Analytical, Numerical, and Experimental Studies of the Working Process in a Pneumatic Abrasive Installation
1
Faculty of Technical Systems and Energy Efficient Technologies, Sumy State University, 116, Kharkivska St., 40007 Sumy, Ukraine
2
Faculty of Manufacturing Technologies with a Seat in Prešov, Technical University of Košice, 1, Bayerova St., 080 01 Prešov, Slovakia
*
Author to whom correspondence should be addressed.
Appl. Sci. 2024, 14(24), 11728; https://doi.org/10.3390/app142411728
Submission received: 13 September 2024
/
Revised: 13 December 2024
/
Accepted: 13 December 2024
/
Published: 16 December 2024
Download keyboard_arrow_down
Figure 1
<p>The design scheme (<b>a</b>) and the dependence between the mass flow rate and pressure ratio (<b>b</b>): 1-1—inlet section; 2-2—outlet section; <span class="html-italic">C</span>—critical point.</p> "> Figure 2
<p>The flowchart of numerical simulations.</p> "> Figure 3
<p>Three-dimensional model (<b>a</b>) and mesh grid (<b>b</b>) of the flow part for the industrial nozzle UDC32-450 with a critical diameter of 6 mm. Dimensions of the simulation model (<b>c</b>).</p> "> Figure 3 Cont.
<p>Three-dimensional model (<b>a</b>) and mesh grid (<b>b</b>) of the flow part for the industrial nozzle UDC32-450 with a critical diameter of 6 mm. Dimensions of the simulation model (<b>c</b>).</p> "> Figure 4
<p>The convergence of momentum and mass.</p> "> Figure 5
<p>Airflow velocities in the flow part of the industrial nozzle UDC32-450 with a critical diameter of 6 mm (<b>a</b>) and a surface roughness of 3.2 μm (<b>b</b>).</p> "> Figure 6
<p>The experimental stand for studying the working nozzle: 1—weights; 2—filler; 3—container with sand; 4—dosing tap; 5—abrasive-jet hose (<b>a</b>), measurement scheme (<b>b</b>): 1—container with abrasive material, 2—moisture separator, 3—compressor, 4, 5, 6—shut-off valves, 7—nozzle, 8—dynamometer, 9—electronic scales, 10—device for measuring the jet reaction, 11—load plate, 12—air intake, 13—air flow meter, 14—safety valve, 15—flow washer, 16, 17, 18, 19, 20—gauges.</p> "> Figure 7
<p>The flowchart of the experimental research.</p> "> Figure 8
<p>The impact of air consumption on the output surface roughness (<span class="html-italic">K</span>—roughness coefficient): points—calculated values; lines—approximation lines.</p> ">
Versions Notes
<p>The design scheme (<b>a</b>) and the dependence between the mass flow rate and pressure ratio (<b>b</b>): 1-1—inlet section; 2-2—outlet section; <span class="html-italic">C</span>—critical point.</p> "> Figure 2
<p>The flowchart of numerical simulations.</p> "> Figure 3
<p>Three-dimensional model (<b>a</b>) and mesh grid (<b>b</b>) of the flow part for the industrial nozzle UDC32-450 with a critical diameter of 6 mm. Dimensions of the simulation model (<b>c</b>).</p> "> Figure 3 Cont.
<p>Three-dimensional model (<b>a</b>) and mesh grid (<b>b</b>) of the flow part for the industrial nozzle UDC32-450 with a critical diameter of 6 mm. Dimensions of the simulation model (<b>c</b>).</p> "> Figure 4
<p>The convergence of momentum and mass.</p> "> Figure 5
<p>Airflow velocities in the flow part of the industrial nozzle UDC32-450 with a critical diameter of 6 mm (<b>a</b>) and a surface roughness of 3.2 μm (<b>b</b>).</p> "> Figure 6
<p>The experimental stand for studying the working nozzle: 1—weights; 2—filler; 3—container with sand; 4—dosing tap; 5—abrasive-jet hose (<b>a</b>), measurement scheme (<b>b</b>): 1—container with abrasive material, 2—moisture separator, 3—compressor, 4, 5, 6—shut-off valves, 7—nozzle, 8—dynamometer, 9—electronic scales, 10—device for measuring the jet reaction, 11—load plate, 12—air intake, 13—air flow meter, 14—safety valve, 15—flow washer, 16, 17, 18, 19, 20—gauges.</p> "> Figure 7
<p>The flowchart of the experimental research.</p> "> Figure 8
<p>The impact of air consumption on the output surface roughness (<span class="html-italic">K</span>—roughness coefficient): points—calculated values; lines—approximation lines.</p> ">
Abstract
:The article presents the results of numerical and experimental studies of a working nozzle for jet-abrasive machining of material surfaces. Nozzle designs with variable geometry were investigated. The aim of the study was to identify reserves for increasing the efficiency of the nozzle to ensure the energy efficiency of the jet-abrasive installation for sustainable production in the context of Industry 5.0. The implementation of numerical modeling made it possible to carry out a series of calculations for the considered nozzle designs using an air-abrasive mixture with flow visualization. The technological parameters of jet-abrasive machining were analyzed. A series of numerical and experimental studies were conducted using the principles of Industry 4.0. Two software packages were used for numerical studies. The results of the calculations that were obtained coincided quite well. Overall, the obtained results made it possible to adjust the settings of the pneumo-abrasive unit in order to get the proper roughness of the processed surface, opt for proper working nozzle design, and determine proper pressure and air consumption for the highest unit efficiency. In a series of studies, the authors proposed a mathematical model for determining the values of mass flow rates of the working medium in the nozzle. The analytical coefficients of the developed model have been obtained. In addition, an approach to determining the main parameters of abrasive blasting based on experimental data was developed. The results obtained were verified by comparing them with the results of experimental studies. It was found that to increase the efficiency of the Venturi nozzle, the outlet cross-section of the considered nozzles should be reduced, and the mass flow rate of the dispersed phase should not significantly affect the speed of the grains of sand at the nozzle outlet.
1. Introduction
Pneumatic abrasive blasting of contaminated material surfaces has always been in demand and is not cheap because it uses capacious energy equipment to ensure the performance of the installation. It is necessary to ensure an uninterrupted supply of compressed air with a pressure of 0.8 MPa and a flow rate of 2.5–3.0 m3/min. Abrasive material should be dry and have a certain grain size. One of the key elements of a pneumatic abrasive machine is its working nozzle, the efficiency of which determines the efficiency of material processing [1]. This leads to the necessity of designing a nozzle that can replace conventional nozzles due to more efficient transformation of the potential energy of the compressed gas into kinetic energy of the outcoming jet for sustainable production within the Industry 5.0 context.
In [2], the author found a high-frequency pressure component in the end throttle resulting from the non-linearity of the hydromechanical system. The results showed a decrease in the pressure value in the end channel, which helps design such devices.
In [3], the implementation of technological equipment for abrasive-jet machining was analyzed in terms of efficiency and fast cleaning.
The research work in [4] proposed a mathematical model of surface roughness during abrasive-jet machining. However, the overall error compared with the physical experiment was 12–16%.
In [5], the Reynolds equations calculated the gas phase dynamics with their closing based on the Wilcox turbulent model. In [6], an optimized design of a new pneumatic system was obtained using programmable logic controllers. The research work in [7] presents an abrasive-jet machining model implemented for machine tool coatings.
In [8], an impact of the jet angle on abrasive-jet processing with velocities in a range of 280 310 m/s was considered using CFD simulations.
In [9,10], some methods dealing with aerodynamic modeling of the two-phase turbulent vortex flow in the separate chamber of the pneumatic centrifugal classifier are considered. Particularly, Zhang et al. [9] analyzed separation mechanics for particles with variable size ranges considering centrifugal forces and pressure gradients in a channel. As a result, it was found that the drag force has much more impact on the particles than the abovementioned forces.
Furthermore, Derksen [10] studied a turbulent vortex flow using large-Eddy simulations and lattice-Bolzman discretization for Reynolds equations. After comparing the numerical simulation results with those of available experimental studies, it was found that the tube’s diameter significantly impacts the average velocity. Additionally, the phenomena of vortex breakdown and core laminarization were observed.
Thus, further and deeper studies of the two-phase medium flow in the working nozzle of the pneumo-abrasive unit are necessary to improve its operating features. There is a need to identify the efficiency indicators of the working nozzle of the pneumo-abrasive unit. The goal is to perform a series of experimental and numerical studies of the working nozzle of the pneumo-abrasive unit using Industry 4.0 principles so that technological parameters of the jet-abrasive processing of the surfaces of materials can be identified.
The list of tasks includes:
- −
- creating a mathematical model to determine the relationship between the mass flow rate in the working nozzle based on the original Saint-Venant–Wanzel formula and its total expansion for an air-abrasive mixture using the proposed polynomial approximation;
- −
- identifying efficiency indicators of the working nozzle of the pneumo-abrasive unit;
- −
- determining the impact of the roughness of the nozzle’s inner surface on its operating characteristics;
- −
- estimating the impact of geometrical and operating parameters of the working nozzle of the pneumo-abrasive unit on its operating characteristics.
The study in [11] considers the features of the development and operation of multistage steam jet ejectors, but it is necessary to expand the ranges of the parameters under study. The operation of shot blasting and a waterjet nozzle are investigated in [12]. It has been shown that the geometric and operating parameters of the studied nozzles significantly impact the performance characteristics of the jet flowing from the nozzle. There is a need for systematic studies of a broader range of values. In [13], the improvement of the performance of the process of microabrasive jet machining of Aluminum 6061 is studied. According to the results of the experiments, numerous factors should influence the surface roughness value. There is a need to create a more advanced design of an abrasive jet nozzle, which, due to the rational proportions of its geometric shapes, would process the surfaces of materials more efficiently and quickly to obtain a given surface roughness. The study in [14] focuses on the mechanism of sand grain advancement in the middle of the nozzle using numerical modeling tools. The results obtained should be used to create new designs of working nozzles. In [15], the author proposed the design of an abrasive blasting nozzle with a permeable insert, which reduces the abrasive material’s friction and increases the nozzle’s efficiency. The disadvantages of this nozzle design are its structural complexity, difficulty of manufacturing, and the need for an additional air hose, which makes the nozzle much heavier and less maneuverable during processing. By performing a series of studies in a wide range of operating conditions and geometric parameters, it is possible to obtain simpler and cheaper designs of abrasive blast nozzles. In [16], a methodology for experimental studies of an ejector with resonant support at low pressure was developed. There is a need to expand the values of the pressure range.
When even a small amount of nozzle wear occurs, air and abrasive material flow through the nozzle increases significantly. Thus, worn nozzles lose their efficiency and need to be replaced immediately.
2. Materials and Methods
2.1. Analytical Studies
Existing analytical studies are predominantly based on the assumption of an ideal nozzle in which losses are not considered due to a significant pressure difference. Under such conditions, the Saint-Venant–Wanzel formula [16] can be applied:
where m is mass flow rate, kg/s; p1, p2 are inlet and outlet pressures, respectively, Pa; ρ1 is inlet gas density, kg/m3; F2 is outlet cross-sectional area of the nozzle, m2; k > 1 is thermodynamic constant.
After introducing the pressure ratio β = p1/p2 and considering the parabolic feature of its impact on the mass flow rate (Figure 1), the following approximation of Equation (1) can be proposed:
where a0, a1, and a2 are unknown parameters.
The parameters a1, a2, and a3 can be determined analytically using the following physical conditions:
where mcr is the critical value of the mass flow rate, kg/s, that corresponds to the critical pressure ratio βcr (in a range of 0.51.0) when the supersonic mode occurs.
These conditions allow for determining the unknown parameters:
Thus, Formula (2) takes the form:
where C > 4 is the following dimensionless parameter determined by the critical pressure ratio:
Since the critical pressure ratio for an air-abrasive mixture significantly differs from the ideal gas, the parameter C should be evaluated using the best approximation of experimental data by Formula (5). In this case, after using the least square approach [17], the following error function should be minimized:
where n is the total number of experimental points; i is experiment no. (i = 1, 2, …, n); βi is the pressure ratio for the i-th experiment; mi is mass flow rate at the i-th experiment, kg/m3.
The minimization condition
allows for evaluating the actual value of the unknown parameter:
Moreover, Formula (6) allows for further determining the actual value of the critical pressure ratio for the air-abrasive mixture:
2.2. Numerical Simulations
The numerical calculations were made using software complexes ANSYS and FlowVision to get the operating parameters of the air-abrasive mixture both inside and off the nozzle. The following nozzles were tested: a Venturi nozzle with a critical diameter of 4 mm and a length of 143 mm, a Venturi nozzle with a critical diameter of 8 mm and a length of 194 mm, a cylindrical nozzle from ceramics with a length of 22 mm, a cylindrical nozzle from steel C40 with a length of 22 mm, a cylindrical nozzle from steel C40 with a length of 11 mm, a cylindrical nozzle from steel C40 with a length of 44 mm, UDC32-450 with a critical diameter of 6 mm with hydraulic smooth walls and a rough inner surface, cylindrical nozzle with an inner diameter of 20 mm, length of 22 mm. The flowchart of the numerical simulations is presented in Figure 2.
Numerical modeling with the ANSYS application algorithm is presented in Figure 3. The first stage included building a 3D model of the nozzle UDC32-45 (Figure 3a). Next, the computational grid was constructed (Figure 3b). Afterwards, a calculation model was selected, and boundary conditions were set.
Next, calculations with convergence control application (Figure 4) were carried out.
The turbulent flow simulation was carried out using the Reynolds equations application of various turbulence models. The flow was calculated for stationary conditions. The carrier medium was air; the abrasive material was sand with grain sizes of 0.1–0.5 mm and the turbulent flow mode. Numerical calculations simulated the movement of the air-abrasive mixture in the flowing part of the nozzle under study. The geometry of the nozzle is limited by the three-dimensional model we created. The software package user sets the boundary conditions related to gas dynamics manually and remain unchanged until the calculation is completed [1,17,18].
The working process was modeled using the well-known Reynolds equations, which include turbulence models. The flow was considered to be stationary. Compressed air was selected as the carrier medium, and sand with a grain size of 0.1–0.5 mm was selected as the working abrasive material. The flow was turbulent. Similar problems have used k-ε, Spalart–Allmaras, and SST models [18,19,20].
Airflow velocities in the flow part of the industrial nozzle UDC32-450 with a critical diameter of 6 mm are presented in Figure 5.
2.3. Experimental Studies
Verification of the obtained results was performed by means of a series of experimental studies with a special experimental stand designed for studies of the working nozzles of the pneumo-abrasive unit (Figure 6).
The stand included a compressed air supply sleeve connecting the receiver with the inlet pipeline; three 50 mm valves to shut part of the pipeline and to control the pressure in it; 25 mm valves to connect the pipeline with the atmosphere; pressure lines; welded steel pipeline sections flanged and sealed with the rubber seals.
The river sand with a grain diameter of 0.2 mm was used as an abrasive material. The inlet pressure was set, and the output pressure was constant (atmospheric). Under these conditions, the air and mixture consumptions were determined.
The flowchart of the experimental research is presented in Figure 7.
3. Results
3.1. Venturi Nozzles
The convergence of the gained results was determined by coincidence of the mass flow of the working mixture at the inlet and the output of the nozzle. The validation of the numerical studies was also performed by comparison of the results of the jet reaction force with absolute pressure at the nozzle inlet. This is because this force affects the time and efficiency of the material processing: the higher the force, the higher the air-abrasive mixture velocity, and the more effective the nozzle.
The comparison of two basic nozzle types, namely the straight nozzle and the Venturi nozzle, is given below.
Table 1 presents the basic results of the physical experiment with the Venturi nozzle with a critical diameter of 4 mm and a length of 143 mm. The results for the critical diameter of 8 mm and the length of 194 mm are summarized in Table 2.
The presented results illustrate the two-times difference in the values of real jet reaction force A and ideal jet reaction force A, which can be explained by the absence of friction and resistance in the ideal process. As the inlet pressure of the nozzle increased, the values of all operating parameters of the jet increased as well.
Further studies dealt with the parameters presented in Table 1, but the diameter was twice as high. As a result, the discrepancies in the values of real and ideal jet reaction forces increased four times.
The discrepancy between the value of the jet reaction force obtained experimentally and the value of calculated real jet reaction force was about 4%. This proves the correctness of the obtained results.
The results demonstrated the exponential dependence of the air-abrasive mixture’s reaction jet force on the nozzle’s absolute pressure. The higher the pressure value, the higher the nozzle jet reaction value. It should be noted that if the nozzle critical diameter increased two times, the jet reaction force increased three times. The consumption coefficient for both tested nozzles was almost the same—0.97. The results obtained during physical experiments and numerical calculations by means of the ANSYS complex were almost identical. Finely fractionated sand grains with a diameter of 0.2 mm were taken for the physical experiment. The fact that fine sand grains did not affect the jet reaction force was established experimentally. This effect became evident with the increase of the sand grain diameter. This resulted in a decrease in the jet reaction force. The effect of the fractional composition of sand on the jet reaction force was considered a further investigation direction. This fact can be explained by the inertial component of the abrasive material particle movement: the heavier the particles, the more kinetic flow energy they take and the more slowly they gather velocity accordingly. Furthermore, the increase in sand supply decreased the quantity of air that was used as a carrier flow. This resulted in a decrease in the jet reaction force.
Thus, the nozzle efficiency coefficient can be found in the physical experiment results presented in Table 1 and Table 2. To calculate an ideal nozzle, i.e., without losses and with maximum efficiency under ideal conditions, the Saint-Venant–Wanzel formula can be applied. Therefore, it is necessary to enter a correction factor to correctly determine the air-abrasive mixture’s mass consumption. The value of this consumption affects the consumption coefficient value of the nozzle as well as the jet reaction force value.
The above visualizations make it evident that there were zones of pressure that decreased when velocity increased. Friction along the nozzle length prevented a rapid flow velocity increase. The visualizations also demonstrate that the nozzle was over-expanded and worked with the inside pressure less than with back pressure (atmospheric). This decreased the nozzle output velocity and its velocity coefficient. As a result, pressure pulsation appeared and had a distinctive jet form.
The diagrams present a good convergence of the calculated and experimental data, indicating a possibility of applying a numerical experiment to further investigate the working nozzles for the pneumo-abrasive unit within a wide range of pressure values. If it is necessary to remove thick dirt layers such as old rust or old paint, the working pressures should be 0.50.6 MPa. When glass, plastic, or aluminum are processed, 0.2 MPa of overpressure for the air-abrasive mixture before the nozzle is sufficient.
3.2. Cylindrical Nozzles
A conventional cylindrical nozzle was also investigated to determine the course of the process of the two-phase medium in order to find ways to increase its efficiency. The main results are summarized in Table 3 and Table 4.
Thus, to reduce losses, it is recommended that the nozzle length be reduced from 22 mm to 11 mm in order to evaluate the impact of friction on the nozzle efficiency. The results for this length are summarized in Table 5 and Table 6. They show a good convergence of the inlet speed of the air-abrasive mixture. However, if the nozzle is two times shorter, the velocity increases by up to 60%, leading to a considerable efficiency increase.
The processing time is when the air and abrasive flow rates specified in the table pass through the nozzle. This is an experimental value. As the nozzle diameter increases, the value of air and abrasive material consumption increases in the experiments. Thus, in the experiments, the values of air pressure, air consumption, abrasive material consumption, material surface treatment time, and nozzle length change. The experiment also testified that this nozzle is more effective in case of local corrosion, such as thick layers of old paint in a small area. For larger areas, it is better to use another nozzle because this one’s diameter is insufficient and wears out quickly. When a similar nozzle was manufactured from steel C40 after carbonization, the machining time can be reached 2 times.
3.3. Impact of the Surface Roughness
Notably, the coating made steel nozzles like ceramic ones in terms of surface processing speed. Its disadvantage is rapid wear after about 100 h of continuous operation depending on coating thickness. The impact of the inner surface roughness of the nozzle UDC32-459 with a critical diameter of 6 mm was also analyzed. The results are summarized in Table 7.
It can be seen from the table that when wall roughness was 3.2 μm, a reduction in the jet force of 14% occurred for the nozzle UDC32-450 with a critical diameter of 6 mm.
The results of the experimental studies of the cylindrical nozzle are presented in Table 8, and the impact of air consumption on the output mass flow rate in Figure 8.
Table 8 and Figure 8 summarize the results of the experimental studies of the material surface with an initial roughness of 50 μm, which was processed with abrasive grains from 0.2 to 0.5 mm and with an initial roughness of 35 μm processed with abrasive grains from 0.1 to 0.2 μm. The roughness of the inner surface of the nozzle was measured using a professional profilometer PCE-RT 2300.
As a result, it is apparent that the roughness of the nozzle surface affected its characteristics; namely, roughness reduced the velocity of the air-abrasive mixture by up to 10% in comparison with that in a smooth hydraulic nozzle.
4. Discussion
Verification of the obtained parameters was carried out by comparing the results of the numerical study with the results of the physical test. In this case, the k-ε turbulence model [21] was chosen.
Considerable differences were obtained between the values of the actual jet reaction force of the Venturi nozzle and the ideal jet reaction force. The discrepancy between the value of the jet reaction force A obtained experimentally and the value of the pre-calculated real jet reaction force and output velocity was about 4%. This confirmed the correctness of the calculation results.
It can be seen from the tables that speed values of the air-abrasive mixtures differed by up to 10% in the nozzles made of ceramics and metal. This indicates velocity losses caused by the nozzle’s inner surface roughness, as discussed in the works [22,23,24,25].
The obtained results showed that the roughness of the nozzle wall impacts the value of the working medium velocity; namely, the ceramic nozzle velocity is 15% higher at the output cross-section if compared with the metal surface with higher roughness. The consumption coefficients stay almost the same, correlating with the papers [17,18,19]. It was found that the Venturi nozzle is more sensitive to surface roughness since the differences in the values of its output velocity in the ideal and actual processes make up to 4 times.
The reduction of the cylindrical nozzle length from 22 mm to 11 mm reduced metal surface processing time by 1.5 times, which the reduction of the nozzle hydraulic resistance can explain.
Even if an increase in the cylindrical nozzle diameter does not change the processing time, the air-abrasive mixture consumption rises up to 4 times, which correlated with the papers [20,26]. Notably, since a pneumatic abrasive unit consumes a significant amount of compressed air and abrasive material, it is economically impractical to perform surface treatment of materials using worn nozzles or nozzles with an increased internal diameter.
The reduction of the fractional structure of the abrasive material causes a decrease in the roughness of the processed surface. Thus, the following recommendations may be the following: for removal of the dirt coating, the abrasive fraction of 0.20.5 mm should be applied. The finer abrasive fraction of 0.1−0.2 mm should be used before coating when corrosion is removed from the shells and cavities for finer surface processing.
The results presented above testify to the significant impact of the geometry of the jet-abrasive nozzle on the technological parameters of the material surface processing, and this should be considered while jet-abrasive nozzles are designed and manufactured. The processing times affect the processing cost since a jet-abrasive unit consumes much of the expensive compressed air and abrasive material.
The angle of the fluid profile at the nozzle outlet constantly changes and depends on many geometric and operational factors. The most influential factors on the value of the outlet jet angle at the nozzle cut are its length, diameter, working stream velocity at the nozzle outlet, the distance between the nozzle and the surface to be treated, and the angle of the nozzle related to the surface to be treated. The lower the value of the spray angle, the higher the values of the working mixture velocity and the nozzle flow rate we will get.
The technological parameters of abrasive blasting of material surfaces are the processing time, the resulting surface roughness, and the values of the operating parameters of the abrasive-air mixture at the nozzle cut.
Compressed air is a relatively expensive working medium, as a compressed air supply of 3 to 10 m3/min is required to keep the abrasive blasting machine running. Consuming 30 to 100 kW of electrical power is necessary to obtain this amount of compressed air. Therefore, the search for more advanced designs for the working nozzles of abrasive blasting machines is very relevant, since the air consumption of the machine depends on the working nozzle to the greatest extent.
Overall, a comprehensive methodology for designing working nozzles of a pneumatic abrasive unit has been created based on the integrated application of analytical and experimental methods with computational techniques. The developed approach of evaluating the operating parameters for the working nozzle has allowed for the design of new energy-efficient working nozzles that increase processing efficiency.
The obtained results have been practically implemented for designing abrasive jet nozzles at “Karbaz” Ltd. (Kyiv, Ukraine), “Bosko” Ltd. (Sumy, Ukraine), and “SPE “Metekol” Ltd. (Nizhyn, Ukraine).
Further research will be aimed at developing dust-free pneumatic abrasive-jet units, the operation of which will be based on the obtained scientific and practical results.
5. Conclusions
During the research, a mathematical model for determining the dependence between the mass flow rate in a working nozzle was proposed based on the initial Saint-Venant–Wanzel formula and its general extension for an air-abrasive mixture using the proposed approximation by a polynomial. The corresponding coefficients of the model were obtained analytically. Moreover, an approach for identifying the main parameters, i.e., the critical value of the pressure ratio, was also developed based on the best fit of the proposed analytical dependence with the experimental dataset.
The working parameters of the flow part of the Venturi nozzles with a different geometry depending on the inlet overpressure were also evaluated numerically and experimentally using Industry 4.0 principles. The accuracy of the results calculated by software the complex was about 4% acceptable and fit the results of the experimental studies.
It was additionally determined that to increase the efficiency of the Venturi nozzle, the output cross-section of the considered nozzles should be decreased, as the mass flow rate of the dispersed phase does not have an essential impact on the velocity of sand grains at the nozzle output.
Moreover, the impact of the inner surface roughness of the nozzle on its efficiency was established. Namely, surface roughness contributed to the decrease of the outflow velocity of the air-abrasive mixture by 10% in comparison with the hydraulic smooth nozzle and to an increase in the surface processing time. It was also found that the wall roughness of 3.2 µm decreased the jet reaction force of the nozzle UDC32-450 with a critical diameter of 6 mm by 14% and increased the outflow time by 37%. Thus, it is a negative factor in the nozzle operation.
Author Contributions
Conceptualization, V.B.; methodology, V.B.; software, J.P.; validation, V.B., I.P. and J.P.; formal analysis, V.B. and I.P.; investigation, V.B., J.P., and I.P.; resources, V.B. and I.P.; data curation, V.B. and J.P.; writing—original draft preparation, V.B.; writing—review and editing, J.P. and I.P.; visualization, V.B. and I.P.; supervision, I.P.; project administration, V.B.; funding acquisition, J.P. All authors have read and agreed to the published version of the manuscript.
Funding
The research was funded by the EU NextGenerationEU through the Recovery and Resilience Plan for Slovakia under project No. 09I03-03-V01-00093. This work was also supported by the Slovak Research and Development Agency under contract No. APVV-22-0391, and by projects VEGA 1/0704/22, KEGA 022TUKE-4/2023 granted by the Ministry of Education, Research, Development and Youth of the Slovak Republic.
Institutional Review Board Statement
Not applicable.
Informed Consent Statement
Not applicable.
Data Availability Statement
The dataset is available on request from the authors.
Acknowledgments
The authors acknowledge the support of the Ministry of Education and Science of Ukraine, particularly the project “Development of a mobile ejector-cleaning unit for the restoration of buildings, structures and equipment after fires in the war period”, No. 0124U000636.
Conflicts of Interest
The authors declare no conflicts of interest.
References
- Vanyeyev, S.M.; Meleychuk, S.S.; Baga, V.M.; Rodymchenko, T.S. Investigation of the influence of gas pressure at the inlet in jet-reactive turbine on its performance indicators. Probl. Reg. Energetics 2018, 3, 71–82. [Google Scholar] [CrossRef]
- Zhang, Z.; Bertin, V.; Essink, M.N.; Zhang, H.; Fares, N.; Shen, Z.; Bickel, T.; Salez, T.; Maali, A. Unsteady drag force on an immersed sphere oscillating near a wall. J. Fluid. Mech. 2023, 977, A21. [Google Scholar] [CrossRef]
- Haldar, B.; Ghara, T.; Ansari, R.; Das, S.; Saha, P. Abrasive jet system and its various applications in abrasive jet machining, erosion testing, shot-peening, and fast cleaning. Mater. Today Proc. 2018, 5, 13061–13068. [Google Scholar] [CrossRef]
- Verma, T.; Chawla, O.; Jha, S. Mathematical modelling for prediction of surface roughness in pneumatically configurable polishing process. Wear 2022, 504–505, 204434. [Google Scholar] [CrossRef]
- Rogovyi, A.; Neskorozhenyi, A.; Panamariova, O.; Zoria, M. Hydrodynamic characteristics of pumping bulk materials using vortex chamber ejectors. In Advances in Design, Simulation and Manufacturing VI. DSMIE 2023; Ivanov, V., Pavlenko, I., Liaposhchenko, O., Machado, J., Edl, M., Eds.; Lecture Notes in Mechanical Engineering; Springer: Cham, Switzerland, 2023; pp. 148–157. [Google Scholar] [CrossRef]
- de Freitas, A.G.; dos Santos, R.B.; Riascos, L.A.M.; Munive-Hernandez, J.E.; Kuang, S.; Zou, R.; Yu, A. Experimental design and optimization of a novel solids feeder device in energy efficient pneumatic conveying systems. Energy Rep. 2023, 9, 387–400. [Google Scholar] [CrossRef]
- Zhuang, K.; Wu, Z.; Wan, L.; Weng, J.; Yang, Y.; Tian, C.; Li, Y.; Liu, Z. Investigation of different abrasive jet machining methods applied to milling tool coatings for post-treatment. Surf. Coat. Technol. 2024, 491, 131156. [Google Scholar] [CrossRef]
- Kuji, C.; Izumita, K.; Shimada, K.; Mizutani, M.; Sasaki, K.; Kuriyagawa, T. Influence of the impact angle on machining in powder jet processing. Int. J. Autom. Technol. 2023, 17, 5–13. [Google Scholar] [CrossRef]
- Zhang, Y.; Cai, P.; Jiang, F.; Dong, K.; Jiang, Y.; Wang, B. Understanding the separation of particles in a hydrocyclone by force analysis. Powder Technol. 2017, 322, 471–489. [Google Scholar] [CrossRef]
- Derksen, J.J. Simulations of confined turbulent vortex flow. Comput. Fluids 2005, 34, 301–318. [Google Scholar] [CrossRef]
- Aronson, K.E.; Ryabchikov, A.Y.; Zhelonkin, N.V.; Brezgin, D.V.; Demidov, A.L.; Balakin, D.Y. Features of the development and operation of multistage steam jet ejectors. Therm. Eng. 2023, 70, 245–253. [Google Scholar] [CrossRef]
- Bañon, F.; Sambruno, A.; Batista, M.; Simonet, B.; Salguero, J. Surface quality and free energy evaluation of S275 steel by shot blasting, abrasive water jet texturing and laser surface texturing. Metals 2020, 10, 290. [Google Scholar] [CrossRef]
- Kwon, D.-K.; Lee, J.-H. Performance improvement of micro-abrasive jet blasting process for al 6061. Processes 2022, 10, 2247. [Google Scholar] [CrossRef]
- Han, X.; Xiao, J.; Yu, F.; Zhao, W. Relationships and mechanisms of sand grain promotion on nozzle cavitation flow evolution: A numerical simulation investigation. J. Therm. Sci. 2022, 31, 2385–2410. [Google Scholar] [CrossRef]
- Zabolotnyi, O.; Povstyanoy, O.; Somov, D.; Sychuk, V.; Svirzhevskyi, K. Technology of Obtaining Long-Length Powder Permeable Materials with Uniform Density Distributions. In World Congress on Engineering and Technology; Beltran, A., Jr., Lontoc, Z., Conde, B., Serfa Juan, R., Dizon, J., Eds.; Innovation and its Sustainability 2018. WCETIS 2018. EAI/SpringerInnovations in Communication and Computing 2022; Springer: Cham, Switzerland, 2022; pp. 63–78. [Google Scholar] [CrossRef]
- Xi, X.; Xin, Y.; Duan, D.; Zhang, B. Experimental investigation on the performance of a novel resonance-assisted ejector under low pressurization. Energy Convers. Manag. 2023, 280, 116778. [Google Scholar] [CrossRef]
- Baha, V.; Mižáková, J.; Pavlenko, I. An increase in the energy efficiency of abrasive jet equipment based on the rational choice of nozzle geometry. Energies 2023, 16, 6196. [Google Scholar] [CrossRef]
- Baha, V.; Pitel, J.; Pavlenko, I. Effect of erosion on surface roughness and hydromechanical characteristics of abrasive-jet machining. J. Eng. Sci. 2024, 11, G9–G16. [Google Scholar] [CrossRef]
- Wang, J.; Gong, J.; Kang, X.; Zhao, C.; Hooman, K. Assessment of RANS turbulence models on predicting supercritical heat transfer in highly buoyant horizontal flows. Case Stud. Therm. Eng. 2022, 34, 102057. [Google Scholar] [CrossRef]
- Sokolichin, A.; Eigenberger, G. Applicability of the standard k–ε turbulence model to the dynamic simulation of bubble columns: Part I. Detailed numerical simulations. Chem. Eng. Sci. 1999, 54, 2273–2284. [Google Scholar] [CrossRef]
- Qiang, Z.; Yong, Y. A new simpler rotation/curvature correction method for Spalart–Allmaras turbulence model. Chin. J. Aeronaut. 2013, 26, 326–333. [Google Scholar] [CrossRef]
- Kun, T.; Wenjie, H.; Yurong, W. Optimization of cold spray nozzles based on the response surface methodology. J. Eng. Sci. 2024, 11, F1–F11. [Google Scholar] [CrossRef]
- Arana-Landín, G.; Uriarte-Gallastegi, N.; Landeta-Manzano, B.; Laskurain-Iturbe, I. The contribution of lean management –Industry 4.0 technologies to improving energy efficiency. Energies 2023, 16, 2124. [Google Scholar] [CrossRef]
- Ahmed, F.; Chen, W. Investigation of steam ejector parameters under three optimization algorithm using ANN. Appl. Therm. Eng. 2023, 225, 120205. [Google Scholar] [CrossRef]
- Kosheleva, O.; Kreinovich, V. Error estimation for indirect measurements: Interval computation problem is (slightly) harder than a similar probabilistic computational problem. Reliab. Comput. 1999, 5, 81–95. [Google Scholar] [CrossRef]
- Lehocka, D.; Klich, J.; Pitel, J.; Krejci, L.; Storkan, Z.; Duplakova, D.; Schindlerova, V.; Sajdlerova, I. Analysis of the pulsating water jet maximum erosive effect on stainless steel. In Advances in Manufacturing II. MANUFACTURING 2019; Lecture Notes in Mechanical Engineering; Gapiński, B., Szostak, M., Ivanov, V., Eds.; Springer: Cham, Switzerland, 2019; pp. 233–241. [Google Scholar] [CrossRef]
Figure 1.
The design scheme (a) and the dependence between the mass flow rate and pressure ratio (b): 1-1—inlet section; 2-2—outlet section; C—critical point.
Figure 1.
The design scheme (a) and the dependence between the mass flow rate and pressure ratio (b): 1-1—inlet section; 2-2—outlet section; C—critical point.
Figure 2.
The flowchart of numerical simulations.
Figure 3.
Three-dimensional model (a) and mesh grid (b) of the flow part for the industrial nozzle UDC32-450 with a critical diameter of 6 mm. Dimensions of the simulation model (c).
Figure 3.
Three-dimensional model (a) and mesh grid (b) of the flow part for the industrial nozzle UDC32-450 with a critical diameter of 6 mm. Dimensions of the simulation model (c).
Figure 4.
The convergence of momentum and mass.
Figure 5.
Airflow velocities in the flow part of the industrial nozzle UDC32-450 with a critical diameter of 6 mm (a) and a surface roughness of 3.2 μm (b).
Figure 5.
Airflow velocities in the flow part of the industrial nozzle UDC32-450 with a critical diameter of 6 mm (a) and a surface roughness of 3.2 μm (b).
Figure 6.
The experimental stand for studying the working nozzle: 1—weights; 2—filler; 3—container with sand; 4—dosing tap; 5—abrasive-jet hose (a), measurement scheme (b): 1—container with abrasive material, 2—moisture separator, 3—compressor, 4, 5, 6—shut-off valves, 7—nozzle, 8—dynamometer, 9—electronic scales, 10—device for measuring the jet reaction, 11—load plate, 12—air intake, 13—air flow meter, 14—safety valve, 15—flow washer, 16, 17, 18, 19, 20—gauges.
Figure 6.
The experimental stand for studying the working nozzle: 1—weights; 2—filler; 3—container with sand; 4—dosing tap; 5—abrasive-jet hose (a), measurement scheme (b): 1—container with abrasive material, 2—moisture separator, 3—compressor, 4, 5, 6—shut-off valves, 7—nozzle, 8—dynamometer, 9—electronic scales, 10—device for measuring the jet reaction, 11—load plate, 12—air intake, 13—air flow meter, 14—safety valve, 15—flow washer, 16, 17, 18, 19, 20—gauges.
Figure 7.
The flowchart of the experimental research.
Figure 8.
The impact of air consumption on the output surface roughness (K—roughness coefficient): points—calculated values; lines—approximation lines.
Figure 8.
The impact of air consumption on the output surface roughness (K—roughness coefficient): points—calculated values; lines—approximation lines.
Table 1.
Parameters of the Venturi nozzle with a critical diameter of 4 mm and a length of 143 mm.
| p1, MPa | c2, m/s | c2s, m/s | m, kg/s | ms, kg/s | A, N | As, N | Ae, N |
|---|---|---|---|---|---|---|---|
| 0.2 | 154 | 329 | 0.0226 | 0.0234 | 3.48 | 7.72 | 3.20 |
| 0.3 | 215 | 403 | 0.034 | 0.0352 | 7.13 | 14.2 | 7.40 |
| 0.4 | 255 | 444 | 0.046 | 0.0469 | 12.0 | 2.08 | 12.5 |
| 0.5 | 312 | 471 | 0.057 | 0.0586 | 17.8 | 2.76 | 17.8 |
| 0.6 | 344 | 491 | 0.068 | 0.0703 | 23.4 | 3.46 | – |
A—jet force, N; c2—outlet velocity, m/s; “s”—lower index that indicates an ideal process; “t”—lower index that indicates the test result.
Table 2.
Parameters of the Venturi nozzle with a critical diameter of 8 mm and a length of 194 mm.
| p1, MPa | c2, m/s | c2s, m/s | m, kg/s | ms, kg/s | A, N | As, N | Ae, N |
|---|---|---|---|---|---|---|---|
| 0.125 | 49 | 193 | 0.0036 | 0.0037 | 17 | 71 | – |
| 0.15 | 63 | 257 | 0.0043 | 0.0044 | 27 | 113 | – |
| 0.2 | 83 | 329 | 0.0057 | 0.0059 | 47 | 194 | 44 |
| 0.3 | 114 | 403 | 0.0085 | 0.0088 | 97 | 355 | 84 |
| 0.4 | 132 | 444 | 0.0114 | 0.0117 | 150 | 521 | 140 |
| 0.5 | 156 | 471 | 0.0142 | 0.0147 | 222 | 691 | 221 |
| 0.6 | 184 | 491 | 0.0171 | 0.0176 | 315 | 864 | 321 |
| 0.8 | 228 | 520 | 0.0227 | 0.0234 | 518 | 1216 | – |
| 1.0 | 254 | 539 | 0.0286 | 0.0293 | 726 | 1579 | – |
Table 3.
Parameters of the cylindrical nozzle from ceramics with a length of 22 mm and pressure ratio β = 0.51.
Table 3.
Parameters of the cylindrical nozzle from ceramics with a length of 22 mm and pressure ratio β = 0.51.
| d, mm | t, time | ma, kg/s | mp, kg/s | c2, m/s | |
|---|---|---|---|---|---|
| FlowVision | ANSYS | ||||
| 7 | 5.2 | 0.025 | 0.023 | 476 | 466 |
| 8 | 4.1 | 0.034 | 0.030 | 482 | 472 |
| 10 | 4.3 | 0.052 | 0.047 | 490 | 485 |
| 12 | 4.8 | 0.073 | 0.068 | 500 | 494 |
d—nozzle diameter, mm; t—processing time, min; ma, mp—mass flow rates of air and particles, kg/s.
Table 4.
Parameters of the cylindrical nozzle from steel C40 with a length of 22 mm and pressure ratio β = 0.51.
Table 4.
Parameters of the cylindrical nozzle from steel C40 with a length of 22 mm and pressure ratio β = 0.51.
| d, mm | t, time | ma, kg/s | mp, kg/s | c2, m/s | |
|---|---|---|---|---|---|
| FlowVision | ANSYS | ||||
| 7 | 8.2 | 0.024 | 0.023 | 366 | 395 |
| 8 | 5.8 | 0.031 | 0.030 | 384 | 399 |
| 10 | 5.8 | 0.049 | 0.047 | 394 | 402 |
| 12 | 7.4 | 0.070 | 0.068 | 412 | 422 |
Table 5.
Parameters of the cylindrical nozzle from steel C40 with a length of 11 mm and pressure ratio β = 0.51.
Table 5.
Parameters of the cylindrical nozzle from steel C40 with a length of 11 mm and pressure ratio β = 0.51.
| d, mm | t, time | ma, kg/s | mp, kg/s | c2, m/s | |
|---|---|---|---|---|---|
| FlowVision | ANSYS | ||||
| 7 | 5.2 | 0.024 | 0.023 | 412 | 421 |
| 8 | 4.1 | 0.033 | 0.030 | 423 | 440 |
| 10 | 4.3 | 0.050 | 0.047 | 436 | 453 |
| 12 | 4.8 | 0.073 | 0.068 | 455 | 472 |
Table 6.
Parameters of the cylindrical nozzle from steel C40 with a length of 44 mm and pressure ratio β = 0.51.
Table 6.
Parameters of the cylindrical nozzle from steel C40 with a length of 44 mm and pressure ratio β = 0.51.
| d, mm | t, time | ma, kg/s | mp, kg/s | c2, m/s | |
|---|---|---|---|---|---|
| FlowVision | ANSYS | ||||
| 7 | 5.2 | 0.020 | 0.023 | 237 | 244 |
| 8 | 4.1 | 0.029 | 0.030 | 261 | 288 |
| 10 | 4.3 | 0.044 | 0.047 | 250 | 276 |
| 12 | 4.8 | 0.055 | 0.068 | 266 | 291 |
Table 7.
The numerical simulation results for the nozzle UDC32-450 with a critical diameter of 6 mm with hydraulic smooth walls and a rough inner surface.
Table 7.
The numerical simulation results for the nozzle UDC32-450 with a critical diameter of 6 mm with hydraulic smooth walls and a rough inner surface.
| Surface Roughness, μm | c2, m/s | ma, m/s | A, N |
|---|---|---|---|
| 0 | 392 | 0.0378 | 16.0 |
| 3.2 | 372 | 0.0374 | 14.0 |
Table 8.
The experimental results for the cylindrical nozzle with an inner diameter of 20 mm, length of 22 mm, and pressure ratio β = 0.51.
Table 8.
The experimental results for the cylindrical nozzle with an inner diameter of 20 mm, length of 22 mm, and pressure ratio β = 0.51.
| No. | Δp, MPa | ma, m/s | No. | Δp, MPa | ma, m/s | No. | Δp, MPa | ma, m/s |
|---|---|---|---|---|---|---|---|---|
| 1 | 0.58–0.60 | 0.0096 | 9 | 0.42–0.44 | 0.0056 | 17 | 0.26–0.28 | 0.0034 |
| 2 | 0.56–0.58 | 0.0096 | 10 | 0.40–0.42 | 0.0050 | 18 | 0.24–0.26 | 0.0032 |
| 3 | 0.54–0.56 | 0.0078 | 11 | 0.38–0.40 | 0.0050 | 19 | 0.22–0.24 | 0.0029 |
| 4 | 0.52–0.54 | 0.0078 | 12 | 0.36–0.38 | 0.0046 | 20 | 0.20–0.22 | 0.0028 |
| 5 | 0.50–0.52 | 0.0078 | 13 | 0.34–0.36 | 0.0046 | 21 | 0.18–0.20 | 0.0025 |
| 6 | 0.48–0.50 | 0.0068 | 14 | 0.32–0.34 | 0.0043 | 22 | 0.16–0.18 | 0.0022 |
| 7 | 0.46–0.48 | 0.0068 | 15 | 0.30–0.32 | 0.0037 | 23 | 0.14–0.16 | 0.0023 |
| 8 | 0.44–0.46 | 0.0063 | 16 | 0.28–0.30 | 0.0034 | 24 | 0.12–0.14 | 0.0019 |
Δp—overpressure limit of air in the receiver, MPa.
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
MDPI and ACS Style
Baha, V.; Piteľ, J.; Pavlenko, I. Analytical, Numerical, and Experimental Studies of the Working Process in a Pneumatic Abrasive Installation. Appl. Sci. 2024, 14, 11728. https://doi.org/10.3390/app142411728
AMA Style
Baha V, Piteľ J, Pavlenko I. Analytical, Numerical, and Experimental Studies of the Working Process in a Pneumatic Abrasive Installation. Applied Sciences. 2024; 14(24):11728. https://doi.org/10.3390/app142411728
Chicago/Turabian StyleBaha, Vadym, Ján Piteľ, and Ivan Pavlenko. 2024. "Analytical, Numerical, and Experimental Studies of the Working Process in a Pneumatic Abrasive Installation" Applied Sciences 14, no. 24: 11728. https://doi.org/10.3390/app142411728
APA StyleBaha, V., Piteľ, J., & Pavlenko, I. (2024). Analytical, Numerical, and Experimental Studies of the Working Process in a Pneumatic Abrasive Installation. Applied Sciences, 14(24), 11728. https://doi.org/10.3390/app142411728
Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.