Analysis of the Inﬂuence of the Channel Layout and Size on the Hydraulic Performance of Emitters

: In this paper, a split-ﬂow channel layout with one (group) inlet and two (group) outlets is adopted, based on computational ﬂuid dynamics technology, and compared with the current commonly used channel with one (group) inlet and one (group) outlet emitter. On the premise of the same outlet spacing, the pressure–ﬂow relationship curve and slope of the split-ﬂow emitter were analyzed under the three channel layouts of non-return, single-sided re-entry, and bilateral re-entry, with different channel widths and lengths. When exploring the inﬂuence of the channel layout and size on the hydraulic performance of split-ﬂow emitters, the results showed that when the split-ﬂow emitter with a non-return channel is adopted and the hydraulic performance is not reduced, the single-side channel length is half that of the one-in-one-out emitter, meaning the channel width needs to be reduced by 15%. When the channel layout is a single-sided channel re-entry, the hydraulic performance is better than that of the one-in-one-out emitter; if the hydraulic performance of the two remains unchanged, the channel width can be increased by 10% or the single-sided channel length can be reduced by 20%. When the channel layout is a bilateral channel re-entry, the channel width can be increased by nearly 30% if the hydraulic performance of the 2 is consistent, and the single-side channel length is increased by about 50%. When the split-ﬂow emitter adopts a non-return channel layout, the channel width needs to be reduced to ensure the hydraulic performance is consistent. If the layout of single-sided channel re-entry or bilateral channel re-entry is adopted, the hydraulic performance is better than that of the one-in-one-out emitter and the hydraulic performance of the two is consistent. Thus, the channel length can be reduced or the channel width increased, which is beneﬁcial for improving the anti-clogging performance of the emitter.


Introduction
Drip irrigation technology is a high-efficiency water-saving irrigation technology in the current agricultural irrigation field. With the development of smart agriculture, the drip irrigation system has gradually transformed from a single irrigation function to multi-functional, such as for irrigation, fertilization, gas supplementation, and pesticide application [1,2]. The emitter is the core technology and key piece of equipment in a drip irrigation system [3]; its channel can effectively eliminate excess energy at the inlet, reduce the flow deviation rate of the emitter in the entire pipe network, and ensure a uniform outflow [4]. The structure of the channel of the emitter directly affects the irrigation quality and steady flow performance of the drip irrigation system [5,6], which, in turn, affect the promotion and application of drip irrigation technology [7].
The sensitivity of the outlet flow of the emitter to its working pressure is represented by the hydraulic performance [8], which is usually expressed by the pressure-flow relationship as:

Emitter Layout and Size Parameters
In this paper, when we refer to the size of the labyrinth emitter used in the side-type drip irrigation belt of Xinjiang Tianye Group, the channel depth of the one-in-one-out emitter (No. Z) and split-flow emitter (Nos. A, B, C and D) is 1 mm, and the space between the outlets of each emitter is 300 mm (or close to 300 mm, to ensure the integrity of the channel unit). The former has a channel width of 1 mm and a channel horizontal length of 300 mm. The latter takes different channel widths and lengths according to different channel layouts: non-return (Type A), single-sided re-entry (Types B and C), and bilateral re-entry (Type D). A schematic diagram of the channels of various types of emitters is shown in Figure 1, and the parameters of the one-in-one-out emitter are given in Table 1. channel without reducing the hydraulic performance of the emitter, to provide a reference basis for the further development of high-performance emitters.

Emitter Layout and Size Parameters
In this paper, when we refer to the size of the labyrinth emitter used in the side-type drip irrigation belt of Xinjiang Tianye Group, the channel depth of the one-in-one-out emitter (No. Z) and split-flow emitter (Nos. A, B, C and D) is 1 mm, and the space between the outlets of each emitter is 300 mm (or close to 300 mm, to ensure the integrity of the channel unit). The former has a channel width of 1 mm and a channel horizontal length of 300 mm. The latter takes different channel widths and lengths according to different channel layouts: non-return (Type A), single-sided re-entry (Types B and C), and bilateral re-entry (Type D). A schematic diagram of the channels of various types of emitters is shown in Figure 1, and the parameters of the one-in-one-out emitter are given in Table 1. Table 1. Parameters of the one-in-one-out emitter.

Emitter Number
Channel Width (mm) Total Number of Units L1 (mm) Outlet Spacing (mm) Z 1.0 50 300 300 Figure 1. Schematic diagram of the channel layout of one-in-one-out and split-flow emitters. Notes: Type A-D, four channel layouts for split-flow emitter; L1, outlet spacing (or one-in-one-out emitter channel length); L2, single-sided channel length of the Type A emitter; L3, single-side channel turnback length of the Type B emitter; L4, single-side channel not turn-back length of the Type C emitter; L5, single-side channel turn-back length of the Type C emitter; L6, single-side channel length of the Type C emitter; L7, single-side channel turn-back length of the Type D emitter.

Governing Equations and Boundary Conditions
In this study, the FLUENT software [30,31] based on computational fluid dynamics was used to numerically simulate the water flow in the aforementioned various types of emitters, and the pressure-flow relationship curve of the emitter was obtained. The advantages and disadvantages of the hydraulic performance of the emitter were then further analyzed. The movement of water flow inside the emitter can be regarded as the movement of viscous incompressible fluid. This paper mainly studied the hydraulic Figure 1. Schematic diagram of the channel layout of one-in-one-out and split-flow emitters. Notes: Type A-D, four channel layouts for split-flow emitter; L 1 , outlet spacing (or one-in-one-out emitter channel length); L 2 , single-sided channel length of the Type A emitter; L 3 , single-side channel turnback length of the Type B emitter; L 4 , single-side channel not turn-back length of the Type C emitter; L 5 , single-side channel turn-back length of the Type C emitter; L 6 , single-side channel length of the Type C emitter; L 7 , single-side channel turn-back length of the Type D emitter.

Governing Equations and Boundary Conditions
In this study, the FLUENT software [30,31] based on computational fluid dynamics was used to numerically simulate the water flow in the aforementioned various types of emitters, and the pressure-flow relationship curve of the emitter was obtained. The advantages and disadvantages of the hydraulic performance of the emitter were then further analyzed. The movement of water flow inside the emitter can be regarded as the movement of viscous incompressible fluid. This paper mainly studied the hydraulic performance of the emitter at room temperature; regardless of the temperature field change caused by the energy exchange of water flow, the motion law conforms to the conservation Agriculture 2022, 12, 541 4 of 13 of mass and momentum, and does not consider the mass force, so the governing equations include the continuity equation and Navier-Stokes.

Governing Equations
Continuity equation: Navier-Stokes equation: where t is time, s; ρ is the density of water, kg/m 3 ; ν is the kinematic viscosity, m 2 /s; p is the fluid pressure, Pa; u i , u j is the flow velocity tensor; and x i , x j is the coordinate tensor.
The existing research indicates that selection of the standard k-ε turbulence model (a semi-empirical turbulence model) for the simulation calculation of the labyrinth channel emitter in this paper would be most consistent with the actual situation [32]. When the fluid is incompressible and user-defined source terms are not considered, the basic transport equations for solving the turbulent kinetic energy k and dissipation rate ε are: k equation: ε equation: Among them: where k is turbulent energy, J; ε is the turbulent dissipation rate; µ t is turbulent viscosity Pa·s; t is time, s; µ is viscosity N·s/m 2 ; x i , x j is the coordinate tensor; and G k is the production term of the turbulent energy k caused by the average velocity gradient. The empirical constants are C 1ε = 1.44, C 2ε = 1.92, C µ = 0.09, σ k = 1.0, and σ ε = 1.3.

Mesh and Boundary Conditions
We used a structured hexahedral mesh [33]. To reduce the influence of the mesh on the flow calculation results, with mesh sizes of 0.1, 0.09, 0.08, 0.07, 0.06, 0.05, and 0.04 mm, the flow of the emitter was calculated for each when the inlet pressure was 5, 10, or 15 m H 2 O. Considering instances when the mesh size was 0.04 or 0.05 mm, the difference in the flow of the emitter between the two mesh sizes was 0.29%, which is less than 0.5% [34]. We considered this did not affect the calculation results, and the mesh size was this set to 0.05 mm in this research. When the boundary layer parameters were selected, the thickness of the first boundary layer was taken as 0.01 mm, and for each layer, it was increased by 1.5 times; hence, with 6 layers, the total thickness of the boundary layer was 0.208 mm.
The calculations were performed using an uncoupled implicit steady-state solver, and the inlet and outlet turbulence parameters were defined by the hydraulic diameter and turbulence intensity, with the latter being 5%. The inlet boundary conditions were set to a 5-15 m H 2 O pressure inlet, and the outlet boundary was set to the atmospheric pressure. The wall was a non-slip boundary. For the flow in the wall area, the standard wall Agriculture 2022, 12, 541 5 of 13 function [35] was used, and the wall roughness was 0.01 mm. The numerical calculation used the finite volume method to discretize the governing equations. The convection term and other parameters were discretized using the second-order upwind style, and the coupling of velocity and pressure was solved by the SIMPLE algorithm, with a convergence accuracy of 10 −4 .

Calculation Results and Physical Model Test Verification
To ensure the correctness of the calculation results, the physical model of the one-inone-out channel emitter was verified in our work. The channel of the model emitter was 1.2 mm wide, 1.8 mm deep, and 301.2 mm long. The model is pictured in Figure 2. and turbulence intensity, with the latter being 5%. The inlet boundary conditions were set to a 5-15 m H2O pressure inlet, and the outlet boundary was set to the atmospheric pressure. The wall was a non-slip boundary. For the flow in the wall area, the standard wall function [35] was used, and the wall roughness was 0.01 mm. The numerical calculation used the finite volume method to discretize the governing equations. The convection term and other parameters were discretized using the second-order upwind style, and the coupling of velocity and pressure was solved by the SIMPLE algorithm, with a convergence accuracy of 10 −4 .

Calculation Results and Physical Model Test Verification
To ensure the correctness of the calculation results, the physical model of the one-inone-out channel emitter was verified in our work. The channel of the model emitter was 1.2 mm wide, 1.8 mm deep, and 301.2 mm long. The model is pictured in Figure 2. The test system mainly included a water tank, pump, water supply and return pipelines, test model, and precision pressure gauge. A schematic diagram is shown in Figure  3.  The test system mainly included a water tank, pump, water supply and return pipelines, test model, and precision pressure gauge. A schematic diagram is shown in Figure 3. and turbulence intensity, with the latter being 5%. The inlet boundary conditions were set to a 5-15 m H2O pressure inlet, and the outlet boundary was set to the atmospheric pressure. The wall was a non-slip boundary. For the flow in the wall area, the standard wall function [35] was used, and the wall roughness was 0.01 mm. The numerical calculation used the finite volume method to discretize the governing equations. The convection term and other parameters were discretized using the second-order upwind style, and the coupling of velocity and pressure was solved by the SIMPLE algorithm, with a convergence accuracy of 10 −4 .

Calculation Results and Physical Model Test Verification
To ensure the correctness of the calculation results, the physical model of the one-inone-out channel emitter was verified in our work. The channel of the model emitter was 1.2 mm wide, 1.8 mm deep, and 301.2 mm long. The model is pictured in Figure 2. The test system mainly included a water tank, pump, water supply and return pipelines, test model, and precision pressure gauge. A schematic diagram is shown in Figure  3.  The flow was measured twice under each inlet pressure, the time taken for each flow measurement was no less than 2 min, the difference between the two measured flows was no more than 2%, and the average value of 2 times was taken as the discharge flow (L/h) of the emitter.
The results of our numerical simulation and model test are shown in Table 2 and Figure 4. It can be seen from Table 2 that the maximum error between them is 2.4%, Agriculture 2022, 12, 541 6 of 13 which verifies the correctness of our selection of mesh, in terms of its size and the calculation method. was no less than 2 min, the difference between the two measured flows was no more than 2%, and the average value of 2 times was taken as the discharge flow (L/h) of the emitter. The results of our numerical simulation and model test are shown in Table 2 and Figure 4. It can be seen from Table 2 that the maximum error between them is 2.4%, which verifies the correctness of our selection of mesh, in terms of its size and the calculation method.

Computational Results and Analysis
By fitting the simulation results for Type Z and Types A, B, C, and D split-flow emitters in the pressure range of 5-15 m H2O, their pressure-flow relationship curves, flow coefficient k, and flow state index x could be obtained. The slope of the pressure-flow relationship curve for each emitter at different working pressures was calculated according to: where k is the flow coefficient; x is the flow state index; q is the flow rate of the emitter, L/h; and h is the inlet pressure of the emitter, m H2O. The advantages and disadvantages of the hydraulic performance of the one-in-one-out and split-flow emitters were compared and analyzed in terms of the outlet flow (design flow) at the inlet pressure of 10 m H2O and the slope of the pressure-flow relationship curve.

Hydraulic Performance of the Type A Emitter
The Type A emitter simply changed one inlet and one outlet to one inlet and two outlets. Parameters, such as the single-sided channel length (L2), total number of units, and outlet spacing of the emitters with different channel widths are shown in Table 3; Figure 5 shows the pressure-flow relationship curve; and the slope of the pressure-flow relationship curve, along with a comparison of parameters under different working pressures, is shown in Table 4.

Computational Results and Analysis
By fitting the simulation results for Type Z and Types A, B, C, and D split-flow emitters in the pressure range of 5-15 m H 2 O, their pressure-flow relationship curves, flow coefficient k, and flow state index x could be obtained. The slope of the pressureflow relationship curve for each emitter at different working pressures was calculated according to: where k is the flow coefficient; x is the flow state index; q is the flow rate of the emitter, L/h; and h is the inlet pressure of the emitter, m H 2 O. The advantages and disadvantages of the hydraulic performance of the one-in-one-out and split-flow emitters were compared and analyzed in terms of the outlet flow (design flow) at the inlet pressure of 10 m H 2 O and the slope of the pressure-flow relationship curve.

Hydraulic Performance of the Type A Emitter
The Type A emitter simply changed one inlet and one outlet to one inlet and two outlets. Parameters, such as the single-sided channel length (L 2 ), total number of units, and outlet spacing of the emitters with different channel widths are shown in Table 3; Figure 5 shows the pressure-flow relationship curve; and the slope of the pressure-flow relationship curve, along with a comparison of parameters under different working pressures, is shown in Table 4.    Results can be seen in Tables 3 and 4 for the split-flow emitter with a non-return channel, on the premise that the one-sided channel length (L2) is half that of the channel length of the one-in-one-out emitter (L2 = L1/2). The channel width is equal to the channel width of the one-in-one-out emitter, or the former is 90% of the latter, meaning the slope of the pressure-flow relationship curve and the design flow both increase (A1 and A2 emitters). The maximum increase in the slope of the curve is 22.73%, and the design flow  Results can be seen in Tables 3 and 4 for the split-flow emitter with a non-return channel, on the premise that the one-sided channel length (L 2 ) is half that of the channel length of the one-in-one-out emitter (L 2 = L 1 /2). The channel width is equal to the channel width of the one-in-one-out emitter, or the former is 90% of the latter, meaning the slope of the pressure-flow relationship curve and the design flow both increase (A1 and A2 emitters). The maximum increase in the slope of the curve is 22.73%, and the design flow increases by 25.19%. If the outlet spacing of the 2 is kept constant (or close) under this condition, the slope of the curve and design flow are consistent or close, meaning the channel width of the Type A emitter needs to be reduced to 0.85 mm, 15% less than that of the Type Z emitter. This shows that when the channel layout of the emitter is changed from 1 outlet to 2, if the hydraulic performance remains unchanged, the channel width needs to be reduced by about 15% when the single-sided channel length is reduced by nearly 50%, and the reduction of the channel width will be detrimental to the anti-clogging performance of the emitter [36] (the effect of reducing the channel length on the anti-clogging performance of the emitter was not considered).

Hydraulic Performance of Type B and Type C Emitters
In view of the problems with the Type A emitter, we lengthened the single-sided channel length of the split-flow emitter to be the same as that of the Type Z emitter, to form a Type B emitter. The single-sided channel length of the Type B emitter was L 1 or 2L 3 (L 1 = 2L 3 ). Then, we lengthened the emitter to be longer than the Type A emitter but shorter than the Type Z emitter to form a Type C emitter. The single-sided channel length of the Type C emitter was L 6 , i.e., L 4 + L 5 (L 6 = L 4 + L 5 < L 1 ). We ensured that the outlet spacing was the same as that of the Type Z emitter, with single-sided channel re-entry. The total number of units, channel width, outlet spacing, and other parameters are shown in Table 5. The pressure-flow relationship curve in the inlet pressure range of 5-15 m H 2 O is shown in Figure 6. The curve slope and its parameter comparison with the Type Z emitter are shown in Table 6. increases by 25.19%. If the outlet spacing of the 2 is kept constant (or close) under this condition, the slope of the curve and design flow are consistent or close, meaning the channel width of the Type A emitter needs to be reduced to 0.85 mm, 15% less than that of the Type Z emitter. This shows that when the channel layout of the emitter is changed from 1 outlet to 2, if the hydraulic performance remains unchanged, the channel width needs to be reduced by about 15% when the single-sided channel length is reduced by nearly 50%, and the reduction of the channel width will be detrimental to the anti-clogging performance of the emitter [36] (the effect of reducing the channel length on the anti-clogging performance of the emitter was not considered).

Hydraulic Performance of Type B and Type C Emitters
In view of the problems with the Type A emitter, we lengthened the single-sided channel length of the split-flow emitter to be the same as that of the Type Z emitter, to form a Type B emitter. The single-sided channel length of the Type B emitter was L1 or 2L3 (L1 = 2L3). Then, we lengthened the emitter to be longer than the Type A emitter but shorter than the Type Z emitter to form a Type C emitter. The single-sided channel length of the Type C emitter was L6, i.e., L4 + L5 (L6 = L4 + L5 < L1). We ensured that the outlet spacing was the same as that of the Type Z emitter, with single-sided channel re-entry. The total number of units, channel width, outlet spacing, and other parameters are shown in Table  5. The pressure-flow relationship curve in the inlet pressure range of 5-15 m H2O is shown in Figure 6. The curve slope and its parameter comparison with the Type Z emitter are shown in Table 6.  It can be seen from Tables 5 and 6 that if the channel of the split-flow emitter adopts single-sided channel re-entry, when the outlet spacing, channel width and single-sided channel length are all consistent with those of the Type Z emitter, the slope of the curve and design flow of the former are less than those of the latter. The slope is reduced by 11.10% at the maximum, and the design flow is reduced by 9.93% (B1 emitter). This shows It can be seen from Tables 5 and 6 that if the channel of the split-flow emitter adopts single-sided channel re-entry, when the outlet spacing, channel width and single-sided channel length are all consistent with those of the Type Z emitter, the slope of the curve and design flow of the former are less than those of the latter. The slope is reduced by 11.10% at the maximum, and the design flow is reduced by 9.93% (B1 emitter). This shows that changing the channel layout from one-in-one-out to split-flow(one-in-two-out) is beneficial for improving the hydraulic performance of the emitter.
On the other hand, we can increase the channel width or reduce the channel length of the emitter without improving the hydraulic performance of the B1 emitter, that is, to ensure that the hydraulic performance of the B1 and Z emitters is consistent or largely Agriculture 2022, 12, 541 9 of 13 the same. When the outlet spacing of the 2 types of emitters and single-sided channel length is the same, the channel width can be increased by 10% (B2 emitter). When the channel width is increased by 20%, its hydraulic performance will be greatly reduced (B3 emitter). When the outlet spacing of the 2 types of emitters and the channel width are the same, the maximum channel length (L 6 ) can be reduced from 300 to 240 mm, a reduction of 20% (C2 emitter). When the channel length (L 6 ) is reduced from 300 to 270 mm (10% reduction), the design flow is 5.08% lower than that of the Type Z emitter, and the slope of the pressure-flow relationship curve is reduced by 6.72% (C1 emitter). When the channel length (L 6 ) is reduced from 300 to 210 mm by 30%, the slope of the pressure-flow relationship curve and the design flow both increase (by 7.2% and 5.81%, respectively), and the hydraulic performance decreases (C3 emitter). To further improve its anti-clogging performance, on the premise that the hydraulic performance of the split-flow emitter and one-in-one-outlet emitter, along with the outlet spacing, remained unchanged, we adopted a bilateral channel re-entry layout. In doing so, we were trying to increase the channel width by increasing the channel length of the split-flow emitter, thus forming the Type D emitter. The single-sided channel length of the Type D emitter was L 1 /2 + 2L 7 . For parameters, such as the total number of units of the emitter, single-sided channel length, and outlet spacing for different channel widths, see Table 7. The pressure-flow relationship curve within the inlet pressure range of 5-15 m H 2 O is shown in Figure 7, and Table 8 shows the slope of the curve and compares it with the parameters of the Type Z emitter.     It can be seen from Tables 7 and 8 that when the split-flow emitter adopts bilateral channel re-entry, and the single-sided channel length is increased by about 50% compared with the channel length of the one-in-one-out emitter, if the width of the 2 channels is the same, the design flow of the former is reduced by 26.02%, and the maximum slope of the pressure-flow relationship curve is reduced by 25.78% (D1 emitter). If the former channel width is increased by 10 or 20%, the designed flow is reduced by 14.25 or 5.6%, respectively, and the maximum slope of the pressure-flow relationship curve is reduced by 13.34 or 4.1% (D2 and D3 emitters), indicating that the hydraulic performance is still better than that of the one-in-one-out emitter. When the channel width of the split-flow emitter increases by 30%, the design flow and maximum slope of the pressure-flow relationship curve increase by 7.8 and 7.45%, respectively, with an increase of less than 10% (D4 emitter). This shows that the split-flow emitter with bilateral channel re-entry can increase the channel width by nearly 30% if the single-sided channel length increases by nearly 50%, under the condition that the hydraulic performance and outlet spacing are the same as those of the one-in-one-out emitter.