In this paper, the effects of internal flow in underwater flexible pipe are mathematically formulated. Internal flow is assumed steady. Pressure force, centrifugal force, Corioli's force and inertia moments from internal flow on 3D nonlinear moving pipe are rigorously derived. Numerical simulations of a 3D nonlinear flexible pipe are performed in time domain. Forced excitation analyses for flexible pipe subject to current are carried out with variation of mass density and internal flow velocity.


This paper concerns about the mathematical formulation of internal flow effects on dynamic behaviors of underwater flexible pipes and numerical simulations. For typical examples flexible marine risers for production of offshore oil and gas, flexible pipes for production of deepwater and flexible conduit pipes for deep ocean mining are found. The internal flow through a curved and moving pipe will result in forces whose magnitude and direction will depend on pipe curvature, angular velocity, wall roughness, density and velocity of flow and underwater depth. Sparks (1979, 1984) gives the mathematical and physical interpretations of the widely used concepts of effective tension and effective stress for convenient investigation of static pressures. They investigated numerically the quasi-static and dynamic effects of single slug flow on the response of flexible riser. Patel and Seyed (1989) present a frequency domain method for the 2D analysis of the flexible risers subject to a time varying internal flow. Seyed and Patel (1992a) show through time domain analysis that an extreme slug flow may be capable of exciting pipe responses exceeding wave induced motions. Seyed and Patel (1992b) present mathematical formulation of internal flow effects for 2D problems. Hong (1992) uses the rate of momentum change of internal flow to formulate the forces and moments to pipe and shows a concept of effective bending stiffness of pipe.

This content is only available via PDF.
You can access this article if you purchase or spend a download.