Numerical simulation of the effects of sandy water on regulator labyrinth channel in micro-sprinkler systems

In a micro-sprinkler irrigation system, laying branch pipes may result in considerable hydraulic loss and pressure differences. This phenomenon causes crops at different locations in the pipeline to receive different amounts of water and nutrients, affecting both the overall yield and quality of crops (Martin et al. 2007). To alleviate this problem, pressure-compensated micro-sprinkler irrigators are commonly applied to maintain a consistent flow rate within the required range of operating pressures. This pressure compensation function is mainly achieved by a labyrinth channel and deformation of the elastic gasket inside the pressure compensation chamber. In the labyrinth channel, the movement and deposition of impurities are important factors affecting the stability of the irrigator. For example, in the fertigation system, adhesion and accumulation of incompletely melted grain-fertilizer inside the channel cause blockage and corrosion, which affect the efficiency of the irrigator (Zhai et al. 1999). Therefore, the flow characteristics of impurities in the irrigator channel need to be studied.

Anti-clogging performance is an important factor for evaluating the performance of irrigators. In a micro-irrigation system, the channel size of the irrigator is usually small. Due to the diversity of irrigation water sources, irrigation water contains many suspended solid particles, which increase the possibility for occurrence of emitter blockage (Nakayama & Bucks 1991). Li et al. (2008) simulated the turbulence and velocity distribution within labyrinth emitters and found that the smooth arc connection of flow paths enhances the self-cleaning ability of channels. Zhangzhong et al. (2015) analyzed the internal flow field of non-compensating emitters, and showed that the shape of the low-speed region changes with changing pressure, which affects the hydraulic characteristics of the emitter. Therefore, the flow field of the irrigator must be studied under different working pressures. Liu & Huang (2009) showed that a large flow emitter achieved better anti-clogging performance than a small flow emitter under the same irrigation time. Niu et al. (2013) studied the relationship between muddy irrigation water and clogging of the emitter, and identified a sensitive sediment particle diameter range, which more likely causes emitter blockage. The concentration of particles smaller than 0.1 mm is a significant factor for the occurrence of blockages. Based on prior research outlined above, the physical structure of the channel, flow rate, operating pressure, and characteristics of the flowing medium in the irrigation system are key parameters that affect clogging.

Practical micro-irrigation systems are often equipped with sufficient filtering devices and backwashing operations to reduce the probability of clogging events. However, the abrasive and erosive effect of suspended particles (e.g., sand or incompletely melted fertilizer) in the flow channel is a further problem, which affects the stability of the irrigator. It is difficult to measure debris movements inside the flow channel directly. Therefore, numerical simulation is often preferred. Ge et al. (2009) experimentally studied the collision between sand particles and the micro-channel wall, and measured the collision coefficient to provide accurate setting conditions for simulations. Various simulation methods applied to studies of particle movements in sandy water (e.g., Zhao et al. 2016) established the mass transfer equation of particles based on the Diffusive Flux Model (DFM) and simulated the flow of high-concentration suspensions in a straight micro channel. Zhao et al. (2016) used the Discrete Element Model (DEM) to simulate the passage rate of sand particles in the labyrinth channel. Yan et al. (2007) used the Discrete Phase Model (DPM) to simulate the movement of suspended particles with different mass concentrations in the labyrinth channel of an emitter. The erosion of the wall caused by suspended solid particles in the multiphase flow has been assessed via DPM (Bozzini et al. 2003). These studies have shown that Computational Fluid Dynamics (CFD) can be used to accurately predict the impact erosion of particles on the channel wall, which is related to their impact velocity, sediment concentration, and the target material.

Monitoring and visualizing the internal flow inside the irrigator are necessary for studying the trends of internal flow and particle migration. Particle Image Velocimetry (PIV) (Santiago et al. 1998) and Particle Tracking Velocimetry (PTV) (Ge et al. 2009) can realize the visualization of the particle movement inside the emitter. The internal channel size of the emitter is too small to carry out related experiments, although the research method using an equal scale physical model developed by Roushangar et al. (2020) has overcome this problem. However, the followability, visibility, and uniformity (Hadad & Gurka 2013) of fluorescent particles still create challenges for an accurate description of the flow field. Using numerical simulation, Yang et al. (2020) achieved accurate results for the energy dissipation of turbulent kinetic energy and the internal flow velocity in the irrigator. By using numerical simulation (Niu et al. 2010), multiple low-velocity zones and vortex zones can be observed, which have been considered as potential reasons for energy dispassion and clogging.

The aim of this research is to study the internal sandy flow of a large-flowrate irrigator, as most of the current research is based on drip irrigation emitters. Compared to drip irrigation (flow rate <12 L/h), micro-sprinkler irrigation uses a larger flow rate (<250 L/h), which results in different flow characteristics and intense scouring behavior inside the flow channel. This study investigated the effects of sandy water on a new labyrinth channel of the micro-sprinkler irrigator. The energy dissipation, sand deposition, and channel erosion levels were analyzed for different incoming flow conditions (i.e., sandy water with different sediment concentrations and particle diameters under several operating pressure and flow rate conditions). The behavior of sand movement in the channel is summarized, and optimal pressure and filtering requirements in the micro-sprinkler irrigation system are proposed. These results provide additional reference for the stable operation of micro-sprinkler irrigation systems.

The modeled geometry for this simulation is based on the channel structure of a pressure-compensated micro-sprinkler irrigator (Shanghai Huawei Co., Ltd, Shanghai, China. Int. Cl. A01G 25/02 (2006.01)) as shown in Figure 1(a). This pressure compensation irrigator consists of a base connected to the capillary, a pressure-compensated flow rate regulator, and a micro-sprinkler. As shown in Figure 1(b), the flow rate regulator contains a pressure compensation chamber, a labyrinth flow channel, and an elastic gasket, which is the key component enabling the pressure compensation function. The rated pressure compensation range of this regulator is 200–400 kPa. It has been proposed that the occurrence of blockages is independent of whether large-flowrate emitters have a pressure compensation function. Consequently, only the internal flow field of the labyrinth channel (a double-outlet, symmetrical W-shaped arc flow channel structure) was studied. Figure 2 shows a three-dimensional model of the labyrinth channel, constructed by NX.10.0 software, where the diameter of the inlet is 1.9 mm and the length of the channel is 14 mm.

Based on ANSYS Fluent 17.1 software, two simulations of sand movements in the labyrinth channel were carried out. Figure 3 shows a flowchart of the simulation process.

To study the energy dissipation and sand deposition in the channel, transient simulations of water-sand two-phase flow were carried out under different incoming flow conditions. The specific computational setups are listed in Table 1. Solid particles belong to river sand with a density of 2,500 kg/m³. The volume fraction of sand in the water remains far below 5%, indicating that the flow medium is diluted phase flow. Hence, the Eulerian Multiphase Flow model was used to simulate the deposition of sand particles in the channel. Li et al. (2008) found that the flow state inside the channel is turbulent, and suggested that a suitable turbulence model is required to obtain accurate numerical simulation results. Al-Muhammad et al. (2016) compared several turbulence models and found that the results of standard k–ε and Re-Normalization Group (RNG) k–ε models are most consistent with experimental data. Considering the turbulence anisotropy effect and the high strain rate (or the large curvature of the flow surface), the present study used RNG k–ε as viscosity model to improve the accuracy in case of swirling and large curvature. The phase coupled semi-implicit method for pressure linked equations (SIMPLE) scheme was employed for coupling between pressure and velocity. The second-order upwind scheme was employed for spatial discretization items. The Gidaspow drag model was selected for calculating the drag force between solid phase and liquid phase.

The simulation grids were acquired by ANSYS ICEM 17.1 software, which includes a simplified structured grid of the main channel for DPM simulation, and an unstructured grid of the whole channel for Eulerian multiphase flow simulation. To ensure calculation accuracy and reduce processor calculation cost, independent tests on the calculation mesh were performed to identify the optimal mesh. In Table 2, five types of meshes with different cell sizes were used to simulate the internal flow of channels under 200 kPa. Outlet velocity was monitored to evaluate the computational accuracy of the optimal mesh. The unstructured Mesh 4 with 3 × 10⁵ grids and the structured Mesh 4 with 2.3 × 10⁵ grids were selected as computational grids for numerical simulations.

Figure 5 depicts the relationship between operating pressure and turbulent kinetic energy (TKE) dissipation ratios under different conditions. Energy dissipation in the channel can be reflected by the TKE dissipation ratio, which is defined as the ratio of the difference in TKE between inlet and outlet to the inlet TKE. When the pressure is below 300 kPa, the TKE dissipation ratio remains steady at 0.75 despite pressure changes. Consequently, about 75% of the energy of the flowing medium is converted to internal energy and then dissipated. If the pressure exceeds 300 kPa, the TKE dissipation ratio gradually decreases with increasing pressure. This indicates that the TKE difference between the outlet and the inlet of the flow channel becomes small, and the energy dissipation effect of the flow channel worsens. For a constant pressure condition exceeding 300 kPa, if the concentration of sand particles increases, both the TKE dissipation ratio and the energy dissipation effect decrease. Similarly, the TKE dissipation ratio decreases significantly if the diameter of sand particles increases.

Figure 6 shows the vorticity contour in the channel at a pressure of 300 kPa. At the inlet of the flow channel, because of the restricted channel structure, the flow direction of the incoming flow abruptly changes from Z direction to X-Y direction and forms many backflows and vortices. The mixing of flows is an effective energy dissipation behavior at the inlet position. Therefore, the vorticity value in this region is much higher than that of the surrounding area. The existence of vortices as well as the viscous stresses in the boundary layer between fluid and wall cause locally high vorticity values. For example, at curve transition sections, streamlines are smooth and without vortices. However, the vorticity here is highest at around 8–20 (10³ s⁻¹) and water velocity reaches 10–12 m/s, implying that the flow is scouring the wall of the flow channel at high speed. Li et al. (2018) identified flushing of the channel as an effective way to reduce clogging. Therefore, in the flow field of the labyrinth channel, turbulent flow with high vorticity not only causes energy dissipation but also strengthens the self-washing and reduces sedimentation of sand by flushing the channel wall. Moreover, the vorticity value is proportional to the energy dissipation and inversely proportional to the sediment concentration.

Pressure is one of the important factors affecting the distribution of sand particles in the labyrinth channel. The contours of the sand phase volume fraction under different pressure conditions are compared, to assess the relationship between pressure and sand deposition. It is found that 300 kPa is the critical pressure at which the location of sand deposition changes. Figure 7(a) shows the sand distribution characteristics in the channel for pressures below 300 kPa. Sand particles are mainly settled along the outer side of the bend and the straight channel, and sand deposition is proportional to sediment concentration. At the same concentration, the sediment distribution in the channel is similar, but smaller particle sizes are more likely to cause clogging. Since these small sand particles also have lower kinetic energy, once they enter the low-velocity zone, they cannot escape, resulting in clogging. Figure 7(b) shows the sand distribution in the channel for pressures above 300 kPa, where sand particles are mainly deposited in the downstream face of the bent channel, which is completely different. At high pressure levels, the kinetic energy of the flow is large. Thus, there is an obvious speed difference in the inner bend of the channel. The velocity of the upstream face exceeds that of the downstream face. Consequently, a low-velocity zone forms at the downstream face, where sand particles are deposited.

As I≥ 0.25, blockage occurs inside the emitter flow channel. Figure 8 shows that the clogging rate I is related to the operating pressure, and 300 kPa is the critical pressure threshold, determining whether blockage occurs. If the operating pressure remains below 300 kPa, the occurrence of clogging inside the channel depends on the conditions of the incoming flow (i.e., both sediment concentration and sand diameter). If the flowing medium is sandy water with high sediment concentration, flow with smaller sand diameters achieves a higher blockage rate, and blockage is more likely to occur in the channel. The possible reason for this phenomenon is that the kinetic energy of small sand particles is weak. After entering the low-velocity region, sand particles do not have enough kinetic energy to escape. Thus, their deposition in the velocity dead zone leads to a risk of blockage. If the flowing medium is sandy water with low sediment concentration, flow with a larger sand diameter results in a greater blockage rate. The possible reason is that at low sediment concentration, small sand particles are directly washed out of the channel because of their better flow behavior, whereas large sand particles are more likely to deposit inside the channel because of gravity and collision. However, when the operating pressure exceeds 300 kPa, the clogging rates at any operating conditions remain below 0.25; that is, clogging is less likely to occur in the channel.

In summary, the location of sand accumulation in the labyrinth channel of the emitter can be obtained through numerical simulation. The probability of the blockage of a single emitter under different sandy water conditions can be calculated. The clogging rate can be used to evaluate the optimal operating pressure and the critical filtering standard of the irrigation system.

Figure 9 shows the Stokes number of the particle swarm at the inlet of the channel according to DPM simulation. The result shows that the standard deviation of the Stokes number of sand between different inlet velocity conditions is not significant; that is, remains within 0.13. If the diameter of sand particles exceeds 0.04 mm (which accounts for ∼70% of the particle swarm), the Stokes number of sand exceeds 1, implying that such sand particles do not move well with the flow in the flow channel. The followability of sand particles in the fluid affects the trajectory of particles. Therefore, it can be assumed that during the flow process, the probability for collision between sand particles and channel increases with a large Stokes number. This also implies that the erosive effect of sand particles on the wall of the channel is mainly caused by sand particles with a diameter exceeding 0.04 mm.

In the labyrinth channel, the bend section has a direct collision with the flow, and the erosion will be more severe here than at the straight section. Therefore, DPM simulation focused on monitoring the erosion rate on the wall of the arc channel. The results are presented in Tables 3 and 4. Table 3 shows the relationship between flow velocity and erosion rate on the channel wall. These results reflect that changing the inlet velocity has less effect on the sand erosion rate. If the sand concentration is 10 g/L, the average erosion rate remains around 3.66 × 10⁻⁸ kg/m²-s, independent of the inlet velocity. Table 4 shows an obvious proportional relationship between sediment concentration and erosion rate. With increase in sand concentration, the erosion on the channel wall increases because more solid particles collide with the channel surface. However, according to the research of Zheng et al. (2008), with increase in sediment concentration, the interaction between solid particles will consume considerable kinetic energy. Therefore, the erosion rate will not change significantly. To reduce erosion of the labyrinth channel surface and prolong the service life of the emitter, the concentration of impurities in the pipeline needs to be controlled, without having to adjust the operating flow rate of the micro-sprinkler irrigation system. Furthermore, the materials of the emitter should be adjusted by the corresponding water source quality to strengthen the adaptability of the emitter.

This study evaluated the flow characteristics of sandy water in a W-shaped labyrinth channel through CFD numerical simulation. The distribution of accumulated sand and erosion problems in the channel were investigated under different flow conditions. The simulation data show that because of the effects of the labyrinth flow channel structure on sandy water, the reflow mixing behavior and shear action inside the channel increase energy dissipation and reduce the risk of sand accumulation. The optimal operating pressure of the micro-sprinkler irrigation system is estimated from the deposition distribution and the erosion rate of sand by numerical simulation. Applying this optimal operating pressure reduces the sand deposition and erosion in the labyrinth channel while ensuring the basic hydraulic performance of the emitter. In this specific case study, the optimal operating pressure for the micro-sprinkler emitter is 300 kPa. The erosion of sand particles on the channel surface is proportional to the sediment concentration and independent of the flow velocity. Micro-sprinkler irrigation systems should formulate a relevant filtration standard of sand concentration rather than restrict the diameter of sand particles, as this reduces the configuration requirements of the filtration device and the system construction cost. The data and conclusions of this research are all drawn from numerical simulation, and corresponding experimental research may be implemented in the future to assess the actual flow conditions inside the labyrinth channel.

Simulation work and writing-original draft preparation, Lin Hua; funding acquisition and writing review, Hong Li, Chao Chen, and Yue Jiang; provision of the product physical model, Zhonghua Zhang.

The authors declare no conflict of interest.

This work was financially supported by the National Natural Science Foundation of China (grant Nos. 51939005, 51809119, and 51679109), the Postgraduate Scientific Research and Innovation Project of Jiangsu Province (grant No. KYCX21_3345), the National Key Research and Development Project of China (grant No. 2017YFD0201500), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (grant No. PAPD-2018-87).

All relevant data are included in the paper or its Supplementary Information.