Two-phase fluid resonance frequency and improved elastic water model for pipes conveying fluid with entrapped air

This is the authors' abstract. We don't add key points for this paper.

The entrapped air in pipe has a significant impact on the dynamic characteristics of the pipeline system, as it can induce transient high pressures and pressure oscillations similar to water hammer during system opening and closing. In this study, plane wave equations for the liquid and air phases in pipe are formulated with considering various conditions of entrapped air. The approximate solution for the resonance frequency of the two-phase fluid is derived via the separation variables method and the coupling relationship at the air–liquid interface. The resonance frequencies obtained from the approximate solution closely match those from the finite element method, confirming the accuracy and universality of the presented approximate solutions. Furthermore, based on the criterion of consistent first-order resonance frequency, an improved elastic water model and the corresponding analysis process of fluid dynamic response are proposed by correcting the first resonance frequency of the dynamic model of pipes conveying fluid with entrapped air. The predicted results are consistent with experimental data and computational fluid dynamics results, thus validating the proposed model. Compared with existing models, the improved elastic water model proposed in this paper can obtain accurate calculation results under all entrapped air conditions, overcoming the limitation of existing models that are only applicable to a single entrapped air condition. It is found that the air–liquid interface angle influences the fluid resonance frequency and dynamic response significantly. As the angle of the air–liquid interface increases, the pressure peak and oscillation frequency of the pipe fluid response decrease remarkedly.