**Hao Li 1,2, Hong Li 1,\*, Xiuqiao Huang 2, Qibiao Han 2, Ye Yuan <sup>1</sup> and Bin Qi 3,\***


Received: 30 October 2019; Accepted: 27 December 2019; Published: 2 January 2020

**Abstract:** To study the appropriate numerical simulation methods for venturi injectors, including the investigation of the hydraulic performance, mixing process, and the flowing law of the two internal fluids, simulations and experiments were conducted in this study. In the simulations part, the cavitation model based on the standard k–ε turbulence and mixture models was added, after convergence of the calculations. The results revealed that the cavitation model has good agreement with the experiment. However, huge deviations occurred between the experimental results and the ones from the calculation when not considering the cavitation model after cavitation. Thus, it is inferred that the cavitation model can exactly predict the hydraulic performance of a venturi injector. In addition, the cavitation is a crucial factor affecting the hydraulic performance of a venturi injector. The cavitation can ensure the stability of the fertilizer absorption of the venturi injector and can realize the precise control of fertilization by the venturi injector, although it affects the flow stability and causes energy loss. Moreover, this study found that the mixing chamber and throat are the main areas of energy loss. Furthermore, we observed that the internal flow of the venturi injector results in the majority of mixing taking place at the diffusion and outlet sections.

**Keywords:** venturi injector; cavitation; numerical investigation; mixing process; internal flow

### **1. Introduction**

Fertigation is becoming increasingly common, and fertilizer devices are becoming increasingly important [1]. A venturi injector, a commonly used device for fertilizer application, uses the turbulent diffusion of the jet to transfer energy and mass. This injector is broadly applied in fertigation systems because of its advantages such as simple structure, convenient operation, low cost, and no need for external power [2–4]. However, the internal flow involves the mixing of two flows with different pressures, although the internal structure of the venturi injector is simple with no moving parts. Thus, the internal flow is complex, energy loss is large, and the mass transfer energy efficiency is low [5], making it necessary to assess the flow characteristics of the venturi injector.

To date, venturi injectors have been studied widely, especially focusing on fertilizer absorption performance [6–8]. Neto and Porto [9] observed that the area ratio of a venturi injector exerts a major impact on the fertilizer suction efficiency; the authors also presented a simple methodology for the design and construction of low-cost ejectors from PVC, to reduce costs and enhance the fertilizer suction performance of fertigation systems. Ozkan et al. [10] investigated venturi injectors' structure parameters, including the impact of the inlet diameter, the diameter of the suction pipe, and the ratio of the throat diameter to the inlet diameter. In a field experiment, Parish et al. [11] investigated the injection methods, injection rate, and solution volume on the fertigation uniformity and reported that venturi injectors have a better fertilizer distribution and that the injection rate exerts a significant impact on the fertilizer distribution uniformity. Li et al. [12] investigated the performance of three different fertilization devices (venturi injector, proportional pump, and differential pressure tank) in laboratory and field experiments of a micro-irrigation system; they reported that the type of fertilization device and the manufacturing variability of emitters exert a considerable impact on the fertilizer distribution uniformity.

Using dynamics theory [13,14] for model analysis and modern testing and signal processing technology [15,16] has become a common research tool these days. With the technological advancement of computers and computational fluid dynamics (CFD), complex flows that could previously only be acquired by experimental methods can be simulated precisely [17–19], especially the internal flow fields in fluid machinery and microfluidics [20,21], such as two-phase flow [22–24], pressure fluctuation [25], energy loss [26–28], and so on. Other studies have mainly focused on the flow inside venturi injectors. Huang et al. [29,30] numerically analyzed the influence of the structural parameters on the absorption capacity. Yan et al. [31] used a high-speed video camera to investigate the development of the cavitation inside a venturi injector. Zwart et al. [32] presented a new multiphase flow algorithm to predict cavitation and validate the transient cavitation in a venturi. Simpson and Ranade [33] developed CFD models to simulate the cavitating flow in various venturi injectors. Shi et al. [34] established a semi-empirical model to predict cavitation in different venturi injectors. Furthermore, Dastane et al. [35] developed a CFD modeling scheme to successfully simulate flows in a cavitating venturi. Various study reports on venturi injectors revealed that CFD methods have been used extensively to investigate the impact of key structure and working parameters on the performance, including the diffusion, shape of the nozzle, ratio of the throat length to diameter, and contraction ratio [36–39]. However, few studies have focused on the effect of the mixing process between water and fertilizer liquid. Of note, the mixing process seriously affects the uniformity of the water and fertilizer distribution in the irrigation system, necessitating further investigation. Hence, this study aims to extend the solution method and test the reliability of calculated models. Moreover, this study investigates the mixing of two flows with different pressures.

#### **2. Experimental Setup**

We studied the working process and the fertilizer suction/hydraulic performance in a venturi injector using water as a working fluid. In this study, a closed-loop system was considered to assess the venturi injector. The system contained water circulation and measuring subsystems. Figure 1 presents the configuration of the closed-loop system.

**Figure 1.** Schematic of the experimental system. **1**. Variable-frequency, constant-pressure water supply device; **2**. Valve 1; **3**. Turbine flowmeter; **4**. Pressure gauge; **5**. Venturi injector; **6**. Pressure gauge; **7**. Turbine flowmeter; **8**. Valve 2; **9**. Valve 3; **10**. Tank.

In the experiment, water was driven by a variable-frequency, constant-pressure water supply device. We mounted two pressure gauges (precision: 0.4%) on the inlet and outlet lines of the venturi injector to measure the local pressures accurately. Likewise, the flow rates at the inlet and outlet

lines of the venturi injector were measured by two turbine flowmeters (precision: 0.2%). In addition, valves of the main pipeline were used to regulate the flow rate of the experimental system and control the import and export pressures of the venturi injector. The tank's water level was maintained constant to isolate the suction flow rate from the water level impact. Accordingly, a water pipe was set from the main pipeline to the water tank. Notably, the vertical distance between the water level and the venturi injector axis was 500 mm.
