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Acoustic analysis of particle-wall interactions of plug flow in vertical pneumatic conveying
Chemical Engineering Science 211 (2020) 115260
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Acoustic analysis of particle-wall interactions of plug flow in vertical pneumatic conveying Yao Yang a, Peng Zhang a, Lelu He a, Jingyuan Sun a,⇑, Zhengliang Huang a, Jingdai Wang b, Yongrong Yang b a Zhejiang Provincial Key Laboratory of Advanced Chemical Engineering Manufacture Technology, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, PR China b State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, PR China
h i g h l i g h t s Unsteady flow was identified by pressure drop and acoustic emission detection. Pressure drop for vertical pneumatic conveying was well predicted using active Kw. The established acoustic model supports a potential online measurement for Kw.
a r t i c l e
i n f o
Article history: Received 22 May 2019 Received in revised form 26 September 2019 Accepted 30 September 2019 Available online 11 October 2019 Keywords: Plug flow Unsteady flow Particle-wall interactions Acoustic emission Pressure drop
a b s t r a c t The plug flow was investigated in both the single plug and the continuous plug experiments. In the single plug flow, the pressure drop might rise for two times with a longer plug, and the second increase was proved to be caused by the collision between the falling particles and the plug by acoustic emission detection. In continuous plug flow, the interaction between the bulk of the plug and the pipe wall was dominated by the friction. And the sources of acoustic signals in continuous plug flow can be mainly divided into two parts: the collision between the falling particles and the plug and the friction between the bulk of plug and the wall. Based on this, the acoustic model was derived and the energy fraction can be predicted accurately. And the model further provides a possibility for the non-intrusive, real-time and online detection of Janssen coefficient. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Compared to the dilute-phase pneumatic conveying, densephase operation has the advantages of lower energy cost and reduced erosion of the transported materials because of lower gas velocity (Klinzing et al., 2010). Thus, the dense-phase pneumatic conveying has received more attention and it has been widely applied in many industrial processes such as conveying of pulverized coal in the pulverized coal gasification process (Cong et al., 2013; Pu et al., 2010). However, unsteady plug flow usually occurs due to uneven distribution of solid materials in the conveying pipe, which brings about large pressure fluctuations and results in the increasing risk of blockage (Qiu et al., 2019; Sun et al., 2019; Wypych and Yi, 2003). Therefore, a detailed understanding of the hydrodynamics in plug flow pneumatic conveying is essential for ⇑ Corresponding author. E-mail address: [email protected] (J. Sun). https://doi.org/10.1016/j.ces.2019.115260 0009-2509/Ó 2019 Elsevier Ltd. All rights reserved.
the design, optimization and operation of the dense-phase pneumatic conveying systems. Plug flow is a kind of typical unsteady flow (Konrad et al., 1980; Levy, 2000). Especially in the vertical pneumatic conveying process, when the solid-gas ratio (particle concentration) is high, the flow regime will change from suspension flow to plug flow directly, resulting in sharp increase of pressure drop. In addition, due to the existence of gravity in the vertical direction, the plug is easy to decompose, then induces large fluctuation of pressure drop. And the shape, number, length and velocity of the plug vary in time and space. For example, Daoud et al. (1993) found that for a certain solids flow rate, the plug length decreased as the increase of gas velocity and increased as the increase of conveying distance. Mason et al. (1991) convinced their results and pointed out that a long gap existed between two short pressure waves, indicating that the plugs were decomposed as the increase of conveying distance. Levy et al. (2000) found that the plug shape and length varied along the conveying direction based on numerical modeling
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method. Li et al. (2013) found that the increase of friction factor would lead to the increase of plug length and the decrease of plug velocity. For predicting the pressure drop of plug flow, one of the most precise models is the force balance model developed by Konrad (1987). The accuracy of this model depends on the Janssen coefficients at the wall, which equals to the radial stress at the wall divided by the axial stress. Therefore, numerous experimental set-ups and detection methods were used to measure the particle-wall stresses during the pneumatic conveying process. Roberts et al. (1966), Roberts and Jones (2003) studied the forces needed for transporting a plug for the first time. They used pistons to simulate the plug transportation in a vertical pipe with a diameter of 46 mm and measured the forces needed. Besides, they compared the forces needed for transporting an aerated plug and an un-aerated plug, the results showed that aeration reduced the force needed. Rabinovich et al. (2012) used several kinds of particles to repeat Roberts’s experiment. They found that the particle size had no effects on particle-wall friction force while plug length had a big influence on that force. Though they had used aeration to simulate the real transport of plugs, the plugs investigated in these studies were different from that in real plug flow. In order to overcome these problems, Vasquez et al. (2003) mounted three stress sensors in the external wall of a horizontal pipe for the online measurement of particle-wall friction force. They found that the axial stress and radical stress acting on the plugs increased as the increase of plug length, and the radical stress increased as the increase of gas velocity. Pahk et al. (2012) further investigated the influence of particle shape, particle size, particle type and plug length on particle-wall interactions, and compared the stress in different positions of the conveying pipe. They found that the friction forces at the top and side were larger than that in the bottom. Based on these analyses, they (Pahk et al., 2013) extended their measurement system to the investigation of industrial pneumatic conveying systems and convinced the above results. However, particle-wall interactions in the plug flow of vertical conveying process and their influence on pressure drop has not been studied in the literatures. What’s worse, although the Janssen coefficient is regarded as an important parameter for the prediction of pressure drop, the related method to measure it is scanty. Acoustic emission (AE) signals, induced by frequent particleparticle and particle-wall contacts, are very sensitive to the particle motions in gas-solid two phase systems (He et al., 2009). Furthermore, we have found that the original acoustic signals can be divided into two parts by wavelet decomposition and they stand for particle-wall collision and particle-wall friction, respectively (He et al., 2014; He et al., 2016). Therefore, the acoustic emission detection has been proved to be an efficient way in investigating the particle-wall interactions and particle motions in the gassolid fluidized bed and in the pneumatic conveying process (Dong et al., 2015; Jiang et al., 2007; Wang et al., 2010). Based on all above, this work aims at investigating the plug flow in vertical pneumatic conveying by acoustic analysis of particlewall interactions. Firstly, the influence of particle-wall interactions on the stability of the transported single plug was investigated. Secondly, the influence of particle-wall interactions on the stability of continuous plug flow was also studied. In the end, a new AE energy model for plug flow was established based on the particle-wall interaction analysis of plug flow, and the energy fraction predicted by the model fitted well with the experimental values. Moreover, based on this energy model, a new method for the measurement of Janssen coefficient was developed, which was of value importance for the prediction of pressure loss in the plug flow.
2. Experiments 2.1. Materials and procedure A schematic diagram of the vertical pneumatic conveying system is shown in Fig. 1. The conveying pipe consists with a horizontal Plexiglas pipe (1.2 m in length, 25 mm in inner diameter (I.D.) and the thickness of the pipe is 2 mm) at the bottom, and the main testing section of a vertical Plexiglas pipe (3.0 m in length, 25 mm in I.D. and the thickness of the pipe is 2 mm). In aforementioned investigations (e.g. Roberts et al. (1966), Roberts and Jones (2003)), they used the conveying pipe with the inner diameter of 46 mm, but during the experiments we found that a larger inner diameter would induce more fluctuations and the single plug was very hard to be generated. Therefore, the conveying pipe with an inner diameter of 25 mm was used. Each time when experiments related to the single plug involved, the gas flow rate was set at a certain value before the experiment, then bypass valve (valve 4) was closed to make gas bypass. Polypropylene (PP) particles were added in the horizontal pipe to form a single plug with a certain length. Then valve 4 was opened to transport the plug into vertical pipe. When all the signals were sampled, particles retained in the pipe were collected and above procedures were repeated for another run which meant particles were re-added to the horizontal pipe and formed a new plug. In the experiments, the superficial gas velocity ranged from 6.0 to 12.0 m s1 and the plug length ranged from 100 to 300 mm. The physical properties of PP particles are summarized in Table 1. The PP particles were sieved with mean diameter of 1500.0 lm and have a narrow size distribution. This set-up can also be used to do the experiments with real plug flow. At that time, the feeding vessel was involved and pre-addition of plug in the horizontal pipe was not necessary. 2.2. Measurement devices The pressure drops DP1 and DP2 were measured by the pressure sensors as shown in Fig. 1, the distances between each two couples of pressure sensors were 1.2 m and 0.05 m, respectively. According to the Shannon sampling theorem, the sampling frequency should be greater than 2 times of the highest frequency in the signal, so as to ensure that the sampled digital signal can retain the complete information. Therefore, 400 Hz is selected as the sampling frequency. The sampling time is determined according to the specific experimental conditions. Under the experimental conditions of this work, the time for a single plug to pass the pressure detection section does not exceed 10 s, so this paper selects 10 s as the sampling time. The online AE system for collection and analysis developed by UNILAB Research Center of Chemical Engineering in Zhejiang University (Yang et al., 2004) includes 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 corporation). The output of acoustic sensor is electrical signals whose unit is V. The software used is the Labview. Therefore, in combination with the calculation method of acoustic energy (which will be introduced in the next part), the unit of acoustic energy is V2. Besides, the AE sensor was mounted on the outer surface of the vertical pipe with a couple of rubber rings to isolate the noises, and the installation location was 1.2 m above the elbow bend at the bottom. The sampling frequency was chosen as 900 kHz on basis of Shannon sampling theorem, and the sampling time was 10 s. Besides of above methods, the high-speed camera (PHOTRON FASTCAM Mini WX100) was also used in this work to acquire the conveying
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Fig. 1. Schematic diagram of the vertical plug conveying system. 1 – Air compressor, 2 – Buffer tank, 3 – Gas flow meter, 4 – Ball valve, 5 – Pressure sensor, 6 – Acoustic sensor, 7 – Preamplifier, 8 – Main amplifier, 9 – A/D conversion module, 10 – Computer, 11 – Rubber, 12 – Receiving Vessel, 13 – Feeding Vessel.
Table 1 Physical properties of PP particles. Material
Mean diameter (lm)
Density (kg m3)
Pan’s classification (1999)
Terminal velocity (m s1)
Void fraction
PP
1500.0
900
PC2
5.6
0.5
pictures and based on the images analysis software the plug velocity and particle velocity could be calculated.
published references (Dong et al., 2015; Kuang et al., 2008; He et al., 2016; He et al., 2009).
3. Data processing methods
4. Results and discussion
Power spectrum density (PSD) analysis and wavelet transform were the main signal processing methods used in this work. The former one is a frequency-domain analysis method which has proved to be an efficient way in dealing with acoustic signals. And the ordinate of the power spectrum is the acoustic energy at each frequency. Then the acoustic energy at each frequency is summed, the acoustic energy is obtained. While the latter one provides an approach which can represent a signal simultaneously in time and in frequency. Using the wavelet transform, the acoustic signals can be subjected to 10 scales. And the energy fractions of the 1–3 scales are the energy fraction of collision, the energy fractions of the 4–5 scales are the energy fraction of friction. Base on this, the average impact angle (the angle between the contact direction of the particle-wall and the vertical direction) can be calculated. Details of these two methods can be found in numerous
4.1. Unsteady flow in single plug conveying experiments 4.1.1. Variation of pressure drop Fig. 2 shows the variation of pressure drop with time when a single plug was transported across the detection section. Obviously, six stages can be seen in the figure. The first stage was 3.00–3.35 s. During this stage the pressure drop increased slowly because the particles in the front of the plug entered the detection section. In the second stage (3.35–3.38 s), the pressure drop increased sharply due to the entrance of the bulk of the plug. In the third stage (3.38–3.63 s), the pressure drop stayed approximately unchanged at a high value, which meant that the plug was transported across the detection section. Then in the fourth stage (3.63–3.70 s), the pressure drop decreased sharply due to the plug left the detection section. In the fifth stage (3.70–4.20 s),
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Fig. 2. Variation of the pressure drop with time (Lini: initial plug length-10 cm, Ug: gas velocity-10 m/s).
the slowly decrease of pressure drop resulted from the fact that particles in the wake of plug were leaving the detection section. At last, all the particles left the detection section and thus the pressure drop remained unchanged. Fig. 3 shows the variation of pressure drop with time when plugs with different lengths were transported at various superficial gas velocities. It can be seen that when the plug length was small, pressure drop increased as the increase of gas velocity. No plug breakages were seen in the experiments and thus the figures were similar as Fig. 2. However, when plug length was large, second increase of pressure drop can be seen in Fig. 3(b) and their amplitudes were even half of the first increase. During the experiments, plug breakages were observed under these conditions. After the breakages, the void age increased, which further led to the decrease of local gas velocity as well as the gas-solid drag forces. This would result in the falling of particles in the wake of the plug. When the falling particles had collisions with the plugs moving upwards, extra energy loss appeared and thus the pressure drop increased at second time. These phenomena were in accordance with results of Konrad et al. (1989). The second increase of pressure drop would lead to large fluctuations of pressure drop and increase the risk of pipe blockage. Therefore, in the following sections, the second increase of pressure drop is recorded as unstable flow while the others are recorded as stable flow.
4.1.2. Variation of local pressure drop and acoustic energy Fig. 4 shows the variation of DP1, DP2 and acoustic energy with time for stable conveying. The pipe pressure drop DP1 can be used to identify the change of particle concentration in the whole detection section roughly while the local pressure drop DP2 can be used to identify the change of local particle concentration roughly. It can be seen in the figures that DP2 increased sharply when plug went across the lower sensor, and decreased sharply when plug left it. What’s more, the variation of acoustic energy agrees well with DP2. The variations of DP1, DP2 and acoustic energy with time for unstable conveying was shown in Fig. 5. It can be seen that when pipe pressure drop DP1 increased at second time, local pressure drop DP2 increased at the same time. Besides, the negative value of DP2 can be seen in the figures, indicating that pressure waves were propagated downwards. These negative pressure drops were caused by the collisions between the falling particles and the plugs. Meanwhile, the acoustic energy increased at the same time, which means that these collisions can be detected by acoustic signals. The increasing gas velocity causes the increase of particle motions and the particle-wall interactions, resulting in an increase of pressure drop as well as the acoustic signals.
4.1.3. Variations of particle motions Fig. 6 shows the variation of acoustic energy and energy fraction of particle-wall interactions (He et al., 2014) with time for stable conveying and unstable conveying. For the stable conveying processes, as shown in Fig. 6(a), energy fraction of particle-wall collision increased while energy fractions of particle-wall friction decreased before the increase of acoustic energy, which meant that before the bulk of the plug entered the detection section, particles in the front of plug mainly collided with the pipe wall (the first stage in Fig. 2) due to the large local void age in the front of plug. When the plug went across the detection section, energy fraction of particle-wall collision decreased and energy fraction of particle-wall friction increased, resulting in friction domain flow (the 2–4 stages in Fig. 2). For the unstable flow, as shown in Fig. 6(b), the variations of energy fractions of particle-wall collision and friction were similar as those in the stable flow before the bulk of the plug entered the detection section. However, when the pressure drop was increased at second time, particle-wall collision energy fraction increased and friction energy fraction decreased. It resulted in collision domain flow again, which meant that the collisions between falling particles and plug were the main reason for the increase of pressure drop at second time. Moreover, results in Fig. 6 also show that the variation of particle-wall interaction appears prior to the variations of pressure drop and acoustic energy, thus measurement of particle-wall interaction can be a better way for measurement of flow regime transition. Fig. 7 shows the variation of particle-wall impact angles with time under different conditions. For the stable conveying processes, as shown in Fig. 7(a), particle-wall impact angle increased when particles in the front of the plug arrived at the lower sensor. For the unstable conveying processes, as shown in Fig. 7(b), the particle-wall impact angle also increased when particles in the front of the plug arrived at the lower sensor. After that, the particle-wall impact angle increased largely when the pressure drop increased at second time, and the amplitude was larger than that of the first time, which resulted from the fact that collisions at second time were more violently. 4.2. Unsteady flow in real continuous plug flow 4.2.1. Particle motions in plug flow Previous results are obtained from experiments with a single plug, are they in accordance with the real industrial process with continuous plugs? Fig. 8 shows the variation of pressure drop and acoustic energy with time for plug flow (experimental conditions: gas velocity 5.5 m/s, solid flow rate 0.007 kg/s, plug length 14 cm). In this part, L is the length of the measurement section,
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Fig. 3. Variation of pressure drop with time when plugs with different lengths were transported at various superficial gas velocities. (a) Lini: initial plug length – 10 cm, (b) Lini: initial plug length – 25 cm.
which is 1.2 m. DP is the pressure drop in the measurement section and the sampling time is 120 s. Continuous plug flow is unstable and more than 20 plugs passes through the measurement section during the sampling time. It can be seen that the pressure drop increased firstly and then decreased during 0 to 0.75 s which meant a plug was transported through the detection section. But compared with Fig. 2, the fluctuation of pressure drop in real plug flow was not completely the same to that in the single plug experiments, which might be caused by the interaction between two adjacent plugs. But the figure also showed that the pressure drop increased when the plug moving in and decreased when moving out. Besides, during the experiments we observed that when the
plug arrived at the acoustic emission sensor, the fluctuation of acoustic energy was observed, as the sharp increase of acoustic energy at about 0.25 s in Fig. 8. Fig. 9 shows the variation of acoustic energy and energy fraction of particle-wall interactions with time for plug flow. It can be seen that, particle-wall collision energy fraction increased and friction energy fractions decreased before the increase of acoustic energy. Fig. 10 shows the variation of acoustic energy and average impact angle with time for plug flow. It can be seen that the particles in the front of plug collide with the pipe wall and resulted in the increase of impact angle. As the plug went through the pipe, particle-wall interactions were domain by particle-wall friction
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dP dra 4sw þ þ þ qb g ¼ 0 dx dx D
ð1Þ
where P is the pressure drop, ra is the axial stress, and sw is the shear stress of the wall. For the stable flow, Konrad (1987) proposed an equation to calculate normal stress ra as follows.
ra ¼
bqs ð1 ebulk Þðv plug v p;t Þ2 ð1 ebulk bÞ
ð2Þ
where ebulk is the void fraction of loose packed solids, vp,t and vplug are the velocities of falling particles and plug respectively measured by images processing, b is the volume fraction of particles between plugs, which can be estimated by the following equation (Richardson, 1954).
U g þ v plug v p;t ¼ ð1 bÞ2:4 v t
ð3Þ
where vt is the particle terminal velocity, Ug is the superficial gas velocity. In Eq. (1), the shear stress of the wall sw can be calculated as Eq. (4).
sw ¼ lK w ra þ cw
Fig. 4. Variation of DP1, DP2 and acoustic energy with time for stable conveying. (a) Ug: gas velocity – 6 m/s, Lini: initial plug length – 10 cm, (b) Ug: gas velocity 10 m/s, Lini: initial plug length – 10 cm.
ð4Þ
where cw is the cohesive force, for PP particles used in this work it equals to 0, l is the friction coefficient, and Kw is the Janssen coefficient. The Janssen coefficient can be divided into the active one and the passive one according to impact angle. According to E and Wang (2010), Kw_active and Kw_passive are 0.271 and 3.69 respectively for PP particles. Based on Eqs. (1)–(4), the variations of actual value and predicted value of pressure drop with axial stress are calculated and shown in Fig. 11. It can be seen that the predicted value using active Janssen coefficient fit with experiment results very well, indicating that under the experimental conditions of this work, the axial wall stress was larger than the normal stress which was convinced with the results of Roberts and Jones (2003). 4.3. Acoustic model of particle-wall interaction for plug flow
Fig. 5. Variations of DP1, DP2 and acoustic energy with time for unstable conveying. (a) Ug: gas velocity – 6 m/s, Lini: initial plug length – 25 cm, (b) Ug: gas velocity – 10 m/s, Lini: initial plug length – 25 cm.
and resulted in the decrease of impact angle. As the plug left the pipe, particle-wall impact angle remained small. These results were similar as that of single plug experiments, indicating that the acoustic methods could also be used for the detection of particle motions in plug flow. 4.2.2. Prediction of pressure drop for continuous plug flow Konrad et al. (1980, 1989) developed a pressure drop prediction model for plug flow based on force balance analysis, which can be expressed as Eq. (1).
Above results have shown that the acoustic energy and energy fraction are related to particle motions and particle-wall interaction in the plug, but the quantitative relationship between them is confused. In this part, the forces on particles and the plug will be analyzed to establish the acoustic model which describing the plug flow. For the plug flow in vertical pipe (see Fig. 12), there are two distinct particle phases that co-exist in the flow field. One is the dispersed particle phase mainly existing between two adjacent plugs, which will fall down and collide with the lower plug. The others are particles existing inside the bulk of the plug and moving upwards. The behaviors of particles in different forms differ from each other. To be specific, particles in the dispersed phase may impact with the wall at an angle and particle-wall collision is enhanced, while particles in the plug phase will mainly rub with the wall as a whole. What’s more, in the above sections, we have found that the collisions between particles and the plug had the most important influence on the pressure drop of gassolid two phase flow in the plug flow. Therefore, the following assumptions have been made before establishing the theory model: (1) Based on the images analysis, we found that the plug velocity increased as the increase of plug length and solids mass flow rates have little influences on it. Thus, the plug velocity was assumed as:
v plug ¼ kplug Lplug
ð5Þ
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Fig. 6. Variation of acoustic energy and energy fraction of particle-wall interactions with time. (a) stable conveying, Ug: gas velocity – 6 m/s, Lini: initial plug length – 10 cm, (b) unstable conveying, Ug: gas velocity – 6 m/s, Lini: initial plug length – 25 cm.
Fig. 7. Variation of acoustic energy and average impact angle with time. (a) Ug: gas velocity – 6 m/s, Lini: initial plug length – 10 cm, (b) Ug: gas velocity – 6 m/s, Lini: initial plug length – 25 cm.
Fig. 8. Variation of pressure drop and acoustic energy with time in real plug flow (Ug: gas velocity – 5.5 m/s, solid flow rate – 0.007 kg/s, Lplug: plug length – 14 cm).
Meanwhile, Daoud et al. (1993) found that the plug length decreased as the increase of gas velocity under a certain solids mass flow rate. Thus, the plug length was assumed as:
Fig. 9. Variation of acoustic energy and energy fraction of particle-wall interactions with time.
ð6Þ
From Eq. (7), the plug velocity will decrease as the increase of gas velocity under a certain solids mass flow rate, which is convinced with our former results.
where ms and mg is the mass flow rate of solid phase and gas phase respectively, and a is the model factor. Combining Eqs. (5) and (6), we have
(2) Particles in the dispersed phase have the uniform axial velocity, which can be estimated by the following equation (Eq. (8) is the transformation of Eq. (3)).
Lplug
ms ¼a mg
v plug ¼ akplug
ms mg
ð7Þ
v p;t ¼ Ug þ v plug ð1 bÞ2:4 v t
ð8Þ
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However, the angle of particles interacting with the pipe wall differs from one another due to the complex particle-particle collisions. It is supposed that the particles are divided into n categories according to the different particle-wall impact angles, aj and xj are the particle-wall impact angle of the j-th category particles and the percentage of particles impacting on the wall at this angle. Thus, the particle velocity perpendicular to the pipe wall is:
v p;n;j ¼ v p;t tanaj ;
Fig. 10. Variation of acoustic energy and average impact angle with time.
j ¼ 1; 2; 3; . . . n
ð9Þ
(3) Particles in the dispersed phase are formed by the falling particles in the wake of the upper plug, and these particles are received by the next plug. Thus, particles in the dispersed phase which have a downwards velocity of vp,t will collide with the plug which have an upwards velocity of vplug, and moved upwards at a velocity of vplug after the collisions. What’s more, the axial stress caused by the collisions would be transferred to normal stress and resulted in additional pressure drop due to the increase of particle-wall frictions. In the next part, a pipe section with a length of LT is taken into consideration, where the length of the plug is Lplug. Based on above assumption, particle motions which induce the acoustic signals are divided into three parts: particle-wall interaction in the dispersed phase, particle-wall interaction in the plug, as well as the interaction between dispersed phase and the plug, and they are considered separately. (a) Particle-wall interactions in dispersed phase The interaction between dispersed particles and the wall is similar with that in the suspension flow of vertical conveying, which can be expressed as the derivation of He et al. (2014). The acoustic energy caused by particle-wall collision in dispersed phase in a time interval t can be expressed as Eq. (10).
Fig. 11. Variation of actual value and predicted value of pressure drop with axial stress.
Ep;collision ¼ 2gtmC p AðLT Lplug Þ
n X
v 3p;n;j xj
ð10Þ
j¼1
where g is the transformation efficiency from the collision pressure to acoustic pressure detected by AE sensor (Wang et al., 2009), m is the particle mass, Cp is the particle number concentration of dispersed phase, A is the area of the acoustic sensor. And the acoustic energy caused by particle-wall friction in dispersed phase can be expressed as Eq. (11).
Ep;friction ¼ 2lgtmv p;t C p AðLT Lplug Þ
n X
v 2p;n;j xj
ð11Þ
j¼1
(b) Interactions between the dispersed phase and plug phase According to assumption 3, acoustic pressure caused by the collision between a single particle and plug can be expressed as follows:
ppplug ¼
gmf pplug ðv p;t þ v plug Þ DA
ð12Þ
where DA is the contact area between the particles and the pipe wall, and the average collision frequency between particles in the dispersed phase and plug can be obtained as follows:
f pplug ¼ C p DAðv p;t þ v plug Þ
ð13Þ
Thus, acoustic flux in unit time can be expressed as follows: Fig. 12. Schematic diagram of particle-wall interactions in plug flow.
J pplug ¼ ppplug DAðv p;t þ v plug Þ ¼ gmðv p;t þ v plug Þ3 C p DA
ð14Þ
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Assuming that k1 of the collision energy is detected by the acoustic sensor, then acoustic energy caused by the collision between dispersed particles and plug during the sampling time t can be expressed as follows:
Z
t
Z
A
Epplug;collision ¼ k1
J pplug dAdt 0
0
¼ k1 gtmðv p;t þ v plug Þ3 C p A
ð15Þ
(c) Particle-wall interactions in the plug phase According to assumption 3, the friction force between the plug and the pipe wall is:
F plug ¼ lK w Nplug ¼ lK w mf p;plug ðv p;t þ v plug Þ
ð16Þ
where Kw is the Janssen coefficient, Nplug is the normal stress between plug and the wall. The power caused by friction force can be expressed as follows:
Pplug ¼ F plug v plug ¼ lK w mðv p;t þ v plug Þ2 v plug C p DA
ð17Þ
Then the acoustic energy caused by friction between the plug and pipe wall during the sampling time t can be expressed as follows:
Eplug;f ¼ g
Z 0
t
Z 0
A
P plug dAdt ¼ lK w gtmv plug C p Aðv p;t þ v plug Þ2
ð18Þ
In the current work, acoustic collision energy was mainly caused by the collision between dispersed particles and plugs. Thus, the total collision energy can be simplified as:
Ecollision ¼ Ep;collision þ Epplug;collision
ð19Þ
Epplug;collision ¼ k1 gtmðv p;t þ v plug Þ3 C p A Similarly, the total friction energy can be simplified as:
Efricition ¼ Ep;friction þ Eplug;friction
ð20Þ
Eplug;friction ¼ lK w gtmv plug C p Aðv p;t þ v plug Þ2
Thus, the acoustic energy fraction of particle-wall collision Dc is:
Dc ¼
Ecollision 1 ¼ Ecollision þ Efriction 1 þ lkK w v vþplug p;t v 1
Fig. 13. Schematic diagram of the calculation of k1.
sensor. Since the acoustic signal is rapidly attenuated in the air, it can be assumed that only the acoustic signal near the wall will be received by the AE sensor. That is, only the acoustic signal generated by the particles falling into the annular region as shown in Fig. 13 will be received by the AE sensor. Then the probability that the particles fall into the annular region is:
P¼
pR2 pðR dÞ2 p R2
where R is the radius of the conveying pipe and d is the average particle size. According to the experimental conditions in this work, the probability that the particles fall into the annular region is 0.23. However, the particles do not fall uniformly, so the value of k1 is further reduced. Taking this value as the initial value, the minimum deviation from the true value as the target, the optimal value of k1 is fitted as 0.1. It means that the accuracy of this method is strongly dependent on k1. In essence, k1 might be obtained accurately combined with concentration analysis in the cross-section of the conveying pipe. Moreover, if k1 can be obtained accurately, the Janssen coefficient can be measured by the acoustic emission detection since Eq. (21) can be re-arranged as Eq. (23). Based on AE detection, the energy fraction of collision (Dc) can be calculated, and based on Eq. (23), the Janssen coefficient can be calculated. This shows a possibility for the non-intrusive, real-time and online detection of Janssen coefficient.
ð21Þ Kw ¼
plug
Table 2 compared the experimental Dc from analysis of acoustic signals and the predicted Dc calculated from Eq. (21). During the calculation, the velocity of particles and plugs were calculated from images analysis, particle-wall friction factor was 0.3 (Pahk et al., 2013). k1 was chosen as 0.1, and the Janssen coefficient Kw_active was 0.271 according to Section 4.2.2. It can be seen from the table that the predicted value of Dc fits with the experimental value very well, indicating that the simplification of Eqs. (19) and (20) was reasonable. Namely, the collision acoustic signals were mainly induced by collisions between dispersed particles and plugs, while the friction acoustic signals were mainly generated by friction between plugs and the wall. It is worth mentioning that k1 is the proportion of acoustic energy induced by particle-plug collisions and detected by the AE
Table 2 Comparison of experimental value and predicted value of Dc in plug flow. Gas velocity (m s1)
Experimental value
Predicted value
Error (%)
4.0 4.5 5.0
0.707 0.697 0.691
0.714 0.692 0.687
0.74 0.42 0.43
ð22Þ
k1 ðv p;t þ v plug Þ
lv plug
1 1 Dc
ð23Þ
5. Conclusions Based on pressure drop measurement and AE detection, this work first investigated the vertical transportation of a single plug. Results showed that for plug with larger length, the unsteady flow appeared when the plug decomposed and partial particles in the front of the plug fell down and collided with the bulk of the plug. The unsteady flow could induce the second increase of the pressure drop through the whole pipe, the local negative pressure drop, and the sharp increase of acoustic energy. Decomposing the acoustic signals by wavelet analysis, it was found that the plug-wall interaction was dominated by friction, while in the front and back end of the plug the particle-wall interaction was dominated by collisions. Applying the AE detection and pressure drop measurement to the real continuous plug flow, the results were almost the same to those in the single plug conveying process. Therefore, the AE technology might be a good way for the detection of unsteady flow in the real plug conveying just the same to pressure drop measurement. Moreover, the pressure drop was predicted by Konrad’s
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model and it was proved that for the plug flow in the vertical conveying process, the axial wall stress was larger than the normal stress, thus smaller deviation between the predicted and the measured pressure drop was acquired when using the active Janssen coefficient. Based on above measurement, the sources of acoustic signals in the plug flow were divided into two parts: the collision between dispersed particles and the plug, and the friction between the plug and the wall. Furthermore, an acoustic model was established which describing the relationship between the acoustic energy fraction of collision (Dc) and the Janssen coefficient. The predicted Dc agreed well with the experimental one with a relative deviation lower than 0.8%, under the fitted k1 of 0.1. Therefore, the established model was proved to be corrected and it further provides a possibility for the non-intrusive, real-time and online detection of Janssen coefficient. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The authors acknowledge the support and encouragement of the National Natural Science Foundation of China, China (21808197), The National Science Fund for Distinguished Young, China (21525627) and the Science Fund for Creative Research Groups of National Natural Science Foundation of China, China (61621002). References Cong, X., Guo, X., Lu, H., Gong, X., Liu, K., Sun, X., Xie, K., 2013. Flow patterns of pulverized coal pneumatic conveying and time-series analysis of pressure fluctuations. Chem. Eng. Sci. 101, 303–314. Daoud, K., Ould Dris, A., Guigon, P., Large, J., 1993. Experimental study of horizontal plug flow of cohesionless bulk solids. KONA. Powder. Part. J. 11, 119–124. Dong, K., Zhang, Q., Huang, Z., Liao, Z., Wang, J., Yang, Y., Wang, F., 2015. Experimental investigation of electrostatic effect on particle motions in gassolid fluidized beds. AIChE J. 61, 3628–3638. E, D., Wang, H., 2010. Design and analysis of polypropylene. Process. Eq. Pip. 47, 21– 22. He, Y., Wang, J., Cao, Y., Yang, Y., 2009. Resolution of structure characteristics of AE signals in multiphase flow system—from data to information. AIChE J. 55, 2563– 2577. He, L., Zhou, Y., Huang, Z., Wang, J., Lungu, M., Yang, Y., 2014. Acoustic analysis of particle–wall interaction and detection of particle mass flow rate in vertical pneumatic conveying. Ind. Eng. Chem. Res. 53, 9938–9948. He, L., Yang, Y., Huang, Z., Liao, Z., Wang, J., Yang, Y., 2016. Multi-scale analysis of acoustic emission signals in dense-phase pneumatic conveying of pulverized coal at high pressure. AIChE J. 62, 2635–2648.
Jiang, X., Wang, J., Jiang, B., Yang, Y., Hou, L., 2007. Study of the power spectrum of acoustic emission (AE) by accelerometers in fluidized beds. Ind. Eng. Chem. Res. 46, 6904–6909. Klinzing, G.E., Rizk, F., Marcus, R., 2010. Pneumatic Conveying of Solids: A Theoretical and Practical Approach. Springer, London/New York. Konrad, K., 1987. An exploratory analysis of dense phase pneumatic conveying through vertical pipelines. J. Pipelines. 6, 99–104. Konrad, K., Totah, T.S., 1989. Vertical pneumatic conveying of particle plugs. Can. J. Chem. Eng. 67, 245–252. Konrad, K., Harrison, D., Nedderman, R., Davidson, J., 1980. Prediction of the pressure drop for horizontal dense phase pneumatic conveying of particles. Pneumotransport. 5, 225–244. Kuang, S., Chu, K., Yu, A., Zou, Z., Feng, Y., 2008. Computational investigation of horizontal slug flow in pneumatic conveying. Ind. Eng. Chem. Res. 47, 470–480. Levy, A., 2000. Two-fluid approach for plug flow simulations in horizontal pneumatic conveying. Powder. Technol. 112, 263–272. Li, K., Kuang, S., Zou, R., Pan, R., Yu, A., 2013. Numerical study of vertical pneumatic conveying: effect of friction coefficient. AIP Conf. Proc. 1542, 1154–1157. Mason, D. John, 1991. A Study of the Modes of Gas-solids Flow in Pipelines. Thames Polytechnic. Pahk, J.B., Klinzing, G.E., 2012. Frictional force measurement between a single plug and the pipe wall in dense phase pneumatic conveying. Powder. Technol. 222, 58–64. Pahk, J.B., Vasquez, N.A., Jacob, K., Klinzing, G.E., 2013. Frictional force measurement for multiple plugs in dense phase pneumatic conveying of polymer particles: an industry application. Ind. Eng. Chem. Res. 52, 199–206. Pan, R., 1999. Material properties and flow modes in pneumatic conveying. Powder. Technol. 104, 157–163. Pu, W., Zhao, C., Xiong, Y., Liang, C., Chen, X., Lu, P., Fan, C., 2010. Numerical simulation on dense phase pneumatic conveying of pulverized coal in horizontal pipe at high pressure. Chem. Eng. Sci. 65, 2500–2512. Qiu, J., Sun, K., Wang, T., Gao, H., 2019. Observer-based fuzzy adaptive eventtriggered control for pure-feedback nonlinear systems with prescribed performance. IEEE. T. Fuzzy. Syst. 1–1. https://doi.org/10.1109/ TFUZZ.2019.2895560. Rabinovich, E., Freund, N., Kalman, H., Klinzing, G., 2012. Friction forces on plugs of coarse particles moving upwards in a vertical column. Powder. Technol. 219, 143–150. Richardson, J., 1954. Sedimentation and fluidisation: Part I. Trans. Inst. Chem. Eng. 32, 35–53. Roberts, A., Jones, M., 2003. Analysis of forced flow of granular materials in vertical pipes without and with air permeation. Particul. Sci. Technol. 21, 25–44. Roberts, A., 1966. Developments in materials handling research at Wollongong University College. In: 2nd Annual Conference, Illawarra Group, The Institution of Engineers, Australia. Sun, K., Mou, S., Qiu, J., Wang, T., Gao, H., 2019. Adaptive fuzzy control for nontriangular structural stochastic switched nonlinear systems with full state constraints. IEEE. T. Fuzzy. Syst. 27, 1587–1601. https://doi.org/10.1109/ TFUZZ.2018.2883374. Vásquez, N., Sánchez, L., Klinzing, G.E., Dhodapkar, S., 2003. Friction measurement in dense phase plug flow analysis. Powder. Technol. 137, 167–183. Wang, J., Ren, C., Yang, Y., Hou, L., 2009. Characterization of particle fluidization pattern in a gas solid fluidized bed based on acoustic emission (AE) measurement. Ind. Eng. Chem. Res. 48, 8508–8514. Wang, J., Ren, C., Yang, Y., 2010. Characterization of flow regime transition and particle motion using acoustic emission measurement in a gas-solid fluidized bed. AIChE J. 56, 1173–1183. Wypych, P., Yi, J., 2003. Minimum transport boundary for horizontal dense-phase pneumatic conveying of granular materials. Powder. Technol. 129, 111–121. Yang, Y., Hou, L., Yang, B., Liu, C., Hu, X., Wang, J., Chen, J., 2004. A system and technology of acoustic emission measurement applied in fluidized bed reactors. Patant CN1544140.
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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Acoustic analysis of particle-wall interactions of plug flow in vertical pneumatic conveying Yao Yang a, Peng Zhang a, Lelu He a, Jingyuan Sun a,⇑, Zhengliang Huang a, Jingdai Wang b, Yongrong Yang b a Zhejiang Provincial Key Laboratory of Advanced Chemical Engineering Manufacture Technology, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, PR China b State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, PR China
h i g h l i g h t s Unsteady flow was identified by pressure drop and acoustic emission detection. Pressure drop for vertical pneumatic conveying was well predicted using active Kw. The established acoustic model supports a potential online measurement for Kw.
a r t i c l e
i n f o
Article history: Received 22 May 2019 Received in revised form 26 September 2019 Accepted 30 September 2019 Available online 11 October 2019 Keywords: Plug flow Unsteady flow Particle-wall interactions Acoustic emission Pressure drop
a b s t r a c t The plug flow was investigated in both the single plug and the continuous plug experiments. In the single plug flow, the pressure drop might rise for two times with a longer plug, and the second increase was proved to be caused by the collision between the falling particles and the plug by acoustic emission detection. In continuous plug flow, the interaction between the bulk of the plug and the pipe wall was dominated by the friction. And the sources of acoustic signals in continuous plug flow can be mainly divided into two parts: the collision between the falling particles and the plug and the friction between the bulk of plug and the wall. Based on this, the acoustic model was derived and the energy fraction can be predicted accurately. And the model further provides a possibility for the non-intrusive, real-time and online detection of Janssen coefficient. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Compared to the dilute-phase pneumatic conveying, densephase operation has the advantages of lower energy cost and reduced erosion of the transported materials because of lower gas velocity (Klinzing et al., 2010). Thus, the dense-phase pneumatic conveying has received more attention and it has been widely applied in many industrial processes such as conveying of pulverized coal in the pulverized coal gasification process (Cong et al., 2013; Pu et al., 2010). However, unsteady plug flow usually occurs due to uneven distribution of solid materials in the conveying pipe, which brings about large pressure fluctuations and results in the increasing risk of blockage (Qiu et al., 2019; Sun et al., 2019; Wypych and Yi, 2003). Therefore, a detailed understanding of the hydrodynamics in plug flow pneumatic conveying is essential for ⇑ Corresponding author. E-mail address: [email protected] (J. Sun). https://doi.org/10.1016/j.ces.2019.115260 0009-2509/Ó 2019 Elsevier Ltd. All rights reserved.
the design, optimization and operation of the dense-phase pneumatic conveying systems. Plug flow is a kind of typical unsteady flow (Konrad et al., 1980; Levy, 2000). Especially in the vertical pneumatic conveying process, when the solid-gas ratio (particle concentration) is high, the flow regime will change from suspension flow to plug flow directly, resulting in sharp increase of pressure drop. In addition, due to the existence of gravity in the vertical direction, the plug is easy to decompose, then induces large fluctuation of pressure drop. And the shape, number, length and velocity of the plug vary in time and space. For example, Daoud et al. (1993) found that for a certain solids flow rate, the plug length decreased as the increase of gas velocity and increased as the increase of conveying distance. Mason et al. (1991) convinced their results and pointed out that a long gap existed between two short pressure waves, indicating that the plugs were decomposed as the increase of conveying distance. Levy et al. (2000) found that the plug shape and length varied along the conveying direction based on numerical modeling
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method. Li et al. (2013) found that the increase of friction factor would lead to the increase of plug length and the decrease of plug velocity. For predicting the pressure drop of plug flow, one of the most precise models is the force balance model developed by Konrad (1987). The accuracy of this model depends on the Janssen coefficients at the wall, which equals to the radial stress at the wall divided by the axial stress. Therefore, numerous experimental set-ups and detection methods were used to measure the particle-wall stresses during the pneumatic conveying process. Roberts et al. (1966), Roberts and Jones (2003) studied the forces needed for transporting a plug for the first time. They used pistons to simulate the plug transportation in a vertical pipe with a diameter of 46 mm and measured the forces needed. Besides, they compared the forces needed for transporting an aerated plug and an un-aerated plug, the results showed that aeration reduced the force needed. Rabinovich et al. (2012) used several kinds of particles to repeat Roberts’s experiment. They found that the particle size had no effects on particle-wall friction force while plug length had a big influence on that force. Though they had used aeration to simulate the real transport of plugs, the plugs investigated in these studies were different from that in real plug flow. In order to overcome these problems, Vasquez et al. (2003) mounted three stress sensors in the external wall of a horizontal pipe for the online measurement of particle-wall friction force. They found that the axial stress and radical stress acting on the plugs increased as the increase of plug length, and the radical stress increased as the increase of gas velocity. Pahk et al. (2012) further investigated the influence of particle shape, particle size, particle type and plug length on particle-wall interactions, and compared the stress in different positions of the conveying pipe. They found that the friction forces at the top and side were larger than that in the bottom. Based on these analyses, they (Pahk et al., 2013) extended their measurement system to the investigation of industrial pneumatic conveying systems and convinced the above results. However, particle-wall interactions in the plug flow of vertical conveying process and their influence on pressure drop has not been studied in the literatures. What’s worse, although the Janssen coefficient is regarded as an important parameter for the prediction of pressure drop, the related method to measure it is scanty. Acoustic emission (AE) signals, induced by frequent particleparticle and particle-wall contacts, are very sensitive to the particle motions in gas-solid two phase systems (He et al., 2009). Furthermore, we have found that the original acoustic signals can be divided into two parts by wavelet decomposition and they stand for particle-wall collision and particle-wall friction, respectively (He et al., 2014; He et al., 2016). Therefore, the acoustic emission detection has been proved to be an efficient way in investigating the particle-wall interactions and particle motions in the gassolid fluidized bed and in the pneumatic conveying process (Dong et al., 2015; Jiang et al., 2007; Wang et al., 2010). Based on all above, this work aims at investigating the plug flow in vertical pneumatic conveying by acoustic analysis of particlewall interactions. Firstly, the influence of particle-wall interactions on the stability of the transported single plug was investigated. Secondly, the influence of particle-wall interactions on the stability of continuous plug flow was also studied. In the end, a new AE energy model for plug flow was established based on the particle-wall interaction analysis of plug flow, and the energy fraction predicted by the model fitted well with the experimental values. Moreover, based on this energy model, a new method for the measurement of Janssen coefficient was developed, which was of value importance for the prediction of pressure loss in the plug flow.
2. Experiments 2.1. Materials and procedure A schematic diagram of the vertical pneumatic conveying system is shown in Fig. 1. The conveying pipe consists with a horizontal Plexiglas pipe (1.2 m in length, 25 mm in inner diameter (I.D.) and the thickness of the pipe is 2 mm) at the bottom, and the main testing section of a vertical Plexiglas pipe (3.0 m in length, 25 mm in I.D. and the thickness of the pipe is 2 mm). In aforementioned investigations (e.g. Roberts et al. (1966), Roberts and Jones (2003)), they used the conveying pipe with the inner diameter of 46 mm, but during the experiments we found that a larger inner diameter would induce more fluctuations and the single plug was very hard to be generated. Therefore, the conveying pipe with an inner diameter of 25 mm was used. Each time when experiments related to the single plug involved, the gas flow rate was set at a certain value before the experiment, then bypass valve (valve 4) was closed to make gas bypass. Polypropylene (PP) particles were added in the horizontal pipe to form a single plug with a certain length. Then valve 4 was opened to transport the plug into vertical pipe. When all the signals were sampled, particles retained in the pipe were collected and above procedures were repeated for another run which meant particles were re-added to the horizontal pipe and formed a new plug. In the experiments, the superficial gas velocity ranged from 6.0 to 12.0 m s1 and the plug length ranged from 100 to 300 mm. The physical properties of PP particles are summarized in Table 1. The PP particles were sieved with mean diameter of 1500.0 lm and have a narrow size distribution. This set-up can also be used to do the experiments with real plug flow. At that time, the feeding vessel was involved and pre-addition of plug in the horizontal pipe was not necessary. 2.2. Measurement devices The pressure drops DP1 and DP2 were measured by the pressure sensors as shown in Fig. 1, the distances between each two couples of pressure sensors were 1.2 m and 0.05 m, respectively. According to the Shannon sampling theorem, the sampling frequency should be greater than 2 times of the highest frequency in the signal, so as to ensure that the sampled digital signal can retain the complete information. Therefore, 400 Hz is selected as the sampling frequency. The sampling time is determined according to the specific experimental conditions. Under the experimental conditions of this work, the time for a single plug to pass the pressure detection section does not exceed 10 s, so this paper selects 10 s as the sampling time. The online AE system for collection and analysis developed by UNILAB Research Center of Chemical Engineering in Zhejiang University (Yang et al., 2004) includes 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 corporation). The output of acoustic sensor is electrical signals whose unit is V. The software used is the Labview. Therefore, in combination with the calculation method of acoustic energy (which will be introduced in the next part), the unit of acoustic energy is V2. Besides, the AE sensor was mounted on the outer surface of the vertical pipe with a couple of rubber rings to isolate the noises, and the installation location was 1.2 m above the elbow bend at the bottom. The sampling frequency was chosen as 900 kHz on basis of Shannon sampling theorem, and the sampling time was 10 s. Besides of above methods, the high-speed camera (PHOTRON FASTCAM Mini WX100) was also used in this work to acquire the conveying
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Fig. 1. Schematic diagram of the vertical plug conveying system. 1 – Air compressor, 2 – Buffer tank, 3 – Gas flow meter, 4 – Ball valve, 5 – Pressure sensor, 6 – Acoustic sensor, 7 – Preamplifier, 8 – Main amplifier, 9 – A/D conversion module, 10 – Computer, 11 – Rubber, 12 – Receiving Vessel, 13 – Feeding Vessel.
Table 1 Physical properties of PP particles. Material
Mean diameter (lm)
Density (kg m3)
Pan’s classification (1999)
Terminal velocity (m s1)
Void fraction
PP
1500.0
900
PC2
5.6
0.5
pictures and based on the images analysis software the plug velocity and particle velocity could be calculated.
published references (Dong et al., 2015; Kuang et al., 2008; He et al., 2016; He et al., 2009).
3. Data processing methods
4. Results and discussion
Power spectrum density (PSD) analysis and wavelet transform were the main signal processing methods used in this work. The former one is a frequency-domain analysis method which has proved to be an efficient way in dealing with acoustic signals. And the ordinate of the power spectrum is the acoustic energy at each frequency. Then the acoustic energy at each frequency is summed, the acoustic energy is obtained. While the latter one provides an approach which can represent a signal simultaneously in time and in frequency. Using the wavelet transform, the acoustic signals can be subjected to 10 scales. And the energy fractions of the 1–3 scales are the energy fraction of collision, the energy fractions of the 4–5 scales are the energy fraction of friction. Base on this, the average impact angle (the angle between the contact direction of the particle-wall and the vertical direction) can be calculated. Details of these two methods can be found in numerous
4.1. Unsteady flow in single plug conveying experiments 4.1.1. Variation of pressure drop Fig. 2 shows the variation of pressure drop with time when a single plug was transported across the detection section. Obviously, six stages can be seen in the figure. The first stage was 3.00–3.35 s. During this stage the pressure drop increased slowly because the particles in the front of the plug entered the detection section. In the second stage (3.35–3.38 s), the pressure drop increased sharply due to the entrance of the bulk of the plug. In the third stage (3.38–3.63 s), the pressure drop stayed approximately unchanged at a high value, which meant that the plug was transported across the detection section. Then in the fourth stage (3.63–3.70 s), the pressure drop decreased sharply due to the plug left the detection section. In the fifth stage (3.70–4.20 s),
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Fig. 2. Variation of the pressure drop with time (Lini: initial plug length-10 cm, Ug: gas velocity-10 m/s).
the slowly decrease of pressure drop resulted from the fact that particles in the wake of plug were leaving the detection section. At last, all the particles left the detection section and thus the pressure drop remained unchanged. Fig. 3 shows the variation of pressure drop with time when plugs with different lengths were transported at various superficial gas velocities. It can be seen that when the plug length was small, pressure drop increased as the increase of gas velocity. No plug breakages were seen in the experiments and thus the figures were similar as Fig. 2. However, when plug length was large, second increase of pressure drop can be seen in Fig. 3(b) and their amplitudes were even half of the first increase. During the experiments, plug breakages were observed under these conditions. After the breakages, the void age increased, which further led to the decrease of local gas velocity as well as the gas-solid drag forces. This would result in the falling of particles in the wake of the plug. When the falling particles had collisions with the plugs moving upwards, extra energy loss appeared and thus the pressure drop increased at second time. These phenomena were in accordance with results of Konrad et al. (1989). The second increase of pressure drop would lead to large fluctuations of pressure drop and increase the risk of pipe blockage. Therefore, in the following sections, the second increase of pressure drop is recorded as unstable flow while the others are recorded as stable flow.
4.1.2. Variation of local pressure drop and acoustic energy Fig. 4 shows the variation of DP1, DP2 and acoustic energy with time for stable conveying. The pipe pressure drop DP1 can be used to identify the change of particle concentration in the whole detection section roughly while the local pressure drop DP2 can be used to identify the change of local particle concentration roughly. It can be seen in the figures that DP2 increased sharply when plug went across the lower sensor, and decreased sharply when plug left it. What’s more, the variation of acoustic energy agrees well with DP2. The variations of DP1, DP2 and acoustic energy with time for unstable conveying was shown in Fig. 5. It can be seen that when pipe pressure drop DP1 increased at second time, local pressure drop DP2 increased at the same time. Besides, the negative value of DP2 can be seen in the figures, indicating that pressure waves were propagated downwards. These negative pressure drops were caused by the collisions between the falling particles and the plugs. Meanwhile, the acoustic energy increased at the same time, which means that these collisions can be detected by acoustic signals. The increasing gas velocity causes the increase of particle motions and the particle-wall interactions, resulting in an increase of pressure drop as well as the acoustic signals.
4.1.3. Variations of particle motions Fig. 6 shows the variation of acoustic energy and energy fraction of particle-wall interactions (He et al., 2014) with time for stable conveying and unstable conveying. For the stable conveying processes, as shown in Fig. 6(a), energy fraction of particle-wall collision increased while energy fractions of particle-wall friction decreased before the increase of acoustic energy, which meant that before the bulk of the plug entered the detection section, particles in the front of plug mainly collided with the pipe wall (the first stage in Fig. 2) due to the large local void age in the front of plug. When the plug went across the detection section, energy fraction of particle-wall collision decreased and energy fraction of particle-wall friction increased, resulting in friction domain flow (the 2–4 stages in Fig. 2). For the unstable flow, as shown in Fig. 6(b), the variations of energy fractions of particle-wall collision and friction were similar as those in the stable flow before the bulk of the plug entered the detection section. However, when the pressure drop was increased at second time, particle-wall collision energy fraction increased and friction energy fraction decreased. It resulted in collision domain flow again, which meant that the collisions between falling particles and plug were the main reason for the increase of pressure drop at second time. Moreover, results in Fig. 6 also show that the variation of particle-wall interaction appears prior to the variations of pressure drop and acoustic energy, thus measurement of particle-wall interaction can be a better way for measurement of flow regime transition. Fig. 7 shows the variation of particle-wall impact angles with time under different conditions. For the stable conveying processes, as shown in Fig. 7(a), particle-wall impact angle increased when particles in the front of the plug arrived at the lower sensor. For the unstable conveying processes, as shown in Fig. 7(b), the particle-wall impact angle also increased when particles in the front of the plug arrived at the lower sensor. After that, the particle-wall impact angle increased largely when the pressure drop increased at second time, and the amplitude was larger than that of the first time, which resulted from the fact that collisions at second time were more violently. 4.2. Unsteady flow in real continuous plug flow 4.2.1. Particle motions in plug flow Previous results are obtained from experiments with a single plug, are they in accordance with the real industrial process with continuous plugs? Fig. 8 shows the variation of pressure drop and acoustic energy with time for plug flow (experimental conditions: gas velocity 5.5 m/s, solid flow rate 0.007 kg/s, plug length 14 cm). In this part, L is the length of the measurement section,
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Fig. 3. Variation of pressure drop with time when plugs with different lengths were transported at various superficial gas velocities. (a) Lini: initial plug length – 10 cm, (b) Lini: initial plug length – 25 cm.
which is 1.2 m. DP is the pressure drop in the measurement section and the sampling time is 120 s. Continuous plug flow is unstable and more than 20 plugs passes through the measurement section during the sampling time. It can be seen that the pressure drop increased firstly and then decreased during 0 to 0.75 s which meant a plug was transported through the detection section. But compared with Fig. 2, the fluctuation of pressure drop in real plug flow was not completely the same to that in the single plug experiments, which might be caused by the interaction between two adjacent plugs. But the figure also showed that the pressure drop increased when the plug moving in and decreased when moving out. Besides, during the experiments we observed that when the
plug arrived at the acoustic emission sensor, the fluctuation of acoustic energy was observed, as the sharp increase of acoustic energy at about 0.25 s in Fig. 8. Fig. 9 shows the variation of acoustic energy and energy fraction of particle-wall interactions with time for plug flow. It can be seen that, particle-wall collision energy fraction increased and friction energy fractions decreased before the increase of acoustic energy. Fig. 10 shows the variation of acoustic energy and average impact angle with time for plug flow. It can be seen that the particles in the front of plug collide with the pipe wall and resulted in the increase of impact angle. As the plug went through the pipe, particle-wall interactions were domain by particle-wall friction
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dP dra 4sw þ þ þ qb g ¼ 0 dx dx D
ð1Þ
where P is the pressure drop, ra is the axial stress, and sw is the shear stress of the wall. For the stable flow, Konrad (1987) proposed an equation to calculate normal stress ra as follows.
ra ¼
bqs ð1 ebulk Þðv plug v p;t Þ2 ð1 ebulk bÞ
ð2Þ
where ebulk is the void fraction of loose packed solids, vp,t and vplug are the velocities of falling particles and plug respectively measured by images processing, b is the volume fraction of particles between plugs, which can be estimated by the following equation (Richardson, 1954).
U g þ v plug v p;t ¼ ð1 bÞ2:4 v t
ð3Þ
where vt is the particle terminal velocity, Ug is the superficial gas velocity. In Eq. (1), the shear stress of the wall sw can be calculated as Eq. (4).
sw ¼ lK w ra þ cw
Fig. 4. Variation of DP1, DP2 and acoustic energy with time for stable conveying. (a) Ug: gas velocity – 6 m/s, Lini: initial plug length – 10 cm, (b) Ug: gas velocity 10 m/s, Lini: initial plug length – 10 cm.
ð4Þ
where cw is the cohesive force, for PP particles used in this work it equals to 0, l is the friction coefficient, and Kw is the Janssen coefficient. The Janssen coefficient can be divided into the active one and the passive one according to impact angle. According to E and Wang (2010), Kw_active and Kw_passive are 0.271 and 3.69 respectively for PP particles. Based on Eqs. (1)–(4), the variations of actual value and predicted value of pressure drop with axial stress are calculated and shown in Fig. 11. It can be seen that the predicted value using active Janssen coefficient fit with experiment results very well, indicating that under the experimental conditions of this work, the axial wall stress was larger than the normal stress which was convinced with the results of Roberts and Jones (2003). 4.3. Acoustic model of particle-wall interaction for plug flow
Fig. 5. Variations of DP1, DP2 and acoustic energy with time for unstable conveying. (a) Ug: gas velocity – 6 m/s, Lini: initial plug length – 25 cm, (b) Ug: gas velocity – 10 m/s, Lini: initial plug length – 25 cm.
and resulted in the decrease of impact angle. As the plug left the pipe, particle-wall impact angle remained small. These results were similar as that of single plug experiments, indicating that the acoustic methods could also be used for the detection of particle motions in plug flow. 4.2.2. Prediction of pressure drop for continuous plug flow Konrad et al. (1980, 1989) developed a pressure drop prediction model for plug flow based on force balance analysis, which can be expressed as Eq. (1).
Above results have shown that the acoustic energy and energy fraction are related to particle motions and particle-wall interaction in the plug, but the quantitative relationship between them is confused. In this part, the forces on particles and the plug will be analyzed to establish the acoustic model which describing the plug flow. For the plug flow in vertical pipe (see Fig. 12), there are two distinct particle phases that co-exist in the flow field. One is the dispersed particle phase mainly existing between two adjacent plugs, which will fall down and collide with the lower plug. The others are particles existing inside the bulk of the plug and moving upwards. The behaviors of particles in different forms differ from each other. To be specific, particles in the dispersed phase may impact with the wall at an angle and particle-wall collision is enhanced, while particles in the plug phase will mainly rub with the wall as a whole. What’s more, in the above sections, we have found that the collisions between particles and the plug had the most important influence on the pressure drop of gassolid two phase flow in the plug flow. Therefore, the following assumptions have been made before establishing the theory model: (1) Based on the images analysis, we found that the plug velocity increased as the increase of plug length and solids mass flow rates have little influences on it. Thus, the plug velocity was assumed as:
v plug ¼ kplug Lplug
ð5Þ
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7
Fig. 6. Variation of acoustic energy and energy fraction of particle-wall interactions with time. (a) stable conveying, Ug: gas velocity – 6 m/s, Lini: initial plug length – 10 cm, (b) unstable conveying, Ug: gas velocity – 6 m/s, Lini: initial plug length – 25 cm.
Fig. 7. Variation of acoustic energy and average impact angle with time. (a) Ug: gas velocity – 6 m/s, Lini: initial plug length – 10 cm, (b) Ug: gas velocity – 6 m/s, Lini: initial plug length – 25 cm.
Fig. 8. Variation of pressure drop and acoustic energy with time in real plug flow (Ug: gas velocity – 5.5 m/s, solid flow rate – 0.007 kg/s, Lplug: plug length – 14 cm).
Meanwhile, Daoud et al. (1993) found that the plug length decreased as the increase of gas velocity under a certain solids mass flow rate. Thus, the plug length was assumed as:
Fig. 9. Variation of acoustic energy and energy fraction of particle-wall interactions with time.
ð6Þ
From Eq. (7), the plug velocity will decrease as the increase of gas velocity under a certain solids mass flow rate, which is convinced with our former results.
where ms and mg is the mass flow rate of solid phase and gas phase respectively, and a is the model factor. Combining Eqs. (5) and (6), we have
(2) Particles in the dispersed phase have the uniform axial velocity, which can be estimated by the following equation (Eq. (8) is the transformation of Eq. (3)).
Lplug
ms ¼a mg
v plug ¼ akplug
ms mg
ð7Þ
v p;t ¼ Ug þ v plug ð1 bÞ2:4 v t
ð8Þ
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However, the angle of particles interacting with the pipe wall differs from one another due to the complex particle-particle collisions. It is supposed that the particles are divided into n categories according to the different particle-wall impact angles, aj and xj are the particle-wall impact angle of the j-th category particles and the percentage of particles impacting on the wall at this angle. Thus, the particle velocity perpendicular to the pipe wall is:
v p;n;j ¼ v p;t tanaj ;
Fig. 10. Variation of acoustic energy and average impact angle with time.
j ¼ 1; 2; 3; . . . n
ð9Þ
(3) Particles in the dispersed phase are formed by the falling particles in the wake of the upper plug, and these particles are received by the next plug. Thus, particles in the dispersed phase which have a downwards velocity of vp,t will collide with the plug which have an upwards velocity of vplug, and moved upwards at a velocity of vplug after the collisions. What’s more, the axial stress caused by the collisions would be transferred to normal stress and resulted in additional pressure drop due to the increase of particle-wall frictions. In the next part, a pipe section with a length of LT is taken into consideration, where the length of the plug is Lplug. Based on above assumption, particle motions which induce the acoustic signals are divided into three parts: particle-wall interaction in the dispersed phase, particle-wall interaction in the plug, as well as the interaction between dispersed phase and the plug, and they are considered separately. (a) Particle-wall interactions in dispersed phase The interaction between dispersed particles and the wall is similar with that in the suspension flow of vertical conveying, which can be expressed as the derivation of He et al. (2014). The acoustic energy caused by particle-wall collision in dispersed phase in a time interval t can be expressed as Eq. (10).
Fig. 11. Variation of actual value and predicted value of pressure drop with axial stress.
Ep;collision ¼ 2gtmC p AðLT Lplug Þ
n X
v 3p;n;j xj
ð10Þ
j¼1
where g is the transformation efficiency from the collision pressure to acoustic pressure detected by AE sensor (Wang et al., 2009), m is the particle mass, Cp is the particle number concentration of dispersed phase, A is the area of the acoustic sensor. And the acoustic energy caused by particle-wall friction in dispersed phase can be expressed as Eq. (11).
Ep;friction ¼ 2lgtmv p;t C p AðLT Lplug Þ
n X
v 2p;n;j xj
ð11Þ
j¼1
(b) Interactions between the dispersed phase and plug phase According to assumption 3, acoustic pressure caused by the collision between a single particle and plug can be expressed as follows:
ppplug ¼
gmf pplug ðv p;t þ v plug Þ DA
ð12Þ
where DA is the contact area between the particles and the pipe wall, and the average collision frequency between particles in the dispersed phase and plug can be obtained as follows:
f pplug ¼ C p DAðv p;t þ v plug Þ
ð13Þ
Thus, acoustic flux in unit time can be expressed as follows: Fig. 12. Schematic diagram of particle-wall interactions in plug flow.
J pplug ¼ ppplug DAðv p;t þ v plug Þ ¼ gmðv p;t þ v plug Þ3 C p DA
ð14Þ
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Y. Yang et al. / Chemical Engineering Science 211 (2020) 115260
Assuming that k1 of the collision energy is detected by the acoustic sensor, then acoustic energy caused by the collision between dispersed particles and plug during the sampling time t can be expressed as follows:
Z
t
Z
A
Epplug;collision ¼ k1
J pplug dAdt 0
0
¼ k1 gtmðv p;t þ v plug Þ3 C p A
ð15Þ
(c) Particle-wall interactions in the plug phase According to assumption 3, the friction force between the plug and the pipe wall is:
F plug ¼ lK w Nplug ¼ lK w mf p;plug ðv p;t þ v plug Þ
ð16Þ
where Kw is the Janssen coefficient, Nplug is the normal stress between plug and the wall. The power caused by friction force can be expressed as follows:
Pplug ¼ F plug v plug ¼ lK w mðv p;t þ v plug Þ2 v plug C p DA
ð17Þ
Then the acoustic energy caused by friction between the plug and pipe wall during the sampling time t can be expressed as follows:
Eplug;f ¼ g
Z 0
t
Z 0
A
P plug dAdt ¼ lK w gtmv plug C p Aðv p;t þ v plug Þ2
ð18Þ
In the current work, acoustic collision energy was mainly caused by the collision between dispersed particles and plugs. Thus, the total collision energy can be simplified as:
Ecollision ¼ Ep;collision þ Epplug;collision
ð19Þ
Epplug;collision ¼ k1 gtmðv p;t þ v plug Þ3 C p A Similarly, the total friction energy can be simplified as:
Efricition ¼ Ep;friction þ Eplug;friction
ð20Þ
Eplug;friction ¼ lK w gtmv plug C p Aðv p;t þ v plug Þ2
Thus, the acoustic energy fraction of particle-wall collision Dc is:
Dc ¼
Ecollision 1 ¼ Ecollision þ Efriction 1 þ lkK w v vþplug p;t v 1
Fig. 13. Schematic diagram of the calculation of k1.
sensor. Since the acoustic signal is rapidly attenuated in the air, it can be assumed that only the acoustic signal near the wall will be received by the AE sensor. That is, only the acoustic signal generated by the particles falling into the annular region as shown in Fig. 13 will be received by the AE sensor. Then the probability that the particles fall into the annular region is:
P¼
pR2 pðR dÞ2 p R2
where R is the radius of the conveying pipe and d is the average particle size. According to the experimental conditions in this work, the probability that the particles fall into the annular region is 0.23. However, the particles do not fall uniformly, so the value of k1 is further reduced. Taking this value as the initial value, the minimum deviation from the true value as the target, the optimal value of k1 is fitted as 0.1. It means that the accuracy of this method is strongly dependent on k1. In essence, k1 might be obtained accurately combined with concentration analysis in the cross-section of the conveying pipe. Moreover, if k1 can be obtained accurately, the Janssen coefficient can be measured by the acoustic emission detection since Eq. (21) can be re-arranged as Eq. (23). Based on AE detection, the energy fraction of collision (Dc) can be calculated, and based on Eq. (23), the Janssen coefficient can be calculated. This shows a possibility for the non-intrusive, real-time and online detection of Janssen coefficient.
ð21Þ Kw ¼
plug
Table 2 compared the experimental Dc from analysis of acoustic signals and the predicted Dc calculated from Eq. (21). During the calculation, the velocity of particles and plugs were calculated from images analysis, particle-wall friction factor was 0.3 (Pahk et al., 2013). k1 was chosen as 0.1, and the Janssen coefficient Kw_active was 0.271 according to Section 4.2.2. It can be seen from the table that the predicted value of Dc fits with the experimental value very well, indicating that the simplification of Eqs. (19) and (20) was reasonable. Namely, the collision acoustic signals were mainly induced by collisions between dispersed particles and plugs, while the friction acoustic signals were mainly generated by friction between plugs and the wall. It is worth mentioning that k1 is the proportion of acoustic energy induced by particle-plug collisions and detected by the AE
Table 2 Comparison of experimental value and predicted value of Dc in plug flow. Gas velocity (m s1)
Experimental value
Predicted value
Error (%)
4.0 4.5 5.0
0.707 0.697 0.691
0.714 0.692 0.687
0.74 0.42 0.43
ð22Þ
k1 ðv p;t þ v plug Þ
lv plug
1 1 Dc
ð23Þ
5. Conclusions Based on pressure drop measurement and AE detection, this work first investigated the vertical transportation of a single plug. Results showed that for plug with larger length, the unsteady flow appeared when the plug decomposed and partial particles in the front of the plug fell down and collided with the bulk of the plug. The unsteady flow could induce the second increase of the pressure drop through the whole pipe, the local negative pressure drop, and the sharp increase of acoustic energy. Decomposing the acoustic signals by wavelet analysis, it was found that the plug-wall interaction was dominated by friction, while in the front and back end of the plug the particle-wall interaction was dominated by collisions. Applying the AE detection and pressure drop measurement to the real continuous plug flow, the results were almost the same to those in the single plug conveying process. Therefore, the AE technology might be a good way for the detection of unsteady flow in the real plug conveying just the same to pressure drop measurement. Moreover, the pressure drop was predicted by Konrad’s
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Y. Yang et al. / Chemical Engineering Science 211 (2020) 115260
model and it was proved that for the plug flow in the vertical conveying process, the axial wall stress was larger than the normal stress, thus smaller deviation between the predicted and the measured pressure drop was acquired when using the active Janssen coefficient. Based on above measurement, the sources of acoustic signals in the plug flow were divided into two parts: the collision between dispersed particles and the plug, and the friction between the plug and the wall. Furthermore, an acoustic model was established which describing the relationship between the acoustic energy fraction of collision (Dc) and the Janssen coefficient. The predicted Dc agreed well with the experimental one with a relative deviation lower than 0.8%, under the fitted k1 of 0.1. Therefore, the established model was proved to be corrected and it further provides a possibility for the non-intrusive, real-time and online detection of Janssen coefficient. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The authors acknowledge the support and encouragement of the National Natural Science Foundation of China, China (21808197), The National Science Fund for Distinguished Young, China (21525627) and the Science Fund for Creative Research Groups of National Natural Science Foundation of China, China (61621002). References Cong, X., Guo, X., Lu, H., Gong, X., Liu, K., Sun, X., Xie, K., 2013. Flow patterns of pulverized coal pneumatic conveying and time-series analysis of pressure fluctuations. Chem. Eng. Sci. 101, 303–314. Daoud, K., Ould Dris, A., Guigon, P., Large, J., 1993. Experimental study of horizontal plug flow of cohesionless bulk solids. KONA. Powder. Part. J. 11, 119–124. Dong, K., Zhang, Q., Huang, Z., Liao, Z., Wang, J., Yang, Y., Wang, F., 2015. Experimental investigation of electrostatic effect on particle motions in gassolid fluidized beds. AIChE J. 61, 3628–3638. E, D., Wang, H., 2010. Design and analysis of polypropylene. Process. Eq. Pip. 47, 21– 22. He, Y., Wang, J., Cao, Y., Yang, Y., 2009. Resolution of structure characteristics of AE signals in multiphase flow system—from data to information. AIChE J. 55, 2563– 2577. He, L., Zhou, Y., Huang, Z., Wang, J., Lungu, M., Yang, Y., 2014. Acoustic analysis of particle–wall interaction and detection of particle mass flow rate in vertical pneumatic conveying. Ind. Eng. Chem. Res. 53, 9938–9948. He, L., Yang, Y., Huang, Z., Liao, Z., Wang, J., Yang, Y., 2016. Multi-scale analysis of acoustic emission signals in dense-phase pneumatic conveying of pulverized coal at high pressure. AIChE J. 62, 2635–2648.
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