Study on the natural frequencies of pipes conveying gas-liquid two-phase slug flow

The natural frequencies of pipes conveying gas-liquid two-phase slug flow are explored, considering the significance of the intermittent characteristic of gas-liquid two-phase slug flow particularly. The widely used finite element method is employed to establish the theoretical model. The local flow parameters including local gas and liquid velocities and local liquid holdup varying with time and position along the pipe are calculated to obtain the global matrix equation of motion for the system. An experiment is conducted to verify the theoretical model. The results show that the time domain values of the natural frequency would keep periodicity during the process of slug flow. Root-mean-square of the natural frequency is employed to represent the characteristic of the piping system natural frequency. If the superficial gas velocity is given, root-mean-square of the natural frequency will decrease with the increase of the superficial liquid velocity. Yet if the superficial liquid velocity is given, root-mean-square of the natural frequency will increase firstly and then decrease with the increase of superficial gas velocity when the superficial liquid velocity is relatively large. Thus a critical superficial gas velocity exists for these conditions. The range of superficial gas velocity that could make the system become unstable may be predicted preliminarily by analyzing this critical value. Sufficient analysis of slug parameters and geometrical parameters of the pipes is necessary to obtain the critical superficial gas velocity. Finally, the divergent instability of the piping system is predicted based on the above analysis.