavity model (2D-DGCM), the selection of grid number is independent of the inclusion of the friction model and only depends on the assumption of the cavitation model.; The 2D-DVCM and 2D-DGCM can accurately predict the time of cavity formation and collapse.; A procedure for evaluating the accuracy of numerical results is proposed considering the complexity of pressure fluctuation.;
PDF