Dynamics of spinning pipes conveying flow with internal elliptical cross-section surrounded by an external annular fluid by considering rotary inertia effects

Abstract

In this work, the vibration and stability of spinning pipes with an internal elliptical cross-section concurrently subjected to internal flow and external annular fluid are analyzed by considering rotary inertia effects and the non-uniformity of internal flow velocity distribution. To model the system, axial force, internal pressure, hygro-thermal loads, viscoelastic properties, and gravitational effects were incorporated. The coupled dynamic equations of transverse motions of the pipe were derived by exploiting the extended Hamilton's principle. With the aid of the Laplace transform and Galerkin discretization method, eigenvalues and stability conditions of the system were determined. Moreover, the divergence instability conditions of the system were acquired analytically. Then, the current investigation results were compared and verified with existing experimental and theoretical data in open literature. The impacts of key parameters, such as stabilizer characteristics, boundary conditions, geometrical features, and external fluid mass ratio, on the vibration frequencies and instability thresholds, were evaluated. It was concluded that, contrary to the internal circular cross-section case, the divergence instability region can be observed in the stability evaluation of the system with the internal elliptical cross-section. It was found that considering the rotary inertia effects reduces the critical velocities of the system. Also, the results showed that by increasing the stabilizer damping, the detached stable region is detected in the stability map of cantilevered pipes. The present research results can be beneficial for the optimal design of industrial equipment such as drill string pipes.