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The purpose of this study is to develop a new approach for simulating the ion flow field with the floating conductors based on the existing inversion method.

The space charge keeps charging the floating conductors until the dynamic balance is reached. The corresponding floating potential boundary condition is linearized as the combination of the equipotential constraints and natural boundary condition, which can be directly imposed in the inversion process.

The numerical results demonstrate that the modified inversion algorithm performs well in the ion flow field with the floating conductors and the floating potential converges within five steps’ iterations. The proposed approach is applied to investigate the effect of the grounded line to the floating conductors in the practical high voltage direct current (HVDC) transmission lines.

The modified inverse algorithm provides a general way to deal with the Kapzov hypothesis and the floating boundary condition simultaneously within one loop, which can be applied to the multiphysics systems with different kinds of irregular boundary conditions.

The per-unit-length earth return mutual impedance of the overhead conductors plays an important role for analyzing electromagnetic transients or couplings of multi-conductor systems. It is impossible to have a closed-form expression to evaluate this kind of impedance. The purpose of this paper is to propose an efficient numerical approach to evaluate the earth return mutual impedance of the overhead conductors above horizontally multi-layered soils.

The expression of the earth return mutual impedance, which contains a complex highly oscillatory semi-infinite integral, is divided into two parts intentionally, i.e. the definite and the tail integral, respectively. The definite integral is calculated using the proposed moment functions after fitting the integrand into the piecewise cubic spline functions, and the tail integral is replaced by exponential integrals with newly developed asymptotic integrands.

The numerical examples show the proposed approach has a satisfactory accuracy for different parameter combinations. Compared to the direct quadrature approach, the computational time of the proposed approach is very competitive, especially, for the large horizontal distance and the low height of the conductors.

The advantage of the proposed approach is that the calculation of the highly oscillatory integral is completely avoided due to the fact that the moment function can be evaluated analytically. The contribution of the tail integral is well included by means of the exponential integral, though in an asymptotic way. The proposed approach is completely general, and can be applied to calculate the earth return mutual impedance of overhead conductors above a soil structure with an arbitrary number of horizontal layers.

The study aims to decrease the effect of solid particles on a butterfly valve, which will cause seal failure and leakage, providing a reference for anti-wear design.

In this paper, computational fluid dynamics discrete element method (CFD-DEM) simulation was conducted to study the solid–liquid two-phase flow characteristics and erosion characteristics of a butterfly valve with a different opening.

Abrasion at 10% opening is affected by high-speed jets in upper and lower parts of the pipeline, where the erosion is intense. The impact of the jet on the upper part of 20% opening begins to weaken. With the top backflow vortex disappearing, the effect of lower jet is enhanced. Meanwhile, the bottom backflow vortex phenomenon is obvious, and the abrasion position moves downward. At 30% opening, the velocity is further weakened, and the circulation effect of lower flow channel is more obvious than that of the upper one.

It is the first time to use DEM to investigate the two-phase flow and erosion characteristics at a small opening of a butterfly valve, considering the effect of inter-particle collision. Therefore, this study carries on the thorough analysis and discussion. At the same opening degree, with increasing of the particle size, the abrasion of valve frontal surface increases when the size is less than 150 µm and decreases when it is greater than 150 µm. For the valve backflow surface, this boundary value becomes 200 µm.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2020-0264/

The purpose of this paper is to analyze the mechanism of particle erosion in butterfly valve pipelines under hydraulic transportation conditions. The results will affect the sealing and safety of butterfly valve pipelines and hopefully serve as reference for the anti-erosion design of butterfly valve pipelines.

Through the discrete element method (DEM) simulation that considers the force between particles, the detached eddy simulation (DES) turbulence model based on realizable k-epsilon is used to simulate the solid-liquid two-phase flow-induced erosion condition when the butterfly valve is fully opened. The simulation is verified by building an experimental system correctness. The solid-liquid two-phase flow characteristics, particle distribution and erosion characteristics of the butterfly valve pipeline under transportation conditions are studied.

The addition of particles may enhance the high-speed area behind the valve. It first increases and then decreases with increasing particle size. With increasing particle size, the low-velocity particles change from being uniformly distributed in flow channel to first gathering in the front of the valve and, then, to gathering in lower part of it. Fluid stagnation at the left arc-shaped flange leads to the appearance of two high-speed belts in the channel. With increasing fluid velocity, high-speed belts gradually cover the entire valve surface by focusing on the upper and lower ends, resulting in the overall aggravation of erosion.

Considering the complexity of solid-liquid two-phase flow, this is the first time that the DEM method with added inter-particle forces and the DES turbulence model based on realizable k-epsilon has been used to study the flow characteristics and erosion mechanism of butterfly valves under fully open transportation conditions.