Numerical investigation on the pressure loss of coarse particles hydraulic lifting in the riser with the lateral vibration

Highlights

• Dynamic grid technique is used to simulate the lateral vibration of the riser.

• The pressure loss in the dynamic riser is more than in the static riser.

• As the amplitude of the lateral vibration increase, the pressure loss arises.

• As the period of the lateral vibration increase, the pressure loss decreases.

• As the order of the model shape increases, the pressure loss enhances obviously.

Abstract

This study focuses on the effect of the riser lateral vibration on the pressure loss of coarse particles hydraulic lifting by the numerical simulation. Euler-Euler two-fluid model based on kinetic theory is used to simulate the flow behavior of coarse particles in the riser, and the numerical model has been validated by using the experimental data. The dynamic grid technique is employed to simulate the lateral vibration of the riser. According to results of numerical simulation, the lateral vibration leads to the cyclical fluctuation of the pressure loss of coarse particles hydraulic lifting, and the average pressure loss of the dynamic riser is bigger than the static riser in general. The influence of the vibration amplitude, vibration period and modal shape on the pressure loss is analyzed, and the cause of pressure loss is also discussed.

Introduction

The ocean is very rich in mineral resources, it will become sustainable development mineral resources for human in the future. At present, deep-sea mineral mining generally adopts the scheme of hydraulic lifting in the riser [1]. The length of riser can be several kilometers according to the operation requirement, the lateral vibration of riser definitely occurs under the action of current, which is called vortex-induced vibration. It will cause the new flow behavior of the liquid-solid two-phase flow (the mixture of mineral coarse particles and seawater). And the flow behavior is a very critical in the design of mineral particles hydraulic lifting system.

Several studies were dedicated to study the hydraulic conveying of coarse particles. Alajbegović [2] measured the phase distribution for liquid-solid flow having spherical particles (2 mm in diameter) in a vertical pipe by LDA. The volume fraction profiles showed that at low flow rates the ceramic particles had an almost uniform distribution, while increasing the flow rate causing coring. In contrast, the phase distribution of the light polystyrene particles had wall peaking for both the low and high flow rates. Asakura [3] employed discrete particle model to simulate the motion of coarse particles in the hydraulic lifting pipe. He found that particles moved toward the center of the pipe without the action of coarse particles to the fluid. In contrast, particles had an almost uniform distribution. Xia [4] also used the discrete particle method to simulate the movement of manganese nodules in hydraulically lifting in the vertical pipeline, and believed that the particles had a tendency to move toward the center of the pipeline.

In the past few years, some scholars have used the experimental method and numerical simulation to investigate the pressure loss of liquid-solid two-phase flow in the vertical pipeline. Messa [5] presented a new two-fluid model for the simulation of fully-suspended liquid–solid slurry flows in horizontal pipes. The improvements considerably increase the accuracy of the pressure gradient predictions, without affecting the model's capability in reproducing the other features of these flows, namely solid volume fraction distribution and velocity distribution. Yuan [6] measured the pressure loss of the liquid-solid two-phase flow in the swing pipeline, it was found that the pressure loss was greater than in the static pipe. Zhao and Xia [7] also found this phenomenon in their experiment. They thought that particles produced radial motion due to the drag force of the water, the number of contacts between granules and the pipeline wall rised, so the axial impulse of the liquid-solid two-phase flow decreased and the pressure loss increased. They also found that the pressure loss enhanced with increase of the frequency on the condition that the amplitude was the same. They also used the Lagrangian-Euler model to track the granular trajectories, and did the research about the axial impulse variation of the fluid-solid two-phase flow in the swing pipeline. According to characteristics of the force which acts on particles, a methematical model is established. Xu [8] used the Euler-Euler two-fluid flow to study the influence of parameters of hydraulic transmission system on the pressure loss in submarine natural gas hydrate exploitation. Liu [9] employed Euler-Euler two-fluid flow model to simulate the two dimensional liquid-solid flow having coarse particles in the hydraulic lifting riser. He did the research about the influence of the riser lateral vibration on flow behavior of the liquid-solid flow in the riser. It was found that the vibration changed the distribution of particle volume fraction, local particle volume fraction increased significantly. Kaushal [10] numerically simulated pipeline slurry flow of mono-dispersed fine particles at high concentration using Mixture and Eulerian two-phase models. Euler-Euler two-fluid model gives fairly accurate predictions for both the pressure drop and concentration profiles at all efflux concentrations and flow velocities.

However, very little work has been done on the effect of the riser lateral vibration on the pressure loss of coarse particles hydraulic lifting. The Euler-Euler two-fluid model based on kinetic theory is used here to simulate the liquid-solid two-phase flow in the riser. The numerical model used in this study will be validated by comparing the numerical result with the experimental data from Ref. [2]. The dynamic grid technique is employed to simulate the lateral vibration of the riser. On the basis of models, the influence of the lateral vibration on the pressure loss will be discussed.