Assessment of polydisperse drag models for the size segregation in a bubbling fluidized bed using discrete particle method

Author’s Accepted Manuscript Assessment of polydisperse drag models for the size segregation in a bubbling fluidized bed using discrete particle method Yong Zhang, Yuemin Zhao, Liqiang Lu, Wei Ge, Junwu Wang, Chenlong Duan www.elsevier.com/locate/ces

PII: DOI: Reference:

S0009-2509(16)30623-6 http://dx.doi.org/10.1016/j.ces.2016.11.028 CES13251

To appear in: Chemical Engineering Science Received date: 27 September 2016 Revised date: 5 November 2016 Accepted date: 14 November 2016 Cite this article as: Yong Zhang, Yuemin Zhao, Liqiang Lu, Wei Ge, Junwu Wang and Chenlong Duan, Assessment of polydisperse drag models for the size segregation in a bubbling fluidized bed using discrete particle method, Chemical Engineering Science, http://dx.doi.org/10.1016/j.ces.2016.11.028 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Assessment of polydisperse drag models for the size segregation in a bubbling fluidized bed using discrete particle method Yong Zhanga,b, Yuemin Zhaoa, Liqiang Lub, Wei Geb,c, Junwu Wangb*, Chenlong Duana* a

School of Chemical Engineering and Technology, China University of Mining and Technology, Xuzhou,

221116, P. R. China b

State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese

Academy of Sciences, Beijing 100190, P. R. China c

University of Chinese Academy of Sciences, Beijing, 100049, P. R. China

jwwang@ ipe.ac.cn [email protected] *Corresponding author. Tel.: +86 10 82544842; fax: +86 10 62558065.

Abstract Polydisperse gas-particle flow is often encountered in industry and many polydisperse drag models have been developed in literature. In this work, discrete particle method was employed to assess polydisperse drag models for the segregation and mixing of binary gas-particle flow in a bubbling fluidized bed. The degree of particle segregation and the characteristic bubble frequency using different polydisperse drag models were analyzed. It was shown that the results predicted by the model of Rong et al (Chemical Engineering Science, 2014, 116: 508-523) are in a best agreement with experimental data with 5.3% errors on average, and two dominant bubble frequencies were found by analyzing the fluctuations of average particle height. Graphical abstract

Keywords: Drag force model; Fluidization; Gas-solid flow; Multiphase flow; CFD-DEM method 1. Introduction Fluidized bed technologies have been widely used in chemical engineering, energy utilization and environmental protection. In these practical applications the sizes of particles are normally polydisperse rather than monodisperse and segregation may occur in the reactors. The particle segregation phenomenon has attracted many researchers to investigate because segregation rates and degrees directly affect the efficiency of reaction and heat transfer (Das et al., 2008; Zhou and Wang, 2015). For example, in metallurgical industry the minerals of wide-size distribution need to be classified into several products with different sizes (Sahu et al., 2015), but in coal gasification, it required that the multi-size coal particles mixed well to ensure uniform heat transfer and reaction (Lundberg et al., 2016). Some experimental results have found that lower gas velocity promotes segregation whereas higher gas velocity facilitates mixing process (Goldschmidt et al., 2003; Leboreiro et al., 2008).

In an attempt to figure out the mechanism of segregation and mixing process, numerical methods have been developed such as Eulerian-Eulerian (EE) model (Cooper and Coronella, 2005; Huilin and Gidaspow, 2003; Santos et al., 2016) and Eulerian-Lagrangian (EL) model (Deen et al., 2007; Peng et al., 2016). EE models treat the fluid and solid as interpenetrating continua, therefore, they have great advantages in terms of computational cost as compared to CFD-DEM method, but coarse-grained EL methods , such as MP-PIC method (Snider, 2001; Sundaresan, 2011), can be computationally more effective than EE models, due to the usage of the concept of parcels and of the allowed larger time step. Besides, some researchers have pointed out that EE models have some difficulties in predicting the segregation process and segregation rates quantitatively (Bokkers et al., 2004; Peng et al., 2016). On the other hand, EL models are often used by treating solid phase and gas phase as discrete particles and continuum respectively. By adopting Lagrangian method, EL models are believed to be better in the prediction of segregation and mixing of particles (Deen et al., 2007; Xu and Yu, 1997; Zhu et al., 2007) . Furthermore, the drag models are thought as the pivotal factor in closing the interactions between gas and particles no matter of EE model or EL model. A variety of drag models were put forward through fitting either experimental data or direct numerical simulation (DNS) results (Cello et al., 2010; Gidaspow, 1994; Rong et al., 2014; Sarkar et al., 2009). There were also a lot of articles concentrating on the validation and comparison of these drag modes (Beetstra et al., 2007b; Di Renzo et al., 2011; Leboreiro et al., 2008; van Wachem et al., 2001). However no one was well accepted in view of the continuous appearance of new correlations, because these models usually were generated based on different conditions such as dilute or dense system, gas-solid or liquid-solid system and so on. Besides, a lot of drag models deduced from DNS thought static particles (Beetstra et al.,

2007a; Hoef et al., 2005; Rong et al., 2013, 2014), it is of a large difference from the actual fluidized beds. This paper study the applicability and accuracy of several drag models derived from experiments or DNS recently. The simulation of the prediction of minimum fluidization velocity by different drag models were conducted firstly. Then the data involved segregation degrees and bubble frequency of experiments were employed to compare the simulation results comprehensively. EL model, also called CFD-DEM method or discrete particle method, was employed in this paper by combining the open software of OpenFOAM and in-house code of DEMMS (Lu et al., 2016; Lu et al., 2014; Xu et al., 2011). It however should be noted that by contrast to our previous studies using the same code (Lu et al., 2016; Lu et al., 2014), in present study, no EMMS drag model has been used, because we are studying the fluidization behaviour of very coarse particles with sufficient scale resolution (Carlos Varas et al., 2016; Wang et al., 2009). 2. Discrete particle method 2.1 Governing equations The simulation method used in this paper could be divided into two parts: the calculation of gas phase in CPUs and the calculation of solid phase in GPUs. The particles information of volume fraction, velocity and the gas sections of velocity and pressure were exchanged by shared memory blocks. The parallel calculation was developed through the platform of CUDA (Compute Unified Device Architecture). The discrete particle equations were calculated on a single particle by Newton’s equation as given below:

mp

dv p dt

 m p g  Fd,i  Fcol  V pP (1)

Ii

dwi  Ti (2) dt

Fd,i 

 0V p ug  vp  (3) s

Fd,i represents the drag force between gas and solid, Fcol is the collision forces among particles.

mpg is the gravitational force and VpP is the pressure gradient force. Soft sphere model is adopted to treat particle-particle and particle wall interactions, details of which can be found in [26]. The governing equations for gas phase are summarized below:

 g  g t

   ( g  g u g )  0 (4)

 g  g u g  t

   ( g

  u u )   P 

n i 1 d,i

g

g

g

g

F



   ( g g )   g  g g (5)

It should be noted that ug is the gas velocity of a grid and Ω represents the volume size of a single grid. 2.2 Drag models for polydisperse particle system Over the last decades the monodisperse drag models were deduced through normalized drag F(εs,Re) based on Stroke-Einstein equation as shown in Eq(6). The exponential and linear expressions are generally developed to derive F(εs,Re) by experimental data or lattice-Boltzmann simulations as equations of (7) & (8). Furthermore the polydisperse drag models are often achieved by modifying the mono-drag models (Beetstra et al., 2007a; Cello et al., 2010; Rong et al., 2014; Sarkar et al., 2009).

F  s , Re  Fdrag / 3dU (6)

F  s , Re  F  s ,0    s  Re (7) F  s , Re  F 0, Re s  (8) The calculation of drag force would convert to solve the normalized drag force F(εs,Re).

According to linear Eq (7), some researchers (Blake, 1921; Burke and Plummer, 1928) gave the expressions as follows: F ( s ,0) 

a s 18(1   s ) 2

 ( s ) 

b (9) 18(1   s ) 2

Ergun (Ergun, 1952) conducted experiments with 640 types particles by pressure analysis and given the exact parameters for a=150 and b=1.75. However on the basis of Eq(8), more researchers concluded the expression of F(0,Re) for a single particle firstly and classified the fluid dynamics to several different regime such as Stroke flow, Allen flow or turbulent flow. Then by measuring the particles terminal velocity in the suspensions, the expression β can be achieved. Wen & Yu (Wen and Yu, 1966) suggested Schiler & Nauman equation (Schiller and Naumann,

1933) for F(0,Re) and β=3.7 for dilute system. Gidaspow et al combined the linear equation of Ergun and exponential equation of Wen & Yu to express the system for 0.2<εs<1 and 0<εs<0.2 (Gidaspow, 1994), respectively. Although some questions were put forward to modify Gidaspow et al model (Hill et al., 2001; Hoomans et al., 1996) , it is still widely applied in various simulation software and industrial productions. More other expressions deduced from DNS adopted similar method to acquire the expression of Eq(7) & (8) by fitting the data of the simulations. Except for above derivations, researchers have also done efforts to modify the pressure gradient term in Eq(1) because for multi-sizes system the pressure drop is closely related to the particle surface area rather than volume fraction and their method could distinctly improve the models’ accuracy (Feng and Yu, 2004). Two methods have been raised by extending the monodisperse drag to achieve polydisperse drag models. Firstly, we could directly calculate drag force of each particle by using mono-disperse drag model to sum all the drag forces of different types of particles. The

parameters of Rei and εsi use the individual particle. The second calculation is to adopt average parameters of system to derive the total drag force fd and then distribute to different types particles through a certain rule, the average parameters of system such as average diameter and Reynolds number Re are given: c  xi  si  s    si s i 1

 c xi   d     i 1 d i 

1

yi 

di d 

Re 

 g g  d  Us l i p (10) 

Uslip represents the module of the slip velocity between gas and particles. Table 1 listed four expressions that will be applied in this paper. Except for Gidaspow et al’s model, the other drag models are all calculated using the second method. Sarkar et al’s model and Rong et al’s model were deduced based on lattice-Boltzmann simulations while the Gidaspow et al’s model is through experiments. Cello et al’s model is a semi-empirical model by fitting the simulation data from Van Der Hoef et al (Hoef et al., 2005) and Hill et al (Hill et al., 2001), plus deriving from model of Turton et al (Turton and Levenspiel, 1986). Fig. 1 presents the drag force ratio of large particle and small particle as functions of Reynolds number and porosity by different models. Table 1. Summary of poly-disperse drag models used in discrete particle simulation

Source

Equations

Gidaspow et al

f d ,i

(Gidaspow, 1994).

Sarkar et al (Sarkar et al., 2009).

Cello et al (Cello et

f d ,i fd fd  f d ,i fd

150(1   g )  1.75 Rei  g  0.8  18 g    Rei C   3.65   0.8 g  24 d 0 g

 yi 10 g (1   g )

 yi 

2

 (1   g ) 2 (1  1.5 g2 ) 

1 0.343 0.413 Re (1   g )  3 g (1   g )  8.4 Re [ ] 3 g (1 4 g ) / 2 2 24(1   g ) 1  10 Re

1   g  1   g  0.27  ( yi2  yi )    g  1  0.27  n xi yi i 1

al., 2010).

f d  K1  K 2 g4  K3 (1   g4 ) K0 

1  g 1  3 g

K2 

K1 

1  128K 0  715K 02  g2 (1  49.5K 0 )

1  0.13 Re 6.66 *104 Re 2 1 1  3.42 *102 Re 6.92 *106

 410 g  9.2 *107 Re K 020  1900 2g  6.6 *102 Re 2 Re 2 K3  ( )( ) 1  Re 6600 g  4.92 *104 Re 43000 g2  1.31*104 Re 2  73800 g3

f d ,i fd

Rong et al (Rong et al., 2014).



fd 

0.5 g

i1 ( xi / yi2 ) n

 0.5(1   g ) yi2  0.5 yi

Re   (Re, g ) Cd 0 g 24

 (Re,  g )  2.65(1   g )  (5.3  3.5 g ) g2 exp  0.5(1.5  log Re) 2  Rei 

 g  gUdi 

Re 

 g  gU  d  

Fig. 1. The drag ratio of large particle and small particle as functions of Reynolds number and porosity (The particles

parameters in Table2 were used for calculation here)

3. Simulation conditions The main aims of this paper were to assess the available polydisperse drag models for

predicting segregation and mixing of binary gas-solid flow in a bubbling fluidized bed and study the size segregation mechanism which may not easily observed through experiments. The simulation results are finally compared to the experiments of Goldschmidt et al (Goldschmidt et al., 2003) where the binary glass particles of 1.5mm and 2.5mm are fluidized by air in a pseudo-2D transparent bed and the image analysis technique was conducted by digital camera. The mass fraction of 50% 1.5mm particles as well as 50% 2.5mm particles are used as the mixture and the experimental minimum fluidization gas velocity is about 0.93m/s. The gas velocities of 1.05m/s, 1.15m/s and 1.25m/s were carried out, and other simulation parameters are all listed in Table 2. Segregation degrees were calculated by recording the heights of the small particles and large particles within 60 seconds and segregation degree was defined as follows: s

S  1 (11) S max  1

where S=/hlarge, Smax=(xlarge+1)/xlarge. and hlarge represent the averaged heights of small particles and large particles respectively, and xlarge is the mass fraction of large particles. Hence when s=0, the system is completely mixed whereas s=1 is for complete segregated system. Because the segregation degrees of experiments were measured by three times for each condition, we adopted the average values of three times to compare with simulation results. Except for the comparison of segregation degree, the bubble frequency was also studied by analyzing the variation of bed heights in Part 4.3. At beginning of simulation, all particles distributed randomly representing completely mixing condition and fallen freely to the bed for accumulating. The boundary conditions are set as no-slip and free-slip for y-coordinate and z-coordinate respectively as studied by Beetstra et al before (Beetstra et al., 2007b).

Table 2. Summary of the parameters used in simulations Bed size (width×height×depth)

0.15m×0.45m×0.015m

Grid numbers(x×y×z)

20×60×2

Gas velocity (m/s)

1.05, 1.15, 1.25

Particles

Large

Small

Diameter (mm)

2.5

1.5

Number

11960

55420

Density(kg/m3)

2523

2523

Young modulus (Pa)

5×108

5×108

Poisson ratio

0.33

0.33

Coefficient of normal restitution

0.97

0.97

Coefficient of friction

0.1

0.1

4. Results and discussion 4.1 Minimum fluidization velocity

Fig. 2. Prediction of the minimum fluidization velocity by different drag models

The variations of the pressure drop with gas velocity using different drag models are presented in Fig. 2. The data of the pressure drop for each gas velocity was the average values of at least 5 seconds after the bed was reaching the statistically stationary state. It can be seen that the minimum fluidization velocity predicted by the drag correlation of Cello et al (1.01m/s) is obviously higher than those obtained by other models (0.95m/s) as well as the experiment result of 0.93m/s. Because the particles were not possible fluidized fully considering the formation of bubbles and some de-fluidized zones of the bed, the highest pressure drop is reasonably smaller than the value of Plift off as shown in Fig. 2. 4.2 Segregation and mixing process

Fig. 3. Segregation degrees as function of time by different polydisperse drag models and their comparison with

experimental data

Fig. 3 presents the simulation results of the segregation degrees by different drag models. In spite of some discrepancies as compared to experiments, the simulation results substantially reflected main features of experiments and the main results were listed as follows: (i) Different particles could segregate easily at lower gas velocities but mix well above a critical gas velocity. At lower gas velocity the bubbles in the bed are smaller and the particles segregation would occur. Small particles are more easily drown to the top layer and large particles sediment at the bottom. It is also easily to understand that the larger gas velocity implies bigger and faster

moving bubbles which cause the mixing process. (ii) The segregation degrees increased monotonously in experiments and reached the maximum values of about 50% for segregation system as shown in Fig. 3. For a gas velocity of 1.15m/s, each drag model can predict the similar maximum value as in the experiment except that Gidaspow et al’s model shows a larger maximum value of near 60%. For a velocity of 1.05m/s, the maximum segregation degrees of simulation results are generally lower than experiments by four models. When gas velocity is equal to 1.05m/s, the particles in the bed moved slowly and the segregation mainly occurred in the top layer while the particles at the bottom remained the state as beginning state.

Fig. 4 The average errors of segregation degrees for different drag models

(iii) For strongly segregation system, it took about 45-50s to reach the maximum segregation degree in experiments. The simulation results of Sarkar et al and Rong et al shown more quickly segregation rates compared with experiments, only 20-30s to reach stable values. On the other hand the particles segregation rate predicted by Cello et al model presented almost the same results as experiments for condition of 1.15m/s. Gidaspow et al’s model predicted the most quickly segregation rates for both 1.05m/s and 1.15m/s compared to other models. In order to explain such differences of segregation rate shown in Fig. 3, it can be deduced that the greater drag ratio implicates larger drag force for larger particles or smaller drag force for small particles. That is to say large particles are more easily drown up to top layer while small particles trend to accumulate at the bottom, which could retard the segregation process. Because the porosity larger than 0.8 is attribute to the bubbles mixing scope, the porosity range from 0.45 to 0.8 should be paid attention to. It can be inferred from Fig .1 that the model of Cello et al would predict lower segregation rate whilst the model for Gidaspow et al calculated higher segregation rate. We also found the ratio values calculated by Sarkar et al and Rong et al were mainly moderate and had similar changes corresponding to the results of Fig. 3. The absolute errors of segregation degrees between experiments and simulations were calculated as shown in Fig. 4. The equation for calculating the average errors (AE) is shown in Eq(12):

AE 

1 n  ( Sex  Ssi ) (12) n i 1

It can be seen that the averaged absolute error for Rong et al’s model was approximately 5.3%, which is lower than other three models. 4.3 Bubble frequency analysis The effect of bubbles on segregation and mixing can be classified as two aspects. Firstly

when two sizes of particles have reached segregation state, namely large particles stay at the bottom while small particles distribute in the top. Because large particles at the bottom have high porosity, gas flow can easily aggregate into bubbles which carry the large particles from bottom to the top eventually promoting mixing process. Secondly if gas velocity is high and big bubbles are generated, the particles would become active or move quickly and large particles as well as small particles can be easily lifted by bubbles, as a result, segregation process is replaced by the mixing process.

Fig. 5. Fourier analysis of the height of overall particles, small particles and large particles by Rong et al model at

different gas velocities

We recorded the averaged heights of the overall particles, small particles and large particles within 60 seconds and the results of Fourier analysis were shown in Fig. 5. It can be seen there is a prodigious peaking values when frequency is close to 0 Hz, this is because the particles were fallen freely to heap up from a certain height at beginning. When gas velocities were 1.05 m/s and 1.15m/s two dominant frequencies can be clearly shown, which was also mentioned in Goldschmidt et al’s article (Goldschmidt et al., 2003). It was thought that the lower frequency was caused by the hardly fluidized bottom area while the higher frequency was mainly due to the effect of the top smaller particles. Taking the case of 1.05m/s as an example, when frequency is equal to 1.95Hz, the signals from overall particles, small particles and large particles correspond to

each peaking values and have similar variation tendency. The above 1.95Hz is marked since the rising bubbles have same impact on the average height of overall particles, small particles and large particles when two types of particles mixed well as shown in Fig. 6(A). However for the higher dominant frequency of about 3.95Hz, the amplitude values of overall particles and small particles are alike at peaking value. The reason can be explained that bubbles mainly result in the fluctuations for the height of small particles when two types of particles separate completely shown in Fig. 6(B). The rising bubbles may also drive the large particles up to decrease the segregation degree.

Fig. 6. The different effects of bubbles on the mixing pattern (A) and segregation pattern (B) For mixing system at higher velocity as shown in Fig. 5(c), there is only one dominant frequency because no obvious separation process occurs at higher velocity and all particles are mixed well. The lower frequency such as 1.95Hz is defined as first frequency in our paper (which is also called bubbles frequency in experiments of Goldschmidt et al) while higher frequency such as 3.95Hz mentioned above is defined as second frequency as results of small particles motion. Table 3 listed the values of first frequency and second frequency by different drag models as well

as experimental data at three gas velocities. It is important to note that the experiments by Goldschmidt et al just recorded the first frequency (bubbles frequency), but we listed first frequency and second frequency in Table 3. Although the segregation degrees calculated by each model had a large difference as shown in Fig. 3, the first frequency predicted by different models were similar as experiments in a whole. Besides, the bubble frequency was almost the same at different gas velocities for both experiment and model prediction as shown in Table 3. This gave us a clue that the segregation degrees is not only affected by the number of bubbles of the bed but also influenced by the characters of bubbles itself such as dimensions or velocity of bubbles and this aspect is our next research direction. Table 3. The calculation of first frequency and second frequency by different drag models

Model

1.05m/s

1.15m/s

1.25m/s

First frequency/(Second frequency) Gidaspow et al

2.05/(3.3)

2.15/(3.95)

2.15

Cello et al

1.75/(2.95)

2.0/(3.62)

2.05

Sakar et al

1.9/(3.70)

2.2/(3.45)

2.0

Rong et al

1.95/(3.95)

1.95/(3.0)

1.90

Experiment

1.8~1.85

2.05~2.15

1.9~2.0

5. Conclusion A parallel CFD-DEM code based on the software of OpenFOAM and DEMMS was used to study the particle segregation and mixing process. The simulation results were compared and validated against the experiments of Goldschmidt et al (Goldschmidt et al., 2003). The following conclusions were made: (1) The variation of the segregation degree with time was simulated by four polydisperse drag

models and compared to experiments. The mixing process at high gas velocity could be precisely described by different drag models but for segregation process at low gas velocity, the models of Sarkar et al and Rong et al had similar variation trends and they were more accurate than Gidaspow et al and Cello et al model. The error analysis shown that the averaged errors of segregation degree for Rong et al model was about 5.3%, less than other models. (2) Two dominant bubble frequencies were observed by analyzing the variation of average particle heights. The first frequency was created when particles mixed well and bubbles could have an effect for both small particles and large particles, but the second frequency is mainly caused by the top small particles fluctuations strongly segregation system. If there is no segregation process of fluidized bed at high gas velocity, only first frequency could be found. The results of bubbles frequency were also compared to the experiments and had a good agreement. Acknowledgment The authors acknowledge the financial Support by National Natural Science Foundation of China (No. 51620105001, 51304196, 91434133, 21406238), Natural Science Foundation of Jiangsu Province (No. BK20160055) and the Priority Academic Program Development of Jiangsu Higher Education Institutions. Reference Beetstra, R., van der Hoef, M.A., Kuipers, J.A.M., 2007a. Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres. AIChE Journal 53, 489-501. Beetstra, R., van der Hoef, M.A., Kuipers, J.A.M., 2007b. Numerical study of segregation using a new drag force correlation for polydisperse systems derived from lattice-Boltzmann simulations. Chemical Engineering Science 62, 246-255. Blake, F.C., 1921. The resistance of packing to fluid flow. Transactions of the American Institute of Chemical Engineers 14, 415-421. Bokkers, G.A., van Sint Annaland, M., Kuipers, J.A.M., 2004. Mixing and segregation in a bidisperse gas–solid fluidised bed: a numerical and experimental study. Powder Technology 140, 176-186. Burke, S.P., Plummer, W.B., 1928. Gas flow through packed columns. Industrial and Engineering

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of

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Highlights 

A parallel CFD-DEM model was used to simulate polydisperse system.

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The effects of polydisperse drag models on the size segregation were studied.

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Two dominant bubble frequencies were found in binary system.