Valve closure based on pump runaway characteristics in long distance pressurized systems

In order to guarantee the safety of pumps, valves are installed at the outlet of each pump in long-distance pressurized water supply systems. However, water hammer pressure caused by improper valve closure can tremendously exceed the standard of the pipeline. In this paper, the effects of valve closure on speed of pump and pressure along the pipeline were investigated. Valve closure formula based on pump runaway characteristics were proposed and verified using numerical simulation. In addition, when valves were closed under the formula proposed in this paper and other closure laws, the minimum speed, minimum and maximum pressure along the pipeline were compared. The results showed that formulas agree well with the numerical results. In the high lift supply systems, compared with the other closure laws, the minimum speed and minimum pressure along the pipeline under valve closure formula were the largest, and the maximum pressure along the pipeline was the smallest. Moreover, in the low lift supply systems, the minimum speed under valve closure formula did not exceed the rated speed. Compared with the other closure laws, the minimum pressure along the pipeline was the largest and the maximum pressure along the pipeline was the smallest.

A three-phase flow model with two miscible phases

The paper concerns the modelling of a compressible mixture of a liquid, its vapor and a gas. The gas and the vapor are miscible while the liquid is immiscible with the gaseous phases. This assumption leads to non symmetric constraints on the void fractions. We derive a three-phase three-pressure model endowed with an entropic structure. We show that interfacial pressures are uniquely defined and propose entropy-consistent closure laws for the source terms. Naturally one exhibits that the mechanical relaxation complies with Dalton’s law on the phasic pressures. Then the hyperbolicity and the eigenstructure of the homogeneous model are investigated and we prove that it admits a symmetric form leading to a local existence result. We also derive a barotropic variant which possesses similar properties.

The Effect of Closure Laws on the Simulation Results of Two-Fluid Model of Gas-Solid Flows

There are two primary approaches in modeling fluid-solid flows based on the method of treating particles suspended in flows. The first approach is the Eulerian-Lagrangian or Discrete Element Method (DEM) approach that tracks individual particles by solving the equations of motion of these particles. The second approach is the Eulerian-Eulerian approach or two-fluid model (TFM) that considers particles as another continuum phase or fluid. The TFM is preferred in modeling and predicting gas-solid flow behaviors in many engineering applications because of its efficiency in handling large-scale complex systems with large number of particles. However, one of the challenges in TFM is the uncertainty related to the selection of closure laws and transport properties of solid phases. In this study we employ the MFIX code, a general-purpose TFM computer code developed at the National Energy Technology Laboratory, to investigate the effect of different drag models and heat transfer models on the simulation results on the flow hydrodynamics and heat transfer of gas-solid fluidized beds. Three drag models (Gidspow model, Syamlal-O’Brien model, and Koch-Hill model) and two heat transfer model (Gunn model and a recently developed model by Sun et al., 2015) are tested. Simulation results from these models are compared with experimental measurements. The accuracy and applicability of these models are assessed and discussed.

Analysis of Water Hammer with Different Closing Valve Laws on Transient Flow of Hydrogen-Natural Gas Mixture

Water hammer on transient flow of hydrogen-natural gas mixture in a horizontal pipeline is analysed to determine the relationship between pressure waves and different modes of closing and opening of valves. Four types of laws applicable to closing valve, namely, instantaneous, linear, concave, and convex laws, are considered. These closure laws describe the speed variation of the hydrogen-natural gas mixture as the valve is closing. The numerical solution is obtained using the reduced order modelling technique. The results show that changes in the pressure wave profile and amplitude depend on the type of closing laws, valve closure times, and the number of polygonal segments in the closing function. The pressure wave profile varies from square to triangular and trapezoidal shape depending on the type of closing laws, while the amplitude of pressure waves reduces as the closing time is reduced and the numbers of polygonal segments are increased. The instantaneous and convex closing laws give rise to minimum and maximum pressure, respectively.