MATHEMATICAL MODELING OF THE ACCEPTABLE PARAMETERS OF THE PLATE SCRUBBER

ABSTRACT

In the article, the influence of the hydraulic resistance of the plate scrubber, which cleans dusty gases in a wet method, on the cleaning efficiency and the energy used for the process was studied, and the optimal parameters of the device were determined using the mathematical planning method. Assuming that the influence of factors on the evaluation criteria in the mathematical planning method is fully described by a second-order polynomial, experiments (V4) are implemented based on the plan. Regression equations that adequately represent the evaluation criteria are HARTLI, with appropriate processing of the experimental results based on the -4 program. Based on the results of the experiment, the optimal parameters of the apparatus for the dust removal process selected for the sample are set to the standard state.

АННОТАЦИЯ

В статье исследовано влияние гидравлического сопротивления пластинчатого скруббера, очищающего запыленные газы мокрым способом, на эффективность очистки и энергозатраты на процесс, а также определены оптимальные параметры устройства с помощью математического уравнения. метод планирования. Полагая, что влияние факторов на критерии оценки в методе математического планирования полностью описывается полиномом второго порядка, эксперименты (V4) реализуются на основе плана. Уравнения регрессии, адекватно представляющие критерии оценки, представляют собой HARTLI с соответствующей обработкой экспериментальных результатов на основе программы -4. По результатам эксперимента оптимальные параметры аппарата процесса обеспыливания, выбранные для образца, устанавливаются в штатное состояние.

Keywords: plate scrubber, plate, HARTLI-4, wet method, hydraulic resistance, superphosphate dust, local resistance coefficient, working surface, nozzle

Ключевые слова: скруббер пластинчатый, пластина, ХАРТЛИ-4, мокрый способ, гидравлическое сопротивление, пыль суперфосфата, коэффициент местного сопротивления, рабочая поверхность, насадка.

Introduction

The cleaning efficiency of wet dust gas cleaning devices and the energy used for the process are determined according to the constructional structure of the device. One of the main tasks of the scientific research conducted in this field is to increase the cleaning efficiency and reduce the energy consumption per unit volume of the apparatus.

On the basis of these tasks, many scientific research works and information presented in the literature [1,2,3,4,5,7] were systematically analyzed on the basis of the MatLab program, and on the basis of these, an improved design scheme of the scrubber with a cylindrical plate with a simple structure and low energy consumption was developed, and a physical model of the device was developed (Fig. 1) [14,15]. Hydraulic resistance, the effect of hydraulic resistance on energy consumption and cleaning efficiency were studied in the experimental apparatus. In determining the cleaning efficiency and energy consumption, the equations proposed in the research work of KTSemrau [2,7] were used.

Figure 1. Overview of the laboratory model

During the experiments, within the following limits of the variable factors, the diameter of the liquid nozzle d_n=3 mm, the liquid consumption Q_liq=0.071÷0.189 m³/h, the intermediate step increased by 0.021 m³/h, the diameter of the plate valve hole d_f=2, 3 and 4 mm, the plate valve installation angle to the device β=15^o; The number of 30^o and 45^o plates is 2 according to the angle of installation, the intermediate step was increased by an average of 5.5 m/s to the gas speed υ_г=7.4÷28.8 m/s.

Superphosphate mineral fertilizer dust was selected as dust gas, and its density was determined as ρ_г=3.38 kg/m³ for a mixture of air and superphosphate mineral fertilizer dust (in which the amount of gas and dust mixture is 2697.79 mgr [2,8,14] in 1 m³ of air). Taking into account the influence of the external environment during the experiments, the temperature for the water and gas system was set at 200С±2. Experiments RD 34.20. 519-97 “Испытания гидравлического сопротивления трубороводов. Машины и аппараты для измерения расхода газов и давления. Программа и методы испытаний” [2,6,9,10,11,12]. The results of the experiment are presented in Tables 1 and 2. Taking into account the multifactor nature of the conducted experiments, the results obtained for the minimum and maximum gas velocities are presented in the tables.

Table 1.

Experimental results obtained on the effect of hydraulic resistance on cleaning efficiency and energy consumption. V_gas=7.4 m/s const.

Table 2

Experimental results obtained on the effect of hydraulic resistance on cleaning efficiency and energy consumption. y_gas=28.8 m/s const.

In order to evaluate the influence of the variable factors on the cleaning efficiency and energy consumption in the apparatus, it was determined using the method of mathematical planning of multifactorial experiments [11,12,13,15].

In theoretical studies and multi-factor experiments, it was found that the diameter of the squeegee plate hole (X1), dust gas velocity (X2), angle of installation of the squeegee plate on the device (X3) and liquid consumption (X4) are the factors that most affect the cleaning efficiency and energy consumption of the device. Based on the above-mentioned practical and theoretical studies and the results of multi-factor experiments, the change ranges of these factors were determined. Table 3 shows the levels and intervals of change of the factors.

Table 3.

Factor levels and change intervals

The hydraulic resistance of the device (Y1), the energy spent on dust cleaning (Y2) and the cleaning efficiency of the device (Y3) were taken as the evaluation criteria when conducting multi-factor experiments. Assuming that the influence of factors on the evaluation criteria is fully described by a second-order polynomial, experiments (V₄) was implemented based on the plan [2].

In order to reduce the influence of uncontrollable factors on the evaluation criteria, the sequence of conducting experiments was determined using a random number table, and separate experiments were conducted to determine the optimal parameters for cleaning scoperphosphate dust. The results of the experiment are presented in Table 4.

Table 4.

Experimental results obtained using a table of random numbers

The following regression equations that adequately represent the evaluation criteria are HARTLI, treating the results of the experiment accordingly– Received under 4 programs:

The hydraulic resistance of the rotary plate scrubber is determined by the following regression equation, Pa;

2470,775+209,5003 X1+1601,823X2-326,934X3+141,8045X4+ +161,0046X1X1+574,1728X2X2+295,7188X3X3+ +147,6249X4X4-461,386X1X2-317,93X1X3+440,4072X1X4+0,087585X2X3-343,963X2X4- 151.66X3X4

The energy consumption for the superphosphate dust cleaning process is determined according to the following regression equation, kJ/1000m³

525.1424+13.20617X1+356.413X2-73.1211X3+0.467121X4+ +43.71852X1X1+129.4685 X2X2+68.82625 X3X3+32.07387 X4X4-115.137 X1X2-62.4607 X1X4+81 X1X45 -17.2835 X2X3-101.424 X2X4-4.25413 X3X4

Superphosphate dust removal efficiency is determined by the following regression equation, %

99.66916+1.401656 X1+15.14628 X2-0.76481X3+0.679833X4-0.31127X1X1-10.3738 X2X22.408061X3X3+3.242856X4X4-1.47839X1X3+1.455893X1X3+1.455893X2X084+ ,03727X2X4-5,81982X3X4

Using the regression equation obtained for the superphosphate dust cleaning process and energy consumption, graphs of dependence of cleaning efficiency and energy consumption on the variable factors in the apparatus were constructed. The results are presented in Figures 2, 3 and 4.

Figure 2. Dependence of hydraulic resistance on variable factors

a–dependence of hydraulic resistance on the diameter of the plate hole; b – dependence of hydraulic resistance on gas speed; v - dependence of hydraulic resistance on the angle of installation of the spherical plate on the apparatus; g – dependence of hydraulic resistance on liquid consumption

Figure 3. Dependence of energy consumption on variable factor

a–dependence of energy consumption on the diameter of the plate hole; b – dependence of energy consumption on gas speed; v - dependence of energy consumption on the angle of installation of the spherical plate on the apparatus; g – dependence of energy consumption on liquid consumption

Figure 4. Dependence of cleaning efficiency on variable factor

a–the dependence of cleaning efficiency on the diameter of the plate hole; b – dependence of cleaning efficiency on gas speed; v - dependence of the cleaning efficiency on the angle of installation of the spherical plate on the apparatus; g – dependence of cleaning efficiency on liquid consumption

As can be seen from the analysis of the obtained regression equations and graphs, all factors have a significant impact on the evaluation criteria. In addition, fluid consumption, dust air velocity, diameter of the plate hole and the angle of installation of the plate on the apparatus are in a complex relationship with the studied factors.

In order to determine the optimal values of factors affecting the researched processes, i.e. hydraulic resistance of the apparatus, cleaning efficiency and energy consumption, regression equations (1), (2) and (3) were solved separately for the superphosphate dust cleaning process. In this case, the condition that the superphosphate dust cleaning efficiency is higher than 98.78% was accepted according to the requirements of GOST-62-198-142 [2]. This task was solved using the Excel program "search for a solution" (poisk reshenia) function on the PK "Pentium IV" computer, and the coded variable factors acceptable values in the form were obtained and changed from coded values to natural values Table 5.

Table 5.

Converting from coded values to natural values

Thus, the optimal parameters of the apparatus for the dust removal process selected for the sample were brought to the standard state and can be written as follows.

For the superphosphate dust removal process;

• The diameter of the hole of the spherical plate, df=3.75 mm
• Dust gas velocity, y=22.6 m/s
• The angle of mounting the spherical plate to the device, b=20 degrees
• liquid consumption, Q_c=0.163 m³/hour for one nozzle. If we take into account that the number of nozzles in the device is 4, then the liquid consumption is Q_c=0.652 m³/ hour

At these values of the factors, the energy consumption of the device was 4.2 kW/h, the cleaning efficiency was 99.6691%, and its hydraulic resistance was 2.47 kPa.

Conclusion

According to the experimental results, the cleaning efficiency is 6.03% higher than the existing wet cleaning devices, 1m³ it was found that the liquid used for air cleaning is 2 times less and the energy consumption is 0.8 times less, which fully satisfies the technical requirements for this type of equipment.

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