On the stability of rotating pipes conveying fluid in annular liquid medium

This study provides a stability analysis of flexible rotating pipes taking into account the simultaneous effects of internal and external fluid loading. Using the Euler-Bernoulli beam assumptions, governing equations for flexural vibrations of rotating pipes are obtained. The internal flow characteristics and the double gyroscopic effect are taken into account when deriving the structural equations coupled with the internal flow. External fluid loading is determined by a special linearization of the Navier-Stokes equations. Considering the circular wall of the pipe as an impermeable boundary to the flow, fluid-induced forcing functions are obtained and then applied to the structural equations of motion to get a full description of the coupled field problem. Both analytical and semi-analytical solutions are utilized to get the stability results for the coupled equations of motion. Interesting findings are reported by providing stability results for two separate categories of pipes: with purely external fluid, and simultaneous internal-flow and external-fluid loading, and some conclusions are drawn.