*Article* **Influence of Particle Charge and Size Distribution on Triboelectric Separation—New Evidence Revealed by In Situ Particle Size Measurements**

#### **Johann Landauer \* and Petra Foerst**

Chair of Process Systems Engineering, TUM School of Life Sciences Weihenstephan, Technical University of Munich, Gregor-Mendel-Straße 4, 85354 Freising, Germany; petra.foerst@tum.de

**\*** Correspondence: johann.landauer@tum.de; Tel.: +49-8161-71-5172

Received: 20 May 2019; Accepted: 15 June 2019; Published: 19 June 2019

**Abstract:** Triboelectric charging is a potentially suitable tool for separating fine dry powders, but the charging process is not yet completely understood. Although physical descriptions of triboelectric charging have been proposed, these proposals generally assume the standard conditions of particles and surfaces without considering dispersity. To better understand the influence of particle charge on particle size distribution, we determined the in situ particle size in a protein–starch mixture injected into a separation chamber. The particle size distribution of the mixture was determined near the electrodes at different distances from the separation chamber inlet. The particle size decreased along both electrodes, indicating a higher protein than starch content near the electrodes. Moreover, the height distribution of the powder deposition and protein content along the electrodes were determined in further experiments, and the minimum charge of a particle that ensures its separation in a given region of the separation chamber was determined in a computational fluid dynamics simulation. According to the results, the charge on the particles is distributed and apparently independent of particle size.

**Keywords:** triboelectric separation; particle size distribution; particle charge; binary mixture; in situ particle size measurement; charge estimation

#### **1. Introduction**

Electrostatic effects were first recognized by the ancient Greek philosophers, who generated electricity by rubbing amber with fur. Thales of Miletus is often called the discoverer of the triboelectric effect [1,2]; however, this ancient observation has not been completely understood. Triboelectric charging of conductive materials is described by work function [3,4]. At conductor–insulator and insulator–insulator contacts, triboelectric charging has been described with "effective work function" [5,6], electron transfer [7], ion transfer [8,9], and material transfer [10,11]. Furthermore, contact charging is affected by environmental conditions such as humidity [12–14] and physical impact [15–17].

Triboelectric charging is undesired in process engineering because it interferes with pneumatic conveying [18,19], fluidized beds [20,21], mixing [22,23], and tablet pressing [24]. Moreover, it is a surface effect, indicating that particle surface plays a critical role. The known factors affecting triboelectric charging are particle area (indicated by particle size) [25–30], surface roughness [31–33], chemical composition [34], and elasticity (indicated by contact area) [35–38]; however, most experimental studies assumed uniform particles or contact surfaces. In most applications, the particles are not monodispersed and have no defined surface; however, the particles are dispersed in size, surface area, elasticity, crystallinity, and morphology.

To use triboelectric charging and subsequent separation as a tool to separate particles due to their chemical composition, surface morphology, crystallinity, or particle morphology, it is necessary to

understand the influence of particle size distribution or powder composition as well as the influence of non-ideal conditions. All these factors show the necessity of triboelectric separation experiments with real, but defined, powders (like starch and protein) in order to use triboelectric separation to enrich, e.g., protein in lupine flour [39] and to take into account further influencing factors. Furthermore, the use of a starch–protein mixture as a model substrate for triboelectric charging is anticipated to have a possible application to enrich protein out of cereals or legumes. This ability of triboelectric separation has been demonstrated [39–46].

Hitherto, lots of studies have been carried out with well-defined particles or with inhomogeneous and undefined organic systems. Supplementary to these findings, real powders with a defined chemical composition and dispersity in particle size should be investigated. The discussion of influencing factors, such as particle morphology or further particle properties, suggest that particle surface charge is affected by the particle size distribution, in turn influencing the triboelectric charging effect. As the particle charge strongly affects the subsequent separation step, particles with different charges become separated at different regions on the electrodes, depending on the flow profile in the separation chamber and the electric field strength. Therefore, we hypothesize that if particle size (as a proxy of surface area) influences the charging and the subsequent separation properties, then particles of different sizes will be separated at different regions on the electrodes.

#### **2. Materials and Methods**

#### *2.1. Materials*

Whey protein isolate (Davisco Foods International, Le Sueur, MN, USA) with a protein content of 97.6 wt % was ground as that described in Landauer et al. [47]. Barley starch (Altia, Finland) with a starch content of 97.0 wt % was narrowed in particle size distribution in a wheel classifier (ATP 50, Hosokawa Alpine, Augsburg, Germany) under the conditions described in Landauer et al. [47].

#### *2.2. Methods*

#### 2.2.1. Separation Setup

The simple experimental setup, originally demonstrated by Landauer et al. [47,48], comprises of an exchangeable charging section and a rectangular separation chamber. The dispersion of powders added to the gas flow is facilitated by a Venturi nozzle. The charging tube (of diameter 10 mm and length 230 mm) was composed of polytetrafluoroethylene (PTFE). An electrical field strength of 109 V/m was applied to the parallel-plate capacitor in a rectangular separation chamber (46 mm × 52 mm × 400 mm). The protein contents of the binary protein–starch mixtures were varied as 15, 35, and 45 wt %, and were determined as described in [48]. Briefly, the powder was dispersed in NaCl buffer (pH 7, 0.15 M) and the protein concentration was photometrically determined at 280 nm. To measure the protein content along the electrodes, the powder was sampled in three colored areas (see Figure 1a).

The amount of particles separated along the electrodes was determined by measuring the height of the separated powder. The measuring points are shown in Figure 1a and marked with gray circles. The powder deposition height was measured homogenously along each electrode in order to get a topography. Note that the powder height was determined using a micrometer screw (according to DIN 863-1:2017-02). The mean was calculated from the results of three independent separation experiments (*n* = 3). Error bars indicate the confidence intervals of the Student's *t*-test with an α = 0.05 significance level.

**Figure 1.** (**a**) Schematic of the sampling points along the electrodes. The powder deposition height on the electrode was measured at the points marked by gray circles. Colored areas mark the areas of powder sampling along the electrode. (**b**) Schematic of the separation chamber and the charging tube. The in situ particle size near the electrodes was measured at positions I, II, and III. Measurements near the anode and cathode were enabled by switching the polarity of the electrical field. The electric force *F*el and weight force *F*<sup>g</sup> acting on each particle in the separation chamber are visualized.

#### 2.2.2. In Situ Particle Size Analysis

To investigate whether the particles agglomerate along the charging tube, we analyzed the in situ particle size distributions along the charging tube. For this purpose, parts of the charging and separation setup were installed in the measuring gap of a HELOS laser diffraction system (Sympatec, Clausthal-Zellerfeld, Germany). The charging and dispersing setup has been described in previous studies [47,48]. In the charging section, the particle size distributions were determined at the outlet of the Venturi nozzle (inlet of the charging section) and at the outlet of the charging tube. In the separation chamber, the particle size distribution was measured as a function of length. The schematic in Figure 1b shows the measuring positions I, II, and III along the electrodes in the separation chamber. The measuring points were chosen to be close to the electrodes and in the first half of the separation chamber. Due to the triboelectric separation, the particle concentration is decreasing along the separation chamber. Thus, the particle concentration, which is required to determine the particle size distribution, was not accessible. The particle size distributions on the anode and the cathode were obtained by switching the polarity of the electrical field with an electrical field strength of 217.4 kV/m. The mean of six independent separation experiments (*n* = 6) was calculated and the error is indicated by the confidence intervals of the Student's *t*-test with an α = 0.05 significance level using error bars.

#### 2.2.3. Flow Simulation and Estimation of the Particle Charge

The change in cross section between the charging tube and the separation chamber is very rigorous. The flow profile in the separation chamber, which might affect the separation characteristics and the particle size distribution along the electrodes (Figure 1b), was investigated in a computational fluid dynamics (CFD) simulation (ANSYS Fluent, version: 17.0, supplier: Ansys, Inc., Canonsburg, PA,

USA) of a realizable k–ε model. The particle motion in the separation chamber was visualized by tracking particles in the flow simulation. The inserted spherical particles followed a Weibull size distribution with a minimum, mean, and maximum (measured in the initial particle size distribution) of 1, 16, and 40 μm, respectively. The powder density was considered as the mean of the true density (1465 kg/m3), which was measured by a gas pycnometer (Accupyc 1330, Micromeritics Instrument Corp., Norcross, GA, USA). The minimum charge at which the particle will be deflected in the measuring region was determined by simulating the in situ particle size distribution at different gravity levels (emulating different particle charges). The Coulomb force aligns with the weight force, as shown in Figure 1b. The absolute value of the charge *q* of the particles is estimated as follows:

$$q = \frac{\varkappa\_3}{6E} \pi \rho\_s g(n-1) \tag{1}$$

where *<sup>x</sup>* is the mean particle size, <sup>ρ</sup>*<sup>s</sup>* is the true density, <sup>→</sup> *E* is the electrical field, <sup>→</sup> *g* is gravity, and the scaling factor *n* is the increase in particle charge. The scaling factor in the simulation was varied between 1 and 44. Note that the polarity of the charge depends on the electrical field's polarity.

#### **3. Results**

#### *3.1. Particle Size Distribution*

#### 3.1.1. Agglomeration within the Charging Tube

Figure 2 shows the volume–weight density distributions at the Venturi nozzle outlet (panel a) and at the outlet of the charging tube (panel b) in the 15 and 30 wt % powders. In both particle size distributions, the particle size decreased with increasing initial protein content. The particle size distributions were similar at the outlets of the nozzle and the charging tube. The mean particle size (peak position) and the maximum particle size are the same at the tube inlet and the tube outlet. By comparing the distribution of finer particles, an increase in finer particles is visible. Thus, a dispersion along the charging tube is measured. The reason for this dispersion could be the high particle–particle collision number within the charging tube, due to the high turbulence [47]. The results in Figure 2 indicate breaking up particle agglomerates of fine particles during the charging step that could promote electrostatic separation. Contrarily, no electrostatic agglomeration that could impair electrostatic separation is observed.

**Figure 2.** Volume–weight density distribution at (**a**) the Venturi nozzle outlet and (**b**) the outlet of the charging tube. Increasing the initial protein content (from 15 to 30 wt %) refined the particle size distribution. The distributions at the nozzle and tube ends are not obviously different.

#### 3.1.2. Particle Size Distribution along the Electrodes

Figure 3 shows the volume–weight density distributions of the powder close to the cathode (a) and the anode (b) in measuring regions I, II, and III (Figure 1b). Increasing the initial protein content refined the particle size distributions at both the cathode and anode, as evidenced by the higher peak at ~6 μm in the 30 wt % compared to the 15 wt % distribution. This higher peak indicates a higher amount of finer protein particles (cf. Figure 2). In the sample with an initial protein content of 15 wt %, the particle size decreased along the investigated regions I, II, and III (note the lower peak height at 16 μm than that at 6 μm). This stepwise decrease in particle size was observed along both the cathode and the anode, as well as in the sample with higher initial protein content (30 wt %). The peak increases from 15 to 30 wt % are more clearly observed at 6 μm compared to 16 μm because increasing the protein content increases the amount of smaller particles. Comparing the particle size distributions at the cathode and the anode, the particles were finer on the cathode regardless of the initial protein content. These results suggest a higher protein content on the cathode (cf. Figure 2). The protein content of the separated powder on the cathode and the anode is approximately 80 and 2.5 wt %, respectively. Thus, protein is enriched on the cathode and starch is enriched on the anode [47,48]. However, the enhancement of finer protein particles near the cathode cannot be correlated with the protein content because the used protein powder is finer than the starch powder. Nevertheless, the particle size distributions at each measuring position in the separation chamber depended on the initial protein content. Thus, the particle size is influenced by the polarity of the electric field, the distance from the charging tube outlet, and (most strongly) the initial protein content. The region in which the particles separate plays a subordinate role on the particle size distribution. Furthermore, the particle size distributions on the anode and cathode resembled the initial distributions determined at the outlets of the Venturi nozzle and the tube.

**Figure 3.** Volume–weight density distributions recorded near the cathode (**a**) and the anode (**b**) in regions I, II, and III. Closed and open symbols denote initial protein contents of 15 and 30 wt %, respectively. Increasing the initial protein content reduces the particle size at both anode and cathode. The particle size distributions differ in the three measuring regions.

#### *3.2. Powder on the Electrodes*

#### 3.2.1. Powder Height

Figure 4 shows the powder height along the cathode and the anode. On the cathode, the distribution of powder was approximately homogeneous along the electrode. The powder height varied most extensively at the second measuring point, and was least variable at the first and fourth measuring points. This significant but extremely low variation should not be overinterpreted; however, the powder height severely decreased along the anode. The powder height was constant at the first two measuring points, and then dropped to zero over the next two measurement points. Thus, the powder heights on the cathode and the anode exhibited very different profiles, suggesting different charges of the particles separated on the two electrodes. In particular, the negatively charged particles exhibited a higher net charge than the positively charged particles.

**Figure 4.** Powder height along the cathode and the anode. Powder height is approximately constant on the cathode, but mostly separates over the first half of the anode.

#### 3.2.2. Protein Content

Figure 5 shows the protein content on the cathode in the three measurement areas at initial protein contents of 15 and 30 wt %. The protein content was consistently higher for the sample with the higher initial protein content. Independently of the initial protein content, the protein content increased in the second area (relative to the first area). In the third area, the protein content decreased at the initial protein content of 15 wt %, but remained high at the higher initial protein content. If we compare the protein content with the powder height, the two quantities are apparently independent because the powder height was approximately constant along the electrode, whereas the protein content extensively varied.

**Figure 5.** Protein content on the cathode in three different measurement areas for initial protein contents of 15 and 30 wt %. The protein content increases form the first to the second area regardless of initial protein content. In the third area, the protein content decreases (15 wt %) or remains the same (30 wt %).

#### *3.3. Estimation of the Charge Correlated with the In Situ Particle Size Distribution*

To estimate the minimum charge at which particles will separate in the separation chamber (enabling an in situ particle size analysis), the particles were tracked in a CFD study. Figure 6 shows the trajectories of spherical particles with different accelerations (varied by changing the electrical force in Equation (1)). In a homogenous electrical field, the net charge of the particles is a multiple of the elementary charge. Uncharged particles might be undetectable in every measuring region. Particles with a net charge of 1.45 <sup>×</sup> 103 *q*<sup>e</sup> can be detected in regions II and III, whereas those with charges of 7.26 <sup>×</sup> 103 *q*<sup>e</sup> and 1.16 <sup>×</sup> 10<sup>4</sup> *q*<sup>e</sup> might be measurable only in region II. Particles with a net charge of 3.77 <sup>×</sup> 10<sup>4</sup> *q*<sup>e</sup> and higher are visible in region I. When generating Figure 6 and calculating the associated particle charge, we assumed spherical particles with a mean diameter of 16 μm corresponding to the mean particle size of the powders used for the experiments. According to Equation (1), the particle size affects both the charge on a single particle and the particle trajectories. In all cases, varying the particle size only slightly affected the trajectories.

The background of Figure 6 shows the velocity profile in the separation chamber. The profile shows a jet at the charging tube outlet followed by homogeneity. The jet formed at the outlet of the tube affected the particle trajectories considerably. Regardless of their net charge, the particles remained within the jet to ~100 mm from the outlet. Then, they lost speed and were deflected toward the electrode by the Coulomb force. Thus, the simulation visualized the influence of the particle net charge on the particle trajectories within a complex velocity profile. Observing these particle trajectories, we can understand how particles might be charged to ensure their separation in the measuring regions of in situ particle size analyses.

**Figure 6.** Trajectories of 16 μm diameter spherical particles with different particle charges (multiples of the elementary charge calculated by Equation (1)). The measuring regions I, II, and III of the in situ particle size distribution are indicated by the white open circles. Depending on their net charges, certain particles are not detectable in every measuring region. The background visualizes the velocity profile. The jet formed at the outlet of the charging tube is clearly visible.

#### **4. Discussion**

To use triboelectric separation as a tailor-made particle separation tool, one must separate the particles by their specific chargeabilities. Accordingly, it is necessary to disperse the particles before the charging step and avoid their agglomeration during the charging step. The selected setup enables the appropriate conditions for dispersal and aggregation prevention (Figure 2). Hence, detailed investigations of the separation step are required to establish triboelectric separation as an industrial separation technique.

Assuming that the charge distribution of fine particles is sourced from the triboelectric charging of the particles and that the charge distribution also possibly depends on the particle size and the chemical composition [34], the particle size distributions were determined at different locations close to the electrodes (Figure 3). As expected, the particle size distribution was coarser on the anode than on the cathode, because increasing the protein content refined the particle size distribution (Figure 2) and the protein was enriched on the cathode [47,48]. Moreover, along the measuring regions close to the electrodes, the decreased particle size accompanying the refined particles was demonstrated for different initial protein contents. These results were identical on the cathode and the anode, suggesting (as a first hint) that the net charges of the particles after triboelectric charging are independently distributed of the particle sizes.

The local distribution of the separated powder on the electrodes indicates the strength of the particle charges because particles with a higher and lower net charge are separated at the inlet and the near-outlet of the electrode, respectively. The powder height profiles on the cathode and the anode exhibited very different characteristics (Figure 4). The powder was dispersed almost homogeneously on the cathode but was separated close to the inlet on the anode. The absence of powder at the anode outlet indicates that the negative particles were more highly charged than the positive ones. The same results were reported in single-particle charge measurements [49]. This result further indicates independent distributions of the particle charges and sizes because the particle size distributions were similar on the cathode and anode (Figure 3). Furthermore, the homogeneously distributed powder exhibited a distributed protein content with a peak in the middle of the electrode at 15 wt % initial protein content, and level peaks in the second and third parts of the electrode at 30 wt % initial protein content (Figure 5). This suggests a lower net charge of protein particles than of starch particles (Figure 6). These results are underpinned by the decreased particle size (higher protein content) along the cathode than along the anode (Figure 3). The particle trajectories were affected by the inhomogeneous flow profile in the separation chamber; however, in the flow simulation, they were predominantly influenced by the charge. Moreover, they showed a charge-dependent separation region. To summarize, the binary powder mixture with a polydispersed particle size distribution showed no clear relationship between particle size and particle charge in the separation region. These results contradict previous studies, which reported that smaller particles are predominantly negatively charged [25–30]. The results support an effect of particle size on triboelectric charging, but no clear tendency was found regarding the fine and coarse particles. Thus, the hypothesis of this study, i.e., that particle size distribution (as a measure of surface area) plays a major role in triboelectric charging and subsequent separation, is questionable. Indeed, there is a dependence of particle size along the electrodes, but the results show a more complex connection between the particle material and particle size.

#### **5. Conclusions**

The dispersing and agglomeration characteristics of powders with different initial protein contents were consistent along the charging tube. The in situ particle size measurements were consistent at different regions in the separation camber. After estimating the minimum charge for particle separation, it was found that large charge differences were required for separation in every measuring region of the chamber. This wide charge distribution might lead to different separation regions of the particles, as indicated by the roughly homogeneous powder height on the cathode and the steep decrease in powder height on the anode. These results show a complex dependency of triboelectric charging and

subsequent separation on the size and material of the particles. As the mechanism of triboelectric or contact charging has not been accurately determined, determining the primary influencing factors is very challenging. The present results indicate the high complexity of triboelectric charging and indicate that particle size is not a highly important factor in triboelectric separation but affects the triboelectric charging through surface-area differences.

**Author Contributions:** Conceptualization, J.L.; methodology, J.L.; data curation, J.L.; writing—original draft preparation, J.L.; writing—review and editing, J.L. and P.F.; visualization, J.L.; supervision, P.F.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors would like to thank Lukas Hans for help with performing in situ particle size measurement and Heiko Briesen for the possibility to carry out this study.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Research on the Pressure Dropin Horizontal Pneumatic Conveying for Large Coal Particles**

#### **Daolong Yang 1,\*, Yanxiang Wang <sup>1</sup> and Zhengwei Hu <sup>2</sup>**


Received: 17 April 2020; Accepted: 28 May 2020; Published: 30 May 2020

**Abstract:** As a type of airtight conveying mode, pneumatic conveying has the advantages of environmental friendliness and conveying without dust overflow. The application of the pneumatic conveying system in the field of coal particle conveying can avoid direct contact between coal particles and the atmosphere, which helps to reduce the concentration of air dust and improve environmental quality in coal production and coal consumption enterprises. In order to predict pressure drop in the pipe during the horizontal pneumatic conveying of large coal particles, the Lagrangian coupling method and DPM (discrete particle model) simulation model was used in this paper. Based on the comparison of the experimental results, the feasibility of the simulation was verified and the pressure drop in the pipe was simulated. The simulation results show that when the flow velocity is small, the simulation results of the DPM model are quite different from that of the experiment. When the flow velocity is large, the large particle horizontal pneumatic conveying behavior predicted by the model is feasible, which can provide a simulation reference for the design of the coal pneumatic conveying system.

**Keywords:** pneumatic conveying; large coal particles; Euler–Lagrange approach; DPM; pressure drop

#### **1. Introduction**

Coal is an important fossil energy and many countries have strong dependence on coal resources [1]. The open-conveying way is the most common conveying way for coal particles. The main conveying equipment is a belt conveyor. In the process of mining, unloading, separation and conveying, the pulverized coal and dust escape into the air, causing environmental pollution and serious dust explosion accidents [2]. The coal particles come in direct contact with the atmosphere, which leads to coal dust diffusion, pollution of the surrounding environment, waste of resources and coal dust explosion accidents [3].

How to convey coal cleanly, efficiently and safely has become an urgent environmental problem, one that needs to be solved. It also puts forward higher requirements for environmental protection, economy and reliability of coal conveying equipment. As a kind of airtight conveying mode, pneumatic conveying has the advantages of environmental friendliness and no-dust overflow [4]. Applying the pneumatic conveying system to the field of coal particle conveying can avoid the direct contact between coal particles and the atmosphere [5]. It is of great significance to improve the surrounding environment of coal enterprises, avoid safety production accidents and realize the green use of coal resources.

Many scholars have made contributions in the field of particle pneumatic conveying. Rabinovich [6] proposed the generalized flow pattern of vertical pneumatic conveying and a fluidized bed system that considers the effects of particle and gas properties, pipe diameter and particle concentration. Pahk [7] studied the friction between the plug and the pipe wall in the dense phase pneumatic conveying system. The results showed that the friction between the plug and the pipe wall increased with the contact area, and the friction between the spherical particles was greater than that of the cylindrical particles. Njobuenwu [8] used the particle trajectory model and wear model to predict the wear of elbows with different square sections in dilute particle flow. The results show that the maximum wear position is in the range of 20◦–35◦ of elbows. Watson [9] carried out the vertical pneumatic conveying test of alumina particles with a particle size of 2.7 mm, measured the solid-phase mass flow rate, gas-phase mass flow rate and inlet and outlet pressure, as well as the pressure distribution and other parameters, and proved that the dense plug flow pneumatic conveying system has advantages in conveying coarse particles. Ebrahimi [10] established a horizontal pneumatic conveying test-bed based on a laser Doppler velocimeter, and carried out the conveying experiments of spherical glass powder with particle size of 0.81 mm, 1.50 mm and 2.00 mm. Ogata [11] studied the influence of different glass particle properties on the fluidization dense-phase pneumatic conveying system in a horizontal rectangular pipeline. Makwana [12] studied the causes of the fluctuation of the pneumatic conveying in the horizontal pipeline and showed that the pressure loss in the pipeline increased sharply with the formation of sand dunes, and the pressure drop value was related to the axial position of sand dunes. Anantharaman [13] studied the relationship between particle size, density, sphericity and minimum pickup speed of particles in the pneumatic conveying system and showed that the influence of particle size on pickup speed is greater than that of particle density. Akira [14,15] compared the pneumatic conveying system with a soft wing and sand dune model with the traditional pneumatic conveying system and showed that the pressure loss of the pneumatic conveying system with a soft wing and sand dune model was less than that of the traditional pneumatic conveying system at low air speed. Yang [16] carried out simulation and experimental research on the pneumatic suspension behavior of large irregular coal particles and obtained the suspension speed of coal particles under different particle sizes. Yang [17,18] studied the influence of structural parameters of a coal particle gas–solid injection feeder on the pure flow field injection performance and particle injection performance through multifactor orthogonal experiments.

Previous work in the field has looked at fine particle [19,20], powder [21,22] and seed [23,24], all of which are less than 5 mm in size and are within the range of Geldart A to Geldart C. However, there are a few studies on large sizes (larger than Geldart D) [25,26]. When using the common computational fluid dynamics and discrete element method (CFD-DEM) simulation, due to the coupling method between the discrete element method and the finite element method, the simulation time is long and there is a lot to calculate, so it is difficult to get the results quickly. In order to quickly predict the pressure drop in horizontal pneumatic conveying for large (5–25 mm) coal particles, this paper uses the coupling method based on the Euler–Lagrange approach, DPM (discrete particle model) and the particle trajectory equations. The experiment and the simulation of horizontal pneumatic conveying for large coal particles was carried out to verify the feasibility of the simulation method. The multi-factor simulations were carried out to analyze the effects of particle size, flow field velocity, solid-gas rate and pipe diameter on pressure drop.

#### **2. Theory**

The flow field provides the energy required by the particles' motion, and the exchange of momentum and energy between the flow field and particles occurs in the pneumatic conveying flow field. In the Euler–Lagrange approach, the fluid phase is treated as a continuum by solving the Navier–Stokes equations, while the dispersed phase is solved by tracking a large number of particles through the calculated flow field. The dispersed phase can exchange momentum, mass and energy with the fluid phase.

#### *2.1. Gas Phase Equations*

The gas phase is a continuous medium, considering the influence of solid phase to flow field, and the continuity equation adds the volume fraction term ξ to exclude the gas volume occupied by the solid phase. It is assumed that the temperature of both gas and solid phases in pneumatic conveying is the same as that of the atmosphere, and no exothermic reaction occurs between the two phases. Therefore, the energy equation of gas and solid phases can be ignored.

#### (1) Gas phase continuity equation

According to the law of mass conservation, the gas phase continuity equation can be obtained and is shown in Equations (1) and (2).

$$\frac{\partial \xi \rho}{\partial t} + \nabla \cdot \rho \varepsilon v = 0;\tag{1}$$

$$
\nabla \equiv \frac{\partial}{\partial \mathbf{x}} \stackrel{\rightarrow}{i} + \frac{\partial}{\partial y} \stackrel{\rightarrow}{j} + \frac{\partial}{\partial z} \stackrel{\rightarrow}{k} \tag{2}
$$

where ρ is the density of gas phase, *v* is the velocity of gas phase and ξ is the volume fraction term.

#### (2) Gas phase momentum equation

The momentum equation of the gas phase can be obtained from the law of momentum conservation, which is similar to the continuity equation.

$$\frac{\partial \underline{\xi}\rho v}{\partial t} + \nabla \cdot \rho \underline{\xi}\mu v = -\nabla \rho + \nabla \cdot (\underline{\xi}\mu \nabla v) + \rho \underline{\xi}\underline{g} - \mathcal{S}\_{\text{m}}.\tag{3}$$

The momentum transfer *Sm* refers to the sum of the fluid drag in the fluid unit.

$$S\_m = \frac{\sum F\_d}{V}.\tag{4}$$

#### (3) Turbulence transmission equations

The Realizable *k*-ε model [27] has the advantage of a more accurate prediction for the divergence ratio of flat and cylindrical jets, and its transmission equations are shown in Equations (5)–(7).

$$\frac{\partial}{\partial t}(\rho k) + \frac{\partial}{\partial \mathbf{x}\_j}(\rho k \mathbf{v}\_j) = \frac{\partial}{\partial \mathbf{x}\_j} \left[ \left( \mu + \frac{\mu\_t}{\sigma\_k} \right) \frac{\partial k}{\partial \mathbf{x}\_j} \right] + \mathbf{G}\_k + \mathbf{G}\_b - \rho \varepsilon - \mathbf{Y}\_M + \mathbf{S}\_k \tag{5}$$

$$\frac{\partial}{\partial t}(\rho \varepsilon) + \frac{\partial}{\partial \mathbf{x}\_{\dot{\jmath}}}(\rho \varepsilon \mathbf{v}\_{\dot{\jmath}}) = \frac{\partial}{\partial \mathbf{x}\_{\dot{\jmath}}} \Big[ (\mu + \frac{\mu\_{\ell}}{\sigma\_{\ell}}) \frac{\partial \varepsilon}{\partial \mathbf{x}\_{\dot{\jmath}}} \Big] + \rho \mathbf{C}\_{1} \mathbf{S} \varepsilon - \frac{\rho \mathbf{C}\_{2} \varepsilon^{2}}{k + \sqrt{\nu \varepsilon}} + \frac{\mathbf{C}\_{1\varepsilon} \mathbf{C}\_{3\varepsilon} \mathbf{G}\_{b} \varepsilon}{k} + \mathbf{S}\_{\ell} \cdot \tag{6}$$

where

$$\begin{cases} \mathcal{C}\_1 = \max\left[0.43, \frac{\eta}{\eta+5}\right] \\ \eta = \sqrt{2S\_{ij}S\_{ij}}\_{\mathcal{E}\_l} \end{cases} . \tag{7}$$

#### *2.2. Motion Equations of Solid Phase*

The solid phase is a discrete phase as the motion law of solid particles obeys Newton's second law.

#### (1) Particle Force Balance

The trajectory of the solid phase is predicted by integrating the force balance on the particle which is written in a Lagrangian reference frame. This force balance equates the particle inertia with the forces acting on the particle and can be written as

$$\frac{\mathbf{d}\overrightarrow{u}\_p}{\mathbf{d}t} = \frac{\overrightarrow{u} - \overrightarrow{u}\_p}{\tau\_r} + \frac{\overrightarrow{g}(\rho\_p - \rho)}{\rho\_p} + \overrightarrow{F}\_\prime \tag{8}$$

where <sup>→</sup> *F* is an additional acceleration term, <sup>→</sup> *g* is the force of gravity on the particle, → *u*− → *up* <sup>τ</sup>*<sup>r</sup>* is the drag force per unit particle mass and τ*<sup>r</sup>* is the particle relaxation time [28], which is defined as

$$
\tau\_{\tau} = \frac{\rho\_p d\_p^2}{18\mu} \frac{24}{\mathcal{C}\_d \text{Re}'} \tag{9}
$$

where <sup>→</sup> *u* is the fluid phase velocity, <sup>→</sup> *up* is the particle velocity, μ is the molecular viscosity of the fluid, ρ is the fluid density, ρ*<sup>p</sup>* is the density of the particle and *dp* is the particle diameter. Re is the relative Reynolds number, which is defined as

$$\text{Re} = \frac{\rho\_p d\_p \left| \overrightarrow{\text{u}} - \overrightarrow{\text{u}}\_p \right|}{\mu}. \tag{10}$$

For non-spherical particles, Haider and Levenspiel [29] developed the correlation

$$\mathcal{C}\_{D} = \frac{24}{\text{Re}\_{\text{splr}}} (1 + b\_1 \text{Re}\_{\text{splr}}^{b\_2}) + \frac{b\_3 \text{Re}\_{\text{splr}}}{b\_4 + \text{Re}\_{\text{splr}}},\tag{11}$$

where

$$\begin{aligned} b\_1 &= \exp(2.3288 - 6.4581\phi + 2.4486\phi^2); \\ b\_2 &= 0.0964 + 0.5565\phi; \\ b\_3 &= \exp(4.9050 - 13.8944\phi + 18.4222\phi^2 - 10.2599\phi^3); \\ b\_4 &= \exp(1.4681 + 12.2584\phi - 20.7322\phi^2 + 15.8855\phi^3). \end{aligned} \tag{12}$$

The shape factor φ is defined as

$$
\phi = \frac{\mathbf{s}}{\mathbf{S}}\tag{13}
$$

where *s* is the surface area of a sphere having the same volume as the particle and *S* is the actual surface area of the particle.

The additional forces <sup>→</sup> *F* in the particle force are virtual mass and pressure gradient forces which are not important when the density of the fluid is much lower than the density of the particles. For this study, the virtual mass and pressure gradient forces are ignored.

(2) Particle Torque Balance

Particle rotation is a natural part of particle motion and can have a significant influence on the trajectory of a particle moving in a fluid. The impact is even more pronounced for large particles with high moments of inertia. In this case, if particle rotation is disregarded in simulation studies, the resulting particle trajectories can significantly differ from the actual particle paths. The torque <sup>→</sup> *T* results from equilibrium between the particle inertia and the drag.

$$
\stackrel{\rightharpoonup}{T} = I\_p \frac{\mathbf{d} \overrightarrow{\omega}\_p}{\mathbf{d}t} = \frac{\rho\_f}{2} (\frac{d\_p}{2})^5 \mathbf{C}\_\omega \overrightarrow{\Omega}\_\prime \tag{14}
$$

where *Ip* is the moment of inertia, <sup>→</sup> ω*<sup>p</sup>* is the particle angular velocity, ρ*<sup>f</sup>* is the fluid density, *dp* is the particle diameter, *<sup>C</sup>*<sup>ω</sup> is the rotational drag coefficient, <sup>→</sup> *T* is the torque applied to a particle in a fluid domain and <sup>→</sup> Ω is the relative particle–fluid angular velocity calculated by:

$$
\overrightarrow{\Omega} = \frac{1}{2}\nabla \times \overrightarrow{\boldsymbol{u}}\_f - \overrightarrow{\boldsymbol{\omega}}\_p. \tag{15}
$$

The particles will have impact with the wall and other particles in the pipe. The collision recovery factor is obtained by Forder's recovery factor equations [30].

$$\begin{aligned} \varepsilon\_{\text{\tiny{\tiny{\tiny{\tiny{\Gamma}}}}} &= 0.988 - 0.780 + 0.19 \theta^2 - 0.024 \theta^3 + 0.027 \theta^4; \\ \varepsilon\_{\text{\tiny{\Gamma}}} &= 1 - 0.780 + 0.84 \theta^2 - 0.21 \theta^3 + 0.028 \theta^4 - 0.022 \theta^5, \end{aligned} \tag{16}$$

where *en* is the normal recovery factor, *er* is the tangential recovery factor and θ is the impact angle.

#### **3. Simulations**

#### *3.1. Simulation Model*

The Euler–Lagrange approach, DPM and the two-way coupling method were used in the simulations. The boundary conditions and injection parameters are shown in Figure 1. The simulation pipe diameters were 70, 100 and 150 mm, and the length was 6 m. The wall roughness of seamless steel pipes used in the experiments was 0.05 mm. The particle density was 2100 kg/m3.The solid-gas rate was the ratio of the particle's mass flow ratio between the air mass flow ratio during pneumatic conveying. The particles were injected into the pipe inlet uniformly. The transmission medium was air, which was considered an incompressible gas. The gas density was 1.225 kg/m<sup>3</sup> and the dynamic viscosity was 1.8 <sup>×</sup> <sup>10</sup>−<sup>5</sup> kg/m<sup>3</sup> (20 ◦C, 1 atm).

**Figure 1.** Simulation model.

The DPM model is based on ANSYS FLUENT and the meshes of the simulation models are the hexahedral orthogonal meshes. The simulation considered the interaction between the gas and particle phase; however, the shape characteristics of particles was ignored.

#### *3.2. E*ff*ects of Particle Size and Flow Field Velocity on Pressure Drop*

The different particle sizes and flow field velocities were used in the simulations to obtain the effects of particle size and flow field velocity on pressure drop. The simulation parameters are shown in Table 1.

**Table 1.** Simulations parameters.


As an example, the variation trend of pressure drop was analyzed by taking the simulation results under the condition of 10 mm particle size and 50 m/s flow field velocity. The variation trend in the stable conveying part in the horizontal conveying pipe is shown in Figure 2. The coupled static pressure, the coupled dynamic pressure and the coupled total pressure refer to the coupling simulation process of the coal particles and the flow field, while the pure flow static pressure, the pure flow dynamic pressure and the pure flow total pressure refer to the simulation process of pure flow fluid conveying.

**Figure 2.** Pressure variation in a horizontal pipe.

Both in coupling and pure flow simulation results, the changes of dynamic pressure were small, which means there was a small change of flow field velocity. The change of the flow field total pressure was mainly due to the change of static pressure. The coupling static pressure and coupling total pressure curves can be divided into three regions. Region I is the pure flow region, region II is the particle dropping and rebounding region and region III is the stable conveying region. Region I is behind the particle factory. Since there is no particle formation, it is still the pure fluid field, meaning the slope of static pressure drop is the same as that of pure flow static pressure. At region II, the particles start to form and exchange momentum and energy with the flow field. Since particles are randomly generated in the particle factory, the interaction between the particles and the flow field is sufficient when the particles enter the flow field. There is an initial collision between particles and wall, so the static pressure of this region declines faster than other regions and the energy conversion efficiency between the flow fluid and the particles is also the highest. Region III is in a stable conveying stage-the particles have sufficient velocity and the particle–particle collisions and the particle–wall collisions are basically in a stable and eased off state. This means the static pressure drop trend of the flow field is to slow down. The unit distance static pressure drop (hereinafter referred to as the pressure drop) of region III under different particle size and flow field velocity is shown in Figure 3.

**Figure 3.** Relationship between pressure drop, particle size and flow field velocity.

The pressure drop increases with the flow field velocity and decreases with the particle size. At a lower flow field velocity (*v* = 20 m/s), the difference in pressure drop under different sizes is small. This is because the flow field is stratified due to the small flow field velocity. Only some particles participate in the interaction with flow field, so the particle size has a small effect on the pressure drop. The stratification state of flow field disappears gradually with the flow velocity, and more particles participate in the interaction with the flow field. However, under the same feeding rate, the smaller the particle size, the higher the number of particles and the easier the interaction with the flow field. More particle collisions probability result in more energy consumption of particles. Therefore, the pressure drop is also higher. However, when the particle size is larger, the number of particles is smaller and the probability of particle collisions is less. This means the energy consumption of particles is also less, which leads the pressure to continue dropping. When the flow velocity increases further, the particle collision probability is more severe. The more energy consumption that is needed leads to a greater pressure drop.

#### *3.3. E*ff*ects of Pipe Diameter and Solid-Gas Ratio on Pressure Drop*

The different solid-gas rates and pipe diameters were used in the simulations to obtain the effects of pipe diameter and solid-gas ratio on pressure drop. The simulation parameters are shown in Table 2. The relationship between pressure drop, pipe diameter and solid-gas rate is shown in Figure 4.

**Table 2.** Simulation parameters.

**Figure 4.** Relationship between pressure drop, pipe diameter and solid-gas rate.

The pressure drop increases with the pipe diameter and the solid-gas rate. Under the same solid-gas ratio, the pressure drop increases greatly with the pipe diameter. This is because the mass flow rate of the flow field increases with the pipe diameter under the fixed flow field velocity. The mass flow rate of particles increases with the flow field due to the fixed solid-gas rate, which leads to a significant increase in pressure drop. The influence of the solid-gas rate on pressure drop is less than that of pipe diameter, but the increase of the solid-gas rate makes the mass flow rate of particles and the pressure drop of the flow field increase. The pressure drop increases slightly with the solid-gas rate under the same pipe diameter *Dp* = 100 and 150 mm. It is because there is enough space for the particles (size = 15 mm) to move in the large diameter pipe when the solid-gas rate increases, so the increment of collision probability is less. The pressure drop increases greatly with the solid-gas rate under the pipe diameter *Dp* = 70 mm. This is because the small pipe diameter and the increase of solid-gas rate both cause an increase in collision probability. The increase of the solid-gas rate leads to an increase in collision probability and also leads to high energy consumption and a drop in pressure.

#### **4. Experimental Verification**

The experimental system of horizontal pneumatic conveying is shown in Figure 1. The total length of the conveying pipelines was 10 m and the diameter was 70 mm. The test system included two pressure transducers, a signal amplifier, a data acquisition instrument and a computer. The position of two pressure transducers and one transparent pipe is shown in Figure 5.

**Figure 5.** Experimental system of horizontal pneumatic conveying.

The air flow is pressurized by the screw air compressor and stabilized by the air receiver which enters into the gas-solid injector through the flow valve. The coal particles gain kinetic energy from air flow and are conveyed into the dust collection box through conveying pipes. There is some back pressure in the dust collection box, but far less than the pressure of air flow. Therefore, the dust collector can be considered as atmospheric pressure. The first pressure transducer is installed 3 m from the outlet of the gas-solid injector and the second is 4 m downstream of the first pressure transducer. The transparent pipe is installed 1.5 m downstream of the first pressure transducer to monitor the particle motion state.

When the output pressure of the air compressor is certain, the opening of the flow valve determines the air flow rate in the pipe. It is called a pure flow field when no particles enter. However, when the particles do enter the flow field, some of flow field dynamic pressure turns to static pressure to transfer momentum and energy to the particles. At this point, it amounts to add back pressure into the pipe. As result, the air flow rate will be reduced by this back pressure. Therefore, the air flow rate of the pure flow field is regarded as the reference standard in the experiments. When the particles enter into the flow field, the opening of the flow valve will be appropriately increased to complement the reduction.

The size of experimental coal particles was 5–10 mm and the feeding rate was controlled by the frequency converter. The mass density of the experimental coal particle was 2100 kg/m3. The experimental scheme is shown in Table 3.


**Table 3.** The experimental scheme of horizontal pneumatic conveying.

#### *4.1. Experiment Results*

In all the experimental results, the pressure signal curves obtained by the two pressure transducers were basically the same trend, but the output pressure of the air compressor and feeding rate had obvious influence on the pressure signal curves. Due to the highest output pressure of the air compressor and the largest feeding rate in the No.8 experiment, the pressure signal curves obtained by the two pressure sensors are best visualized. Therefore, the No.8 experiment is taken as an example to analyze the trend of pressure drop in the pipe during the pneumatic conveying experiment. The static pressure signals of first and second pressure transducers are shown in Figure 6.

**Figure 6.** Pressure signal in horizontal pneumatic conveying pipe.

The pressure signal curves were clearly divided into pure flow part and conveying part. At 0–5 s, the pressure value gradually increased, which was the initial stage of single-phase gas flow in the pipe. After that, the pressure value was relatively stable, although there was noise fluctuation. Basically, the pressure value floated up and down at zero, which indicates that the air flow was fully developed and the stable flow field was formed, which is called the pure flow part. The pressure value rose rapidly and maintained its high value when the particles entered the flow field. The pressure curve has a large fluctuation with the particle conveying which eliminates the noise fluctuation. It is because the coal particles in the pipeline hinder the flow field that the pressure value of this part increased. This is called the conveying part. Next, the pressure value gradually decreased with the decline of coal particles in the pipe, and then the pure flow part was restored.

The unit-distance pressure drop (Δ*p*/*l*) of the horizontal pneumatic conveying experiment was the ratio of the pressure difference obtained by the two pressure transducers of the distance between the two measuring points, which is shown in Figure 7. According to the zero temperature drift of pressure transducers (±0.15%FS/ ◦C), sensitivity temperature drift of pressure transducers (±0.15%FS/ ◦C) and signal fluctuation (±1.0%) in the measurement process, the pressure error measured in the experiment (20 ◦C) was estimated to be ±7%. Pressure drop curves have the same trend, where the pressure drop is first reduced and then increased. The pressure drop increased with the feeding rate under the same flow field velocity.

**Figure 7.** Relationship between pressure drop and flow field velocity.

#### *4.2. Comparison Pressure Drop*

The comparative simulations were carried out using the simulation particles with the diameter of 5–10 mm and the R-R particle size distribution [31]. The simulation scheme is the same as Table 3. The pressure drop comparison between the simulation and the experiment results is shown in Figure 8. The experiment variation trend of the pressure drop shows the parabola shape with the flow field velocity, and the simulation variation trend shows a linear growth pattern. From the numerical analysis, the pressure drop of simulation results were very different from the experimental results when the flow velocity was small. However, the simulation and experimental results changed gradually when the flow velocity increased. This indicates that the simulation results of DPM are similar to experiment results when flow velocity is large. Therefore, larger flow field velocities are used in the subsequent simulation to ensure the accuracy of the simulation results.

**Figure 8.** Comparison of pressure drop between experiment and simulation.

#### **5. Discussion and Limitation**

#### *5.1. Discussion of Simulation Results Accuracy*

The pressure drop obtained by simulation and experiments varied greatly with respect to flow field velocity. This is because the DPM used in this paper does not consider particle shape characteristics. Particle shape characteristics play a key role in particle–particle and particle–wall collisions. When the flow velocity is low, the stratification of flow field leads to more frequent particle–particle and particle–wall interactions, and some of the particles even accumulate at the pipe bottom. Therefore, the accuracy of DPM simulation results is very low at low flow field velocity. However, when the flow velocity increases, the particles get more energy from the flow field and some particles are suspended in the flow field, which leads to a decrease in collision probability. Therefore, the DPM simulation results are similar to the experimental results at the high flow field velocity.

#### *5.2. Limitation of Experiments*

Coal is an inflammable and explosive material. Coal dust will inevitably be produced in the pneumatic conveying process and there is a chance of sparks when large sized particles make an impact with the pipe wall at high speed. This in turn could cause accidents such as pipeline explosions. Therefore, under the premise of ensuring a safe experiment, the pneumatic conveying experiment of large sized particles cannot be carried out, only simulation research can be carried out.

#### *5.3. Future Research*

The goal of this paper is to find a simple and effective numerical simulation method to predict the pneumatic conveying of large coal particles. According to the results of the experimental and simulation comparison, this is only the first step in finding a suitable model. The simulation model used in this paper is only suitable for high-speed flow field, and we will continue to study and modify the simulation model to obtain an effective and fast prediction model for all conditions in the pneumatic conveying of large particles.

#### **6. Conclusions**

This paper uses the coupling method based on the Euler–Lagrange approach, DPM and particle trajectory equations to quickly predict the pressure drop in horizontal pneumatic conveying for large coal particles. The multi-factor simulations are carried out to analyze the effects of particle size, flow field velocity, solid-gas rate and pipe diameter on pressure drop. In the simulation results, the change of the flow field total pressure was mainly due to the change of static pressure. The pressure curves can be divided into three regions: the pure flow region, the particle dropping and rebounding region and the stable conveying region.

In the stable conveying region, the pressure drop increases with the flow field velocity and decreases with the particle size. At lower flow field velocity, the difference of pressure drop under different particle sizes is small. In the stable conveying region, the pressure drop increases with the pipe diameter and the solid-gas rate. The influence of the solid-gas rate on the pressure drop is less than that of the pipe diameter, but the increase of solid-gas rate makes the mass flow rate of particles and the pressure drop of flow field increase.

Comparing simulation results with verified experimental results of pressure drop, the pressure drop of simulation results greatly differs from experimental results when the flow velocity is small. However, the simulation and experimental results gradually become more similar when the flow velocity increases. This indicates that the DPM model is feasible in predicting horizontal pneumatic conveying for large coal particles at large flow field velocity.

**Author Contributions:** Methodology, D.Y.; software, D.Y.; validation, Y.W.; writing—original draft preparation, D.Y.; writing—review and editing, Y.W. and Z.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (51705222), the National Natural Science Foundation of Jiangsu Province (BK20170241) and the National Natural Science Foundation of the Jiangsu Normal University (17XLR028).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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