A method and system for predicting the trajectory of water droplets sprayed by a rotary head

Abstract

The present application relates to a kind of rotating sprinkler water droplet movement trajectory prediction method and prediction system, wherein the prediction method is by collecting nozzle structure, operation and environmental parameters, construct the water droplet initial velocity model combined with the rotation effect of sprinkler disc, establish the water droplet particle size distribution model with probability weight combined with actual spraying law, obtain the three-dimensional trajectory of water droplet of multiple particle size by solving water droplet flight motion control equation, the global spraying process is restored by the discrete of sprinkler rotation period, combined with drop point statistics and weighted water volume superposition, calculate the spray water depth and the uniformity coefficient of sprinkling irrigation.The present application effectively reduces the simulation calculation error, can predict the water droplet trajectory of nozzle, spray range and spray uniformity, and is suitable for rotating sprinkler spray performance evaluation and parameter optimization.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of agricultural water-saving irrigation engineering and fluid mechanics, specifically to a method and system for predicting the trajectory of water droplets sprayed by a rotating sprinkler head. Background Technology

[0002] Large sprinkler irrigation machines are important equipment for water-saving irrigation in agriculture. The rotary sprinkler head, as a key spraying component, directly affects the irrigation range, water distribution, and irrigation uniformity. When the rotary sprinkler head is working, water is sprayed out after passing through the flow channel of the spray disc. The continuous rotation of the spray disc causes the launch direction and initial velocity of the water droplets to change constantly when they leave the spray disc, thus affecting the flight trajectory and landing point distribution of the water droplets in space.

[0003] Existing methods for predicting water droplet motion mostly focus on fixed nozzles, typically simplifying the initial velocity of the droplets to a radial velocity along the jet direction, and then calculating the droplet trajectory based on this. These methods struggle to reflect the influence of the rotation of the nozzle disk on the initial velocity direction and impact point distribution of the droplets, leading to significant biases in the predictions of the range and water volume distribution of rotating nozzles.

[0004] Furthermore, the water droplets sprayed from a rotating nozzle are not of a single size, but rather composed of droplets of different sizes. Different droplet sizes differ in terms of air resistance, flight time, and landing point. If only a single droplet size or average droplet size is used for calculation, it is difficult to accurately describe the motion characteristics of the actual sprayed water droplet group. Summary of the Invention

[0005] To address the problem that existing methods for predicting water droplet motion based on fixed sprinklers struggle to characterize the influence of the rotation effect of the spray disk on water droplet motion, leading to significant deviations in droplet trajectory prediction, this invention proposes a method and system for predicting the trajectory of water droplets sprayed from a rotating sprinkler. This method establishes an initial velocity model of the water droplets incorporating the spray disk rotation effect within a fixed reference frame, constructs a droplet size distribution function incorporating the influence of working pressure and nozzle diameter, numerically solves the water droplet motion equation based on ballistic trajectories, and employs a ground grid water volume overlay method. This enables the prediction of the water droplet trajectory, range, and uniformity coefficient of the sprayed water volume distribution from the rotating sprinkler.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention relates to a method for predicting the trajectory of water droplets sprayed from a rotary sprinkler head, comprising the following steps: Obtain the structural, operational, and environmental parameters of the rotary nozzle; By combining the rotational motion characteristics of the spray disk and the jet ejection characteristics of the rotary nozzle, a water droplet initial velocity model incorporating the spray disk rotation effect is constructed to characterize the influence of the spray disk rotation on the initial motion state of the water droplets. Based on the actual droplet size distribution of water sprayed by a rotary nozzle, a droplet size distribution model adapted to the rotary nozzle is constructed to generate a group of water droplet samples with probabilistic representativeness and match the corresponding droplet size weights. The motion control equations for the free flight phase of water droplets under a fixed reference frame are established. The motion control equations are numerically solved based on the initial motion parameters, particle size characteristics and environmental parameters of the water droplets to obtain the three-dimensional motion trajectories of water droplets with different working conditions and different particle sizes. Discretize the spraying process of the nozzle's complete rotation cycle, simulate the instantaneous spraying motion of water droplets at different ejection moments within the entire cycle, and obtain the full-domain water droplet motion trajectory data under the rotating spraying condition. Based on the spatial statistics and water volume superposition analysis of the water droplet landing point, the characteristics of ground spray water distribution are obtained and the sprinkler uniformity coefficient is solved, so as to predict the water droplet trajectory, effective spray range and spray uniformity of the rotating sprinkler head.

[0007] In one possible implementation, the structural parameters include the spray disc radius, nozzle installation height, spray elevation angle, and nozzle diameter; the operating parameters include the working pressure, spray disc rotation speed, initial droplet velocity, and calculation time step; and the environmental parameters include air density, aerodynamic viscosity, and ambient wind speed.

[0008] In one possible implementation, constructing a model of the initial velocity of water droplets that incorporates the rotational effect of the spray disc includes the following steps: Calculate the working angular velocity of the spray disc based on the spray disc rotation speed, and solve for the tangential velocity generated by the rotation of the spray disc by combining the spray disc radius; The total ejection velocity of the water droplets is decomposed based on the nozzle's jet elevation angle to obtain the resultant velocity in the horizontal plane. The radial velocity of the water droplet is solved based on the vector composition relationship, and the azimuth angle of the water droplet's ejection velocity is determined by combining the cosine theorem. The three-dimensional initial velocity components of the water droplets when they leave the spray disc are determined based on the angles between the horizontal surface velocity and the X and Y axes, the nozzle spray elevation angle, and the horizontal surface velocity, combined with the spray disc rotation angle. The initial spatial position of the water droplet when it leaves the spray plate is obtained by solving for t and the nozzle installation height H. The rotation of the spray plate is converted into a dynamic change in the initial velocity direction and initial position of the water droplet. The angle between the horizontal plane velocity and the X and Y axes is determined based on the azimuth angle of the water droplet's ejection velocity.

[0010] In one possible implementation, the droplet size distribution model uses the Gamma distribution as its basic form to construct the probability density function. Taking into account the influence of working pressure and nozzle diameter, the probability density function is: Wherein, the water droplet size is d, the working pressure is P, and the nozzle diameter is D. The shape parameter is used to characterize the peak shape and dispersion of the water droplet size distribution curve. is a scale parameter used to characterize the scale of water droplet size distribution; Multiple representative water droplets of different particle sizes are generated based on the probability density function, and weights are assigned to the corresponding water droplets according to the occurrence probability of each particle size, so that the water droplet sample group conforms to the actual spraying particle size distribution characteristics.

[0011] In one possible implementation, when solving the motion control equations for the free flight phase of the water droplet, the initial velocity of the water droplet, the representative particle size obtained from the probability density function of the water droplet size distribution, and the probability weight are used as input parameters. The four-order Runge-Kutta method is used to solve the three-dimensional motion trajectory of the water droplet at each launch time and for each particle size through time iteration. The critical state of the water droplet landing is captured, and the actual landing coordinates of the water droplet are obtained by linear interpolation correction of the coordinates before and after landing.

[0012] In one possible implementation, the discretization of the spraying process during the complete rotation cycle of the nozzle includes: uniformly discretizing the complete rotation cycle of the nozzle into several equally spaced water droplet ejection times, matching the rotational attitude of the spray disc with the initial motion parameters of the water droplets at each time, solving the water droplet motion trajectory time by time, and then integrating the trajectories of all ejection times to obtain global water droplet motion data.

[0013] In one possible implementation, the spatial statistics and water volume superposition analysis of the water droplet landing point includes: dividing the horizontal ground statistical area into statistical grids, classifying each water droplet into the corresponding statistical grid according to the coordinates of the water droplet landing point, and accumulating the water volume in each statistical grid by combining the probability weights of water droplet volume and particle size to obtain the spraying water depth of each statistical grid, thereby calculating the irrigation uniformity coefficient.

[0014] In one possible implementation, after dividing the horizontal ground statistical area into statistical grids, before classifying each water droplet into its corresponding statistical grid based on the droplet's landing point coordinates, and accumulating the water volume within each statistical grid by combining droplet volume and particle size probability weights to obtain the spraying water depth of each statistical grid, and before calculating the irrigation uniformity coefficient, the method further includes: Based on the maximum and minimum X-axis values ​​of water droplet landing points in the statistical region of the horizontal ground, and the minimum and minimum Y-axis values ​​of water droplet landing points, a statistical grid is extended along the X-axis and Y-axis directions, respectively.

[0015] As a second aspect, this application relates to a prediction system for the trajectory of water droplets sprayed from a rotary sprinkler head, which is used to implement the above-mentioned prediction method, and includes: The parameter acquisition module is used to collect and preprocess the structural parameters, operating parameters, and environmental parameters of the rotary nozzle to build a dataset of predictive basic parameters. The initial velocity modeling module is used to construct an initial velocity model of water droplets that incorporates the spray disc rotation effect, and to solve for the three-dimensional initial velocity and initial spatial position of the water droplets after they leave the nozzle. The particle size distribution modeling module is used to construct a water droplet particle size distribution model based on the Gamma distribution and generate a representative group of water droplet samples with probability weights. The equations of motion module is used to construct the control equations for the free flight of water droplets under a fixed reference frame, and to use the Runge-Kutta method to solve the trajectory numerically, so as to obtain the three-dimensional motion trajectory of water droplets under different working conditions and different particle sizes. The rotating spraying simulation module is used to discretize the nozzle rotation cycle, simulate the instantaneous spraying process of water droplets at different ejection times throughout the entire cycle, and output the global water droplet motion trajectory data. The water distribution analysis module is used to complete the grid statistics of water droplet landing points, calculate water volume superposition, solve the spraying water depth and irrigation uniformity coefficient, and output the prediction results of sprinkler head water droplet trajectory, effective spraying range and spraying uniformity.

[0016] The present invention has the following advantages due to the adoption of the above technical solutions: 1. This invention acquires parameters such as the structure, operation, and environment of the rotating sprinkler head, constructs an initial velocity model of water droplets combined with the rotation effect of the spray disc, to characterize the influence of the sprinkler head rotation on the initial motion state of the water droplets. Simultaneously, based on the actual water droplet size distribution law of the sprinkler head, a corresponding water droplet size distribution model is established, generating a representative water droplet sample group with probability weights and matching the weights. Then, the motion control equations for the free flight stage of water droplets under a fixed reference frame are constructed, and numerical solutions are performed to obtain the three-dimensional motion trajectories of water droplets with different working conditions and different particle sizes. Subsequently, discrete simulations are performed on the complete rotation cycle of the sprinkler head to obtain global water droplet motion trajectory data. Finally, by combining spatial statistics of water droplet landing points and water volume superposition analysis, the characteristics of ground water volume distribution are obtained, and the irrigation uniformity coefficient is calculated. Thus, an integrated prediction of the rotating sprinkler head's water droplet motion trajectory, spray range, and spray uniformity can be achieved.

[0017] 2. In the process of solving the initial velocity of the water droplet, this invention combines the tangential velocity component of the spray disk rotation, so that the initial motion state of the water droplet when it leaves the spray disk takes into account both the radial jetting effect of the water flow and the rotational traction effect of the spray disk. This restores the actual water output dynamic characteristics of the rotating nozzle, effectively overcoming the technical defects of the traditional fixed nozzle ballistic model that cannot adapt to the rotating spraying condition and the distortion of motion state simulation, thus improving the simulation accuracy of water droplet trajectory from the source.

[0018] 3. This invention constructs a droplet size distribution model based on the Gamma distribution using measured sprayed water droplet size data. It integrates the nozzle working pressure and nozzle diameter into the calculation model for average droplet size and coefficient of variation, using the average droplet size and coefficient of variation to solve for the shape and scale parameters of the Gamma distribution. Simultaneously, this invention generates representative water droplet samples based on the probability intervals of the droplet size distribution and matches them with corresponding probability weights. This allows droplets of different sizes to participate in trajectory iteration and grid water volume superposition calculations according to their actual spraying proportions. It abandons the idealized assumption of using a single average droplet size in traditional simulations, effectively avoiding trajectory deviations and water volume statistical errors caused by single-size calculations. This makes the simulation results of droplet group movement and ground water volume distribution more closely resemble actual spraying conditions.

[0019] 4. This invention, through discretization of the nozzle's rotation period, high-precision solution of instantaneous water droplet trajectories, and weighted superposition of ground grid water volume, can output multiple core performance indicators of the rotating nozzle, such as effective spraying range, water droplet landing point distribution, overall ground water volume distribution, and irrigation uniformity coefficient. The simulation results show good consistency with the measured results, and can distinguish the differences in spray uniformity under different nozzles and operating conditions, providing reliable theoretical and simulation support for nozzle structure optimization, operating condition matching, and irrigation system performance evaluation. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the numerical solution for the motion trajectory of a single water droplet in a rotary nozzle according to one embodiment of the present invention. Figure 2 This is a flowchart of a method and system for predicting the trajectory of water droplets from a rotating nozzle according to an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the decomposition of the initial velocity of water droplets combined with the rotation effect of the spray disc in one embodiment of the present invention; Figure 4 This is a comparison chart of the fitting effects of candidate particle size distribution functions in one embodiment of the present invention; Figure 5 This is a schematic diagram of the nozzle rotation cycle discretization and instantaneous jet trajectory in one embodiment of the present invention; Figure 6 This is a schematic diagram of the landing point grid statistics in one embodiment of the present invention; Figure 7 This is a comparison and verification diagram of the predicted sprinkler uniformity coefficient and the measured sprinkler uniformity coefficient in one embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0022] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," "third," "fourth," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect.

[0023] In modern agricultural water-saving irrigation, rotary sprinklers are often used as key spraying components. Their spraying performance directly affects the irrigation range, water distribution, and irrigation uniformity. However, existing methods for predicting droplet motion mostly focus on fixed sprinklers, typically simplifying the initial droplet velocity to a radial velocity along the spray direction and calculating the droplet trajectory based on this. This method struggles to reflect the influence of the rotating sprinkler head's rotation on the initial velocity direction and impact point distribution of the droplets, leading to significant deviations in the prediction of the rotary sprinkler's range and water distribution. Therefore, to address these technical problems, this invention provides a rotary sprinkler spraying... A method and system for predicting water droplet trajectories are developed. By establishing an initial velocity model of water droplets incorporating the rotation effect of the spray disc under a fixed reference frame, and using the water droplet size distribution function, the water droplet motion equation based on ballistic trajectory, and the ground grid water volume superposition method, reliable predictions of the water droplet trajectory, range, and uniformity coefficient of spray water distribution of a rotating sprinkler head are achieved. This restores the water droplet trajectory and ground water volume distribution law of the rotating sprinkler head, significantly improving the accuracy and reliability of sprinkler performance prediction, and providing reliable numerical simulation support for the optimization and engineering application of agricultural water-saving irrigation equipment.

[0024] It should be noted that the rotary sprinkler head is equipped with a spray disc, which is the core moving water outlet component of the rotary sprinkler head. During operation, it can rotate continuously with the sprinkler head, playing a role in stabilizing, diverting and guiding the internal water flow. At the same time, the tangential velocity brought by the rotation of the spray disc will combine with the radial velocity of the jet, directly changing the trajectory of the water droplets in the air and the distribution of the landing point on the ground. It is a key structure that determines the sprinkler head's spray range, the overall water distribution, and the uniformity of irrigation.

[0025] like Figures 1 to 7 As shown, the method for predicting the trajectory of water droplets sprayed by a rotary nozzle according to the present invention specifically includes the following steps: S1. Obtain the structural parameters, operating parameters, and environmental parameters of the rotary nozzle.

[0026] Specifically, structural parameters include the spray disk radius, nozzle installation height, spray elevation angle, and nozzle diameter. These parameters are used to construct the geometric working model of the rotating nozzle, which can be used to solve for the tangential velocity of the spray disk rotation, the initial three-dimensional angle of the water droplet, and the initial spatial position. This determines the initial motion state of the water droplet when it leaves the spray disk and the theoretical limit spray range, ensuring that the initial velocity modeling conforms to the actual structural characteristics of the nozzle. Operating parameters include working pressure, spray disk rotation speed, initial water droplet velocity, and calculation time step. The working pressure determines the basic ejection velocity of the water droplet and, together with the initial water droplet velocity, determines the kinetic energy of the water droplet. The spray disk rotation speed is used to calculate the angular velocity of the spray disk, enabling dynamic simulation of the combined effect of the spray disk rotation. The calculation time step is the core operating parameter for full-cycle, high-precision dynamic trajectory simulation. Environmental parameters include air density, aerodynamic viscosity, and ambient wind speed. These parameters can be used to calculate air resistance and aerodynamic losses during the flight of water droplets, thereby correcting the flight attenuation of water droplets of different sizes, avoiding deviations caused by ideal, interference-free simulations, and making the structure of water droplet trajectories, landing point distribution, and water volume superposition more consistent with the actual sprinkler irrigation environment.

[0027] S2. Combining the rotational motion characteristics of the spray disc and the jet ejection characteristics of the rotary nozzle, a water droplet initial velocity model incorporating the spray disc rotation effect is constructed to characterize the influence of the spray disc rotation on the initial motion state of the water droplets.

[0028] When a rotary nozzle is working, the initial motion state of a water droplet at the moment it leaves the spray plate is affected not only by the ejection direction of the spray plate channel but also by the combined effect of the spray plate's rotational motion. Therefore, by constructing a water droplet initial velocity model that incorporates the spray plate rotation effect, and combining the characteristics of the spray plate rotational motion with the characteristics of the water jet ejection, the dynamic control law of the spray plate rotation on the magnitude, direction of motion, and initial spatial position of the water droplet ejection velocity is quantified. This restores the actual initial motion state of the water droplet when it leaves the spray plate, providing accurate initial boundary conditions for the subsequent numerical solution of the water droplet flight trajectory.

[0029] In the specific modeling process, to characterize the spray disc rotation effect, the initial velocity of the water droplets is decomposed into radial velocity along the spray disc flow channel, tangential velocity generated by the spray disc rotation, and vertical velocity determined by the spray elevation angle. First, the working angular velocity of the spray disc is calculated based on its rotational speed, and then the tangential velocity generated by the spray disc rotation is solved using the spray disc radius. The velocity decomposition relationship is as follows: Figure 3 As shown. Let the radius of the spray disc be r and the rotational speed be n, then the working angular velocity of the spray disc is... Let V1 be the tangential velocity generated by the rotation of the spray disc. Secondly, the total ejection velocity of the water droplets is decomposed based on the nozzle's spray elevation angle to obtain the resultant velocity in the horizontal plane. Let the total velocity of the water droplets at the instant they leave the nozzle be V0, and the spray elevation angle be... The resultant velocity of the water droplet in the horizontal plane is .

[0030] Next, the radial velocity of the water droplet is solved based on the vector composition relationship, and the azimuth angle of the water droplet's ejection velocity is determined by combining the cosine theorem. Since the water droplet velocity is in the horizontal plane, it is composed of the tangential velocity V1 and the radial velocity V2, satisfying... Therefore, the radial velocity V2 can be calculated as follows: To further determine the initial velocity direction of the water droplet, let the tangential velocity V1, radial velocity V2, and the resultant velocity on the horizontal plane form a velocity triangle, and let... Let V be the angle between the resultant velocity V on the horizontal plane and the radial direction. Then, by the law of cosines, we can obtain the angle. for: .

[0031] Finally, by combining the spray disc rotation angle and the nozzle installation height, the three-dimensional initial velocity components and initial spatial position of the water droplet when it leaves the spray disc are obtained, thus transforming the spray disc rotation into a dynamic change in the initial velocity direction and initial position of the water droplet. Let t be the time it takes for the water droplet to accelerate from the spray disc surface until it leaves the spray disc, i.e., combining... Figure 3 The time t required for the water droplet to move from position 1 to position 2 is and the angle that the spray disc rotates through during this time period is . t, the angle between the radial velocity of the water droplet as it leaves the spray nozzle and the Y-axis is . Then the angle between the resultant velocity V on the horizontal plane and the Y-axis is... Correspondingly, the angle between the resultant velocity V on the horizontal plane and the X-axis is... Therefore, the components of the initial velocity of the water droplet in the fixed three-dimensional coordinate system are: If the nozzle installation height is H, then the initial position of the water droplet when it leaves the spray plate can be represented as: .

[0032] Through the above modeling method, the constructed water droplet initial velocity model combined with the spray disk rotation effect completely transforms the dynamic mechanical effect of continuous spray disk rotation into the dynamic changes of the initial velocity magnitude, ejection direction and initial spatial position of the water droplets. This not only retains the influence of continuous rotation of the spray disk on the water droplet motion state, but also avoids directly solving the complex flow process inside the spray disk. Thus, it provides accurate and complete dynamic initial boundary conditions for subsequent solutions of water droplet free flight trajectory, spray simulation and water distribution calculation.

[0033] S3. Based on the actual droplet size distribution of water sprayed by the rotary nozzle, construct a droplet size distribution model adapted to the rotary nozzle, generate a group of water droplet samples with probabilistic representativeness, and match the corresponding droplet size weights.

[0034] Water droplets sprayed from a rotating nozzle are not of a single size. Different droplet sizes experience significantly different levels of air resistance and flight attenuation. Using a single droplet size or average droplet size for trajectory calculation makes it difficult to accurately reflect the motion characteristics of the water droplet group during actual spraying. Therefore, this invention, based on measured water droplet size data, establishes a water droplet size distribution model based on the Gamma distribution. Furthermore, it incorporates working pressure and nozzle diameter into the droplet size distribution parameters, enabling the water droplet size distribution to dynamically adjust according to changes in the nozzle's operating conditions.

[0035] Let the droplet size be d, the working pressure be P, and the nozzle diameter be D. Then the Gamma distribution probability density function of the droplet size is: Where α is the shape parameter, used to characterize the kurtosis and dispersion of the water droplet size distribution curve, and θ is the scale parameter, used to characterize the scale of the water droplet size distribution. Furthermore, for the Gamma distribution, its mean particle size and variance satisfy: ,in, The average particle size is This represents the standard deviation of particle size.

[0036] To further describe the dispersion of particle size distribution, the coefficient of variation (CV) is introduced, which is defined as: Then, substituting the average particle size and variance of the Gamma distribution into the formula for the coefficient of variation, we can obtain: The shape parameter of the Gamma distribution can be expressed by the coefficient of variation as: Furthermore, considering both the average particle size and variance of the Gamma distribution, the scale parameter of the Gamma distribution can be expressed as: .

[0037] Therefore, by calculating the average droplet size and coefficient of variation of water droplets based on the current spraying conditions, the shape and scale parameters of the Gamma distribution under these conditions can be calculated in reverse using the average droplet size and coefficient of variation. This allows for the establishment of a droplet size distribution law that adapts to the actual spraying characteristics of the rotary nozzle. The average droplet size is used to control the overall position of the droplet size distribution curve, while the coefficient of variation is used to control the degree of dispersion of the droplet size distribution curve. Together, they determine the complete probability distribution of droplet size.

[0038] For any type of rotary nozzle, spraying tests are conducted under different operating conditions, and measured samples of water droplet size are collected. Let n be the total number of samples obtained under the i-th test condition. i A sample of water droplet size, denoted as d. ij where j = 1, 2, ..., ni The average particle size and standard deviation under this working condition can be obtained from the statistical analysis of the measured data: Accordingly, the particle size variation coefficient under the i-th operating condition is: Under different working pressures and different nozzle diameters, and CV i Then, a functional relationship between the average particle size and the working pressure and nozzle diameter can be further established.

[0039] For a typical rotary nozzle, the average particle size function can be expressed as: ,in, Let P be the average particle size under working pressure P and nozzle diameter D, and A, m, and n be coefficients obtained by fitting measured particle size data. This formula is used to describe the influence of changes in working pressure and nozzle diameter on the overall position of water droplet particle size distribution.

[0040] However, the average particle size still cannot fully describe the droplet size distribution. The average particle size only reflects the overall position of the droplet size distribution curve, but not the peak height, width, or dispersion of the curve. Therefore, the coefficient of variation is further used to describe the dispersion of the droplet size distribution, and a functional relationship is established between the coefficient of variation and the working pressure and nozzle diameter: ,in, Let P be the particle size variation coefficient under working pressure P and nozzle diameter D, and B, r, and s be coefficients obtained by fitting measured particle size data. This formula is used to describe the influence of changes in working pressure and nozzle diameter on the dispersion of water droplet particle size distribution.

[0041] Therefore, according to the above formula, the shape parameter of the Gamma distribution under any working pressure and nozzle diameter conditions can be expressed as: The scale parameter can be expressed as Substituting the shape and size parameters into the Gamma distribution probability density function of the water droplet size, we can obtain the water droplet size probability density function that incorporates the effects of working pressure and nozzle diameter: Therefore, it can be seen that the shape and scale parameters in the Gamma distribution are no longer fixed constants, but functions of the working pressure P and the nozzle diameter D. In other words, for any rotating nozzle, given the working pressure and nozzle diameter, the average particle size is first calculated using the average particle size function. Then calculate the particle size variation coefficient. Then, the shape parameters under the corresponding working conditions are calculated. and scale parameters Finally, the droplet size probability distribution under this working condition is determined by the droplet size probability density function. Next, multiple sets of representative droplets of different sizes are generated according to the probability density function, and weights are assigned to the corresponding droplets according to the occurrence probability of each size, so that the droplet sample group conforms to the actual spraying particle size distribution characteristics.

[0042] The above-described process for constructing the water droplet size distribution model is applicable to various rotary nozzles, meeting the requirements for spray particle size differences among different models of rotary nozzles. Therefore, for rotary nozzles of different structures and specifications, it is only necessary to refit the correlation between the working conditions and particle size characteristic parameters based on the measured water droplet size test data of the corresponding nozzle, so as to quickly adapt and establish a dedicated water droplet size distribution model for the corresponding nozzle. This makes the water droplet size distribution model of the present invention have good versatility and model adaptability.

[0043] The following section uses the R3000 damped rotary nozzle as an example to illustrate the specific fitting process of the aforementioned general particle size distribution model. To determine the influence of working pressure and nozzle diameter on water droplet size distribution, experimental statistics were conducted on the water droplet size distribution of the R3000 damped rotary nozzle under different working pressures and nozzle diameters. The statistical results of water droplet size distribution under different working pressures and nozzle diameters are shown in the table below.

[0044] Table 1. Statistical results of water droplet size distribution parameters of R3000 damped rotary nozzle under different operating conditions.

[0045] The data in the table presents statistical results of water droplet size tests conducted on the R3000 damped rotary nozzle under different operating pressures and nozzle diameters. The results show that both operating pressure and nozzle diameter affect the average droplet size and its distribution morphology. As the operating pressure increases, the water flow breaking effect intensifies, leading to an overall decrease in the average droplet size; simultaneously, the droplet size distribution tends to be more concentrated, and the coefficient of variation decreases overall. Changes in nozzle diameter alter the jet flow rate, velocity, and dispersion process of the spray disc, thus affecting the dispersion and size of the water droplet size distribution.

[0046] Based on the above experimental data, the average particle size function was fitted to obtain the expression for the average particle size of the R3000 damped rotary nozzle: Where P is the working pressure, in psi; and D is the nozzle diameter, in mm. The average droplet size is expressed in mm. Therefore, according to the formula for the average droplet size of the R3000 damped rotary nozzle, it can be shown that within the experimental range of this embodiment, the average droplet size decreases as the working pressure increases; changes in nozzle diameter affect the jet flow rate, flow velocity, and dispersion process of the spray disc, thereby affecting the average droplet size.

[0047] Meanwhile, based on the above experimental data, the coefficient of variation function was fitted, and the expression for the coefficient of variation of the R3000 damped rotary nozzle was obtained as follows: ,in, Let be the coefficient of variation of particle size under working pressure P and nozzle diameter D. The coefficient of variation function shows that, within the experimental range of this embodiment, as the working pressure increases, the droplet breakup process becomes more complete, the particle size distribution tends to be more concentrated, and the coefficient of variation decreases. Changes in nozzle diameter will alter the jet breakup and spray disc dispersion processes, thereby affecting the dispersion of particle size distribution.

[0048] By substituting the average particle size function and coefficient of variation function of the R3000 damped rotary nozzle into the shape and scale parameters of the Gamma distribution, the shape and scale parameters of the R3000 damped rotary nozzle under different working pressures and nozzle diameters can be obtained, and the probability density function of the water droplet size under these conditions can be obtained.

[0049] For example, for nozzle #44, its diameter is 8.731 mm. At a working pressure of 20 psi, the average particle size under this condition is calculated to be approximately 0.537 mm using the formula for the average particle size of the R3000 damped rotary nozzle; the coefficient of variation under this condition is calculated to be approximately 0.604 using the expression for the coefficient of variation of the R3000 damped rotary nozzle. Furthermore, the shape parameter of the Gamma distribution is calculated to be approximately 2.743 using the formula for the shape parameter function of the Gamma distribution, and the scale parameter is calculated to be approximately 0.196 mm using the formula for the scale parameter function of the Gamma distribution. Therefore, the probability density function of the droplet size under the condition of 20 psi and nozzle #44 can be obtained using the droplet size probability density function.

[0050] Through the aforementioned data processing and parameter fitting, the average particle size function is used to characterize the overall offset position and overall particle size level of the water droplet size distribution curve, while the coefficient of variation function is used to describe the distribution width and dispersion of the particle size distribution curve. The shape and scale parameters obtained from the solution work together to completely determine the global particle size probability distribution characteristics of water droplets sprayed by the rotating sprinkler head. Based on the constructed water droplet size probability density distribution law, the entire water droplet size range can be divided into several continuous intervals. Within each interval, statistically representative characteristic particle sizes are selected, and weighting coefficients are assigned to the corresponding characteristic particle sizes according to the actual probability proportion of each particle size interval. By using weighted multi-size water droplet samples to participate in subsequent single-droplet trajectory iteration calculations and global ground grid water volume overlay statistics, the flight differences and water volume overlay differences of different particle sizes during actual spraying are restored, significantly improving the prediction accuracy of spray water volume distribution and irrigation uniformity coefficient.

[0051] S4. Establish the motion control equations for the free flight phase of the water droplets under a fixed reference frame. Based on the initial motion parameters, particle size characteristics, and environmental parameters of the water droplets, numerically solve the motion control equations to obtain the three-dimensional motion trajectories of water droplets with different working conditions and particle sizes.

[0052] After detaching from the spray disk, the water droplet moves in a fixed reference frame. Its flight process is mainly affected by gravity, air resistance, buoyancy, and ambient wind speed. Using the initial conditions of the water droplet, its particle size characteristics, and environmental parameters as input conditions, the changes in its velocity and position are solved step by step. By comparing the water droplet's relative air velocity to reflect the effects of air resistance and wind speed, the control equations for the water droplet's dynamic motion are constructed, specifically: .

[0053] When numerically solving the above-mentioned water droplet motion control equation, the initial velocity of the water droplet obtained from the initial velocity model in S2 above, and the representative particle size and probability weight obtained from the particle size distribution model in S3 are used as input parameters. The fourth-order Runge-Kutta method is used to iterate the motion control equation over time. Specifically, the complete flight time of the water droplet is divided into several small uniform time steps. The motion control differential equation is solved iteratively step by step using the fourth-order Runge-Kutta iterative formula. The velocity change and displacement change of the water droplet in each time step are calculated in turn. The three-dimensional flight velocity and spatial coordinate position of water droplets with different launch times and different particle sizes are updated in real time. The iterative calculation continues until the water droplet lands, completely reproducing the dynamic flight process of the water droplet in the complex field environment, so as to obtain the motion trajectory of water droplets with different launch times and different particle sizes in three-dimensional space.

[0054] Simultaneously, after obtaining the trajectory of the water droplet in three-dimensional space, the critical state of the droplet's landing is captured. Linear interpolation is performed based on the spatial coordinates of the two calculation steps before and after landing to correct the theoretical landing point position of the droplet, resulting in the corrected landing coordinates. Specifically, let the heights of the water droplet at the previous and current moments be z... n and z n+1 Then the coefficient of difference is: The landing location is: This invention utilizes the spatial coordinates of two adjacent computational steps before and after the droplet's landing to perform linear interpolation correction. This can lock the actual landing time of the droplet, correct the landing point deviation caused by discrete time step iteration, effectively compensate for the inherent accuracy defects of the fourth-order Runge-Kutta fixed time step numerical solution, eliminate the need to encrypt the global iteration step size, reduce a large amount of computational work, and thus significantly improve the calculation accuracy of the single droplet landing coordinates.

[0055] S5. Discretize the spraying process of the nozzle's complete rotation cycle to simulate the instantaneous spraying motion of water droplets at different exit moments within the entire cycle, and obtain the full-domain water droplet motion trajectory data under the rotating spraying condition.

[0056] Specifically, the single complete rotation cycle of the nozzle is uniformly discretized into several equally spaced water droplet ejection times, such as... Figure 5 As shown, water droplets have different exit azimuths at different times. For each discrete exit moment, the corresponding spray disk rotation attitude and the initial motion parameters of the water droplets are matched, and the instantaneous spray trajectory of the water droplets is numerically solved moment by moment. This invention matches the corresponding spray disk rotation attitude and the initial motion parameters of the water droplets for each discrete exit moment, which can closely match the actual working state of the nozzle and avoid the model simplification error caused by simulation of a single water outlet angle. By integrating the independent motion trajectories of water droplets corresponding to all different exit moments, covering the entire cycle of dynamic spraying process of the nozzle, and combining and stitching them together, a complete global water droplet motion trajectory data is obtained.

[0057] S6. Based on the droplet landing point, spatial statistics and water volume superposition analysis are carried out to obtain the distribution characteristics of ground spray water volume and solve the sprinkler uniformity coefficient, so as to predict the water droplet trajectory, effective spray range and spray uniformity of the rotating nozzle.

[0058] This invention projects all valid water droplet landing points onto a statistical area on a horizontal ground surface, and lets the coordinates of the i-th water droplet landing point be... Maximum range is Let the range of the x and y coordinates of all effective water droplet landing points be respectively and The grid size is and ,in, and Based on the spraying range and statistical accuracy, when the statistical area is divided into M grids horizontally and N grids vertically... and It can be represented as: This process divides the horizontal ground spraying area into several rectangular statistical grids of uniform size. Each grid serves as the smallest unit for water volume statistics, and the grid to which each water droplet belongs is determined based on its corrected landing coordinates.

[0059] Furthermore, after dividing the horizontal ground statistical area into statistical grids, before classifying each water droplet into its corresponding statistical grid based on the droplet's landing point coordinates, and accumulating the water volume within each statistical grid by combining droplet volume and particle size probability weights to obtain the spraying water depth of each statistical grid, and then calculating the irrigation uniformity coefficient, the process further includes: Based on the maximum and minimum X-axis values ​​of water droplet landing points in the statistical region of the horizontal ground, and the minimum and minimum Y-axis values ​​of water droplet landing points, a statistical grid is extended along the X-axis and Y-axis directions, respectively.

[0060] In this embodiment, to avoid missing water droplet landing points near the boundary, the statistical area is expanded outward by one unit grid size based on the maximum and minimum coordinate ranges of all valid landing points, forming the final ground water volume statistical area. Specifically, This allows for the complete collection of all water droplet landing points, avoiding the omission of boundary water droplets in the statistics, ensuring the accuracy of the total water volume calculation for the grid, and improving the calculation accuracy of water distribution and sprinkler uniformity coefficient.

[0061] Subsequently, water droplets are assigned to their respective grids based on their landing locations, and the water volume is accumulated according to the probability weights of droplet volume and particle size. Let the diameter of the i-th water droplet be D. i The probability weights are The cumulative water volume in the grid is: The spraying water depth corresponding to the grid cell is: The water volume within each grid cell is accumulated by combining the probability weights of water droplet volume and particle size. After completing the statistics of all effective water droplet landing points, the spraying depth of each grid cell is obtained, and the irrigation uniformity coefficient is further calculated. For the landing point grid statistics method, please refer to [link to relevant documentation]. Figure 6 The formula for calculating the uniformity coefficient of sprinkler irrigation is: , where h i Let i be the water depth of the i-th effective grid. The effective grid represents the average water depth, and N represents the number of effective grid cells.

[0062] By combining the probability weights of water droplet size with the weighted summation of grid water volume, the actual distribution of water droplet size is closely observed, effectively improving the practicality of grid water depth calculation. Simultaneously, the sprinkler uniformity coefficient is solved based on the standardized grid water depth, providing a quantitative and intuitive calculation with standardized procedures. The sprinkler uniformity coefficient is used to quantitatively evaluate the spraying performance of the sprinklers, directly reflecting the uniformity of water distribution on the field surface.

[0063] Based on the above-mentioned prediction system for the trajectory of water droplets sprayed by a rotary nozzle, the present invention also provides a prediction system for the trajectory of water droplets sprayed by a rotary nozzle, in order to realize the aforementioned prediction method for the trajectory of water droplets sprayed by a rotary nozzle. The prediction system includes a parameter acquisition module, an initial velocity modeling module, a particle size distribution modeling module, a motion equation module, a rotary spraying simulation module, and a water volume distribution analysis module.

[0064] Specifically, the parameter acquisition module collects and preprocesses the structural, operational, and environmental parameters of the rotating sprinkler head, constructing a dataset of basic prediction parameters. This provides unified, complete, and directly callable input conditions for subsequent modeling, trajectory solving, and water volume statistics modules, ensuring the continuous and stable operation of the entire prediction process. It also improves the model's versatility and adaptability under different sprinklers and field conditions. The initial velocity modeling module constructs an initial velocity model of water droplets that incorporates the spray disc rotation effect. It can solve for the three-dimensional initial velocity and initial spatial position of water droplets after they leave the sprinkler head. By constructing the initial velocity model, it overcomes the initial state calculation deviation caused by traditional simulations that only use static water velocity and do not consider the tangential velocity of the spray disc rotation. It restores the actual ejection motion state of water droplets from the rotating sprinkler head, reducing simulation errors from the source of trajectory calculation and improving the accuracy of subsequent simulations of water droplet flight trajectories and landing positions. The particle size distribution modeling module is used to construct a water droplet particle size distribution model based on the Gamma distribution, generating a representative water droplet sample group with probability weights. This module uses the Gamma distribution to generate the actual particle size distribution of water droplets produced by the corresponding nozzle, selects multiple representative water droplet sizes and matches them with corresponding probability weights, constructing a sample set that reflects the actual proportion of water droplets of different sizes. This provides standardized water droplet sample input for subsequent grid-based water volume weighted accumulation and trajectory solving. The motion equation module is used to construct the control equations for the free flight motion of water droplets in a fixed reference frame and uses the fourth-order Runge-Kutta method to complete the trajectory numerical solution, obtaining the three-dimensional motion trajectory of water droplets under different working conditions and with different particle sizes. It outputs the water droplet's position and motion state data throughout the entire process, providing trajectory basis data for subsequent impact point analysis and full-cycle spraying simulation. The rotational spraying simulation module discretizes the nozzle rotation period, simulates the instantaneous spraying process of water droplets at different launch times throughout the entire cycle, and outputs global water droplet motion trajectory data. The water distribution analysis module is used to complete the grid statistics of water droplet landing points, calculate water volume superposition, solve the spraying water depth and irrigation uniformity coefficient, and output the prediction results of sprinkler head water droplet trajectory, effective spraying range and spraying uniformity.

[0065] In addition, the motion equation module includes a built-in trajectory iteration unit. This unit iteratively updates the droplet's motion state according to a preset time step, using the initial velocity of the droplet output from the initial velocity modeling module, the representative particle size output from the particle size distribution modeling module, and the corresponding probability weights as input parameters to progressively solve for the complete trajectory of the droplet. Furthermore, the motion equation module also includes a landing point correction unit. This unit identifies the critical state of the droplet's landing, extracts the spatial coordinates of two adjacent calculation steps before and after the droplet's landing, and corrects the theoretical landing point position of the droplet using a linear interpolation algorithm. This eliminates the landing point truncation error caused by numerical iteration at fixed time steps, resulting in high-precision landing coordinates.

[0066] The water distribution analysis module includes a grid division unit and a probability weight overlay unit. The grid division unit first counts the maximum and minimum coordinates of all valid water droplet landing points to define the basic statistical range. Then, it expands outward by one grid size around the coordinate extreme values ​​to form the final statistical area, avoiding the omission of water droplet landing points at the boundary and ensuring that all water droplets can be included in the grid water volume statistics. The probability weight overlay unit calculates the volume of a single water droplet based on the diameter of each droplet, and adds up the water volume of the droplets falling into the same grid according to the corresponding particle size probability weight to obtain the total water volume of the grid. Then, it calculates the spraying water depth of each grid unit. After all grid statistics are completed, the irrigation uniformity coefficient is calculated based on the grid water depth to quantitatively characterize the uniformity of the sprinkler head spraying.

[0067] Each module of the prediction system of this invention corresponds one-to-one with the aforementioned prediction method, forming a complete computational closed loop from parameter input, initial state modeling of water droplets, numerical solution of trajectory, dynamic simulation of the entire rotation cycle to grid-based water volume weighted statistics and quantitative evaluation of spraying performance. This allows the entire system to be implemented without field trials, and can quickly predict the spraying performance of rotating nozzles under different structures and working conditions, providing reliable simulation support for nozzle structure optimization and field irrigation condition selection.

[0068] In a specific embodiment, the imported rotary sprinkler head equipped with a center-pivot sprinkler irrigation machine is used as the object to illustrate the method and system for predicting the trajectory of water droplets sprayed by the rotary sprinkler head proposed in this invention. This center-pivot sprinkler irrigation machine consists of two truss spans and a cantilever section. The lengths of the two truss spans are 43.3 m and 37.5 m respectively, the cantilever length is 16.5 m, and the total length of the unit is 97.3 m. The sprinkler heads are arranged along the branch pipe direction of the equipment, with the nozzle size gradually increasing from the inside to the outside, adapting to the water distribution needs of fields with a wider irrigation area and greater water demand outside the unit. This simulation selects the imported rotary sprinkler head equipped with the unit as the core calculation object, setting the sprinkler head working pressure to 138 kPa and the installation height to 1.5 m. The environmental conditions are windless to eliminate wind interference and ensure that the simulation results reflect the inherent spraying characteristics of the sprinkler head.

[0069] like Figure 2 As shown, this embodiment performs simulation calculations according to the overall prediction process of the present invention. The overall process for numerically solving the trajectory of a single water droplet is as follows: Figure 1 As shown, the specific implementation steps are as follows: Step 1: Determine the basic calculation parameters for nozzle simulation.

[0070] Based on the structural characteristics of the imported rotary nozzle and its actual operating conditions, the simulation input parameters were uniformly determined, mainly including key parameters such as nozzle working pressure, installation height, spray elevation angle, spray disk radius, spray disk rotation speed, air density, aerodynamic viscosity, ambient wind speed, and numerical calculation time step. This embodiment limits the core operating parameters to: nozzle working pressure 138 kPa, installation height 1.5 m, and ambient wind speed 0 m / s, thereby constructing a simulation foundation that closely reflects reality.

[0071] Step 2: Establish the initial velocity conditions for the water droplets at the moment they leave the spray plate.

[0072] During operation of the imported rotary nozzle, water flows through the nozzle into the spray disc channel, and after gaining tangential velocity with the high-speed rotation of the spray disc, it exits the spray disc. This embodiment considers the combined effect of the spray disc rotation; firstly, the angular velocity of the spray disc is calculated using the spray disc rotational speed n and the spray disc radius r. and rotational tangential velocity Combining the radial ejection velocity V2 of the water flow, the horizontal surface velocity V, and the jet elevation angle The vector decomposition of the water droplet ejection velocity was completed, and the initial velocity components and initial position of the water droplet at the instant it leaves the nozzle in a fixed three-dimensional coordinate system were finally obtained. The initial velocity decomposition relationship of the water droplet is as follows: Figure 3 As shown, this provides initial boundary conditions for subsequent trajectory iteration.

[0073] Step 3: Determine the droplet size distribution of the imported rotary nozzle and construct a droplet size distribution model for the nozzle.

[0074] Based on measured water droplet size data from imported rotary nozzles, candidate particle size distribution functions were fitted and compared, such as... Figure 4 As shown. Through comparative analysis, this embodiment preferably uses the Gamma distribution as the water droplet size distribution model to match the actual water droplet size distribution law of the nozzle.

[0075] In this embodiment, nozzle No. 44 is selected. Based on the standard conversion relationship between nozzle number and orifice diameter, the orifice diameter corresponding to nozzle No. 44 is determined to be 8.731 mm. Substituting the working pressure of 20 psi and the nozzle diameter of 8.731 mm into the corresponding calculation formula, the average particle size of the atomized water droplets under this working condition is found to be 0.537 mm, with a corresponding particle size variation coefficient of 0.604. Based on the above average particle size and variation coefficient, the shape parameter of the Gamma distribution is calculated to be 2.743 and the scale parameter to be 0.196 mm, respectively, and then the water droplet size probability density function under this working condition is constructed.

[0076] Based on this, the particle size range is further refined to determine the representative droplet size and corresponding probability weight of each range, providing sample data support for subsequent multi-particle-size droplet trajectory solving and ground weighted water volume superposition calculation.

[0077] Step 4: Discretize the rotation period and solve for the instantaneous trajectory of the water droplet.

[0078] To reproduce the continuous rotation spraying characteristics of the nozzle, the complete rotation cycle of the nozzle is discretized, resulting in multiple uniformly distributed water droplet ejection times. Different ejection times correspond to different water droplet spray orientations. The discrete spraying diagram is shown below. Figure 5 As shown, for each launch moment and for each representative droplet size, the fourth-order Runge-Kutta numerical algorithm is used to iteratively solve the three-dimensional dynamic control equations of the droplets, obtaining the complete three-dimensional flight trajectory of droplets under all operating conditions and with all droplet sizes.

[0079] Step 5: Correction of water droplet landing point and weighted superposition of grid water volume.

[0080] To address the truncation error caused by the fixed time step of numerical iteration, a method for identifying the critical state of water droplets upon landing and correcting their landing point is developed. When a water droplet reaches the ground, the spatial coordinates of two adjacent computational steps before and after landing are extracted, and a linear interpolation algorithm is used to correct the landing coordinates, thus obtaining the corrected landing point coordinates.

[0081] Then, all valid water droplet landing points are mapped to an adaptively partitioned ground statistical grid, such as Figure 6 As shown, by combining the volume of a single water droplet with the probability weight of its corresponding particle size, the water volume of each grid unit is weighted and accumulated to restore the water volume distribution characteristics of the entire ground spraying area of ​​the nozzle, and the spraying water depth of each grid unit is obtained.

[0082] Step Six: Verification and Analysis of Simulation Prediction Results Simulation calculations were performed based on the prediction method of this invention to verify and analyze the spraying range and spraying uniformity indicators of the sprinkler head. The results show that the effective spraying range of the sprinkler head obtained by the simulation method is 7.4 m, while the measured range in the field is 7.0 m, with a simulation relative error of only 5.7%, indicating that this invention can predict the droplet landing point and spraying range. Regarding spraying uniformity, the measured uniformity coefficient (CU) of the sprinkler head is 81.6%, while the simulated CU value is 71.9%. The simulation results are similar to the measured results, effectively characterizing the actual spraying uniformity performance of the sprinkler head.

[0083] As can be seen from the above embodiments, the prediction method and system proposed in this invention can combine the spray disc rotation effect, water droplet size distribution, water droplet trajectory solution and landing point water volume superposition based on the determined nozzle structure parameters, operating parameters and environmental parameters, to achieve the prediction of the water droplet motion trajectory, range and spray water volume distribution of the rotating nozzle. This enables the invention to provide a basis for the selection of nozzles, optimization of operating parameters and evaluation of spraying performance of center-supported sprinkler irrigation machines, and has strong engineering practicality and versatility.

[0084] In summary, this invention incorporates the tangential velocity of the spray disc rotation into the initial motion state of the water droplets, restoring the actual water output dynamics of the rotating sprinkler head. It achieves dynamic adaptation of the water droplet size through a Gamma distribution associated with operating conditions, ensuring that the water droplet samples closely match the actual spraying probability characteristics. Furthermore, it uses a fourth-order Runge-Kutta method for iterative numerical calculation and landing point interpolation correction, significantly reducing errors in trajectory and range calculations. Finally, it achieves full-domain spraying simulation through rotation period discretization, employing expanded-edge meshes and probability-weighted water volume superposition to address issues of missing boundary statistics and distorted water volume distribution. This effectively compensates for the shortcomings of traditional models, such as low simulation accuracy, poor adaptability to operating conditions, and inaccurate uniformity evaluation. It significantly improves the overall prediction accuracy of water droplet trajectory, spray range, and irrigation uniformity coefficient of rotating sprinklers, reflecting the actual spraying performance of sprinklers under different structures and operating conditions. This provides a reliable theoretical simulation basis for sprinkler structure optimization, operating parameter matching, and irrigation system performance evaluation.

[0085] This invention incorporates the tangential velocity component of the spray disc rotation during the initial velocity calculation of water droplets. This allows the initial motion state of the water droplets at the moment of detachment from the spray disc to simultaneously consider the radial jetting effect of the water flow and the rotational traction effect of the spray disc. This restores the actual water output dynamics characteristics of the rotating nozzle and effectively overcomes the technical defects of traditional fixed nozzle ballistic models that cannot adapt to rotating spraying conditions and have distorted motion state simulations. This improves the accuracy of water droplet trajectory simulation from the source.

[0086] This invention constructs a Gamma droplet size distribution model based on measured sprayed water droplet size data. It integrates the nozzle operating pressure and nozzle diameter into the average droplet size and coefficient of variation calculation model. By dynamically solving the shape and scale parameters of the Gamma distribution using operating conditions, the droplet size distribution is dynamically adjusted according to the nozzle's operating conditions. Simultaneously, this invention generates representative droplet samples based on the probability intervals of the droplet size distribution and matches corresponding probability weights. This allows droplets of different sizes to participate in trajectory iteration and grid water volume superposition calculations according to their actual spraying proportions. It abandons the idealized assumption of a single average droplet size used in traditional simulations, effectively avoiding trajectory deviations and water volume statistical errors caused by single-size calculations. This makes the simulation results of droplet group movement and ground water volume distribution more closely resemble actual spraying conditions.

[0087] This invention, through discretization of the sprinkler head's rotation period, high-precision solution of instantaneous water droplet trajectories, and weighted superposition of ground grid water volume, can output several core performance indicators of a rotating sprinkler head, including effective spray range, water droplet landing point distribution, overall ground water volume distribution, and irrigation uniformity coefficient. The comparison results between the predicted and measured uniformity coefficients of this invention are as follows: Figure 7 As shown, the simulation results are in good agreement with the measured results, and can distinguish the differences in spray uniformity under different nozzles and working conditions, providing reliable theoretical and simulation support for nozzle structure optimization, working condition matching and performance evaluation of sprinkler irrigation systems.

[0088] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the trajectory of water droplets sprayed from a rotary sprinkler head, characterized in that, Includes the following steps: Obtain the structural, operational, and environmental parameters of the rotary nozzle; By combining the rotational motion characteristics of the spray disk and the jet ejection characteristics of the rotary nozzle, a water droplet initial velocity model incorporating the spray disk rotation effect is constructed to characterize the influence of the spray disk rotation on the initial motion state of the water droplets. Based on the actual droplet size distribution of water sprayed by a rotary nozzle, a droplet size distribution model adapted to the rotary nozzle is constructed to generate a group of water droplet samples with probabilistic representativeness and match the corresponding droplet size weights. The motion control equations for the free flight phase of water droplets under a fixed reference frame are established. The motion control equations are numerically solved based on the initial motion parameters, particle size characteristics and environmental parameters of the water droplets to obtain the three-dimensional motion trajectories of water droplets with different working conditions and different particle sizes. Discretize the spraying process of the nozzle's complete rotation cycle, simulate the instantaneous spraying motion of water droplets at different ejection moments within the entire cycle, and obtain the full-domain water droplet motion trajectory data under the rotating spraying condition. Based on the spatial statistics and water volume superposition analysis of the water droplet landing point, the characteristics of ground spray water distribution are obtained and the sprinkler uniformity coefficient is solved, so as to predict the water droplet trajectory, effective spray range and spray uniformity of the rotating sprinkler head.

2. The prediction method according to claim 1, characterized in that, The structural parameters include the spray disc radius, nozzle installation height, spray elevation angle, and nozzle diameter; the operating parameters include the working pressure, spray disc rotation speed, initial droplet velocity, and calculation time step; the environmental parameters include air density, aerodynamic viscosity, and ambient wind speed.

3. The prediction method according to claim 2, characterized in that, The construction of the water droplet initial velocity model incorporating the spray disc rotation effect includes the following steps: Calculate the working angular velocity of the spray disc based on the spray disc rotation speed, and solve for the tangential velocity generated by the rotation of the spray disc by combining the spray disc radius; The total ejection velocity of the water droplets is decomposed based on the nozzle's jet elevation angle to obtain the resultant velocity in the horizontal plane. The radial velocity of the water droplet is solved based on the vector composition relationship, and the azimuth angle of the water droplet's ejection velocity is determined by combining the cosine theorem. The three-dimensional initial velocity components of the water droplets when they leave the spray disc are determined based on the angles between the horizontal surface velocity and the X and Y axes, the nozzle spray elevation angle, and the horizontal surface velocity, combined with the spray disc rotation angle. The initial spatial position of the water droplet when it leaves the spray plate is obtained by solving for t and the nozzle installation height H. The rotation of the spray plate is converted into a dynamic change in the initial velocity direction and initial position of the water droplet. The angle between the horizontal plane velocity and the X and Y axes is determined based on the azimuth angle of the water droplet's ejection velocity.

4. The prediction method according to claim 2, characterized in that, The droplet size distribution model uses the Gamma distribution as its basic form to construct the probability density function. Taking into account the effects of working pressure and nozzle diameter, the probability density function is: Wherein, the water droplet size is d, the working pressure is P, and the nozzle diameter is D. This is a shape parameter function used to characterize the peak shape and dispersion of the water droplet size distribution curve. ) is a scale parameter function used to characterize the scale of water droplet size distribution; Multiple representative water droplets of different particle sizes are generated based on the probability density function, and weights are assigned to the corresponding water droplets according to the occurrence probability of each particle size, so that the water droplet sample group conforms to the actual spraying particle size distribution characteristics.

5. The prediction method according to claim 4, characterized in that, When solving the motion control equations for the free flight phase of the water droplet, the initial velocity of the water droplet, the representative particle size obtained from the probability density function of the water droplet size distribution, and the probability weight are used as input parameters. The fourth-order Runge-Kutta method is used to solve the three-dimensional motion trajectory of the water droplet at each launch time and for each particle size in time iteration. The critical state of the water droplet landing is captured, and the actual landing coordinates of the water droplet are obtained by linear interpolation correction of the coordinates before and after landing.

6. The prediction method according to claim 1, characterized in that, The discretization process of the complete rotation cycle of the nozzle includes: uniformly discretizing the complete rotation cycle of the nozzle into several equally spaced water droplet ejection times, matching the rotation posture of the spray disk and the initial motion parameters of the water droplets at each time, solving the water droplet motion trajectory time by time, and then integrating the trajectories of all ejection times to obtain the global water droplet motion data.

7. The prediction method according to claim 6, characterized in that, The spatial statistics and water volume superposition analysis of the water droplet landing points include: dividing the horizontal ground statistical area into statistical grids, classifying each water droplet into its corresponding statistical grid according to the coordinates of the water droplet landing point, and accumulating the water volume in each statistical grid by combining the probability weights of water droplet volume and particle size to obtain the spraying water depth of each statistical grid, thereby calculating the sprinkler uniformity coefficient.

8. The prediction method according to claim 7, characterized in that, After dividing the horizontal ground statistical area into statistical grids, and before classifying each water droplet into its corresponding statistical grid based on the droplet's landing point coordinates, and accumulating the water volume within each statistical grid by combining droplet volume and particle size probability weights to obtain the spraying water depth for each statistical grid, and then calculating the irrigation uniformity coefficient, the following steps are also included: Based on the maximum and minimum X-axis values ​​of water droplet landing points in the statistical region of the horizontal ground, and the minimum and minimum Y-axis values ​​of water droplet landing points, a statistical grid is extended along the X-axis and Y-axis directions, respectively.

9. A prediction system for the trajectory of water droplets sprayed from a rotary nozzle, characterized in that, The method for implementing the prediction method according to any one of claims 1 to 8 is characterized in that it comprises: The parameter acquisition module is used to collect and preprocess the structural parameters, operating parameters, and environmental parameters of the rotary nozzle to build a dataset of predictive basic parameters. The initial velocity modeling module is used to construct an initial velocity model of water droplets that incorporates the spray disc rotation effect, and to solve for the three-dimensional initial velocity and initial spatial position of the water droplets after they leave the nozzle. The particle size distribution modeling module is used to construct a water droplet particle size distribution model based on the Gamma distribution and generate a representative group of water droplet samples with probability weights. The equations of motion module is used to construct the control equations for the free flight of water droplets under a fixed reference frame, and to use the Runge-Kutta method to solve the trajectory numerically, so as to obtain the three-dimensional motion trajectory of water droplets under different working conditions and different particle sizes. The rotating spraying simulation module is used to discretize the nozzle rotation cycle, simulate the instantaneous spraying process of water droplets at different ejection times throughout the entire cycle, and output the global water droplet motion trajectory data. The water distribution analysis module is used to complete the grid statistics of water droplet landing points, calculate water volume superposition, solve the spraying water depth and irrigation uniformity coefficient, and output the prediction results of sprinkler head water droplet trajectory, effective spraying range and spraying uniformity.

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