Acoustic Analysis of ParticleâWall Interaction and Detection of Particle

Article pubs.acs.org/IECR

Acoustic Analysis of Particle−Wall Interaction and Detection of Particle Mass Flow Rate in Vertical Pneumatic Conveying Lelu He, Yefeng Zhou, Zhengliang Huang, Jingdai Wang,* Musango Lungu, and Yongrong Yang State Key Laboratory of Chemical Engineering, Department of Chemical and Biochemical Engineering, Zhejiang University, Hangzhou 310027, People’s Republic of China ABSTRACT: A novel approach based on the passive acoustic emission (AE) monitoring technique has been established for analyzing particle−wall collision and friction separately in the present work. Using power spectrum density analysis, the main frequency of AE signal caused from particle−wall collision is found to be higher than that generated by particle−wall friction. Besides, a method for quantitatively extracting the information on particle−wall collision and friction has been set up by wavelet transform analysis. On the basis of these analyses, a theoretical approach has been established for relating the AE signals and solids loading ratio in a vertical pneumatic conveying pipe. The model predictions are verified using experimental data and are in good agreement. Particle mass flow rates obtained using this model give errors less than 6.62%. Conclusions can be drawn that the AE technique has great potential in the measurement of hydrodynamics in pneumatic conveying as well as similar particulate processes.

1. INTRODUCTION Pneumatic conveying of particulate materials is widely used in many types of industrial and commercial operations, including agriculture, mining, chemicals, pharmaceuticals, and metal refining and processing.1 The measurement of particle mass flow rate is crucial for improving product quality and process efficiency. However, it is very difficult to measure the solids mass flow rate due to the complicated and random nature of gas−solid two-phase flow processes.2 Over the years, various sensing techniques have been developed and proposed to overcome these difficulties.2,3 Among them, the most promising methods are electrostatic,4,5 microwave,6 active acoustic,7 and tomographic8,9 methods. Nevertheless, these methods are limited in their industrial application because they are either sensitive to the change of environment, expensive, intrusive, or time-consuming. Therefore, the search for a simple and reliable method for monitoring the particle mass flow rate has been recognized as a challenging task within the industrial and academic circle for a long time. As a nonintrusive, real-time monitoring method, the passive acoustic emission (AE) technique has been widely used in various chemical engineering processes, especially in particulate processes.10 This technique can be divided into two very different measurement approaches (high frequency and low frequency approaches) based on the sampling frequencies.11 Nevertheless, a majority of the results indicate that AE signals are very sensitive to particle movement especially for those “high frequency” approaches.12−17 Thus, this method holds a great potential to estimate particle mass flow rate of gas−solid two-phase flow. However, due to a lack of concrete knowledge about the underlying mechanism of signal generation, how to extract useful information from these signals is a confusing problem.18 Esbensen et al.19 proposed a process analysis technology, named acoustic chemometrics, that combines acoustic sensor technology with multivariate calibration analysis for monitoring of pneumatic transport. To be specific, the power spectrum density (PSD) spectra data of the AE signals © 2014 American Chemical Society

were used for a partial least squares regression (PLS-R) to establish the predictive model of particle mass flow rate. Later, the acoustic chemometrics method has been used for the detection of powder breakage during pneumatic conveying by Huang et al.20 However, over 300 parameters in PSD spectra were used for the PLS-R, and thus this method is timeconsuming. To overcome this problem, Wei et al.21 introduced wavelet packet analysis for data processing of AE signals. In the study, acoustic energies of these decomposed signals, instead of the whole PSD spectra, were used for the PLS-R, and thus the calculation speed was improved significantly. Meunier et al.22 developed an intrusive vibration probe to collect acoustic signals generated by the oscillations of the probe. Similar to the previous studies, PSD spectra data, root-mean-square (RMS), and zero-crossing frequency of the signals were used to establish a neural network for prediction of solids concentration. Recently, Hii et al.23 attached AE sensors to two steel meshes, which were placed with a fixed axial distance in the pipe to study the generation of AE signals. Then RMS and energy of the AE signals were related to mass flow rate of solids and particle velocities, respectively. Although these results indicate that the AE method can be used in detecting mass flow rate of solids, the prediction models that were established on the basis of the statistical characteristics and multivariate calibration not only have little physical sense, but also probably have poor generalization performance. To establish a theoretical model for the detection of particle mass flow rate, which has clear physical meaning, the mechanism of AE signal generation should be deeply analyzed. As discussed by He et al.,18 AE signals are generated from different sources in gas−solid two-phase flow, including Received: Revised: Accepted: Published: 9938

December 3, 2013 March 18, 2014 May 15, 2014 May 15, 2014 dx.doi.org/10.1021/ie404088k | Ind. Eng. Chem. Res. 2014, 53, 9938−9948

Industrial & Engineering Chemistry Research

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particle−particle interaction, particle−wall interaction, and macro-circulation pattern. Generally, AE sensors are fixed on the wall; thus particle−wall interaction dominates in these acoustic sources because AE signals generated by particle− particle interaction and macro-circulation pattern attenuate quickly in air.17 From a theoretical perspective, particle−wall interactions can be divided into two parts:24 one is the particle−wall contact interaction in normal direction (particle− wall collision), and the other is the particle−wall interaction along the tangential direction (particle−wall friction). These interactions can be described by theories developed by Hertz25 and Mindlin et al.26 As compared to the theoretical studies, experimental studies are more difficult to perform for obtaining information about particle−wall interactions in gas−solid twophase flow.27 Jiang et al.28 studied AE signals generated in a gas−solid fluidized bed and developed a frequency model of particle−wall interaction. Besides, Wang et al.29 proposed a theory model to quantitatively describe the energy of AE signal generated by particle−wall collision. In these works, despite several efforts being made in understanding the underlying mechanism of signal generation, particle−wall interactions in the normal direction and in tangential direction were not considered separately, but mixed together. Thus, the AE signal generated from different sources was hardly recognizable. In the present work, we focus on the detection of mass flow rate of solids by AE technique in a vertical pneumatic conveying process. The concepts of particle−wall collision and friction are introduced into the analysis of AE for the first time. AE signals generated by particle−wall collision and friction are studied via PSD analysis and wavelet analysis, and characteristics of these signals are obtained. On the basis of these analyses, methods for extracting the information about particle−wall collision and friction by signal decomposition and reconstruction are established. Furthermore, a theoretical model relating the acoustic energy fraction of particle−wall collision/friction to solids loading ratio (φ, mass flow rate of solids divided by mass flow rate of gas) has been proposed and further verified by experiment results, and thus the mass flow rate of solids has been obtained from this model.

Figure 1. Schematic diagram of the vertical pneumatic conveying system: (1) air compressor; (2) buffer tank; (3) gas flow meter; (4) aeration cone; (5) feeding vessel; (6) weighing cell; (7) receiving vessel; (8) dust collector; (9) acoustic sensor; (10) preamplifier; (11) main amplifier; (12) A/D conversion module; (13) computer; (14) camera.

Table 1. Physical Properties of PP Particles

material

surface weighted mean diameter (μm)

volume weighted mean diameter (μm)

density (kg m−3)

sphericitya

Geldart class

polypropylene

569.66

613.65

900

0.862

B

a

Calculated by surface weighted mean particle diameter and volume weighted mean particle diameter measured via a Malvern Mastersizer 2000 particle size analyzer.

2. EXPERIMENTS 2.1. Experimental Setup, Procedure, and Material. A schematic diagram of the vertical pneumatic conveying system is shown in Figure 1. Compressed air was split into three parts: one was supplied to maintain enough conveying pressure for the feeding vessel, another part was used to fluidize the particles in the feeding vessel, and the rest was used as conveying gas. Polypropylene (PP) particles were conveyed through a horizontal Plexiglas pipe (1.2 m in length and 25 mm in inner diameter (i.d.)) at the bottom, then passed through the main testing section of a vertical Plexiglas pipe (3.0 m in length and 25 mm in i.d.) to the top, and finally entered the receiving vessel via a horizontal pipe (0.8 m in length and 25 mm in i.d.) at the top. A digital camera (Canon DIGITAL IXUS 110 IS) having a resolution of 4000 × 3000 pixels was used to record the particle images. The average mass flow rate of particles was measured by weighing the particles from the receiving vessel in a certain period. The physical properties of PP particles are summarized in Table 1. The particle size distribution (measured by Malvern Mastersizer 2000 particle size analyzer) of PP particles is shown in Figure 2, and the test was repeated twice.

Figure 2. Particle size distribution of polypropylene particles.

The gas flow rate was determined by the gas flow meters while the solid mass flow rate was controlled by valve opening, flow rate of the conveying gas, and pressure of feeding vessel. In the experiments, the superficial gas velocity ranged from 2.0 to 14.0 m s−1 and the PP particle mass flow rate ranged from 0.012 to 0.018 kg s−1. Thus, the solids loading ratio varied from 1.26 to 13.30 kg kg−1. All of the experiments were repeated three times, and the average results were used. 2.2. Acoustic Emission Measurement. The online AE system for collection and analysis developed by the UNILAB Research Center of Chemical Engineering in Zhejiang University30 consists of an AE sensor, a preamplifier, a main amplifier, A/D conversion module, and a computer. The gain of preamplifier is 40 dB. The digital resolution of the capture card is 16-bit. The AE sensor used in this work is a piezoelectric accelerometer with a resonance frequency of 140 kHz (AE 144S, Fuji Ceramics Corp.). Besides, the AE sensor was 9939

dx.doi.org/10.1021/ie404088k | Ind. Eng. Chem. Res. 2014, 53, 9938−9948


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mounted on the outer surface of the vertical pipe, and the installation location was 1.2 m above the elbow bend at the bottom. According to the Shannon sampling theory, the sampling frequency was chosen as 900 kHz, and the sampling time was 5 s.

3. ANALYSIS METHODS 3.1. Power Spectrum Density Analysis. Power spectrum density (PSD) analysis is a common used frequency-domain analysis method, which has proved to be a powerful tool in dealing with acoustic signal. PSD analysis can be applied to detect small differences in the energy distribution for different frequency ranges. Moreover, PSD analysis can reveal the characteristics of the AE sources. The PSD of a discrete signal x(n) is given by ⎛ −j 2πnk ⎞ ⎟ , k = 0, 1, ..., N − 1 N ⎠

N−1

X (k ) =

∑ x(n) exp⎜⎝ n=0

(1)

where X(k) is the PSD of signal x(n) in the kth frequency. To obtain results with universality, the PSD of acoustic signals can be normalized as follows:

Figure 3. Schematic diagram of the particle−wall interaction experimental setups. (a) Particle−wall collision; (b) particle−wall friction.

N−1

X ′(k) = X(k)/ ∑ X(k), k = 0, 1, ..., N − 1 n=0

Plexiglas plate was used to collect acoustic signals in this collision process. To reduce the influence of the ambient gas on the particle motion, a shield (i.d. 40 mm) was mounted on the Plexiglas plate. In the experiment of particle−wall friction, the transparent adhesive tape with PP particles stuck on it was put on the Plexiglas plate. The weight then was placed on top of the sticky tape to ensure close contact between PP particles and the Plexiglas plate. Besides, an electric motor was used to maintain the particles and weight move at a certain velocity. Similarly, the acoustic sensor was attached to the back of the Plexiglas plate to collect the acoustic signals of particle−wall friction. 4.1.1. PSD Analysis of Acoustic Signal Characteristics. For acoustic signals generated from interactions between PP particles and the Plexiglas plate, the original signals and their PSDs are shown in Figure 4a and b. The acoustic signal representing one typical collision appears within a short time, while the friction signal results from an interaction lasting a long time. From Figure 4, it can be concluded that the main frequency of particle−wall collision signal is around 90 kHz, while that of particle−wall friction signal is around 25 kHz for PP particles. The frequency of AE signal caused by particle impact is 15−200 kHz according to Boyd et al.,10 which is consistent with our current work. Besides, it should be noted that from the acoustic signal generated by particle−wall collision, the occurrence of a small peak around 25 kHz means the particle−wall friction exists in this process. The results can be explained as follows: on one hand, the roughness of particle surface makes the particles roll on the wall, which leads to the particle−wall friction; on the other hand, the particle impinges on the Plexiglas plate at an angle, creating a tangential particle−wall interaction. Figure 4c shows the acoustic signal generated by pneumatic conveying. The peaks around 25 and 90 kHz can be both seen in the PSD of the signal, which means that the pneumatic conveying signal covers the information on particle−wall friction as well as particle− wall collision. According to Jiang’s frequency model,28 the main frequency of the AE signal generated by particle−wall interaction depends on the contact time of particle−wall interaction. To be specific,

(2)

3.2. Wavelet Analysis. Wavelet analysis provides an approach to signal processing, which allows for the representation of a signal simultaneously in time and in frequency. There are two kinds of wavelet analysis: a continuous wavelet transformation and a discrete one. The continuous version is mainly applied as a discontinuous detector in signal and image processing, and it can be also used as a method to extract self-affine or fractal-like features of signals. The discrete wavelet transform is mostly used for applications in denoising and data compression.31 The discrete wavelet transform is based on a pair of digital filters, which decompose the signal into a low frequency component a1 called the approximated signal, and a high frequency component d1 called the detailed signal. The procedure is then repeated using the approximated signal as the input signal. By doing this recursively up to a desired level N, a hierarchical multiresolution representation of a signal x can be obtained as follows:32 x = d1 + d 2 + ... + dN + aN

(3)

where dk contains a detailed signal in the frequency range around [fs/2k+1, fs/2k], in which fs is the sampling frequency. Additionally, the inverse wavelet transform allows for reconstruction of a signal without loss of information. For every level k of the decomposition, a reconstruction signal is computed from the approximated and detailed coefficients. This is somewhat equivalent to band-pass filtering of the original signal with the frequency window [fs/2k+1, fs/2k].

4. RESULTS AND DISCUSSION 4.1. Characteristic of AE Signal Caused by Particle− Wall Collision and Friction. AE signals generated by particle−wall collision and friction were studied by the experimental setups shown in Figure 3a and b, respectively. In the experiment involving particle−wall collisions, one PP particle fell from a certain height and had collisions with the Plexiglas plate. An acoustic sensor attached to the back of the 9940



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Figure 4. Acoustic signals (left) and their PSDs (right) of interaction between PP particles and Plexiglas plate. (a) Particle−wall collision; (b) particle−wall friction; (c) pneumatic conveying.

decomposed into 1−10 of scales detailed signals (d1−d10) and the 10th scale approximated signal (a10) using Daubechies second-order wavelet transform. For the sake of convenience, the 10th scale approximated signal a10 is recorded as d11. The energy fraction distribution (variation of energy fractions of each scale detailed signal with scales) was used to characterize the spectrum structure of the acoustic signal. The frequency ranges of these 11 scales are shown in Table 2. The energy fraction distribution of particle−wall collision and friction signals are shown in Figure 5. It can be seen that the acoustic signal generated by particle−wall collision has the highest energy fraction in the third scale, which means most energy is in a frequency range from 56.25 to 112.50 kHz.

a particle−wall interaction with shorter contact time results in a signal with a higher main frequency. In this work, PP particles impacted with the Plexiglas plate in a very short time, but scraped with the Plexiglas plate for a longer time. Therefore, the main frequency of acoustic signal caused from particle−wall collision is much higher than that of acoustic signal generated by particle−wall friction. 4.1.2. Wavelet Analysis of Acoustic Signals Characteristics. In this part, discrete wavelet analysis is used to quantitatively investigate the characteristics of acoustic signals generated by particle−wall collision and friction. Daubechies second-order wavelet was chosen because this wavelet gives smaller residuals than other wavelets. 18 Therefore, acoustic signals are 9941



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The weighted fraction w represents the energy fraction of acoustic signal generated by particle−wall collision. Thus, this factor has the potential for describing the variation of particle− wall interaction in the pipe when φ changes. However, due to the different operating conditions in the experiments of particle−wall interaction and pneumatic conveying process, the transformation efficiency η from the energy of particle−wall interaction to acoustic energy detected by AE sensor varies from one to another. This may result in errors when the weighted fraction w is used to quantitatively describe the variation of particle−wall interaction. Nevertheless, this method can still provide qualitative information about acoustic sources. From Figure 5, the original signal generated by pneumatic conveying and the reconstructed signal have similar energy fraction distributions, which means they have similar acoustic source characteristics. Figure 6 shows

Table 2. Frequency Ranges of the 10 Scales Wavelet Decomposition Signals scale

f (kHz)

scale

f (kHz)

d1 d2 d3 d4 d5 d6

450.00−225.00 225.00−112.50 112.50−56.25 56.25−28.12 28.12−14.06 14.06−7.03

d7 d8 d9 d10 d11

7.03−3.52 3.52−1.76 1.76−0.88 0.88−0.44 0.44−0

Figure 5. Comparison of energy fraction distributions of acoustic signals. ■, signal of particle−wall collision; red ●, signal of particle− wall friction; blue ▲, original signal of pneumatic conveying; green ▽, reconstructed signal of pneumatic conveying.

According to the experiment results in section 4.2.1, the peak around 90 kHz representing particle−wall collision is included in this frequency range. On the other hand, the acoustic signal generated by particle−wall friction has the highest energy fraction in the fifth scale, which means most energy is in a frequency range from 14.06 to 28.12 kHz. Again, the peak around 25 kHz representing particle−wall friction is included in this frequency range. From these analyses, one can easily conclude that the information on particle−wall collision and friction is contained in the acoustic signal from pneumatic conveying process. 4.2. Methods for Extracting the Information on the Particle−Wall Interaction. 4.2.1. Information Extraction by Signal Reconstruction. To extract useful information on particle−wall interaction, the signal reconstruction method based on particle−wall collision and friction signals has been used in this part. The reconstructed signal can be regarded as the weighted sum of signals generated by collision and friction between particles and wall:

Figure 6. PSDs of reconstructed signal and original signal generated by pneumatic conveying.

the comparison of PSDs of reconstructed signal and original acoustic signals generated in pneumatic conveying process. It can be seen from the figure that the power spectrum distributions of these two signals are very similar. Besides, it should be noted that the acoustic signals of particle−wall collision and friction used for signal reconstruction have been obtained from previous experiments, which are independent of the pneumatic conveying process. Particle−wall collision and friction are the elementary interactions existing in gas−solid two phases flows; thus this method has a potential to be extended to other gas−solid processes such as fluidized beds and spouted beds. 4.2.2. Information Extraction by Signal Decomposition. Another possible way to extract the information is to separate the information on particle−wall collision and friction by using the decomposition of acoustic signal generated by pneumatic conveying. The discrete wavelet transform is a useful tool, because it can decompose signals into different scales, which are related to frequency as presented in Table 2. Moreover, the inverse wavelet transform can be used for signal reconstruction of the needed scales without loss of information. According to Figure 6, the energy of acoustic signal generated by particle−wall collision is mainly in d1−d3 scales, while the energy of acoustic signal generated by particle−wall friction is mainly in d4−d5 scales. Therefore, d1−d3 scales of acoustic signal generated by pneumatic conveying can be combined as reconstructed signal of particle−wall collision, while d4−d5 scales can be combined as reconstructed signal of particle−wall friction via an inverse wavelet transform. The

di ,rec = w × di ,collision + (1 − w) × di ,friction , i = 1, 2, ..., 11

(4)

where di,rec, di,collision, and di,friction are the energy fractions of the ith scale detailed signals of the reconstructed signal, particle− wall collision signal, and friction signal, respectively. The weighted fraction w is obtained when the variation between reconstructed signal and the original signal of pneumatic conveying process is a minimum. The variation V is then calculated as follows: 11

V=

∑ (di ,rec − di ,pneu)2 i=1

(5) 9942



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Figure 7. Reconstructed acoustic signals of particle−wall interaction (left) and their PSDs (right). (a) Particle−wall collision; (b) particle−wall friction.

information can be used for detecting solids loading, and further to detect particle mass flow rate. 4.3. Application of AE Method in Detection of Particle Mass Flow Rate. 4.3.1. Particle−Wall Interaction in Vertical Pneumatic Conveying. Complex particle−particle, particle− wall, and particle−fluid interactions exist in gas−solid twophase flow. These interactions are sensitive to the change in operating conditions, and thus lead to the unstable hydrodynamic behaviors of gas−solid two-phase flow. From the viewpoint of particle−particle interaction mechanism, gas− solid two-phase flow is classified into the following three cases by Tsuji:33 collision free flow, collision dominated flow, and contact dominated flow. For pneumatic conveying processes, when the solid concentration is very low, this process belongs to collision free flow. As the solid concentration increases, collision dominated flow and contact dominated flow start to occur. This kind of classification reflects the underlying mechanism of the change of flow regimes. However, this classification method is difficult to verify through experiments, because the distinction of the different kinds of particle interactions is not easy to realize by experiments in the current stage.27 Fortunately, the particle−particle and particle−wall interactions behaved similarly, and they were of the same nature according to the simulation results of Kuang et al.34,35 Thus, the clarification of Tsuji33 can be achieved by the analysis of particle−wall interaction. Photographs of particle distribution in the pipe recorded by a camera for different solid loading ratios are shown in Figure 8. It can be seen that when the solids loading ratio is very low (φ is 1.26 kg kg−1, Figure 8a), all of the particles are suspended

reconstructed signals of particle−wall collision/friction and their PSDs are shown in Figure 7. On one hand, sharp peaks can be seen clearly in the reconstructed signal that represent particle−wall collision. These peaks are very similar to the peak in Figure 4a, which indicate that they were generated by similar acoustic sources. Moreover, the peaks in Figure 7a are in different amplitudes, because particles impacted with the wall at different velocities. On the other hand, almost no sharp peaks exist in the reconstructed signal representing particle−wall friction, which means that the acoustic signals of particle−wall collision and particle−wall friction are separated completely. Therefore, the energy fraction of acoustic signal generated from particle−wall collision and particle−wall friction can be defined as follows: Dc =

Ecollision = d1 + d 2 + d3 Etotal

(6)

Df =

Efriction = d4 + d5 Etotal

(7)

where Dc and Df are the energy fractions of acoustic signal generated by particle−wall collision and friction. Ecollision, Efriction, and Etotal represent the energy of acoustic signal generated by particle−wall collision, particle−wall friction, and the total energy in pneumatic conveying process, respectively. Also, di represents the energy fraction of the ith scale detailed signal. A method for quantitatively extracting the information on particle−wall collision and friction is now established. This 9943



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Figure 9. Schematic diagram of particle−wall interaction.

vp,t = k p,tUg

(8)

where vp,t and Ug are the tangential velocity of particles in the dispersed phase and superficial gas velocity, and kp,t is the solids/gas velocity ratio, which is dependent on the diameter of the particles. However, the angle of particles interacting with the pipe wall varies due to the complex particle−particle collisions. It is supposed that αj and xj are the particle−wall impact angle and the percentage of particles impacting on the wall at this angle. Thus, the particle velocity perpendicular to the pipe wall is

Figure 8. Particle distribution in the pipe with different solids loading ratio (φ: (a) 1.26 kg kg−1; (b) 3.12 kg kg−1; (c) 5.13 kg kg−1; (d) 7.48 kg kg−1; (e) 10.17 kg kg−1).

uniformly and the particles collide with each other freely. As a result, the particle velocity component perpendicular to the wall is relatively large at this moment, and particle−wall collision is the primary source of particle−wall interaction. As φ increased (Figure 8b−d), the distance between particles became shorter, which leads to an increase of the interparticles collision frequency. The particle velocity component perpendicular to the wall decreases due to the energy loss within each collision, and thus the possibility of particle−wall collisions is decreased. Nevertheless, the solid concentration is not that high, and thus the particles are still dispersed in the flow field. When solids loading ratio becomes higher (Figure 8e), nonuniform particles distribution occurs and clusters form. At this time, particle motion is limited by the surrounding particles, and most of these particles are conveyed along the vertical direction, which is tangential to the wall. Therefore, the possibility of particle− wall friction is increased as φ increases. On the basis of these observations, a conclusion can be drawn; that is, the main type of particle−wall interaction changes from particle−wall collision to particle−wall friction as φ increases. That is to say, when φ increases, the possibility of particle−wall friction increases while particle−wall collision decreases. 4.3.2. AE Model of Particle−Wall Interaction. From the physical image in Figure 8 and the schematic diagram in Figure 9, there are two distinct particle phases that exist in the flow field. One is the dispersed phase in which solid particles are individually presented, while the other is the cluster phase in which the particles act as clusters. Particles in the form of dispersed phase and cluster phase behave different from each other. To be specific, particles in the dispersed phase impact with the wall at an angle, while particles in the cluster phase cause friction with the wall. The following assumptions have been made in this theory model: (1) Particles in the dispersed phase have the same vertical velocity along the pipe, which is given as36

vp,n, j = vp,t tan αj , j = 1, 2, 3, ...n

(9) 37

According to the experimental results of Afsahi et al., it is assumed that the velocity of clusters is proportional to Ug:

vc = kcUg

(10)

(2) Particle concentrations in the dispersed phase and in the cluster phase can be obtained as follows:38

Cp = εgC total

(11)

Cc = (1 − εg)C total

(12)

where Cp, Cc, and Ctotal represent the solid concentration of dispersed phase, cluster phase, and both phases, respectively, and εg is the void fraction. It can be obtained that Cp→Ctotal when εg→1, which indicates that all particles are suspended uniformly. On the other hand, it can be obtained that Cc→Ctotal when εg→0, which indicates that all particles keep in contact with each other and form a large slug. Thus, this assumption is in agreement with the physical phenomena. A pipe section of surface area A was taken into consideration. The valid interaction area of particles as cluster phase and as dispersed phase interacting with wall then can be obtained as follows: Sp = εgA

(13)

Sc = (1 − εg)A

(14)

(3) The normal force that clusters act on the pipe wall is needed to calculate the friction force between clusters and pipe wall. It is assumed that the normal force is generated from the surrounding particles impact with the surface of clusters. To be specific, the force is equal to the normal force that is produced 9944



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4.3.2.1.b. Particle−Wall Friction. For n identical particles (with same diameter dp, mass m, and particle−wall impact angle αj) scraping with an area ΔA of the pipe wall with the normal velocity of vp,n,j, the resulted frictional force Fp,t,j(t) is given by

by dispersed particles impacting on the wall within the same surface area of clusters. 4.3.2.1. Particle−Wall Interactions in Dispersed Phase. 4.3.2.1.a. Particle−Wall Collision. For n identical particles (with same diameter dp, mass m, and particle−wall impact angle αj) impacting on area ΔA of the pipe wall with a normal velocity of vp,n,j, the resultant normal force Fp,n,j(t) is given by Cody et al.:12

⟨Fp,t, j⟩ = μ⟨Fp,n, j⟩ = 2μmvp,n, jfp, j

where μ is the friction factor between particle and wall. Similarly, acoustic energy generated by particle−wall friction in a time interval t can be derived as follows:

m

Fp,n, j(t ) =

∑ 2mvp,n,jδ(t − ti)

n

(15)

i=1

(21)

2 Ep,friction = 2μηtmvp,tCpSp ∑ vp,n, jxj

where δ(t) is a Dirac delta function of t, ti is the arrival time of the ith particle on the wall, and vp,n,j is the normal velocity of particles impacting on the wall for the ith particle. Let f p,j denote the average arrival frequency of the particles on the area ΔA, then the number of collisions is f p,j·T in the time interval T. Hence, the mean force of particles in unit time can be written as

(22)

j=1

4.3.2.2. Particle−Wall Interactions in Cluster Phase. According to assumption (3), dispersed particles impact on the clusters and generate the normal force. Thus, it can be obtained that

Nc, j = 2mvp,n, jfp,c, j

(23)

fp,c, j = xjCpScvp,n, j

(24)

T

⟨Fp,n, j(t )⟩ =

∫0 Fp,n, j(t ) dt T T

=

where Nc,j is the normal force generated by particles with an impact angle of αj in dispersed phase, Sc is the valid interaction area between clusters phase and pipe wall, and f p,c,j is the average arrival frequency of the particles on Sc. The frictional force Fc generated by the cluster−wall friction then is given by

m

2mvp,n, j ∫ ∑i = 1 δ(t − ti) dt 0

T

= 2mvp,n, jfp, j

(16)

The average arrival frequency of the particles on the area ΔA can be obtained as follows: fp, j = xjCpΔAvp,n, j

n j=1

(17)

η⟨F(t )⟩ = ΔA

n 2 Ec,friction = 2μηtmvcCpSc ∑ vp,n, jxj

In this model, suspended particles interact with the pipe wall in the normal direction and tangential direction, and cause particle−wall collision and friction, respectively, while particles in the cluster phase cause only friction with the wall. Thus, the total acoustic energy of particle−wall collision and friction can be obtained from eqs 20, 22, and 26 as follows:

(18)

Thus, acoustic flux in unit time can be expressed as follows: n

Jn =

n

n

3 ∑ Jn,j = ∑ pn,j ΔAvp,n,j = 2ηmCpΔA ∑ vp,n, jxj j=1

j=1

n 3 Ecollision = Ep,collision = 2ηtmCpSp ∑ vp,n, jxj

j=1

(19)

∫0

Efriction = Ep,friction + Ec,friction n 2 = 2μηtmCp(vp,tSp + vcSc) ∑ vp,n, jxj

Furthermore, the energy fraction of particle−wall collision and friction can be obtained as follows:

Jn dt

∫0 ∫0

Sp

(28)

j=1

t

t

=

(27)

j=1

where Jn,j and Jn are the acoustic flux for the particles in dispersed phase impacting on the wall at an angle of αj and at any angle, respectively. The acoustic energy of particles in the dispersed phase impacting on the pipe wall in a time interval t then can be integrated from acoustic flux: Ep,collision =

(26)

j=1

2ηmvp,n, jfp, j ΔA

(25)

j=1

Similarly, for the cluster phase, acoustic energy of particle− wall friction in a time interval t is given by

where xj is the percentage of particles impacting on the wall at an angle of αj, and Cp is the solid concentration of the dispersed phase. The acoustic pressure pn,j can be estimated using ⟨Fp,n,j(t)⟩ and ΔA with the transformation efficiency from the collision pressure to acoustic pressure detected by AE sensor of η:29 pn, j =

n

2 Fc = μNc = μ ∑ Nc, j = 2μmCpSc ∑ vp,n, jxj

n 3 2ηmCp ∑ vp,n, jxj dA dt

Dc =

j=1 n

((

) ) (29)

3 = 2ηtmCpSp ∑ vp,n, jxj j=1

Ecollision 1 = Ecollision + Efriction a + b′ × 1 − εg /εg

where a = 1 + μ∑j n= 1 tan2 ajxj/∑j n= 1 tan3 ajxj, b′ = μkc∑j n= 1 tan2 ajxj/kp,t∑j n= 1 tan3 ajxj. For dilute phase pneumatic conveying, it can be obtained that εg→1 and Vg/Vp→∞, thus:

(20)

where Sp is the valid interaction area of dispersed particles impacting with the wall. 9945



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Figure 10. Variation of Dc and Df with (a) superficial gas velocity and (b) solids loading ratio (φ).

εg ≈ 1 −

Vp Vg

=1−ϕ×

ρg ρp

The application range of eq 35 is dilute-phase pneumatic conveying, in which the solids loading ratio varied from 1.26 to 13.30 kg kg−1. Comparison between predicted mass flow rate and the actual value is shown in Figure 11. It can be seen that the predicted value fits the actual one well with an average error of 3.78%, and the maximum relative error is 6.62%.

(30)

where φ is the solids loading ratio, kg kg−1. Substitution of eq 30 into eq 29 gives that Dc =

1 a + bϕ

(31)

where b = b′ρg/ρp. Thus, the energy fraction of particle−wall collision and friction can be obtained as follows: Df = 1 − Dc = 1 −

1 a + bϕ

(32)

4.3.3. Detection of Particle Mass Flow Rate. It can be inferred from eqs 31 and 32 that φ is the only factor that influences Dc and Df. Dc decreases with φ while Df increases. As discussed above, void fraction of the pipe decreases and particles tend to aggregate and form clusters when φ increases. Particles in the clusters are prone to have friction and have less chance to impact with the wall. Therefore, Dc decreases and Df increases. In this part, experiments are illustrated to validate this result. Figure 10a and b shows the variation of Dc and Df with increased superficial gas velocity and φ, respectively. It can be seen that Dc and Df remain unchanged when the gas velocity increases from 9 to 13 m s−1, while Dc and Df show significant variation when φ increases from 2.24 to 12.57 kg kg−1, which fits well with the model. Furthermore, it can be seen that Dc is much larger than Df, which means that the current flow regime in this experiment belongs to particle−wall collision dominant flow. The predictive equations from Figure 10b are obtained: Dc =

1 1.18 + 0.014ϕ

Df = 1 −

1 1.18 + 0.014ϕ

Figure 11. Comparison between predicted values and actual values of mass flow rate.

5. CONCLUSIONS In this work, the concepts of particle−wall collision and friction have been introduced into the analysis of AE signals to present a better understanding of the underlying mechanism of signal generation. Moreover, on the basis of these analyses, a theoretical model for quantitatively describing the relationship between AE signals and φ has been proposed in addition to a model for detecting the particle mass flow rate. The main results of the present work can be summarized as follows: (1) Considering particle−wall collision and friction, a general procedure for acoustic signal analysis has been established. First, physical experiments and mathematical analysis of acoustic signals were used to obtain the characteristic frequency band generated from particle−wall collision and friction qualitatively. It has been found that the main frequency of acoustic signal caused from particle−wall collision is much higher than that generated by particle−wall friction. Besides, energy fraction of 1−3 and 4−5 level detailed AE signals represents particle−wall collision and friction, respectively, in the current work. Thus, these analyses have been used to

(33)

(34)

According to the definition of φ, the particle mass flow rate can be obtained: ⎛ d ⎞2 (1/Dc − 1.18) ms = mg ϕ = Ugπ ⎜ ⎟ ρg ⎝2⎠ 0.014

(35) 9946



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di,pneu = energy fraction of the ith scale detailed signal of pneumatic conveying Dc = energy fraction of acoustic signal generated by particle− wall collision Df = energy fraction of acoustic signal generated by particle− wall friction Ecollision = energy of acoustic signal generated by particle− wall collision, V2 Efriction = energy of acoustic signal generated by particle−wall friction, V2 Etotal = energy of acoustic signal generated in pneumatic conveying, V2 f p = frequency of particles impact to the wall, s−1 fs = sampling frequency, kHz J = AE energy flux, V2 s−1 kc = ratio of cluster velocity to superficial gas velocity kp,t = ratio of tangential particle velocity to superficial gas velocity m = particle mass, kg mg = mass flow rate of gas, kg s−1 ms = mass flow rate of solids, kg s−1 p = acoustic pressure, Pa Sc = surface area of cluster phase, m2 Sp = surface area of dispersed phase, m2 t = sampling time of AE, s Ug = superficial gas velocity, m s−1 V = variation between reconstructed signal and the acoustic signal of pneumatic conveying vc = velocity of particles in cluster phase, m s−1 vp,n = normal velocity of particles in dispersed phase, m s−1 vp,t = tangential velocity of particles in dispersed phase, m s−1 w = weight fraction of particle−wall collision signal x = acoustic signal X = power spectrum density of acoustic signal X′ = normalized power spectrum density

quantitatively extract information involving particle−wall collision and friction. (2) A theoretical model, based on particle−wall collision/ friction, has been established to quantitatively describe the variation of acoustic energy fraction with φ. Two distinct particle phases, in the forms of dispersed particles and clusters, have been taken into consideration in this model. Particles in the suspended phase interact with the pipe wall in the normal and tangential directions, and thus cause particle−wall collision and friction, respectively, while particles in the cluster phase cause only friction with the wall. From the theoretical model, the superficial gas velocity is found to have no effect on the energy fraction at different frequencies, as opposed to the solids loading ratio, which has been found to exert a significant effect. Moreover, the model prediction has been verified with experimental data and is in good agreement. The model has been used to obtain φ and particle mass flow rate in vertical pneumatic conveying, and the maximum relative error is 6.62%. It should be pointed out that our studies focused on the dilute-phase pneumatic conveying process. The underlying mechanisms of particle−wall interaction in dense-phase pneumatic conveying and fluidization are more complicated and have not been considered yet. However, the basic interaction between particles and the surrounding environment is the same. Thus, this method holds a great potential for applications in dense-phase pneumatic conveying and other particulate processes.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS It is a pleasure to acknowledge the following scientists and students at Zhejiang University, Zheng Haijun and Gu Yubin. This work could not have been accomplished without their assistance. We acknowledge the support and encouragement of the National Natural Science Foundation of China (21236007), the National Basic Research Program of China (2012CB720500), Zhejiang Province Natural Science Foundation of China (LQ13B060002), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (20110101120020).

Greek Letters

α = particle−wall impact angle, deg εg = void fraction εp = particle concentration η = transformation efficiency μ = friction factor between particle and wall φ = solids loading ratio

Abbreviations

■

NOMENCLATURE a, b = model parameters ai = ith scale approximation signal A = surface area of pipe wall, m2 Cc = particle number concentration of cluster phase, number m−3 Cp = particle number concentration of dispersed phase, number m−3 Ctotal = total particle number concentration, number m−3 di = ith scale detailed signal di,rec = energy fraction of the ith scale detailed signal of reconstruct signal di,collision = energy fraction of the ith scale detailed signal of particle−wall collision di,friction = energy fraction of the ith scale detailed signal of particle−wall friction

■

AE = acoustic emission PLS-R = partial least squares regression PP = polyethylene PSD = power spectral density RMS = root-mean-square

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