Mathematical model for multivariate nonlinear prediction of SMD of X-type swirl pressure nozzles
Introduction
Dust is more or less produced in many links of the industrial production chains. Dust suspended in the air not only endangers the health of workers, but also poses a threat to the safety of production in workplaces (Zhang et al., 2018; Liu et al., 2019). Currently, such dust prevention measures as ventilation, dust collector for purification through dust extraction, spraying dust suppression and dust separation by enclosures, etc. are mainly taken for industrial workplaces in China and elsewhere. Among these measures, the technology of spraying dust suppression has been widely applied in industrial production due to the simple equipment, easy operation, universal applicability and high efficiency, etc. (Zhou et al., 2017; Wang et al., 2018a, 2018b; Yang et al., 2019). Atomizing nozzle is the key component of the technology of spraying dust suppression. As per the atomizing principles, the popularly used nozzles can be divided into pressure type, rotary type, pneumatic type and ultrasonic type, etc. Among them, the pressure atomizing nozzles are widely used due to such characteristics as simple structure and better adaptability, etc. (Charinpanitkul and Tanthapanicha, 2011; Cheng et al., 2011; Ma and Zhai, 2005). The droplet size is an important indicator to evaluate the atomization characteristics and dust control performance of nozzles. For a long time, engineering staff have to rely on complicated experiments to obtain the droplet size performance parameters of nozzles. However, the apparatuses for measuring droplet size are not available on most project sites, which cause much inconvenience to the engineering design and the application of the technology of spraying dust suppression (Wang et al., 2019a, 2019b; Cheng et al., 2010).
In view of the above reasons, researchers have carried out a lot of research work on droplet size prediction models for pressure nozzles, trying to build theoretical calculation models of droplet size based on nozzle structure parameters and operating condition parameters. Sellens (1989) and Li et al. ((1990); Li and Tankin, 1992, respectively) conducted in-depth study of the maximum entropy model, and proposed a new method to predict droplet size distribution with the maximum entropy model. Dumouchel and Malot ((1999); Dumouchel (2006), 2009, respectively), considering the defect of the two-parameter model built by Sellens et al. and Li et al. that it can’t be used to predict the high concentration droplets, built the three-parameter maximum entropy model of droplet size distribution. On this basis, Guo et al. (2012) obtained the droplet size distribution data of swirl pressure nozzles using the plane laser-induced fluorescence method, with the experimental data provided with the regression analysis and the relationship between generalized parameter α and water flow rate obtained, and the three-parameter maximum entropy model for the average particle size constraint was built to predict the droplet size quantity distribution accurately. Liu and Zhang (2005) based on the experimental data and atomization similarity criterion and by using the least square method, obtained an empirical formula for SMD of droplets at the outlet of TF type spiral nozzles. Yang et al. (2013) studied and analyzed such atomization performance as nozzle flow rate, atomized particle size and atomization angle of the spiral nozzles in the wet process fume desulfurization systems of thermal power plants through experiments, and obtained the fitting formula about the relationship between pressure and droplet size. Xiao et al. (2018) deduced the semi-empirical formula for predicting the liquid film breakup length and the SMD of dual-oil-circuit centrifugal nozzles, with three different types of dual-oil-circuit centrifugal nozzles used for verification through tests, and the prediction error was less than 20%. For different types of pressure nozzles, the above researchers built the mathematical model for droplet size prediction, but its application scope is limited due to the following main problems: 1) For the droplet size distribution prediction model built based on maximum entropy model method, some parameters involved in the model still need to be obtained through more tests, which restricts the wide application of the method. 2) The influence factors of droplet size prediction model have not yet been comprehensively taken into account, even only based on a single influence factor of feed water pressure, so the application scope of the prediction model is limited. 3) The droplet size prediction model built can only predict droplet size at nozzle outlet, without taking into account the spatial difference of droplet size distribution, so it still can’t realize the droplet size prediction of the complete spray field.
X-type swirl pressure nozzle is a newly developed nozzle with better atomization characteristics and dust suppression performance. Due to its short industrial application time, there are few reports on the droplet size prediction models for this type of nozzles (Xie et al., 2014; Qin and Loth, 2016). Nie et al. (2017) compared the atomization characteristics of four types of commonly used pressure nozzles and found that X-type swirl pressure nozzle was suitable for large-area dust suppression in medium and short distance. Under the same working conditions, the X-type swirl pressure nozzle can obtain the smallest droplet size. Apply the X-type swirl pressure nozzles to the coal mining machine for external spray dust suppression, and field tests showed that this type of nozzle has better dust suppression performance. The members of the research group measured the flow coefficient and atomization angle of the X-type swirl pressure nozzles in the early stage, and obtained the flow coefficient and the calculation formula of the atomization angle of this type of nozzles by fitting (Yi et al., 2018). On this basis, combined with the empirical formula of the atomized particle size of single-hole pressure atomizing nozzle, the two-parameter droplet size prediction model based on water supply pressure and outlet diameter is derived (Wang et al., 2018a, 2018b). Through the later experiments, it is found that the two-parameter droplet size prediction model derived from the above method has a large deviation from the experimental results, and it is impossible to accurately predict the droplet size of this type of nozzle.
The X-type swirl pressure nozzle has the X-type spin core inside it, which is of the unique design, and its atomization characteristics are different from those of the conventional swirl pressure nozzles; moreover, the previously built droplet prediction models for pressure nozzles have the disadvantages that the model parameters need to be measured and the influence factors are incomplete, etc. Therefore, the existing pressure nozzle droplet prediction models can’t be directly used for droplet size prediction of X-type swirl pressure nozzles (Kim et al., 2012; Nie et al., 2016; Chang et al., 2008; Wang et al., 2019a, 2019b). In this study, the Malvern droplet size analyzer and orthogonal test design method were used to analyze the droplet SMD change law under the action of such four influence factors as nozzle outlet diameter, feed water pressure, axial distance and radial distance. On this basis, a mathematical SMD predicting model was built by means of the multivariate nonlinear regression analysis method, in order to provide a tool for SMD prediction for this type of nozzles.
Section snippets
Experimental system
The experimental system is composed of water storage tank, BPZ75/12 high pressure water pump, frequency converter, Malvern droplet size analyzer, intelligent electromagnetic flow meter, DX-801XB00150 digital manometer and related pipes and valves, as shown in Fig. 1. The output water pressure of high pressure water pump is regulated by frequency converter, and the feed water pressure is measured and displayed by digital manometer. Malvern droplet size analyzer was used to measure the droplet
Engineering application of the prediction model
The mining face of the coal mine is selected as the prediction model engineering application site. The dust suppression of the coal mining face is generally realized through the external spray device on the coal mining machine. The external spray nozzles are generally installed on the coal mining machine body 2.5 m away from the coal wall, and the working pressure of the nozzles is generally between 1.0 and 8.0 MPa. For the external spray of the coal mining machine, usually the X-type swirl
Conclusions
In this study, the SMD data of X-type swirl pressure nozzle under 25 working conditions were obtained by using the orthogonal design method and the Malvern droplet size analyzer, with the relationship between SMD and various influence factors analyzed. On this basis, a mathematical model for predicting SMD of X-type swirl nozzle is built by means of multivariate nonlinear regression method. The factors influencing the nozzle droplet size include axial distance, radial distance, feed water
Acknowledgments
Financial support for this work, provided by the National Natural Science Foundation of China (No.51574123), and the Open Fund Research Project of Key Laboratory Breeding Base for Mining Disaster Prevention and Control of China (No. MDPC201709), are gratefully acknowledged.
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