The performance of a standard (k-L) turbulence model for predicting slurry pipeline pressure gradients is examined using experimental measurements of velocity and solids concentration distribution for upward vertical flows. Assuming the solids concentration rises abruptly from a value of zero at the pipe wall over a distance corresponding to one half a particle diameter, satisfactory predictions were obtained for sand particles of median diameter up to about 800 um in a 25.8 mm vertical pipeline. No damping of fluid turbulence or additional stresses due to particle-particle interactions were included in the computational model. Velocity distributions are found to be flatter than those of turbulent single-phase flows, because of the variation of mixture properties in the vicinity of the pipe wall.

The capacity limitations of distribution networks, the increasing demands for electricity installation in terms of electricity quality parameters, and the development of electromobility all increase the need to implement systems in order to stabilize and regulate loads for end users. Battery Energy Storage Systems (BESSs), that operate in internal microgrids of enterprises, allow smoothing of electrical power consumption profiles by actively reducing peak demand power. By using BESSs to implement a peak shaving strategy to reduce the peak power consumption of a company in an external network, energy efficiency can be improved by reducing contractual capacity. The aim of this study is to determine the conditions for the use of energy storage, in order to implement a peak shaving strategy for which the installation of the enterprise microgrid is economically efficient. The analysis of the operating conditions of the BESS should take into account the size of the energy storage, the characteristics of the demand profile for the demand systems, the charges related to electricity, and the costs of electricity storage. In the study, the size of the energy storage was related to the power and electrical capacity of the BESS that was used to implement the peak shaving strategy. The article presents the results of research on the method for determining an effective capacity and power of BESSs for enterprise microgrid systems. The technical and cost limitations of the actual microgrid system, which affected the decrease in economic efficiency of the peak shaving strategy in the company research, were taken into account. The simulations of the operation of the electricity storage system, based on real data of the demand of production companies, were based on the rules and market conditions in Poland.

The paper presents validation of a mathematical model describing the friction factor by comparing the predicted and measured results in a broad range of solid concentrations and mean particle diameters. Three different types of solids, surrounded by water as a carrier liquid, namely Canasphere, PVC, and Sand were used with solids density from 1045 to 2650 kg/m³, and in the range of solid concentrations by volume from 0.10 to 0.45. All solid particles were narrowly sized with mean particle diameters between 1.5 and 3.4 mm. It is presented that the model predicts the friction factor fairly well. The paper demonstrates that solid particle diameter plays a crucial role for the friction factor in a vertical slurry flow with coarse solid particles. The mathematical model is discussed in reference to damping of turbulence in such flows. As the friction factor is below the friction for water it is concluded that it is possible that the effect of damping of turbulence is included in the K_B function, which depends on the Reynolds number.