李景海, 刘清霞, 黄修桥, 翟国亮, 韩启彪. 微灌石英砂滤层流态特性与分形阻力模型参数确定[J]. 农业工程学报, 2015, 31(13): 113-119. DOI: 10.11975/j.issn.1002-6819.2015.13.016
    引用本文: 李景海, 刘清霞, 黄修桥, 翟国亮, 韩启彪. 微灌石英砂滤层流态特性与分形阻力模型参数确定[J]. 农业工程学报, 2015, 31(13): 113-119. DOI: 10.11975/j.issn.1002-6819.2015.13.016
    Li Jinghai, Liu Qingxia, Huang Xiuqiao, Zhai Guoliang, Han Qibiao. Flow state characteristics and fractal model parameters determination of quartz sand filter layer used in micro-irrigation[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2015, 31(13): 113-119. DOI: 10.11975/j.issn.1002-6819.2015.13.016
    Citation: Li Jinghai, Liu Qingxia, Huang Xiuqiao, Zhai Guoliang, Han Qibiao. Flow state characteristics and fractal model parameters determination of quartz sand filter layer used in micro-irrigation[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2015, 31(13): 113-119. DOI: 10.11975/j.issn.1002-6819.2015.13.016

    微灌石英砂滤层流态特性与分形阻力模型参数确定

    Flow state characteristics and fractal model parameters determination of quartz sand filter layer used in micro-irrigation

    • 摘要: 石英砂是微灌过滤中常用滤料,具有多孔介质属性。该文将多孔介质模型和分形理论相结合,对3种粒径的微灌石英砂滤层的过滤过程展开研究。将Ergun型方程无量纲化,并结合试验确定了石英砂滤层的流态分区。构建了石英砂滤层清洁压降的分形阻力模型,在模型中,过滤通道曲线分形维数、滤层横截面分形维数为待定参数。为了确定二者的值,将Ergun型方程与分形阻力模型相对比,得出了Ergun型方程经验系数的分形表达式,从而确定待定参数的值。首先,结合试验数据,拟合出湍流区经验系数的值,根据经验系数的分形表达式,确定了过滤通道曲线分形维数、滤层横截面分形维数等参数,得出了湍流区分形模型的表达式。然后,以湍流流区分形参数的值为边界值,确定了Forchheimer流区过滤通道曲线分形维数表达式和滤层横截面分形维数的值,并得出了Forchheimer流区分形模型的表达式。在此基础上,分析了滤层过滤特性:1)根据Forchheimer流区过滤通道曲线分形维数的变化规律,得出了在Forchheimer流区滤层存在成熟期的结论;2)探讨了滤层最佳过滤速度和最佳清洁压降的计算方法,构建了石英砂滤层过滤性能函数,并利用过滤性能函数计算出了滤层的最佳过滤速度和最佳清洁压降。3种滤层最佳过滤速度分别为0.02、0.024和0.027 m/s,最佳清洁压降分别为6 045、9 660、14 500 Pa。研究为微灌砂过滤器运行和设计优化提供了技术依据。

       

      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.

       

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