Numerical simulation of velocity field of sand grains in backwashing process of sand filter layer in micro-irrigation based on granular flows theory

The velocity distribution of sand grains in the backwashing flow field is key to the backwashing performance of sand filter layer, such as the expansion height, distribution uniformity and the stability of fluidized state. To analyze the velocity distribution of sand grains in the backwashing process and find out the optimal backwashing speed, numerical simulation was used in this paper. Moreover, a geometric model of sand filter was established and the mesh division of the geometric model was carried out through Gambit software. Because the backwashing process of quartz sand filter layer is a solid-liquid multiphase flow system composed of water and quartz sand, we can conclude that the Eulerian model is suitable for the numerical simulation of the velocity field of sand grains by comparing the applicability of the current multiphase flow numerical simulation models such as Eulerian model, Mixture model and VOF(volume of fluid) model. At the same time, because the backwashing process of quartz sand filter layer is both a dynamic and a stable process, the transient simulation solver was adopted. Additionally, the granular flow theory was used to seal the momentum equation of the model, because of the formation of granular flows in the backwashing process. The simulation objects was the quartz sand filter layer whose thickness was 400 mm, and the equivalent grain diameter was 1.06 mm. In order to verify the reliability of simulation results, laboratory experiments of backwashing were conducted in Farmland Irrigation Research Institute, Chinese Academy of Agricultural Sciences, Xinxiang, China. The parameters such as the backwashing speed and the total height of the filter layer were measured during the experiments. And the simulation results were compared with the experimental results. Comparison results showed that the maximum simulation error of the sand grains velocity was 9.8%. So the numerical simulation results were proved to be reliable. On this basis, three cross-sections, with the height of 15, 25 and 35 cm, were selected in the filter layer and the axial velocity distribution of sand grains was analyzed. The fluidization ratio of backwashing for this simulation was 1.3, 1.5, 1.7 and 1.9 respectively. Based on the magnitude and direction of the velocity of sand grains in the three cross-sections, we can figure out whether the sand filter layer is completely fluidized or not. The stability of the fluidization state of the filter layer can be estimated by the consistency of the movement trend of sand grains in the three cross-sections and the stability of the rising zone of granular flows. The results showed that the bigger the fluidization ratio of backwashing is, the less time needed for completely fluidizing the filter layer. As a consequence, only if the fluidization ratio of backwashing is not less than 1.7, the filter layer might reach a stable state of fluidization. In a stable flow, the rising zone and the descending zone formed a stable circulation in the filter layer. As the grains swarm moved along a relatively fixed path, the ideal backwashing effect was achieved. It can be seen from the above that the optimal fluidization ratio of backwashing of the filter layer is 1.7. The research provide not only a theoretical basis and technical support for the study of the sand filter but also a reference for the determination of performance parameters for the backwashing.