# Study on the Flow Velocity of Safe and Energy-Saving Transportation of Light-Particle Slurry
## 1 Introduction  
Ice slurry is a solid-liquid mixed two-phase refrigerant consisting of ice crystal particles, water, and a freezing point modifier, where the average characteristic diameter of the ice crystal particles does not exceed 1 mm [1]. Due to its excellent heat transfer characteristics and flow properties, ice slurry is considered a promising and premium fluid [2]. Ice slurry, as a cold storage medium, is one of the most effective means to realize the \"peak shifting and valley filling\" of the power grid [3], and it has been widely used in the fields of cold storage in buildings, food cooling, mine cooling, and medical protection [4]. In addition, polymer-oil-driving technology and hydraulic transportation of gelled crude oil in oil fields [5; 6], polymer particle-water solid-liquid two-phase flow of polypropylene, polyethylene, and other polymers in annular tube reactors [7], solid-liquid two-phase flow of hollow glass beads-water in the preparation of lightweight cement composites for water purification and lightweight cement composites [8; 9], and so on, are all flow problems that are part of the light particles two-phase flow model. Therefore, it is important to find out the optimal flow rate for the safe and energy-efficient transportation of light particle slurries. Therefore, the safe transportation of ice slurries in pipelines plays a crucial role for their application in practice. Critical flow velocity is an important parameter for slurry pipeline transportation, which refers to the minimum safe flow rate required to ensure the flow of slurry. An unreasonable working flow velocity not only leads to solid-phase particles becoming gathered in the pipeline to cause pipeline wear and pipeline clogging [10], but also leads to an increase in conveying resistance and improves the energy consumption of the system; therefore, a reasonable determination of the size of the critical flow velocity is an effective means to ensure the safe and economic transportation of slurry. At present, the definition of critical flow velocity for slurry is not the same as that of other scholars. [PERSON] [11] and [PERSON] [12] used the \"minimum conveying flow velocity\" and \"critical deposition flow velocity\" as the definition of critical flow velocity, respectively. [PERSON] [13] believed that the critical flow velocity is the flow velocity that causes the phenomenon of pipeline erosion and corrosion in the pipeline transportation of solid-liquid two-phase flow. The flow states of ice slurry in the pipe are generally categorized into three, as follows: stationary bed, moving bed, and suspended bed [14]. In the suspended bed, it is subdivided into a non-homogeneous bed and a homogeneous bed, according to the distribution of the ice crystal particles. In order to avoid ice jamming phenomenon and enable the ice slurry to be transported safely and stably, the critical flow velocity of the ice slurry is considered to be the velocity when the flow pattern is exactly changed from a moving bed to a non-homogenized suspended bed [15]. Currently, various scholars have proposed many critical flow rate calculation methods, as well as empirical or semi-empirical formulas [16; 17; 18; 19], which are of some guiding significance for slurry transportation. However, due to the limitation of experimental content and experimental methods, it cannot comprehensively consider all of the factors in pipeline hydraulic conveying, and many formulas have their limitations. [PERSON] [20] analyzed the influence of ice slurry concentration distribution on the flow by numerical simulation and found that the flow tends to show more homogeneous distribution flow with the increase in inlet flow velocity, the increase in ice content rate, and the decrease in particle size. This method can effectively determine the ice slurry flow pattern based on the degree of particle stratification, thus determining the critical flow velocity; however, it is easy to produce errors through the iterative processing of simulation.