Analysis of the dedusting process in a rectangular chamber ﬁ lter

Purifying air from dust is a very important, current topic. There are many methods to minimize the amount of dust, one of them being chamber ﬁ lters. This paper presents the research results of a newly designed rectangular chamber ﬁ lter. The ef ﬁ ciency of the dedusting process is in ﬂ uenced by contamination properties, but also by the construction of the apparatus, inlet, and outlet location, the ratio of certain dimensions, and the gas ﬂ ow rate. The air ﬂ ow containing solid particles is a multi-phase, dif ﬁ cult-to-describe issue, therefore an attempt to determine the trajectory of particle movement in the apparatus was carried out using the PIV method. A decrease in the dedusting ef ﬁ ciency was observed with the increase of the gas ﬂ ow rate, as well as for smaller diameters of the solid particles. The obtained values of the ef ﬁ ciency of the apparatus are comparable with the values obtained for the constructions discussed in other papers.


INTRODUCTION
Technological processes, as well as numerous anthropogenic activities, are very often associated with the emission of the dust generated during their lifespan 1, 2 .It is an important and difficult topic, because the generated pollutants pose a direct threat to both the broadly understood environment and the people living in its surroundings 3,4 .There are standards that defi ne the limit values for dust concentrations in air, which are set by bodies such as the European Parliament and the Council of the European Union.In Europe, one of the applicable regulations is Directive 2008/50/EC of the European Parliament and the Council concerning ambient air quality and cleaner air for Europe 5 .
An increased awareness of the harmfulness of human activities to the environment, proceeding in accordance with the sustainable development trend, and an improvement of work ergonomics are just some of the factors that infl uence the fact that appropriate solutions for eliminating or reducing the emission of pollutants are still being sought 6, 7 .Industrial areas for which it is particularly important to include underground space and traffi c construction in mountainous areas, tunnel engineering, (especially in Germany and Japan) 8 , the wood industry 9 , the construction industry, and the plastics processing industry 10 .
Dedusting of gases (including air) is performed with the use of devices, or sets of devices, called dust collectors 11 .The basic quantity required in the design or selection of appropriate equipment for the dedusting process of a gas stream is the concentration of particles suspended in it.Additionally, important parameters are dimensions (and their distribution), shape, mass, density, adhesiveness, and physical and chemical properties 12,13 .Many conducted experimental studies, as well as numerical calculations, concerned the impact of the concentration, distribution and characteristics of the movement of dust particles on the course of the dedusting process, as well as on its effi ciency 8 .The effi ciency of the dedusting process, according to the general defi nition, is the ratio of the mass of particles retained in the dust collector to the mass of particles fed to the dust collector.In literature, one can also fi nd the defi nition that effi ciency is a speed of separation 14 .Despite the multitude of studies, there is still no clear information that allows for a full explanation of the dedusting mechanism, the illustration of the trajectory of pollution particles, and the linking of the fl ow distribution with the effi ciency of the process.This is due to, among others, the complexity of the process -i.e. the characteristics of multiphase fl ow 15 .
Dust collectors have been used in industry for a very long time.Their beginning can be associated with the Roots blower, which was developed in 1859 16 .Already existing constructions are still modifi ed in order to improve their effi ciency and to optimize their economic aspect 17 .The effi ciency of a dedusting system is based on the correct transport of dust and the proper separation of dust from the transporting medium.In addition to the properties of solid particles, the effi ciency of a dust collector is determined by air fl ow velocity 18 , and thus the pressure (directly dependent on it) difference occurring at different locations in the system 19 .Temperature and fl ow humidity are also important 20 .
One of the simplest dedusting methods is used in dry gravity dust collectors.Gravity is used to separate solid particles from the gas stream.It is a simple and effective method, but only in the presence of large solid particles.This means that it is mainly used when dealing with particles larger than 50 μm, which are in a suffi ciently high concentration.It is also a very effective process of initial dedusting (fi rst stage of dedusting), which allows the remaining equipment that is operating in the system to be protected against mechanical damage.Moreover, it also reduces the need for frequent cleaning 21 .For the process to take place effectively, certain conditions must be met.The dimensions of the settling chamber, its length L, and height H must be selected so that the dust has time to fall to the bottom, from where it will be irreversibly separated 6 .Similar guidelines should be followed when designing cyclones 22 .
The aim of this research work is to present a rectangular chamber dust collector, which was designed and made on a test scale.The results of laboratory tests for the developed construction will be presented, which in turn allows the device's operation to be characterized.The main focus was on determining the effi ciency of Polish Journal of Chemical Technology, 24, 4, 72-77, 10.2478/pjct-2022-0031 the device, characterizing the fl ow, and linking the most important input variables with the obtained dedust effect.

MATERIALS AND METHODS
The subject of this study concerns a chamber fi lter.It was assumed that a camera will work in the portrait orientation.The dust collector has a rectangular chamber (an alternative to cylindrical fi lters that are discussed in scientifi c publications), the bottom of which is bevelled on four sides (prism shape).The system has inlet and outlet nozzles with an internal diameter of 32 mm, which are located coaxial to the direction of the gas fl ow in its upper part.There is also a chute that allows for the periodic removal of solid particles that were separated in the apparatus.Figure 1 shows the proposed solution.
The designed chamber fi lter was made of colorless plexiglass plates (PMMA).The choice of construction material was related to the requirements for the test stand -strength, mechanical resistance, and transparency (enabling the observation of the process inside the apparatus).The plates were cut with a router in accordance with the assumed dimensions.The elements were then connected with glue.
Figure 2 shows the scheme of the test stand that was used to determine the movement of solid particles inside the chamber fi lter, as well as the dedusting effi ciency.
The experimental stand consisted of an autotransformer (the use of which made it possible to adjust the voltage, and thus the power of the blower's motor), a blower, the tested chamber fi lter, a rotameter, a Sony Action Cam FDR -X3000 camera, scales, and a computer with the appropriate software.The camera was positioned perpendicular to the direction of the tested fl ow.The camera had a matrix with a resolution of 8.2 megapixels, and an Exmar image sensor with a diagonal length of 2.5 inches.A Balanced Optical Steady Shot image stabilizer was also used.The research methodology is presented schematically in Figure 3.
The tests were performed at various gas fl ow rates within the range of 0.83 • 10 -4 -7.2 • 10 -4 m 3 /s.When determining the trajectory of the movement of particles, expanded polystyrene particles were used as the research material.A constant number of particles was assumed and introduced into the dedusting chamber during each test.In turn, quartz sand was used to assess the effi ciency of the apparatus.Material samples were fractionated using sieve analysis.A weighed amount of material was placed in a RETSCH vibrating screen that was equipped with a set of test sieves.The separation was carried out in a given period of time (900 sec) and at a specifi ed frequency (50 Hz).The following fractions were obtained: below 100 • 10 -6 m, 100-150 • 10 -6 m, 150-200 • 10 -6 m, 200-300 •10 -6 m, 300-400 • 10 -6 m, and 400-500 • 10 -6 m.From the sand prepared in this way, samples of 0.001 kg, 0.0025 kg, 0.005 kg and 0.010 kg were weighed.After the set test time (45 seconds) ended, the system was turned off and the sand remaining in the chamber was collected and weighed again.Based on these measurements, the effi ciency of the chamber fi lter was calculated in accordance with the following formula: (1)   where: η -effi ciency, m 0 -starting weight (kg), m n -mass of the collected solid from the dedusting chamber after the dedusting process (kg).

Determining the trajectory of the motion of particles
Based on the analysis carried out in PIVlab software, the directions, terminal points of movement and average velocities of the particles in the apparatus were visualized.Figure 4 shows an example of the velocity distributions of polystyrene particles inside the dedusting chamber at the air fl ow rate of 2.9 • 10 -4 m 3 /s.
After the particles were introduced into the air stream in the dust separator, they fell to the bottom of the apparatus due to the force of gravity.The secondary fl ow picked some of them up, however, their lift was signifi cantly below the air outlet nozzle, which caused the particles to remain in the apparatus after the process was completed.In this case, the maximum recorded speed was 1.4 m/s, which was achieved by the particles at about ¾ of the height of the dedusting chamber.Figure 5 presents a comparison of images obtained at various gas fl ow rates.
It can be seen that at the fl ow rate of 6.8 • 10 -4 m 3 /s., the secondary fl ow caused the polystyrene particles to rise to higher levels of the dedusting chamber than in the case of the fl ow rates of 2.9 • 10 -4 m 3 /s and 6.0 • 10 -4 m 3 /s.In turn, at the fl ow rate of 2.9 • 10 -4 m 3 /s, the particles of expanded polystyrene can be observed at the lowest level of the dedusting chamber.From these examples, it can be concluded that the higher fl ow rates caused the particles to be lifted closer to the gas stream fl owing between the inlet and outlet nozzles.This poses a risk of particle entrainment and reduced effi ciency.The fi gures also show that the highest average linear velocity is at the rate of 6.8 • 10 -4 m 3 /s, and the lowest at the rate of 2.9 • 10 -4 m 3 /s.

Determining of dust removal effi ciency
Based on the obtained experimental data, the effi ciency of the apparatus was calculated according to formula (1).Afterwards, graphs that show the dependence between the effi ciency (η) and the particle diameter of the solid and the airfl ow rate were plotted using the Statistica program.Figure 6 shows the results obtained in the case of the starting weight of a sample of 0.0025 kg. the apparatus.The greater the fl ow rate, the lower its performance.
Figure 7 shows the results obtained for a sample when the initial mass of the solid was equal to 10 g.
When comparing Figures 6 and 7, it can be observed that the initial mass of the sample (dust concentration) also affects the obtained results.Higher efficiency values were obtained with higher concentrations.For example, with the same air fl ow rate for the fraction of 400-500 • 10 -6 m, for a starting weight of 0.0025 kg, an effi ciency of 56% was obtained, and for a starting weight of 0.010 kg -70%.The effi ciency was observed for the 400-500 • 10 -6 m fractions, and for the gas fl ow rate of 0.83 • 10 -4 m 3 /s.In turn, the lowest effi ciency was observed for the fractions of 100 • 10 -6 m (15.2%) and for the fractions of 100 -150 • 10 -6 m (12.4%) when the fl ow rate was 7.2 • 10 -4 m 3 /s.It can be seen that dedusting in the case of larger particle fractions is much more effective than for smaller ones.For example, for the fl ow rate of 6.1 • 10 -4 m 3 /s, the effi ciency for the 400-500 μm fractions was 63.2%, while for the 100-150 • 10 -6 m fractions it was only 27.6%.Apart from particle size, the fl ow rate also has a large infl uence on the effi ciency of Using a nonlinear estimation, a relationship was developed that allows the effi ciency of the apparatus to be calculated as a function of the analyzed parameters.The relationship is described by the following formula: where: η -effi ciency, A = 47.46940,B = 0.62628, C = -0.06554,and 0.010 kg.The infl uence of dust concentration on the effi ciency of the dedusting process was noticed.The last analyzed dependence concerned the infl uence of the particle bulk density on the effi ciency of the process.
Based on the obtained results, it was found that the air fl ow rate had a greater impact on the effi ciency of the process in the case of lower densities of apparent solid particles.The lowest dust removal effi ciency was observed for the sample with the lowest apparent density of 10 kg/m 3 .The research results were compared with the own previous investigations 23, 24 .The obtained values of the effi ciency of the apparatus are comparable with the values obtained for the construction discussed in 24 -a cylindrical chamber fi lter.Moreover, they are signifi cantly higher than in the case of the apparatus presented in the publication 23 .
To sum up, it can be stated that the proposed construction is an interesting and promising alternative to already known solutions.The proposed equation can be successfully used in the design of this type of chamber fi lter, and also when selecting their operating conditions.d p -average particle diameter (m), V g -gas fl ow rate (m 3 /s).The value of the R coeffi cient for the proposed correlation was equal to 0.908.

The infl uence of solid body density on the dedusting process
Three materials of the same spherical shape and differing bulk density were used for the tests.The obtained results are presented in Table 1.
It can be seen that with an air fl ow rate of 0.83 • 10 -4 m 3 /s for samples 1 and 2, a high effi ciency of the dedusting process was obtained, and it amounted to 91%.At a higher gas fl ow rate (7.2 • 10 -4 m 3 /s), signifi cant discrepancies can be observed -for the sample with a lower apparent density, the effi ciency of the apparatus was lower (69%) when compared to the effi ciency obtained for the sample with a higher apparent density (80%).Larger amplitudes between the effi ciency values as a function of the air fl ow rate were obtained for the sample with a lower apparent density.The lowest effi ciency was observed for the sample of foamed polystyrene -52%.Based on the obtained results, it can be concluded that the apparent density of the sample has a signifi cant impact on the dedusting process.

CONCLUSIONS
This study aimed to propose and develop a modifi ed design of a chamber fi lter that allows for the obtaining of higher dust removal effi ciency values when compared to the alternative devices described in the literature.
Based on the performed experiments, it can be seen that an increase in the gas fl ow rate causes an intensifi cation of the secondary fl ow.As a consequence, particles that were originally separated in the settling chamber are lifted from the bottom of the apparatus to higher and higher heights, and this generates the risk of their entrainment and their return to the gas stream.Such a phenomenon leads to negative consequences, i.e. a reduction in the effi ciency of the process.In addition, increasing the gas fl ow rate causes an increase in the average velocity of the particles in the dedusting chamber, which may in turn affect the operation of the device, and in the case of prolonged, more intensive use, may result in faster wear (erosion) and an increase in the failure rate of the apparatus.It was observed that the most visible effect of the changes in the gas fl ow rate occurred for the fractions with the smallest (d <100 • 10 -6 m) and the largest diameters (d = 400-500 • 10 -6 m).
In the case of fractions with smaller diameters, the effi ciency of the apparatus decreased signifi cantly, while for fractions with larger particle diameters, the effi ciency of the process increased.The tests were performed on different initial sample weights of 0.0025 kg, 0.005 kg,

Figure 1 .Figure 2 .
Figure 1.Designed chamber fi lter a) the construction drawing, b) a visualization

Figure 3 .Figure 4 .
Figure 3. Measurement methodology: a) determining the trajectory of the movement of particles, b) determining the effi ciency of the dedusting process

Figure 6 .Figure 5 .
Figure 6.Effi ciency of the dedusting process for samples with a starting mass of 2.5 g

Figure 7 .
Figure 7. Effi ciency of the dedusting process for the samples with an initial mass of 10 g

Table 1 .
The obtained research results