Powering smart pipes with fluid flow: Effect of velocity profiles

Abstract

The dynamics of elastic cantilevered smart pipes conveying fluid with non-uniform flow velocity profiles is presented for optimal power generation. The Navier-Stokes equations are used to model the incompressible flow in the circular smart pipe, and flow profile modification factors are formulated based on the Reynolds number and Darcy friction factor. The coupled constitutive dynamic equations, including the electrical circuit, are formulated for laminar and turbulent flows. Due to viscosity in a real fluid, non-uniform flow profiles induce dynamic stability and instability phenomena that affect the generated power. The system consists of an elastic pipe with segmented smart material located on the circumference and longitudinal regions, the circuit, and the electromechanical components. The modified coupled constitutive equations are solved using the weak form extended Ritz method. For faster convergence, this model is reduced from the exact solution of the pipe structure with proof mass offset. Initial validation with a uniform flow profile from previous work is conducted. With increasing flow velocity, the optimal power output and their frequency shifts are investigated both with and without the flow profile modification factors, to identify the level of instability. Further parametric studies with and without flow pulsation and base excitation are given.