Stability analysis on internal flow-induced cold-water pipe with non-uniform and variable cross-section for OTEC subject to multiple clump weights

Abstract

The stability of variable cross-section cold-water pipes (CWPs) is crucial for ensuring the reliability and safety of Ocean Thermal Energy Conversion (OTEC) systems under complex marine conditions. This paper introduces a novel semi-analytical framework to assess the stability of CWPs subjected to multiple clump weights, which is ignored by previous works. The dynamic response equation is established based on the Euler-Bernoulli beam theory, accounting for both inertia forces and gravitational effects of the clump weights. To efficiently and accurately compute the dynamic stability of variable cross-section CWPs, a hybrid method integrating the Sturm-Liouville Eigenvalues Using Theta matrices (SLEUTH) with the Generalized Integral Transform Technique (GITT) is proposed. The problem is transformed into an auxiliary eigenvalue problem and a second-order differential equation with time-dependent coefficients. Eigenvalues and eigenfunctions are computed at discrete points using the SLEUTH method, while coefficients of the differential equation are determined through numerical techniques like the Newton-Cotes formula, Gaussian functions, and exponential functions. The GITT method is employed to solve the transverse vibration equation. Validation with numerical examples demonstrates rapid convergence and high accuracy. Further investigation reveals that the weight, position, and number of clump weights significantly influence CWP stability, providing key insights for OTEC design improvements.