A Study of Particle Motion and Separation Characteristics in a Vibrating Airflow Composite Force Field

Abstract

Low-quality fine-grained coal cannot be effectively separated in a conventional gas–solid fluidized bed. To enhance the density stratification and separation of low-quality fine-grained coal, this paper introduces a vibration force field to create a vibrating airflow composite force field. By investigating the force characteristics and sorting behavior of particles within this vibrating airflow composite force field, we reveal the mechanical properties of both high-density and low-density particles. An energy dissipation model for the vibrational energy among particles in the bed is established, clarifying how vibration acceleration varies between the front and rear sections of the bed. The experimental results indicate that acceleration at the feeding end is significantly greater than that at the discharging end. This higher acceleration at the feeding end facilitates the stratification and segregation of selected particles, while acceleration at the discharging end provides the necessary energy for the transport of gangue. The acceleration curve for low-density particles exhibits greater fluctuations compared to that for high-density particles; additionally, the forces acting on these particles along the y-axis direction promote density segregation. The forces tend to decrease gradually along the z-axis direction, which aids in particle migration and movement. The particle-sorting effectiveness within this vibrating airflow composite force field initially increases with rising vibration frequencies and gas velocities before subsequently decreasing. Under a frequency of 30 Hz and a gas velocity of 35 cm/s, the ash content and yield of the clean coal product from the bed are 7.1% and 52.6%, respectively, achieving the maximum degree of ash separation.

1. Introduction

Coal is one of the most important fossil energy sources in China, making significant contributions to the development of the national economy [1,2]. However, China’s coal resources are poor, with large reserves of low-quality coal accounting for approximately 40% [3]. Coal preparation is the most effective way to improve the coal utilization efficiency and reduce pollution and energy consumption; in 2022, China’s coal separation rate was about 70% [4]. For a long time, wet separation has been the primary method used in coal preparation, but it requires substantial water resources. More than two-thirds of China’s coal deposits are located in arid regions in the western part of the country, where water scarcity prevails. Thus, wet separation technology struggles to satisfy the demands for large-scale processing. Furthermore, low-grade coals are easily transformed into a slurry upon contact with water, making them unsuitable for wet separation technology. Therefore, there is an urgent need for research on efficient dry separation methods and technologies for coal. The air-dense medium fluidized bed is an efficient dry coal separation technology that applies gas–solid two-phase fluidization for coal selection. It is characterized by the stratification of the selected coal within a fluidized bed of a specific density, where lower-density clean coal products float on the surface, while higher-density gangue settles at the bottom. This process achieves high-efficiency dry separation for coal sizes ranging from −50 to +6 mm [5,6,7,8]. Due to the reduction in the coal particle size, the bed buoyancy effect during the separation process is weakened, which can result in intensified particle mismatching [9]. Consequently, relying solely on gravitational fields for separation yields lower accuracy, and this strategy remains at the experimental research stage [10]. To enhance the stratification and segregation of low-quality fine coal based on density, scholars have proposed introducing external energy into conventional gas–solid fluidized beds to create an externally forced gas–solid fluidized bed. This approach aims to improve the gas–solid contact efficiency, enhance the bed fluidization quality, and increase the separation effect for low-quality fine coal within the bed. This is achieved by incorporating vibration energy into the gas–solid fluidized bed system, thereby forming a vibrating gas–solid fluidized bed suitable for separating fine particles [11,12,13,14].

Both domestic and international researchers have conducted systematic studies on the structural optimization, fluidization characteristics, and separation properties of vibrating fluidized beds. These studies have revealed the dynamic stress distribution patterns within the structures of vibrating fluidized beds and established correlation maps between the vibration parameters and bed load parameters [14,15,16,17]. By analyzing the factors influencing the bed fluidization characteristics, they have assessed the significance of various parameters, such as the distributor plate structure, bed height, material properties, vibration intensity, and expansion ratio. Diego et al. [18] investigated the hydrodynamic characteristics of Geldart A and C class particles in vibrating fluidized beds, proposing a vibration energy transfer model that effectively predicts the propagation velocity of vibrational waves within the bed. They also calculated theoretical values for the amplitude ratio and phase lag. Luo et al. [19,20] studied the separation characteristics of coarse and fine particle feeds in vibrating fluidized beds, introducing a three-tier distribution theory for fine coal particles and conducting research on the continuous separation of fine coal. Yang et al. [21] explored the dry separation of fine coal using a self-generated medium in a vibrating fluidized bed, elucidating the mechanisms by which vibration affects the bed fluidization performance, as well as the migration behavior of coal particles within the bed. Wei et al. [22] conducted a study on the continuous separation of fine coal using a novel air-dense medium vibrating fluidized bed, revealing both the mechanisms by which the vibration energy influences fine coal and its impact on adhesion during the separation process. In addition, sensor calibration can lead to high-quality datasets, which play a crucial role in elucidating the motion characteristics of particles in the bed. Sun et al. proposed an in situ calibration method that combines virtual samples and autoencoders, incorporating two key steps—fault detection and sensor calibration—with a calibration error rate of less than 3% [23]. Typically, the excitation of an applied energy field modifies the motion characteristics of particles [9,24,25]. Li et al. developed a multi-field coupled particle flow model based on the computational fluid dynamics-discrete element method (CFD-DEM). They found that ultrasonic energy improved the overall flow field distribution, resulting in a more uniform particle distribution [24]. Li et al. also explored the fundamental laws governing the evolution of the particle fluidization state in a fluidized bed under a pulsating gas flow, and they demonstrated that the pulsation frequency, particle properties, and initial bed height exert a significant influence on the overall fluidization state of the bed [25].

In response to the challenges associated with the movement characteristics of fine coal particles and the sorting efficiency during the separation process, this study investigates the force characteristics and separation mechanisms of fine coal in a vibrating airflow composite force field. It analyzes the synergistic effects of various operating parameters on the density segregation of fine coal and explores how these parameters influence the sorting effectiveness.

2. Materials and Methods

2.1. Setup

The vibrating fluidized bed test system utilized in this study is illustrated in Figure 1. It comprises four components: the sorting system, air supply system, signal analysis system, and dust removal system. The sorting system consists of a separation bed with 2 mm apertures and an area of 0.3 m², as well as a three-phase asynchronous vibration motor. The motor (VB-552-W) is employed as the vibration source and features an excitation force ranging from 0 to 5 kN and an operating frequency of 50 Hz; it enables the sorting bed to achieve an amplitude of 0.5–4.25 mm. After being uniformly distributed across the sorting bed surface, the fluidizing gas penetrates the bed layer and interacts with the particles within it. Driven by the gas drag force, the bed particles are fluidized; concurrently, under the excitation force of the bed surface, they undergo stratified migration, ultimately forming clean coal and gangue products. The gas velocity is regulated by a rotameter.

The bed is uniformly divided into five radial regions, with quartz force stress sensor probes (PCB-208C01; sensitivity: 112,410 mV/kN, range: 0.04448 kN) installed at 40 mm intervals to measure the vibration state signals under varying bed parameters. Prior to commencing the test, the low-pass filter frequency was set to 50 Hz to eliminate noise interference, and zero balancing was performed on the oscilloscope signal to correct for signal offset. Signals were acquired using an INV3060S16 data acquisition instrument (frequency response: 0.3 Hz to 50 kHz) and subsequently analyzed in both the time and frequency domains using the DASP software (Coinv DASP-V10). The vibration frequency of the bed surface can be adjusted by regulating the frequency converter, with an adjustment range of 1–60 Hz.

During the experiments, the airflow velocity (v) and vibration frequency (f) were adjusted to facilitate the fluidization of the material under the combined effects of the airflow and vibration energy. In accordance with Nyquist’s theorem, the data acquisition frequency for the quartz force sensors was set at 1024 Hz, with a collection duration of 60 s. A self-developed BS-1 spherical inertial sensor was adopted; this was integrated with an inertial measurement unit (IMU), a data processing unit, and a wireless transceiver unit to simulate the real-time motion characteristics of materials. The vibration frequency (10–44 Hz) and gas velocity (20–50 cm/s) were adjusted to further investigate the variations in the ash content and mass fraction of fine coal in the composite force field of a vibrating gas flow.

2.2. Materials

The experiment utilized fine coal samples with a particle size of 6–1 mm and an ash content of 23.35%. By conducting float–sink tests on the fine coal particles, the density distribution for the 6–1 mm fine coal was obtained, as shown in

Table 1. Results of the float and sink test of 6–1 mm coal.

Density (g/cm3)	Ratio (%)	Ash (%)
<1.3	46.48	6.97
1.3–1.4	14.43	9.82
1.4–1.5	1.17	10.34
1.5–1.6	3.14	17.95
1.6–1.7	2.32	25.55
1.7–1.8	7.03	39.71
>1.8	25.43	61.77
Total	100.00	24.43

. When the separation density was set at 1.50 g/cm³, the near-density (ranging from 1.40 to 1.60 g/cm³) content was found to be 17.22%, indicating that the raw coal could be classified as moderately washable coal. Additionally, based on the washability curve of the coal, particles with a density below 1.52 g/cm³ were designated as clean coal products.

2.3. Evaluation Index

In order to investigate the fine coal separation efficiency in a vibrating airflow composite force field, the ash separation degree (S_ash) was employed to evaluate the separation performance [26].

$$S_{ash}=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{\left(\raisebox{1ex}{$A_i$}\!\left/ \!\raisebox{-1ex}{$A_0$}\right.-1\right)}^2}{n-1}}}$$

(1)

where A_i represents the average ash content of each product in a partition, while A₀ denotes the ash content of the raw coal. The variable n refers to the number of partitions along the separation bed. The ash separation degree (S_ash) value indicates the extent to which the particles within the bed have been segregated by density after a certain period of separation [15]. A higher S_ash value signifies that particle separation within the bed is more effective.

3. Results

3.1. Analysis of Forces Acting on Particles in Vibrating Airflow Composite Force Field

In the composite force field of a vibrating airflow, vibration energy is transmitted to the bed through collisions between the bed body and the particles. During the motion of the particles, collisions among them consume a portion of their kinetic energy, resulting in a gradual decrease in energy flow throughout the transfer process. In the axial direction at any height along the bed surface, a segment of infinitesimal bed can be selected for energy analysis. Vibration energy enters from one side of the bed; part of it is dissipated within the bed due to particle collisions during motion, while the remaining portion continues to propagate towards the discharge side of the bed. Given that the volume of the selected bed is sufficiently small, its energy balance equation is as follows [27]:

$$dQ=\mathrm{\lambda }dSd\mathrm{h}$$

(2)

In this context, dQ represents the net energy exchange within the bed, J·s⁻¹, defined as dQ = Q_in − Q_out. Here, Q_in and Q_out denote the input and output energies of the bed, respectively. The parameter λ indicates the energy dissipation rate, J·m⁻³·s⁻¹, determined by particle collisions within the bed. dS is the area of a microelement, m². dh is the length of the microelement, m.

The role of vibration in the sorting process consists of two aspects. Firstly, it provides the energy necessary for the movement of material within the sorting bed, enabling longitudinal shear forces to drive the material layer to slide and be stratified according to its density along the longitudinal direction. Secondly, it generates lateral shear forces that work in conjunction with the reactive force from the grid bars and friction on the bed surface. This synergy facilitates the lateral flipping and migration of materials, achieving graded separation between different layers.

In the process of energy input and output in a bed with an extremely small volume, it is necessary to overcome a portion of the kinetic energy generated by particle collisions, which contributes to energy dissipation within the granular bed. From the energy balance equation for the bed (Equation (2)), it is possible to derive formulas for both the energy flow and the rate of energy dissipation associated with the particles in the bed.

The energy of the particles within the bed (Q) is calculated using an equation analogous to Fourier’s law [28]:

$$Q=k{\displaystyle \frac{dT}{dh}}$$

(3)

By analogy with gases, the average fluctuating kinetic energy of particles is defined via the particle temperature. Here, T is the particle temperature, J [29]:

$$T={\displaystyle \frac{1}{3}}m{\nu }_p^2$$

(4)

where v_p is the pulsation velocity of particle motion, m/s.

k denotes the thermal conductivity coefficient:

$$k={\displaystyle \frac{4MGPd}{\sqrt{\pi m}\left(1+4G\right)T^{\frac{1}{2}}}}$$

(5)

where m is the particle quality, kg; $M=1+{\displaystyle \frac{9\pi }{32}}{\left(1+{\displaystyle \frac{5}{12G}}\right)}^5$; G is the particle gravity, $G=\eta g_0$, N; $g_0={\displaystyle \frac{\left(2-\eta \right)}{2{\left(1-\eta \right)}^3}}$, where η is the volume fraction of bed particles; $\eta ={\displaystyle \frac{1}{6}}\pi d^3{n}_p$, where n_p is the particle number per unit volume, and d is the particle diameter, m.

P represents pressure, Pa, and there exists the following relationship between the pressure and temperature T [28]:

$$P={\displaystyle \frac{6}{\pi d^3}}{\displaystyle \frac{\eta \left(1+\eta +{\eta }^2+{\eta }^3\right)}{\left(1-{\eta }^3\right)}}T$$

(6)

The energy dissipation rate λ can be expressed as [28]

$$\lambda ={\displaystyle \frac{24}{\sqrt{\pi m}}}\left(1-e\right){\displaystyle \frac{P}{1+4G}}G{\displaystyle \frac{T^{\frac{1}{2}}}{d}}$$

(7)

In the bed separation system, the dissipated energy is input into the bed. Once the particle system stabilizes, all the energy input into the separation bed is dissipated through particle collisions within the bed. At the discharge edge of the separation bed, there is no energy exchange between the bed and its external environment; specifically,

Q_discharge = 0.

The energy input from the bed structure to the particle layer is as follows [27,28]:

$$Q={\left({\displaystyle \frac{2}{\pi }}\right)}^{{\displaystyle \frac{1}{2}}}P{\displaystyle \frac{2V^2\left(m+{\overline{V}}^2\right)}{T}}$$

(8)

In this equation, V represents the velocity of bed movement, m/s, while ${\overline{V}}^2$ denotes the average value of the square of the bed’s movement velocity. By combining these equations and applying the energy flow boundary condition at both the back plate and discharge edge of the separation bed, it is possible to calculate the energy dissipation within the bed as follows:

$$Q_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{p}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}=2V^2{\left({\displaystyle \frac{2}{\pi }}\right)}^{{\displaystyle \frac{1}{2}}}{\displaystyle \frac{6}{\pi d^3}}{\displaystyle \frac{\eta \left(1+\eta +{\eta }^2+{\eta }^3\right)}{\left(1-{\eta }^3\right)}}\left(m+{\overline{V}}^2\right)$$

(9)

The aforementioned model was derived based on the assumption that particle collisions are perfectly elastic, neglecting the friction between the particles and the bed, and it is only applicable to vibration with low frequencies and small amplitudes.

3.2. Vibration Characteristics of Particles at Different Positions in the Bed

To investigate the motion characteristics of particles at different positions on the bed surface, high-precision accelerometers were installed at both the feed and discharge ends of the bed. Figure 2 presents the sinusoidal accelerations for two measurement points located at the front and rear sections of the bed surface along the x-, y-, and z-axes. It can be observed that the accelerations at both measurement points along the X-axis are negligible; however, significant acceleration is evident along both the y- and z-axes in these sections. Notably, the acceleration at the feed end exceeds that at the discharge end. At the feeding point, the amplitudes of the y-axis and z-axis accelerations are recorded as 3.18 m/s² and 1.87 m/s², respectively. Conversely, at the discharge point, the amplitudes for the y-axis and z-axis accelerations are measured as 2.37 m/s² and 1.19 m/s², respectively.

The vibration frequency of the particles is closely related to the periodicity of the surface, significantly influencing the material’s motion behavior. As illustrated in Figure 3, when the vibration frequency increases from 24 Hz to 44 Hz, the amplitude range of the acceleration along the y-axis at the feeding end varies from 1.66 m/s² to 5.06 m/s², while that along the z-axis ranges from 0.96 m/s² to 3.39 m/s². Similarly, as shown in Figure 3, at the discharge end, the amplitude range for the y-axis acceleration is between 1.06 m/s² and 4.21 m/s², and the z-axis acceleration range is 0.44 m/s² to 2.33 m/s².

At a constant frequency, the vibration energy decreases progressively from the feeding end towards the discharge end of the bed surface. The acceleration at the feeding end is considerably greater than that at the discharging end, indicating that this region serves as a primary separation space for particle sorting. Here, the acceleration greatly surpasses that found at discharge points, where the materials primarily consist of gangue rock. The main role of vibration is to provide energy for the transport of these gangue materials.

The mechanical properties of particles are a crucial factor that influences their motion behavior. Investigating the characteristics of particle forces in a composite force field is key to revealing their separation mechanisms. By employing spherical inertial sensors with varying densities as tracer particles, it is possible to capture the acceleration signals generated by the movement of these tracer particles, reflecting the force characteristics during the density separation process for particles of different densities, as illustrated in Figure 4. In particular, Figure 4a,b illustrate the motion characteristics of low-density and high-density particles in different directions. It can be observed that the acceleration curve for low-density particles exhibits greater fluctuations compared to that for high-density particles. The research indicates that, along the y-axis, the acceleration of low-density particles in the negative direction significantly exceeds that in the positive direction. This finding suggests that the force acting on low-density particles is oriented negatively along the y-axis, which facilitates their movement in the negative y-direction and promotes density segregation among particles. Furthermore, for low-density particles, the acceleration in the positive z-direction is substantially greater than in the negative z-direction, resulting in a tendency for these particles to move positively along the z-axis. Additionally, as the forces acting on the particles in the z-axis gradually diminish, the particle separation time is extended, and this aids in subsequent product discharge.

To further investigate the particle collision behavior under various operating parameters, a Fourier transform was employed to conduct a frequency-domain analysis on the particle collision force signals, and the dimensionless energy E distribution is presented in Figure 5.

As the gas velocity increases, the interparticle collision energy induced by particle impacts exhibits an initial increase followed by a decrease. The results demonstrate that, with an increase in the gas velocity, the particles in the bed undergo loose fluidization and their movement velocity is increased, leading to an increment in the energy generated by collisions. When the gas velocity is excessively high, under the combined effects of vibration and gas flow, the mean free path of interparticle movement gradually expands, the collision probability between particles declines, and the efficiency in transmitting vibrational energy via particle collisions and activating the movement of surrounding particles is impaired. Consequently, the higher the gas velocity, the lower the external excitation energy acquired by particle movement, which results in a reduction in the particle movement speed and collision energy. With an increase in the vibration frequency, the energy input by bed vibration into the particle bed gradually rises, the particle movement speed is accelerated, and interparticle collisions induce an increase in energy. When the vibration frequency is excessively high, the kinetic energy of the particles continues to increase, the movement of the particles in the bed becomes intense, and the particle collision energy continues to rise; however, the contact efficiency between the gas and solid phases is compromised. The corresponding research results are illustrated in Figure 5.

3.3. Ash Content and Mass Fraction of Selected Products Under Varying Operational Parameters

Figure 6 illustrates the yield and ash content curves of selected products at various vibration frequencies and in different sections of the separation bed. The horizontal axis represents the dimensionless height of the separation bed, while the left vertical axis indicates the yield of products from each layer, and the right vertical axis denotes their corresponding ash content. Based on the coal separation outcomes, products from the first two segments of the bed are classified as clean coal, whereas those from the subsequent five segments are categorized as gangue.

The analysis of the data reveals that, with increasing frequencies, the ash content of the clean coal product initially decreases and then increases, while the yield exhibits a trend of first increasing and then decreasing. Under both low-frequency and high-frequency vibration conditions, the ash content of the clean coal products remains below 10%, with yields also around 10%. Meanwhile, at f = 30 Hz, the ash content and yield are 7.1% and 52.6%, respectively; thus, it can be concluded that, under f = 30 Hz, the clean coal product demonstrates lower ash content and a higher yield, indicating a better separation effect for fine coal.

The results presented in Figure 7 illustrate the ash content and mass fractions of products distributed across different regions of the bed under varying gas velocities. At lower gas velocities, the stratification and segregation of products within different zones of the bed are not pronounced. This observation indicates that low gas velocities fail to facilitate the suspension fluidization of the particle system, leading to the significant presence of defluidized zones within the bed. As the gas velocity increases, e.g., at v = 35 cm/s, the ash content and yield of clean coal reach 7.1% and 52.6%, respectively. The ash content of clean coal is reduced by 26.3% compared to that of raw coal, while the ash content and yield of discharged gangue are 81.5% and 43.9%, respectively. Under high gas velocities, the effectiveness of vibration in particle stratification is diminished, resulting in the clean coal located at the top layer being carried down to the lower layers. This leads to an increased misclassification rate during fine coal separation and reduces the overall separation performance.

3.4. Effectiveness of Vibration Airflow Composite Force Field in Separation of Fine Coal

Figure 8 illustrates the fine coal separation effects under various operating parameters. As shown in the figure, with an increase in the vibration frequency, the ash content of the separated product initially increases and then decreases. This result indicates that, at low vibration frequencies, the fluidization quality of bed particles is poor, which prevents the system from achieving a suitable separation density to stratify fine coal. Consequently, this leads to suboptimal fine coal separation performance. As the vibration frequency increases, larger-scale cyclic mixing behavior occurs among the particles within the bed due to stronger vibrational forces. The inertia migration effect on fine coal makes it susceptible to being carried upward from the bottom layer, where gangue settles; this leads to an increase in the ash content of the clean coal products. Meanwhile, the clean coal located at the top layer tends to be mixed downward as medium particles are reintroduced into lower layers. This results in an increased mismatch rate during fine coal separation and reduces the overall separation effectiveness, while also yielding smaller standard deviations.

4. Conclusions

More than two-thirds of China’s coal is distributed in arid and water-scarce areas in the western region, with large amounts of fine-grained coal of poor quality. Therefore, there is an urgent need for efficient dry coal separation technology to separate fine-grained coal. In this work, the characteristics of particle collision under different airflow vibration parameters were revealed, and the variations in vibration acceleration at the front and rear ends of the bed were analyzed. With an increase in the vibration frequency and gas velocity, the separation efficiency of the vibration airflow composite force field showed a trend of first increasing and then decreasing. Consequently, under the conditions of a frequency f = 30 Hz and a gas velocity v = 35 cm/s, the ash content and yield of clean coal products in the bed were 7.1% and 52.6%, respectively, achieving the maximum ash separation. The research results presented in this paper could provide strong theoretical and technical support for improvements in the quality of dry coal separation for fine-grained coal.