Computational Analysis of the Dynamic Stability of a Horizontal Pipe Conveying Two-Phase Flow

Abstract

A coupled mathematical formulation is employed to investigate the dynamic stability of a clamped–clamped horizontal pipe conveying gas–liquid two-phase flow. The formulation is derived from differential elements of the pipe and the internal fluid to which conservation laws and compatibility conditions are applied. The fluid is modeled using the (no-slip) homogeneous flow approach. The resulting equation is discretized spatially via the modal Galerkin method and integrated in time, and implemented and solved in Wolfram Mathematica(R). Convergence analyses with respect to modal truncation and time-step refinement are conducted to ensure the numerical independence of the predictions. Spectral analysis is then used to identify the critical conditions for loss of stability: instability first appears in the fundamental mode, and its critical threshold is strongly dependent on the flow velocity. The numerical results are compared with data from the literature, showing good agreement and thereby validating both the formulation and its computational implementation.