The fluid stress or flow-induced vibration of annular gap flow always has some influence on the stable working conditions of a hydraulic machine. A time-averaged analysis of flow may not have to explicitly acknowledge these factors. Accordingly, a finite-axial-length annular gap was measured via particle image velocimetry (PIV), with inner boundary motion and a stable outer boundary. As a statistic result regarding the fluid stress, the Reynolds stresses soared in the first region, were sustained in the middle region, but decreased at last. The flow had a higher convective transportation intensity in the radial direction than in other directions. Flow diagnostics were also performed by proper orthogonal decomposition (POD). As a result, the coherent structures were found. Then, the power spectrum density (PSD) functions were also calculated for finding the flow-induced vibration characteristics; the functions had high amplitude in the low-frequency domain and low amplitude in the high-frequency domain, with an order of magnitude between the two amplitudes of 10⁻¹ to 10⁻². In addition, the frequency was higher at a smaller gap width in the middle-frequency domain, but the condition was the opposite in the high-frequency domain. In conclusion, the fluid stresses were changeable and uneven along the flow direction, and flow-induced vibration obviously existed. Remarkably, the turbulence characteristics of the annular gap flow were not “laminar approximating,” while the diameter ratio of the gap was 0.6 to 0.8.

The paper presents the visualization results of the sudden contraction flow field with an annular gap downstream of the contraction cross section. The contraction ratio directly influences the flow phenomena. No stationary vortices were observed upstream of the contraction cross section, and flow separation divided the flow field within the annular gap into a recirculation zone, a shear layer, and a mainstream zone. Vena-contracta point and reattachment point occurred within the flow field of the annular gap. The production of Reynolds stress varied with the contraction ratio, and the momentum exchange mainly occurred in the recirculation zone and the shear layer, while the flow state in the mainstream zone tended to become isotropic. Rapid changes in turbulent kinetic energy primarily occurred in the shear layer, and the production term of turbulent kinetic energy contributed the most. Applying computational fluid dynamics and experimental results, this study has formulated an expression for the contraction coefficient of the proposed model. The axial positions of the vena-contracta point and reattachment point have a strong correlation with the contraction ratio, which can be represented by an exponential function.

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.

The hydraulic capsule pipeline (HCP) is an eco-friendly and sustainable pipeline transport option. The freight-carrying capsule is driven by hydraulic pipe flow. Fluid drag is generated by the principal dynamic force effect on the capsule, which could influence the capsule’s motion speed. To make the HCP more efficient, a transient model for the hydrodynamic force in an HCP was developed in this study. From a numerical simulation, the coherent vortex structures of fluctuating modes were observed, and the velocity iso-surfaces of the coherent vortex of the wake flow exhibited an annular trend in circumferential connection. Then, the hydrodynamic force was analyzed: the steady component and transient component were resolved, and the general trend in forces in terms of the transient components was that the maximum amplitude of forces reduced with an increase in mode order. Through short-term Fourier transform, the frequency components and their variations in terms of the entire time range could be acquired. The transient model in this study provided a perspective to build the connection between the flow structures and the hydrodynamic force. By the transient model, the transient component of hydrodynamic force can be explained as the fluctuation of coherent vortex structures.

As the process before the transporting of the capsule in a hydraulic capsule pipeline system, the capsule’s threshold of motion process is often tested in the horizontal straight pipe. However, the result of the physical test in this work shows that the wheeled capsule more easily start-moves in a horizontal bent pipe. Thus, the numerical simulation and the theory analysis were used to study the wheeled capsule’s threshold of motion process in the bent pipe. The simulation results demonstrate that the velocity magnitude of the water flow was asymmetric between the inner part and the outer part of the section closing on the wheeled capsule. This was unlike the water flow of the section in the straight pipe. From this result, a new mechanical model was proposed that divides the wheeled capsule into two parts. The two parts of the mechanical model correspond to the two parts of the section. Then, the deduction has shown that the bolsters of the inner part of the wheeled capsule in the bent pipe endured lower maximum static friction than those in the straight pipe. The whole wheeled capsule was more unstable in the bent pipe than in the straight pipe because of the additional drag force induced by the centrifugal effect of the bent pipe’s water flow.

This study quantitatively and mechanistically examines the flow structure of annular flow with a moving boundary based on the motion conditions of a blunt body within a pressurized pipe. It conducts numerical simulations under turbulent flow conditions to acquire representative flow field samples of the annular flow, and the results are validated through Particle Image Velocimetry. First, the moving-boundary annular flow is subjected to ensemble averaging, and the ensemble-averaged flow structure is obtained using the Q-criterion to identify coherent flow structures. Second, a low-dimensional flow model employing the Proper Orthogonal Decomposition Galerkin method is developed for the moving-boundary annular flow, and the characteristics of coherent vortices and turbulent transport in representative modes are investigated. The radial coherent vortices showed a symmetric pairing tendency along the circumferential direction in the low-order modes, whereas the circumferential coherent vortices appear layered and superimposed along the axial direction, the axial coherent vortices tend to pair and merge along the axial direction. The turbulent kinetic energy contributions under varying conditions remain around 10% within the initial few orders of the modal sequence and generally fall below 0.1% in the 90th and higher-order modes. The Reynolds stress distribution across the modes in the flow field demonstrates a consistent pattern in which the contribution of Reynolds stress decreases as the number of modal sequences increases.