| A direct-acting pressure regulator (PR) is a key device for agriculture irrigation system used to ensure the equal operating pressure of the emitter or sprinkler nozzle required for high uniformity. Given that numerous researchers chose to fit the characteristic curve with experimental approaches and the design theory and methods of the PR having not been established, a systematical study of the flow characteristics of PR for agricultural irrigation in theory and through numerical simulation are carried out.An analytical model was built to quantitatively describe the working process of the PR. The mathematical equation that feature the inlet pressure of PR, flow rate of PR, and displacement of the plunger to the outlet pressure of PR was derived by theoretical analysis. Several steady simulations with displacement pre-established mesh were completed to obtain the coefficient values of the equation by computational fluid dynamics (CFD) approach. The model was validated by a comparison of experimental measurements, and the predicted results of flow rate show good agreement for the relative deviation within -7.3%. The spring parameters can be determined according to the force-displacement characteristic curve (the F-Lv curve) of the regulating plunger.A fluid-rigid body interaction dynamic model for the PR was developed by applying CFD method. The force balance approach of the regulating plunger and the dynamic mesh technique using a layering algorithm was performed for calculating the motion of the plunger and the displacement of domain boundaries and mesh deformation due to the movement of the plunger. The regulating performance curves were simulated under different flow rate range and the pressure distributions through the regulator at each time step were obtained. The response parameters, including the force acting on the regulating plunger, the displacement of the plunger, and the outlet pressure of the regulator were also obtained. A series of experimental tests match to the conditions of the calculation were performed on pressure regulator. Results shown that the regulating performance curves obtained by simulation were close to that obtained by experimental tests, and the numerical and experimental preset pressure agreed within -13.6%, which was considered to be quite acceptable. The detail pictures of the pressure distributions through the regulator and the dynamic simulative results consist of the force acting on the regulating plunger verse time, the motion characteristics of the plunger, and the outlet pressure of the regulator verse time were analyzed and accounted for the pressure regulating mechanism of the direct-acting PR.For the purpose of investigate the effect of geometric and spring parameters on regulating performance, based on the physical mechanism model of the dynamic numerical model, the modification of boundary condition and the calculating process of the model were carried out. The entire characteristic curves including both the performance line of unregulated segment and performance curve of regulated segment and the preset pressure and the slope of the performance line of the unregulated segment (representation for initial regulating pressure) were obtained. The influence of the structural and physical parameters of the PR on its preset pressure and slope of the performance line of the unregulated segment was investigated qualitatively using the improved numerical method by single-factor and five-level experiment design. The results indicated that the preset pressure rises as the increase of the sectional area of plunger upstream face and downstream face proportionally, which affect the force induced by water pressure difference in the force balance equation. The preset pressure drops as the increase of the height of the flow orifice of the seat, the spring stiffness, and pre-stressed spring length proportionally, which affect the spring force. The slope of the performance line of the unregulated segment improves with increase in the sectional area of plunger upstream face, the height of the flow orifice of the seat, the spring stiffness, and pre-stressed spring length respectively, whereas with a decrease in the sectional area of plunger downstream face. The pattern of variation of the flow area determined by the gap between the seat and the plunger revealed the reason of the influence of the parameters on the performance index.Ultimately, the central composite design of the response surface methodology was used to arrange the numerical experiments to estimate effects of geometrical and spring parameters and their interactions on the performance index quantitatively. Two quadratic polynomial regression equations were fitted for the computational preset pressure and slope of the performance line of the unregulated segment data in terms of variables such as diameter of plunger upstream face, height of flow orifice of seat, diameter of plunger downstream face, spring stiffness, and pre-stressed spring length. Diameter of plunger downstream face and spring stiffness were identified as the key design variables by ANOVA and response surface analysis. Moreover, the optimization model was established and solved using genetic algorithm in combination with superimposed contour plot approach, which considered maximum achievable slope of the performance line of the unregulated segment under a certain preset pressure as the objective function. Results showed that the values of slope of the performance line of the unregulated segment obtained from the optimal configuration of PRs for different preset pressure of 0.05,0.07, and 0.1 MPa increased by 16.5,8.5, and 13.8%, respectively. The performance of PR is improved.The present work forms the theoretical basis and technical support for future design and performance optimization of pressure regulator. Also, the theoretical methods and the numerical models can be used as a reference for design of similar device. |
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