Generalized master curve for threshold superficial velocities in particle–fluid systems

Effects of Water and Fertilizer Flow Rates on the Mixing Process and Fertilization Uniformity of Cotton under Mulch Drip Irrigation

Water and fertilizer flow rates are the most convenient variable to control in the process of drip irrigation under mulch. Suitable water and fertilizer flow rates are beneficial to improve water and fertilizer uniformity. Nine groups of water and fertilizer rate combinations were set in the common water and fertilizer rate range to study the influence of the water and fertilizer rate on fertilization uniformity. The numerical simulation of the mixing process in the main pipe was first carried out based on the multiphase flow theory, and then the field experiment for the different water and fertilizer rate combinations in the machine-picked cotton-planting pattern (one film, three tubes and six rows) was conducted. Through the numerical simulation of the mixing process in the pipeline and the analysis of water and fertilizer uniformity field experiment results, it was found that the uniform mixing length is related to the water and fertilizer flow rate, and the water and fertilizer flow rate had some effect on fertilizer uniformity. In the irrigation system with a main pipe diameter of 100 mm and a fertilizer injection pipe diameter of 20 mm, the water fertilizer flow rate ratio should be between 3–8 to ensure the effect of the mixing process and fertilization uniformity. A water flow rate of 2 m s−1 and fertilizer flow rate of 0.35 m s−1 is recommended during the fertilizer process in northern Xinjiang. This paper shows the feasibility of numerical simulation in the study of cotton water and fertilizer mixing processes, and the results can provide some reference for cotton planting.

Role of Reynolds and Archimedes numbers in particle-fluid flows

Any scientific behavior is best represented by nondimensional numbers. However, in many cases, for pneumatic conveying systems, dimensional equations are developed and used. In some cases, many of the nondimensional equations include Reynolds (Re) and Froude (Fr) numbers; they are usually defined for a limited range of materials and operating conditions. This study demonstrates that most of the relevant flow types, whether in horizontal or vertical pipes, can be better described by Re and Archimedes (Ar) numbers. Ar can also be used in hydraulic conveying systems. This paper presents many threshold velocities that are accurately defined by Re as a simple power function of Ar. Many particulate materials are considered by Ar, thereby linking them to a common behavior. Using various threshold velocities, a flow regime chart for horizontal conveying is presented in this paper.

Experimental and Numerical Analyses on Mixing Uniformity of Water and Saline in Pipe Flow

Liquid—liquid mixing is commonly observed in many applications such as the chlorination of water supplies and the agricultural fertigation. In order to study the mixing law of water-chlorine or water-fertilizer in a turbulent pipeline, saline was selected as a tracer injected into the pipeline. In this paper, the computational fluid dynamics (CFD) software was employed to study flow fields in water-saline pipelines. Four variates (mixing ratio δ, pipe diameter D, volume flow rate in the main pipe Q, saline density ρs) were considered to investigate the effects of multiple variates on mixing uniformity. The coefficient of variation (COV) was selected as the evaluation index of mixing uniformity, effective mixing length (LEML, the distance from the saline inlet to the fully mixed position) was chosen to quantitatively analyze the fully mixed position of water and saline in pipelines. The results of this numerical model agree well with experimental measurements and it shows that this model can effectively predict the concentration field of water and saline in the pipeline. Based on the experimental and simulated results, it was found that for the fixed mixing ratio, saline density and volume flow rate, the values of LEML increased significantly with increasing pipe diameters. Furthermore, dimensional analysis (D-A) was adopted to examine the influences of the four variates on LEML, and their correlation coefficient of the curve-fitting equation was calculated to be 0.996.