Theoretical study on the dynamic behavior of pipes conveying gas-liquid flow

The dynamic behavior of clamped-clamped straight pipes conveying gas-liquid two-phase flow is theoretically investigated, specifically the effect of the flow parameters on the frequency of the system. First, the equation of motion is derived based on the classic Païdoussis formulation. Assuming Euler-Bernoulli beam theory, small-deflection approximation and no-slip homogeneous model, a coupled fluid-structure fourth-order partial differential equation (PDE) is obtained. Then, the equation of motion is rendered dimensionless and discretized through Galerkin's method. That method transforms the PDE into a set of Ordinary Differential Equations (ODEs). The system frequency is obtained by solving the system of ODEs by allowing the determinant to be equal to zero. System frequencies for different geometries, structural properties and flow conditions have been calculated. The results show that the system frequency decreases with increasing two-phase flow velocity. By contrast, the former increases with increasing homogeneous void fraction. These theoretical results are in agreement with experimental findings reported in the literature. Furthermore, even for typical two phase flow conditions, the system can become unstable for inadequate chooses of geometry or material of the pipe.