Modal Analysis of the Hydrodynamic Force of a Capsule in a Hydraulic Capsule Pipeline

Abstract

Hydrodynamic forces influence the efficiency and safety of pipeline transport in ocean engineering. A capsule pipeline is an example of pipeline transportation. In this work, a dynamic model is proposed to explain the oscillating motion of a capsule in a hydraulic capsule pipeline (HCP). The main study was conducted using a modal analysis of hydrodynamic forces acting on a capsule, which could be divided into frictional drag and pressure drag forces. The results indicated the presence of independent modes with different contributions to the hydrodynamic forces. Ultimately, the first to fiftieth modes represented 94~97.3% of the hydrodynamic force contributions. These modes had their own frequency ranges and power spectrum density (PSD) functions, and the frictional drag and pressure drag were both found to coincide with the narrow-band characteristics of the lower-order modes. However, the PSD functions of the frictional drag were found to fulfill the wide-band characteristics corresponding to the higher-order modes. Then, coherent structures were extracted. As the mode order increased, the vortices became more fragile and the frequency became higher. This phenomenon coincided with an increase in the frequency of the time coefficient peak, which became larger. This work could provide new perspectives on the hydrodynamic forces of pipeline transport, especially its dynamic analysis of the interaction between a rigid capsule and fluid flow.