Abstract
Aiming at the nozzlediverted channel system, two diverted channels with different configurations were designed and optimized, and the liquid flow characteristics in the diverted channel were studied. A finite element simulation model was established to analyze the influence of different diverted channel systems on the uniform distribution performance of the liquid, and the two diverted channels were tested for the uniform distribution of liquid flow. The results show that the diverting effect of the two kinds of diverting disk channels is relatively uniform. However, the distribution performance of the fourbifurcated diverting disk channel is better than that of the doublebifurcated diverting disk channel. The pressure loss is relatively less; the energy consumption is less, so the fourbifurcated diverting disk channel system is selected as the optimal design. The experimental results are consistent with the simulation results.
Highlights
 A component diverter plate for diverting liquid in a nozzle is proposed.
 The liquid flow characteristics in the diverted channel were studied.
 Through simulation, it is found that the distribution performance of the fourbifurcated diverter channel is better than that of the twobifurcated diverter channel, and the accuracy of the simulation is verified by experiments.
 In the design of the runner system, the distribution performance of liquid can be improved by increasing the number of runner forks as much as possible under certain conditions.
 The efficiency of the spray head can be improved by improving the distribution performance of liquid in the runner.
1. Introduction
Uniform flow distribution is a widespread and essential problem in many engineering environments. In modern agricultural irrigation systems, uniform flow distribution means irrigating more farmland with less water. Biologists have shown that uniform flow distribution helps to reduce the flow resistance in the vascular system [1]. Examples of industrial processes and equipment requiring uniform flow distribution abound, such as radiators [2], trickle bed reactors [3], electrostatic precipitators (ESP) [4], multichannel platefin heat exchangers [5] and packed columns, which perform better when they exhibit uniform flow distribution during operation. If the flow distribution is uneven, it will cause harmful effects. For example, Kim [6] and others found that when the flow in multiple channels is uneven, it will lead to the heat transfer difference between channels, thus reducing the system's effectiveness and affecting the equipment's use efficiency. Uniform flow distribution is advantageous in providing better heat transfer, temperature control, and pressure loss.
In this paper, two kinds of diverter channels with different configurations are studied, and the uniform distribution performance of the liquid flow is compared using simulation and experiment, which guides the design of the new spray head.
2. Modeling and simulation of diverter channel
2.1. Model of geometry
Fig. 1 shows the distributary channel model optimized according to the principle of symmetry and the construction method [7], where a is a doublebifurcated (twosubchannel) distributary channel, and b is a fourbifurcated (foursubchannel) distributary channel, which is smoothest at the flow steering and inlet.
Fig. 1The geometric model of the diverter channel
a) Double bifurcation channel
b) Four bifurcation channel
According to structural theory, the length is determined by the following formula:
where $k$ is the series of fractal tree networks, ${L}_{k}$ is the length of the channel at each level, $N$ is the number of bifurcated trees, and $D$ is the fractal dimension of length, where $D$= 2. In the doublebifurcated flow channel, ${L}_{1}$= 25 mm is designed here, and ${L}_{2}$= 17.7$$mm and ${L}_{3}$= 12.5$$mm are obtained by calculation. In the fourbifurcated flow channel, $D$ = 2 is also taken as the second grade is twobifurcated, ${L}_{1}$= 32.3 mm is designed here, and ${L}_{2}$= 22.9$$mm is calculated.
2.2. Mathematical solution model
Since the calculation of fluid flow in the threedimensional model at constant temperature is carried out in this paper, energy conservation is not considered. In the simulation, laminar flow model is used Therefore, the governing equation of flow is as follows.
Mass conservation equation:
Momentum conservation equation:
where $\rho $ is the density, $u$, $v$ and $w$ are the components of the velocity vector in the $x$, $y$, and $z$ directions, and $p$ is the pressure on the fluid element.
For the fluid flow in a circular pipe, only the internal shear force is considered, and the value of the fluid shear force $\tau $ on the inner microcontrol body satisfies the following formula:
If you change the length $l$ into $dx$, you can get:
where $\mathrm{\Delta}p$ is the pressure difference between the inlet and outlet of the microcontrol body; $r$ Micro control body radius.
The sheer force inside the tube flow changes linearly along the radial direction and is maximum at the wall surface and zero at the centre. Therefore, the velocity is complete at the centre.
The computational fluid dynamics software Fluent is used to simulate the threedimensional flow in the two models in Fig. 1. Water is used as a liquid working medium, and the inlet flow rate is controlled at 10005000 μL/min. The boundary conditions and other settings are shown in Table 1.
Table 1Boundary conditions and other Settings of the shunt plate during simulation
Parameter category  Settings 
Entrance boundary condition  Volume flow inlet 
Exit boundary condition  Pressure outlet, set the pressure value to zero 
Flow boundary conditions on the wall  All walls have no slip boundary 
Axisymmetric boundary condition  The centre of the pipeline is set to be axisymmetric 
Pressurevelocity coupling  SIMPLEC 
Discrete scheme of pressure equation  Adopt standard format 
Discretization of mass equation and momentum equation  QUICK format is adopted 
3. Simulation results and analysis
In order to study the liquid flow trend in the diverter channel, the simulation results were postprocessed. In this work, two dimensionless parameters are used to evaluate the uniformity of flow distribution, namely, standard flow deviation ${D}_{g}$ and maximum flow ratio $\theta $, which are defined as:
where $N$ is the number of exits, ${V}_{i}$ is the flow velocity of the $i$th exit, ${V}_{ave}$ is the average flow velocity of each exit, and ${V}_{max}$ is the maximum flow velocity at the exit. ${V}_{min}$ is the minimum flow velocity at the exit. When the fluid distribution reaches an ideal uniform state, the closer ${D}_{g}$ is to 0, and $\theta $ is to 1; otherwise, if ${D}_{g}$ deviates from 0 and $\theta $ deviates from 1, the fluid distribution is uneven.
Fig. 2 and Fig. 3 shows the model’s velocity crosssection program and pressure crosssection program along the $xoy$ plane. The model's velocity and pressure crosssection program are roughly symmetrical, indicating that the shunt effect of the model is relatively uniform.
Fig. 2Velocity section nephogram
a) Double bifurcation channel
b) Four bifurcation channel
Fig. 3Pressure section nephogram
a) Double bifurcation channel
b) Four bifurcation channel
In order to better demonstrate this effect numerically, two particular paths were created along the horizontal direction of the $X$axis. The change trend curve of velocity and pressure along the path direction was obtained through analysis, as shown in Fig. 4. It is evident from Fig. 4 that both the velocity curve and the pressure curve are roughly symmetric concerning the line $X=$0, which further indicates that the shunt effect of the model is relatively uniform.
Fig. 4Variation curves of velocity and pressure values along the Xaxis of different models, where 2 represents the twofork flow channel model, and 4 illustrates the fourfork flow channel model
a) Velocity curve
b) Pressure curve
Fig. 5 shows the relationship between the flow distribution uniformity of the optimized shunt channel and the average $Re$ at the outlet. It can be seen that both ${D}_{g}$ and $\theta $ fourfork channels are more minor than doublefork channels, indicating that the liquid distribution performance of the fourfork channel is better than that of the doublefork channel because the fourfork channel has two more groups of channels than the doublefork channel. Based on structural theory, it is shown that increasing the number of channel groups can effectively improve the distribution performance of liquid.
Fig. 5Flow distribution performance of different models
a) Relation between ${D}_{g}$ and exit mean $Re$
b) Relation between $\theta $ and exit mean $Re$
Fig. 6 shows the relationship between the pressure drop of the two kinds of shunt plate channels and the average $Re$ at the outlet. It can be seen that the pressure drop of the fourfork channel is lower than that of the twofork channel. Appropriately increasing the number of channel groups can reduce the pressure drop of the liquid in the distribution process, namely reducing energy dissipation.
Fig. 6The relation between ΔP and outlet average Re of different model flow channels
In the HaganPoiseuille flow, the resistance of the flow passage is:
Then the resistance in the double bifurcation channel is:
The resistance in the fourfork channel is:
where $\mathrm{\Delta}P$ is pressure loss, $Q$ is volume flow, $\mu $ is dynamic viscosity, $L$ is the length of flow passage, and $D$ is the diameter of the flow passage.Obviously, $\mathrm{\Delta}{P}_{D}$>$\mathrm{\Delta}{P}_{F}$, indicating that the pressure drop of the twofork channel is more significant than that of the fourfork channel, that is, more energy is consumed, which theoretically verifies the accuracy of the simulation.
4. Experiment of uniform flow of liquid
4.1. Experimental device
In order to verify the above simulation results, two sets of comparison tests were designed. The experimental platform comprises a liquid supply system, shunt plate system, liquid collection system and measurement system. The practical device is shown in Fig. 7 (the photo is taken at Advanced Manufacturing Research Laboratory, Changchun University of Science and Technology; courtesy of Jianhe Liu).
The injection pump is a liquid supply device. In the experiment, the capacity of the injection pump is set as 20 mL, and all 20 mL liquid is distributed to each small beaker through the shunt plate within a certain period. Water is used as the working fluid, and the mass of the collected liquid is measured by using an electronic balance with a weighing accuracy of 0.1 mg.
The velocity at the outlet of the shunt plate was used to measure the uniform distribution performance of the liquid above. Here, the mass of the liquid collected at the outlet of each shunt plate can be similarly used to evaluate the uniform distribution performance of the liquid, i.e., standard mass deviation ${\overline{D}}_{g}$, maximum mass ratio $\overline{\theta}$. There may be specific errors and contingencies in a single experiment. In order to eliminate the influence brought by this, the experiment was repeated 5 times.
Fig. 7Diagram of experimental equipment for uniform flow of liquid
4.2. Experimental results
Fig. 8 shows the relationship between the number of experiments and ${\overline{D}}_{g}$ and $\overline{\theta}$. It is found that ${\overline{D}}_{g}$ and $\overline{\theta}$ of the fourfork shunt are smaller than those of the doublefork shunt in 5 experiments.
Fig. 8Flow distribution performance of diverter plate under different test times
a) Relation between ${\overline{\mathrm{D}}}_{\mathrm{g}}$ and the number of experiments
b) Relation between $\overline{\mathrm{\theta}}$ and the number of experiments
Table 2 shows the comparison between the simulation and experimental results. The simulation results are consistent with the experimental results, and the fourbifurcated flow channel structure has better distribution performance. Therefore, the correctness of the simulation is verified experimentally.
Table 2Comparison of simulation and experimental results
Results  Standard flow/quality deviation  Maximum flow/mass ratio 
Simulation results  ${D}_{g}\left(4\right)<{D}_{g}\left(2\right)$  $\theta \left(4\right)<\theta \left(2\right)$ 
Experimental results  ${\overline{D}}_{g}\left(4\right)<{\overline{D}}_{g}\left(2\right)$  $\overline{\theta}\left(4\right)<\overline{\theta}\left(2\right)$ 
5. Conclusions
In this paper, the finite element simulation model is established based on Fluent, and the influence of different flow channels on the uniform distribution performance of the liquid is analyzed. At the same time, the uniform distribution of the shunt plate is tested, and the results show that:
1) The diverting effect of the two diverting disk channels is relatively uniform, and both have good liquid distribution performance. The distribution performance of the fourbifurcated diverter channel is better than that of the doublebifurcated diverter channel, indicating that the distribution performance of liquid can be improved by appropriately increasing the number of the flow channel groups based on the construction theory, and the simulation results are consistent with the experimental results.
2) The fourfork diverter channel has less pressure loss than the doublefork diverter channel, that is, less energy consumption, indicating that the flow channel system with better distribution performance means more energy saving. Therefore, combined with the simulation and experimental results, the final use of the fourfork diverter channel system is the optimal design.
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About this article
The authors would like to thank the Science and technology development plan project of Jilin province No. 20190304132YY.
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
The authors declare that they have no conflict of interest.