THE DYNAMICS OF A PIPING SYSTEM WITH INTERNAL UNSTEADY-FLOW

The dynamics of a pipeline conveying one-dimensional unsteady flow is considered. The dynamics of the fluid-pipe system is represented by a set of partial differential equations which consists of the axial and transverse equations of motion of the pipeline and the equations of momentum and continuity of the internal flow. The vibration equations of the pipeline are derived by use of Newton's law of motion, while the fluid equations are derived based on the concept of a deformable moving control volume. The equations are fully coupled to each other and thus can be applied to various fluid-pipe interaction problems which can be generated by the diverse operations of valves and pumps attached to the pipeline. The equations are applied to a simply supported inclined straight pipeline to investigate the stabilities and dynamic responses of the pipeline. The stability analysis is conducted by use of Bolotin's method. The dynamic responses are numerically investigated for both stable and unstable conditions. It is observed that unstable regions in the stability chart expand as the flow velocity and the mass density of the fluid increase, and that natural frequencies of the pipeline increase as the fluid friction acting on the inner surface of pipeline increases.