Abstract:
Abstract: Quartz sand, one kind of porous media, is commonly used in micro-irrigation filter. Selecting optimal filtration speed and pressure drop of clean are important for design and operation of filters. In this study, fluid equation for porous media and fractal models were proposed to determine pressure drop of quartz sand layer. In order to facilitate flow zone division, we introduced dimensionless pressure drop into the original fluid equation of porous media. In this way, the empirical coefficients in fluid equation became meaningful. The dimensionless pressure drop is a linear function of Reynolds number, the changes in function curves indicates the changes in flow zones. Based on the dimensionless equation the flow pattern zone could be divided in combination with filtration tests. On the other hand, in the fractal model, the fractal dimensions of the curve and cross section were undetermined parameters. Their values could be determined by the empirical coefficient by comparing the fluid equation with fractal models. The method was demonstrated by a laboratory experiment conducted in Farmland Irrigation Research Institute, Chinese Academy of Agricultural Sciences, Xinjiang, China in 2014. 3 kinds of quartz sand filter layer with different particle sizes were selected based on commonly used sizes in Xinjiang including equivalent sizes of 1.06, 1.2 and 1.5 mm. The sandy layer had a depth of 400 mm and porosity of 0.44. The flow characteristic of irrigation water in micro-irrigation filter with quartz sand was first analyzed and then the empirical coefficient of turbulent flow region was fitted by the experimental data. The parameters of the fractal model were determined, and the expression of fractal model of turbulent flow region was obtained. Using the values of fractal dimension of the curve and cross section in turbulent flow region, the fractal dimensions of curve and cross section in Forchheimer flow region was determined. And the expression of fractal model of Forchheimer flow region was obtained. Finally, the best filtration rate and clean pressure drop were estimated. Results showed that: 1) The Reynold numbers were 2 and 7.3 for size of 1.06 mm, 2 and 10 for size of 1.2 mm, 2 and 16.3 for size of 1.5 mm when Forchheimer zone changed into Turbulent zone. There was a linear relationship between sand size and Reynold numbers. Based on the relationship, the pressure drop could be well estimated with maximum relative error of 5.84%. In the Forchheimer flow region, the pressure drop was also estimated well with maximum relative error of 8.92%. According to the variation of fractal dimension of the curve in Forchheimer flow region, the filter layer could be considered as in a mature stage. The best filtration speed of the filtration layers with equivalent sizes of 1.06, 1.2, and 1.5 mm were 0.02, 0.024 and 0.027 m/s, the best cleaning pressure drops of the 3 filtration layers were 6045, 9660, and 14500 Pa. The research provided valuble information for design, operation and optimization of sand filter in micro irrigation.