考虑射流破碎和液滴形状的喷灌水运动轨迹改进模型构建及验证

喷洒液滴分布特征是模拟喷头水量和能量分布的基础。为解决现有弹道轨迹模型过度简化运动液滴的破碎过程及形状变化导致模型精度不足的问题，该研究改进了弹道轨迹模型的液滴破碎过程、运动液滴形状参数和运动液滴阻力系数，提出了基于能量加权的等效液滴指标，建立了考虑射流破碎和液滴形状的喷洒水运动轨迹改进模型；采用HY50型蜗轮蜗杆式喷枪验证了模型精度，对比了不同模型的差异。结果表明：喷嘴直径20mm和工作压力0.35MPa时，改进模型的平均绝对误差MAE分别比Fukui模型和Li模型的降低了43.3%和75.1%（落地速度）、51.8%和27.1%（落地位置）和61.4%和76.1%（落地角度）；以4个验证工况中落地速度为例，改进模型、Fukui模型和Li模型的均方根误差RMSE平均值分别为0.53、0.93和2.21 m/s；归一化均方根误差NRMSE平均值分别为0.10、0.17和0.40。研究可为应用弹道轨迹模拟喷洒液滴分布特征提供新思路。

Construction and validation of the improved Ballistic model for sprinkler water trajectory considering jet fragmentation and droplet shape

Spray droplet trajectory can often be used to calculate the water and energy distribution of the nozzle. The spray droplet movement and distribution patterns can greatly contribute to the design of sprinkler systems under windy, evaporative, and sloping conditions. Experimental tests, CFD simulations, and theoretical calculations have been commonly used to explore the characteristics of spray droplets. The ballistic trajectory model in the theoretical calculation has effectively simulated the spray droplet distribution using droplet dynamics, due to the high operational efficiency and small test volume. However, the previous model suffers from an oversimplification of the droplet break-up process and the shape of the motion. It is necessary to further improve the accuracy of the model using more realistic parameters for the jet break-up process and droplet shape. In this study, an energy-weighted droplet equivalence index was proposed to modify the initial conditions of the ballistic trajectory model, the kinematic droplet shape parameters, and the kinematic droplet drag coefficient. A model of spray droplet distribution characteristics was established using the improved equation for the ballistic trajectory. The velocity, particle size, and angle of spray droplet landing were simulated by inputting parameters, such as the nozzle diameter, working pressure, and nozzle elevation angle. The accuracy of the model was verified using an HY50 turbine drive sprinkler. A comparison was made on the differences between the current model and the simulated values of the conventional ballistic trajectory model. The modified model was compared using the characterized drag coefficient under four common operating conditions. An analysis was implemented on the effects of different operating pressures, nozzle diameters, nozzle elevation angles, and mounting heights on the droplet size, velocity, and angle at the end of the range. The results show that the MAE of the improved model was reduced than before by 43.3% and 75.1% (landing velocity), 51.8% and 27.1% (landing position), and 61.4% and 76.1% (landing angle), respectively, in the nozzle diameter of 20 mm and working pressure of 0.35 MPa. Taking the landing velocities from the improved model, the average RMSEs were 0.53, 0.93, and 2.21 m/s, respectively, while the average NRMSEs were 0.10, 0.17, and 0.40, respectively, in the Fukui and Li models under the four optimal conditions. The greater the nozzle diameter and working pressure were, the greater the droplet particle size and landing velocity were at the end of the range, and the smaller the landing angle was. The greatest effect was found in the nozzle working pressure variation on the droplet particle size, the nozzle diameter variation on the droplet landing velocity, and the nozzle elevation angle on the droplet landing angle. The least effect was found in the nozzle mounting height on the end droplet characteristic parameters. Therefore, the jet fragmentation and droplet shape can be expected to focus on when building the model. But the sprinkler system can be inevitably affected by multiple factors, such as the topography, wind, evaporation, and deflector pipes when operating in the field. The droplet distribution of sprinklers should be simulated by the multiple factors at the farm scale, in order to improve the generalizability and practicality of the current model. This finding can provide new ideas to simulate the spray droplet, water, and energy using distributions of ballistic trajectories.