Vibrational analysis of pipes based on the drift-flux two-phase flow model

Linear and nonlinear free vibrations of supported pipes containing two-phase flow were modeled in different flow regimes by including gravitational force, structural and two-phase damping effects. To model the flow, the drift-flux model was utilized. Discretization of the dynamical equation was performed with the help of the Galerkin scheme. The linear vibrational frequency of the system was determined by solving the eigenvalue problem. Also, a mathematical closed-form expression for the nonlinear vibrational frequency is presented. For the validation purpose, theoretical and experimental data were obtained from literature and compared with the results of this work in various operating conditions. A detailed parametric analysis was also carried out to examine the influence of flow parameters, geometry, and physical properties on the dynamics of the system. It was concluded that by increasing the inner and outer pipe diameters, vibrational frequencies of the system decrease and increase, respectively. It was found that a lower liquid phase density leads to an improvement in the vibrational stability of the system. Besides, it was demonstrated that by increasing the void fraction/mixture velocity in the system, linear and nonlinear vibrational frequencies increase/decrease. Furthermore, a higher initial amplitude caused a larger nonlinear frequency shift. The outcomes of the current analysis can be applied as a frame to evaluate and optimize the performance of structures transporting two-phase flows.