Numerical and experimental studies of irregular-shape biomass particle motions in turbulent flows

Engineering Science and Technology, an International Journal 22 (2019) 249–265

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Numerical and experimental studies of irregular-shape biomass particle motions in turbulent flows A. Elfasakhany a,⇑, X.S. Bai b a b

Department of Mechanical Engineering, Faculty of Engineering, Taif University, Box 888, Taif, Saudi Arabia Department of Energy Sciences, Lund University, 221 00 Lund, Sweden

a r t i c l e

i n f o

Article history: Received 18 March 2018 Revised 19 August 2018 Accepted 5 October 2018 Available online 17 October 2018 Keywords: Numerical models Experiments Biomass micro size particles Turbulent flow Irregular-shape

a b s t r a c t This paper discusses numerical and experimental studies of biomass micro scale particles motion in turbulent flows. The biomass micro size particles are extremely anisotropic and typically of irregular shape with sizes varying between 200–6000 lm in length and 125–1400 lm in diameter. Four different types of biomass micro size particles from different sources are applied. Ten different numerical modelling tools for simulation of the biomass micro size particles motion in turbulent flow are presented and validated against experiments. The experiments are carried out using three different techniques: an aerodynamic classifier, vibrating sieve and microscopic image analysis. Results showed considerable discrepancy between the models and the experiments. In consequence, a comprehensive new shape factor correlation for the irregular-shape particles is proposed, which enhances significantly the model results. Parametric studies are also carried out, including influence of particle shape, size, and anisotropy criteria. Moving orientation of the irregular-shape particles in turbulent flow is addressed as well. Results demonstrated that the key issue for modelling of biomass micro size particle motion in turbulent flow is both drag coefficient and particle-projected area. Small size of biomass particle is quickly accelerated and it tends to follow airflow; larger biomass micro size particle is slowly accelerated and it decelerated rapidly because of less response to air stream. Additionally, both small and large biomass micro size particles tend to orient themselves to one preferable direction. Ó 2018 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction One of mandatory steps towards successful simulation of any droplets or powders combustion in turbulent flow is to determine the particle motion accurately. Indeed, the particle motion plays a central role in any process involving relative velocity between solid particles and a viscous medium. The motion of droplets or spherical particles in incompressible viscous medium is now available with a wide knowledge of various aspects [1–3]. However, the corresponding work on the motion of irregular-shape particles, as encountered in most real life application, is much less extensive and emerging picture is also rather incoherent. Most of the progress in this area has been made through the use of empirical formulations; the researchers have developed correlations based on their own experimental data and these have rarely been validated using independent experimental results.

⇑ Corresponding author. E-mail address: [email protected] (A. Elfasakhany). Peer review under responsibility of Karabuk University.

Researchers applied several methods to predict motion of irregular-shape particles in turbulent flow based on shape factor such as sphericity, volumetric shape factor as well as based on other shape parameters. In particular, Moley et al. [4] showed several kinds of shape factors or indicators to characterize particle shape of irregular-shape particles. Clift et al. [5] concluded that the sphericity is not a good basis for predicting the motion of irregular-shape particles, except for oblate shapes with a sphericity approaching unity. Xie and Zhang [6], however, argued that the sphericity is generally the most frequently referred particle shape factor for the irregular-shape particles; this is due to that the other shape factors could be correlated as a function of sphericity shape factor; for example, stokes shape factor is correlated as a function of sphericity shape factor [6]. According to our literature review, yet the different methods have been contrasted with each other. For this reason, a universal correlation encompassing a wide variety of particle shapes and kinematics’ conditions is yet to emerge [7]. One of the needs and/or the first step towards addressing a generalized relation for the irregular-shape particle motion in moving fluid stream is to determine forces acting on the particle motion.

https://doi.org/10.1016/j.jestch.2018.10.005 2215-0986/Ó 2018 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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The forces most influential on the irregular-shape particle motion, according to Rusaas [8] and Rosendahl [9], are body force and drag force. The drag force is characterized as the most important one and, accordingly, many researchers spent a lot of efforts to develop reliable and accurate numerical method for estimating the drag force in viscous fluids. However, most of the previous studies in this area involved just spherical particle, while irregular-shape particle was considered rarely. This is due to that the spherical particle is easier in experimental and numerical studies. In particular, drag coefficient is strongly influenced by several factors such as particle size and shapes so that determining or measuring such value in irregular-shape is very challenging, while it is simple for the regular-shape particle [10]. Reviewing literature on calculating drag coefficient of irregular-shape particles can confirm this outcome, as follows. Grbavcic et al. [11] suggested a model based on a single dimensionless parameter to reduce the complexity for calculating fluid-particle inter phase drag coefficient for the irregularshape particles; the advantage of this model is that it does not require precise data for particle diameter and shape factor. Additionally, such model overcomes the problem of irregular particle shape and produces very good results. However, it is not a complete model since some model’s parameters could not be calculated but they are measured instead. Another method tried to

Ug

Up

Apr

develop a drag expression based on fixed particle shape and orientation that was presented by Ui et al. [12] and Huner and Hussey [13] for irregular-shape particles in axial motion, and by Michael [14] and Shail and Norton [15] for discs shaped. However, the drawback of this method is that these correlations of drag coefficient are not possible to be applied to another shape and/or orientation rather than the one built for. One more approach, presented by Madhav and Chhabra [7], Chien [16], Hartman et al. [17], Haider and Levenspiel [18], Thompson and Clark [19] and Ganser [20], is

AP2

Dp

Lp

AP1 Fig. 1. Schematic view of particle projected area and most probably flying orientation.

Fig. 3. Schematic view of aerodynamic classifier (ADC).

Fig. 2. Images of four tested biomass particles (Enk, Has, Nor and Valb).

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based on developing one correlation for all shapes and orientations; but this approach is less accurate than the specific shape one. A different approach with wide range of parameters such as equivalent volume sphere diameter, sphericity factor, equivalent surface area sphere diameter etc., has been used to define drag coefficient as a function of Reynolds number. This approach was applied successfully for some applications, see e.g., List and Schmeanauer [21], Unnikrishnan and Chhabra [22], Swamee and Ojha [23], Finn [24], Kasper and Yang [25], Sharma and Chhabra [26] and Jones and Knudsen [27]. However, it is not applicable for other applications. Gerhardter et al. [28] studied a drag analysis of crushed coal slag particles with sizes between 400 and 850 lm. The study examined three different drag models from literature for non-spherical pulverized coal particles. In comparison to pulverized coal particles, biomass particles vary considerably in particle shape and thus, the models for non-spherical pulverized coal particles may not applicable for the biomass particles; additionally, the change of the aspect ratio of biomass particles varied from coal and that may affect the motion and conversion of biomass particles. Liu and Shen [29] studied the effect of biomass particle shape on fuel combustion in blast furnaces. The study applied one model feature for non-spherical particle shape and compared the burnout with the spherical particle. Results concluded that it is necessary to include the effect of the non-spherical particle shape, while modelling of biomass combustion in furnaces. The work by Wittig et al. [30] investigated numerically the influence of particle drag coefficient on porosity, Reynolds number and Nusselt number of particle. The particle drag coefficient is modeled using spherical and non-spherical (cubical) shapes. The results showed a significant influence of drag coefficient on porosity, Reynolds number and Nusselt number. Consequently, one key of modeling biomass particle combustion is to model the drag coefficient accurately. Based on literature review discussed above, particle shape and orientation are ones of central keys for defining drag expression and, consequently, calculating the particle force. Particle shape and orientation influence on the migration velocity of irregularshape particle in turbulent flow. Additionally, the migration velocity in the force field is particle-size dependent; in particular, particle size dominates the behaviour of solid micro size particles in gas suspension; micro size particles behave differently in different size ranges and are even governed by different physical laws. For example, particles slightly larger than gas molecules are governed by Brownian motion, while large and visible particles are affected by gravitational and inertial forces [31]. Besides, particle shape, size and orientation can be quite complex and are often defined by extent one parameter that can be used to measure or calculate them. Therefore, there are numerous methods for defining particle shape, size and orientation that depend on the measurement techniques or defining which parameter is more applicable to be included. In particular, particle shape has been acknowledged by including a shape factor in the equation of particle motion. In case of irregular-shape particles, inclusion of this factor in the equation allows one to calculate the desired parameter while characterizing complex particle shapes by a single dimension. Although this provides an indication of the particle’s behaviour under certain condi-

tions, it does not provide sufficient detail to fully characterize the particle. Since the motion of irregular-shape particle in turbulent flow is strongly influenced by the particle orientation, as discussed above, a number of researchers spent a big effort to study the particle orientation in flow field. Some of them showed that the motion or the free fall of irregular-shape particles are mainly through their longitudinal axis normal to the direction of motion [32–36]. Others argued that the irregular-shape particle might fall either with its longitudinal axis parallel or normal to the direction of its motion,

Fig. 4. Simulation of airflow velocity vectors at different sections along the ADC and two views (top and side).

Fig. 5. Tracing of different particle sizes inside the ADC; Dp dents diameter in lm.

Table 1 Diameter (Dp), length (Lp) and mass percentage (MF) of the four tested biomass particles (Enk, Has, Nor and Valb) studied in the experiments. Dp (lm)

Lp (lm)

MF Enk

MF Has

MF Nor

MF Valb

125 250 500 710 850 1000 1400

200 300 700 2000 3000 4000 6000

14.3 21.9 42.6 18.7 2 0.5 0

8.1 14.7 30.9 23.6 8.3 8.1 6.3

32 26.4 30.2 9.2 1.4 0.6 0.2

2 15 37 34 8.5 2.5 1

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depending upon the values of the Reynolds number and the length to diameter ratio [5]. One more group of researchers concluded that the behaviour of irregular-shape particles in flow fluid is within their longitudinal axis along the direction of its motion [37,38]. According to that, the results in this area is highly conflicted and there is no work found in the literature, for instance, dealing with particle orientation when particle moves horizontally rather than vertically. In addition to particle conditions (particle size, shape and orientation) the flow field condition can influence on the particle motion. In case of creeping flow regime (Reynolds number is smaller than 0.1), the modelling calculation is expressed in a form of a correction factor to the Stokes formula for spherical particles [39–42]. The correction factor, in turn, has been correlated with a variety of geometric parameters characterizing the irregular-shape particles. Out of creeping flow regime (Reynolds number is larger than 0.1), where many applications are placed, the correction factor is a function of Reynolds number in addition to the shape and orientation of irregular-shape particle, where the study comes to be more complicated. In literature, there are limited numbers of experimental results available outside the creeping flow regime even for simple shaped particles such as cylinders, prisms, wires, etc. [7]. Based on the early discussions and literature review, irregularshape particle models have been contrasted with each other and a universal correlation encompassing a wide variety of particle shapes, orientations and kinematics’ conditions is yet to emerge [7]. The aim of the current study is to develop a generalized modelling tool for simulation of irregular-shape particle motion in turbulent flow. Such modelling tool is essential for simulation of

biomass combustion in industrial furnaces and boilers, especially biomass is one of the most promising renewable fuel for the next decades, see e.g., [43–57]. Ten different models form literature are presented and tested against experimental data. Experiments are carried out using different techniques. A new shape factor correlation is proposed and validated with all models. The scenario of the current work is by validating each model with the experimental data (for four different biomass fuels). When the model and experimental results are disagreed, this leads to a modification of the model and, in turn, a second round of modelling validation is carried out; the ten models are validated in the same strategy. Sensitivity study on the modelling tool is also carried out with addressing the most influential parameters on the irregularshape particle motion.

2. Mathematical modelling The numerical models for two-phase flows are either based on one way or two-way coupling. In case of particles did not effect on the motion of the gas-phase, the solution procedure was simply to solve for the gas-phase velocities and turbulent quantities and then use those values as an input to solve for the particle motion, i.e. one way coupling is applied. However, in case of high number density of particles, two-way coupling should be used instead. In such case, Eulerian/Lagrangian approach is used where the continuous phase is calculated numerically by solving the Reynolds averaged NavierStokes equation and k-e turbulence model, while the trajectories of the particles are obtained by integrating the equation of motion. In

Fig. 6. Numerical simulation of model 1 at one-way coupling (M1) and two-way coupling (M1 cou) compared with experimental data (Exp) for four biomass types (Enk, Has, Nor and Valb).

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the current study, both ways (one way and two-way coupling) are applied. For the gas phase calculations, we write the conservation equations of mass and momentum and for the discrete phase, we use the general equation of motion as follows.

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The forces will, therefore, be wide numbers; but they can alternatively be described qualitatively by considering only the most influenced ones on the particle motions. The forces most influential on the particle motion, according to Rusaas [8] and Rosendahl [9], are body force and drag force, as discussed early. Therefore, these two forces are considered for calculating particles equation of motion as follows.

@q þ div ðquÞ ¼ 0 @t

ð1Þ

@ qui @ qui uj @p @ sij ¼ þ þ Sui þ @xi @xj @t @xj

ð2Þ

2.1. Body force


 X! d Mp Up Fi ¼ dt i

ð3Þ

The body force is the force due to gravity effect as defined below * [9]; where F b is the body force acting on the particle and g is the gravitational acceleration rate.

where U, q, p and sij are respectively gas velocity, density, pressure and viscous stress tensor. Mp, Up are the mass and velocity of par* ticle respectively and F i are forces acting on the particle motion. In order to consider the influence of particle motion on the gas phase equations, the coupling term (Sui) is added in the momentum equation (Eq. (2)). This term is estimated as the sum of the drag on each particle within the corresponding fluid control volume [58]; however this term equals zero in case of one–way coupling calculations and, in this way, the equations can apply for one way and/or two-way coupling conditions. In general equation of motion (Eq. * (3)) the forces ( F i ) depend on particle bulk and surface parameters (size, shape, roughness, chemistry, etc.), the properties of the surrounding gas (temperature, humidity) and the mechanics of the contacting of the particles (relative particle velocity, contact time).

! F b ¼ Mp g

ð4Þ

2.2. Drag force Based on calculating of spherical particle, the drag force of irregular-shape particle is considered as a function of viscous (friction) and pressure drag as follows [6,10,59].

 
 ! 1 F d ¼ C d Apr qg U g  U p  U g  U p 2

ð5Þ

* where F d is the drag force vector acting on the particle, Cd is drag coefficient, Ug is gas velocity and qg is gas density. Apr is particle projected area to the flow direction (see Fig. 1), which is modelled

Fig. 7. Numerical simulation of model 1 at different particle project area (apr = 0.0, 0.3, 0.5, 0.7, and 1.0) compared with experimental data (Exp) for four biomass types (Enk, Has, Nor and Valb).

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in this study by two different methods; stochastic and deterministic. In stochastic way, since particles are moving randomly in all directions, Apr is changing continually and that depends on a particle flying orientation. In such case, the particle-projected area is modelled as described below and shown in Fig. 1.

Apr ¼ AP1 cosa þ AP2 sina ! ! j s  t pj cosa ¼ ! j t pj AP1 ¼ pD2p =4

sina ¼ AP2 ¼ Lp Dp

ð6Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1  cos2 a !

!

ð7Þ !

t p ¼ Ug  Up

ð8Þ

Ap1, Ap2 are respectively the cross section area and longitudinal surface area of particle; Dp is particle diameter and Lp particle length; ! s is unit vector along particle longitude direction (see Fig. 1). During particle-tracing motion, particle longitudinal axis moves parallel to the flow direction, perpendicular to the flow and sometimes in between where one case may dominate on other cases. Accordingly, Apr is modelled in deterministic way (see Eq. (9) below) as a function of particle radius rp, particle length Lp and model constant apr; the apr varies between 0 and 1 and that depends on the particle flying orientation where it is chosen as a fixed value.

Apr ¼ ð1  apr Þp

r 2p

þ 2apr Lp r p

ð9Þ

In literature, considerable numbers of models are found regarding particle dynamics. However, quite often the problem is to find the right model for simulating irregular-shape and irregular shapes

of the typical biomass particles at acceptable quality for those different kinds of biomass sources. Based on previous works in literature, lots of models are employed to calculate the drag coefficient (Cd) and most (probably all) of these models are implemented and tested in the current study, as listed below. 2.2.1. Model one Rosendahl [9] presented this expression of drag coefficient for different shapes of particles as, sphere, cylinder and ellipsoids shapes. He validated the numerical drag coefficient with measurements and found good agreement; however, this shape correlation is valid only for particle Reynolds number less than or equal to thousand (Re  1000); the model is defined as:

24 f f Re c s pffiffiffiffiffiffi Re Re fc ¼ 1 þ þ 60 6

Cd ¼

ð10Þ For Re 6 1000

ð11Þ

For Re << 1 fc ¼ 1  f 2b Re fn fs ¼ B  1 þ f 1b Re

ð12Þ

f n ¼ 0:857 þ 1:46  103 ðn  2Þ

ð14Þ

f 1b ¼ 0:067 þ 2:65  103 ð100  BÞ

ð15Þ

f 2b ¼ 0:142 þ 5:68  104 ðB  5Þ

ð16Þ

ð13Þ

Fig. 8. Numerical simulation of model 1 at stochastic (apr = R) and deterministic (apr = 0.5) calculation methods compared with experimental data (Exp) for four biomass types (Enk, Has, Nor and Valb).

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B ¼ b=a

ð17Þ

Re is Reynolds number and B, b, a and n are related to shape of particle. For cylindrical particles, these variables could be estimated as:

n ¼ 2;

b ¼ Lp ;

a ¼ Dp ;

Re ¼

 pffiffiffiffiffiffiffiffiffiffi  U g  U p  Dp Lp

mg

ð18Þ

255

A2 ¼ 0:0964 þ 0:5565w

ð21Þ


 A3 ¼ exp 4:905  13:8944w þ 18:42222w2  10:2599w3

ð22Þ


 A4 ¼ exp 1:4681 þ 12:2584w  20:7322w2 þ 15:8855w3

ð23Þ

 pffiffiffiffiffiffiffiffiffiffi U g  U p  Dp Lp

 1=3 2 d Dp w ¼ v2 ¼ 1:6509 2Lp ds

where mg is the gas viscosity.

Re ¼

2.2.2. Model two Haider and Levenspiel [18] proposed the following general expression for spherical and irregular-shape particle. The model was reported as representing nearly 500 data points satisfactorily.

where W is particle sphericity, which it depends on particle shape; dv is the particle volume size, which is the diameter of sphere having the same volume as the irregular-shape particle, and ds is the particle surface size, which is the diameter of sphere having the same surface area as the irregular-shape particle.

Cd ¼

i 24 h A3 1 þ A1 ReA2 þ Re 1 þ ARe4


 A1 ¼ exp 2:3288  6:4581w þ 2:4486w2

mg

;

ð24Þ

ð19Þ ð20Þ

2.2.3. Model three Ganser [20] suggested the following drag correlation and argued that every particle experiences two regimes: a Stokes’ regime where the drag force is linear in velocity and a Newton’s regime where the drag force is proportional to the square of velocity. He thus introduced two shape factors k1 and k2 that are applicable in the stokes and Newton’s regimes, respectively.

Flow

Fig. 9. Schematic view of particle tracing orientation at motion in industrial furnaces.

Fig. 10. Numerical simulation of particle tracing with time at stochastic (apr = R) and deterministic (apr = 0.0, 0.5 and 1.0) calculation methods for particle orientation.

Fig. 11. Numerical simulation of particle distribution for different models (M1–M8) at same particle size (Dp = 500 lm, Lp = 700 lm) and orientation (apr = 0.5).

Fig. 12. Numerical simulation of Reynolds number (Re) against drag coefficient for different models (M1–M8).

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" # i 24 h 0:4305k2 0:6567 Cd ¼ 1 þ 0:1118ðRek1 k2 Þ þ 3305 Rek1 1 þ Rek 1 k2  1 1 2 0:5 k1 ¼ ; þ w 3 3 Re ¼

 pffiffiffiffiffiffiffiffiffiffi U g  U p  Dp Lp

mg

0:5743

k2 ¼ 101:8148ðlogwÞ

;

 1=3 2 d Dp w ¼ v2 ¼ 1:6509 2Lp ds

ð25Þ

ð26Þ

ð27Þ

2.2.4. Model four Swamee and Ojha [23] put forward the following drag expression. They mentioned that this model is applicable in the ranges of 0.2 < W < 1 and 1 < Re < 10000; the model resulting errors are of the order 20%.

48:5 0:8 1 þ 4:5w0:35 Re0:64   0:32  Re 1 þ Re þ 100 þ 100w w18 þ 1:05w0:8

Cd ¼


Re ¼

 pffiffiffiffiffiffiffiffiffiffi U g  U p  Dp Lp

mg

;

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w ¼ Dp =2Lp

Cd ¼

Re ¼

30 þ 67:289expð5:03wÞ Re  pffiffiffiffiffiffiffiffiffiffi U g  U p  Dp Lp

mg

;

ð31Þ

i 24 h 1 þ f8:1716expð4:0655wÞg  Reð0:0964þ0:5565wÞ þ E Re

ð32Þ

73:69  Re  expð5:0748wÞ Re þ 5:378expð6:2122wÞ

ð33Þ

Cd ¼ E¼

 pffiffiffiffiffiffiffiffiffiffi U g  U p  Dp Lp

mg

;

ð28Þ

 1=3 2 d Dp w ¼ v2 ¼ 1:6509 2Lp ds

ð34Þ

2.2.7. Model seven Swamee and Ojha [23] developed the following model for drag coefficient based on set of experimental data for rectangular prisms.

Cd ¼ 2.2.5. Model five Chien [16] proposed the following simple expression of drag coefficient. He did not present much detail about the fluids and the particles used in his expression; however, he stated that the expression is applicable for the range 0.2  W  1 and Re < 5000.

 1=3 2 d Dp w ¼ v2 ¼ 1:6509 2Lp ds

2.2.6. Model six Haider and Levenspiel [18] proposed another general expression for irregular-shape particle and they recommended it themselves than their other correlations (model two).

Re ¼

ð29Þ

ð30Þ

Re ¼

128Re0:8

ð35Þ

1 þ 4:5w0:35  pffiffiffiffiffiffiffiffiffiffi U g  U p  Dp Lp

mg

;

w¼

 1=2 Dp Lp

Fig. 13. Numerical simulation of spherical models 8, 9 and 10 (M8, M9 and M10) against experiments (Exp) for four biomass types (Enk, Has, Nor and Valb).

ð36Þ

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2.2.8. Model eight In the current study, we also tested the spherical particle models for the reason of comparison and evaluation with the irregular-shape ones. For a spherical particle, there are numerous correlations for the drag coefficient and, in the following, one of the widest used models is presented; such model can be found in Griselin [60], Bergstrom [61] and Wu [62].

"

Cd ¼

2=3

24 Re 1þ Re 6

#

Re < 1000

ð37Þ

Cd ¼

24  1 þ 0:1935Re0:6305 Re

Re ¼ 20  260

257

ð41Þ

log10 C d ¼ 1:6435  1:1242w þ 0:1558w2 Re ¼ 260  1:5  103

ð42Þ

log10 C d ¼ 2:4571 þ 2:5558w  0:9295w2 þ 0:1049w3 Re ¼ 1:5  103  1:2  104

ð43Þ

where w = log10 Re; Re is defined as in model eight.

Cd ¼ o:424 Re ¼

Re P 1000

  U g  U p dv

mg

ð38Þ 2.3. New shape factor correlation

ð39Þ

2.2.9. Model nine This spherical particle model was presented by Haider and Levenspiel [18], as follows.

Cd ¼

" # 24  0:4251 1 þ 0:1806Re0:6459 þ Re 1 þ 6880:95 Re

Based on our early studies [65–73], it is found that particle aerodynamic area has a big influence on the particle motion. All of the shape factors proposed in literature for irregular-shape particles were not considered this important parameter; hence, it is suggested a new shape factor in the current work. This new shape factor or sphericity correlation includes particle-projected area and it is defined as:

ð40Þ

where Re is defined as in model eight. 2.2.10. Model Ten This spherical correlation can be found in [5,63,64] and defined as:

w¼

ðAv  As Þ1=2 Apr

ð44Þ

where Av is the particle area of sphere having the same volume as the irregular-shape particle; As is the particle area of sphere having the same surface area as the irregular-shape particle; Apr is projected area of the irregular-shape particle, as defined in Eq. (9).

Fig. 14. Numerical simulation of models 1 and 2 (M1 and M2) against experiments (Exp) for four biomass types (Enk, Has, Nor and Valb).

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3. Experiments Experiments are performed in the current study using different techniques, for collecting detail sets of biomass particle distributions in turbulent flows, as aerodynamic classifier (ADC), vibrating sieve (VS) and microscopic image (MI). Four different kinds of biomass fuels are studied. Such biomass is produced from different sources and the biomass is ground by different mills under different conditions, as temperature, humidity, etc. Accordingly, the four types of biomass particles vary in shape, size, anisotropy and other physical properties [65–73]. Based on that, the modelling tools applied and validated here could be sort of generalized models. The particles are sampled from four different Swedish biomass power plants as: Enkoping (Enk), Hässelby (Has), Norberg (Nor) and Valbo (Valb). The biomass micro size particles from Enk is produced using a hammer mill, while the one from Has is made from a ball-ring mill; the biomass micro size particles from Nor and Valb are crushed directly from raw materials without palletising, as shown in Fig. 2. The experimental rig of aerodynamic classifier (ADC) is schematically shown in Fig. 3. As seen, airflow of 0.6 m/s is supplied from the left side of the rig, which is generated by a fan placed at exit of the ADC. On top wall of the ADC and near the air inlet, biomass particles are injected through a particle feeder with a diameter of 50 mm. Particles are dropped by gravity through the feeder into the ADC and then they are transported horizontally by the airflow. After certain distance and due to gravity,

the particles fall to the bottom of the ADC. On the bottom of the ADC, seven boxes are placed, where the particles of different sizes, shapes and anisotropies are collected. The trajectory of the particles depends mostly on their size, shape, fuel type, anisotropy and trajectory orientation. The mass of the particles in each box is measured and the mass percentage is calculated. The size of the particles in different boxes is categorized using vibrating sieve. The sieve of model Retsch AS 200 Basic is applied in the current study as a simple and useful method to classify the particle size distribution; the results are summarized in Table 1. The shape of the particles is studied using microscopic photography technique. Such image analysis technique gives direct observation and verification of different shapes and anisotropy criteria of the different biomass particles, as shown in Fig. 2. This technique is carried out by taking photographs for each biomass powder using high resolution camera (50.6 megapixel full-frame DSLR camera); then enlarge the images to specify the particle shape and size. The photography image technique is repeated for each particle groups obtained from the sieve. From the sieve measurements and microscope image analysis the mass fractions of the particles in different size groups are determined and the results are presented in Table 1. From analysis of the microscope image of the tested particles, the biomass micro size particles are assumed to be of cylindrical shape in the mathematical modelling and the particle density of the four different biomass are calculated to be about 750 kg/m3. Further details about the experiments could be found in the early studies [65–73].

Fig. 15. Numerical simulation of model 3 (M3) and after implementing our new shape factor correlation (M3 New) compared with experiments (Exp) for four biomass types (Enk, Has, Nor and Valb).

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4. Results and discussions In this section, our experimental and modelling results are presented and discussed. The results are presented and discussed in a systematic order as follows. In the beginning, simulations of gas and solid phases in the experimental rig are presented. Then, testing of one-way coupling and two-way coupling calculations is performed to figure out the method we can apply in the simulation. After that, different particle projected areas are simulated to specify the most dominant orientation of particle in the flow field. Subsequently, the ten different particle models from literatures are simulated and validated against experimental data. Later, our new shape factor correlation is implemented and tested in all models. The strategy applied is by validating each model with the experimental data for four different biomass fuels. When the model and experimental results are disagreed, this leads to using our new shape factor correlation in each model and, in turn, a second round of modelling validation is carried out. In the beginning, as highlighted above, simulation of airflow in the ADC is presented. Fig. 4 shows the air velocity at different sections along the ADC within two views (top and side). As shown, air velocity reaches its lowest value somewhere close to the ADC end, where air fan is placed. It is shown in the upper figure a uniform distribution of velocity vectors, where the velocity is zero on the boundaries and maximum in the middle; in the lower figure, however, the velocity is zero on the upper boundary and increases till reach the maximum on the bottom of the AD (there is no boundary on the bottom of the ADC, as shown in Fig. 3). Fig. 5 shows tracing of different particle sizes inside the ADC. When biomass particles are injected into ADC, they move with air-

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flow stream, but they behave differently. In particular, small particles are quickly accelerated and they tend to follow the airflow. The large particles, however, are slowly accelerated and afterwards they are decelerated due to less response to the air stream. The large particle size is collected in the early stage of the ADC, but small particle size travelled for longer distance in the ADC. At far downstream position into the ADC inlet, as shown in Fig. 5, very low particle velocity is obtained due to effects of drag and body forces on the particle motion as well as lower airflow speed. Particle flying distance depends mostly on, for the same flow conditions, particle size, shape, flying orientation and density. In order to examine particle shape and flying orientation only, we need to freeze the other two factors. By testing only one fuel at time, particle density will be constant and by considering only one size at the time, we can freeze the size effect as well, e.g., we have the effects of particle shape and particle moving orientation only. In reality, particle size groups might be hundreds or more and that large number means more time consuming for our CFD calculations. Several size groups are tested (3, 5, 7, 13 and 26 sizes) and it is found that using 5 sizes or more has no considerable influence on results. According to that, we used in our calculation 7 size groups as presented from the vibrating sieve (VS) measurements (see Table 1). Experimental and modelling results of particle distribution in the ADC are presented in Fig. 6. As seen, four fuel results are introduced; in each fuel result, experimental (Exp) and simulation of model 1 are given. In the simulation, one-way coupling (M1) and two-way coupling (M1 cou) are examined. As shown in the figure, there are no big differences between the both simulation cases, which demonstrates that one-way coupling is satisfactory for the

Fig. 16. Numerical simulation of model 4; captions are similar to those in Fig. 15.

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calculations under our working conditions. Wu [62] showed the limit between using the one-way and the two-way coupling. He concluded that solid-phase (biomass particle) has a negligible influence on the gas-phase when the particle–fluid mass ratio is below O  103. In our study, particle–fluid mass ratio is about 47  (103), e.g., one-way coupling is applicable; accordingly, our coming simulation applies one-way coupling. Since the motion of biomass particle in industrial furnaces and boilers depends strongly on the particle flying orientation, such particle orientation is modelled in this study by two different methods, stochastic and deterministic as discussed early in the modelling section. Validation of particle orientation is shown in Fig. 7. The simulation applied model 1 in deterministic calculation method using different orientations from apr = 0 to apr = 1. When the cylindrical particle moves along its fibre direction, the projected area is smallest, which corresponds to the case of apr = 0; however, when the particle moves with its fibre perpendicular, the projected area is the largest, which corresponds to the case of apr = 1. Three different cases between the two extremes, e.g., apr = 0.3, 0.5, and 0.7, are examined as well. As shown in Fig. 7, all particle orientations showed same order of magnitude compared with the experimental results (Exp) of the four tested biomass fuels; but, the best simulation results are found in two cases apr = 0.5 and apr = 0.7. This means that the particles are flying in a direction neither along its fibre direction nor perpendicular to it but they are flying in between. This figure also demonstrated that if the biomass particle travels in turbulent flow using its fibre direction in align with the flow stream (apr = 0), the particle will move shorter distance, since large number of particles are

collected in the earlier boxes. This is might be due to that the drag force is small as a result of small projected area. On the other hand, if the biomass particle travels with its fibre direction perpendicular to the flow direction (apr = 1), the drag force dominants and, in turn, the particle moves together with the flow for longer distance. In stochastic model, numerical simulation for the random orientation of particle is compared with the experimental data and the deterministic case as well (only at apr = 0.5), as shown in Fig. 8. A seen, results of stochastic case (apr = R) did not show good agreement with the experiments as good as the deterministic one. This may refer to that particles tend to orient themselves to one preferable direction, as illustrated in Fig. 9. Reviewing early work in literatures showed that the behaviour of irregular-shape particles in turbulent flow is mostly as apr = 0 [32–38]. Other researches [5,18,23] showed that particles longitudinal axis are normal to flow field instead (apr = 1). However, current results may conclude that irregular-shape particles are neither normal nor parallel to flow field but they are in between (apr = 0.5 to 0.7). Additionally, particle orientation is not fixed in all cases but it depends on some factors as Reynolds number, length to diameter ratio and physical properties of fluid-particle combinations. This may demonstrate that if larger size of particles is used or same particle size but at different kind of medium, the projected area would be varied Particle flying orientations (apr) are also investigated using different mathematical models (M2 to M7) and results showed the same behaviour as in model 1 (this results are not shown in the paper). Accordingly, one may conclude that the different drag coefficient models have no significant influence on particle orientation and, in turn, our

Fig. 17. Numerical simulation of model 5; captions are similar to those in Fig. 15.

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coming simulation will consider apr = 0.5 for the modelling calculations. Simulation of particle moving orientation (apr) within trajectory time from 0 to 0.5 s (typical time for particle tracing in the ADC) in both stochastic and deterministic methods is presented in Fig. 10. As seen, particle orientation in stochastic method (apr = R) oscillates around apr = 0.9; additionally, in this case the particle is not affected by length to diameter ration, Reynolds number and/or other factors that normally influence on particle orientation. This is the main reason for not applying stochastic model in our numerical simulation. Since the motion of particles depends not only on the flying orientation but also on drag coefficient, numerical simulation using different models of drag coefficients are investigated. Ten different models (7 irregular-shape models, models 1–7, and 3 spherical models, models 8–10) are presented and validated against experiments. Prior to validation, a comparison between such models is carried out. Fig. 11 shows simulation of particle distribution for the different models at same particle size (Dp = 500 lm, Lp = 700 lm), density (750 kg/m3) and orientation (apr = 0.5). As seen, there are big differences between distribution of different models; the spherical model (M8), which is the only spherical model tested and other spherical models showed similar trend, come in middle of all irregular-shape models (M1-M7). Another comparison between the different models is carried out, as shown in Fig. 12. The figure presents the drag coefficient (CD) of different models against Reynolds number. As seen, significant difference between the models are obtained (M8 is presented, while M9 and M10 are very close to it). According to Figs. 11 and 12, the tested models

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have different results, and, in turn, all models should be validated with experiential results to figure out the best one(s) for our biomass irregular-shape particle simulation in turbulent flow. We start firstly to validate spherical models. Fig. 13 shows a validation of spherical models 8, 9 and 10, compared with the experimental data. As seen, the models produced some discrepancy with the experiments for the four tested fuels. This clearly demonstrates that such models could not be applicable for the simulation of the irregular-shape particles. This mainly due to that the spherical models did not take into account some important parameters of non-spherical particle tracings, such as particle flying orientation, projected area, etc. Simulations of models 1 and 2 for the irregular-shape particles are presented in Fig. 14. As seen, both models have a good agreement with the experiments for the four biomass fuels. Simulation of the other irregular-shape models (model 3–7), however, showed discrepancy with the experimental data (M3-M7), as shown in Figs. 15–19. In comparison, spherical models (M8, M9 and M10) showed closer agreement with experiments than the nonspherical models (M3-M7). The reason may refer to that the spherical models are calculated based on an equivalent volume between the spherical and irregular-shape correlations, as defined early in Eq. (39). In more detailed analysis, one can see that the irregularshape particles models are based on spherical models with shape factor correlations; accordingly, such correlation might be the source of discrepancy in results of the irregular-shape models 3–7. This guides us to further detailed studies on the shape factor correlations. Analysis of the irregular-shape models illustrate that the shape factor correlations of models 2, 3, 5 and 6 are based on

Fig. 18. Numerical simulation of model 6; captions are similar to those in Fig. 15.

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Fig. 19. Numerical simulation of model 7; captions are similar to those in Fig. 15.

equivalent volume and surface area between the spherical and irregular-shape; however, the rest of models (models 1, 4 and 7) correlates shape factor as a length of three-principle axis of the particle and that is based on equivalent volume sphere diameter. Additionally, all models could not produce good results with different particle sizes and shapes circumstances where the error could reach up to 80% [10]. This clearly demonstrates the needs of a new shape factor correlation, which might be the reason for discrepancy of other models in literature. A new shape factor correlation, defined in Eq. (44), is proposed in this work by considering the influence of particle-projected area, equivalent volume and surface area, as discussed early in the mathematical modelling section. The significance of this new shape factor is that it considered particle aerodynamic area (particle aerodynamic area has a big influence on the particle motion as discussed early), while other shape factors in literature did not consider this important parameter. After implementing the new shape factor correlation into the irregular-shape models, e.g., we replaced the using ones by our new one, and comparing the results with the experiments, one can find big differences. Figs. 15–19 show models 3–7 using old shape factors (M3, M4, M5, M6 and M7) and new shape factor (M3 New, M4 New, M5 New, M6 New and M7 New) compared with experiments (Exp). As seen, a very good agreement between the models using our new correlation and the experimental data, for the four tested biomass fuels. However, the same models at using old shape factor showed disagreement with the experimental data. It is important to show also that model 7 did not present as good agreement with experiments as other models, after implementing the new shape factor. It is quite clear from Fig. 19 that the model 7 at using the new shape factor produced the same results

as the previous case. Hence, we may conclude that the new shape factor correlation could be used for numerous models but, of course, it could not improve all of them. The new shape factor correlation is also tested with models 1 and 2, e.g., models normally have good agreements with experiments, as shown in Figs. 20 and 21. As seen, the results of modelling simulation with and without our new shape factor correlation are almost identical and all of them are in good agreement with the experiments. Accordingly, one may conclude that the new shape factor correlation can be used in wide range of irregular-shape models and even with the good agreement ones without menace. 5. Conclusions Irregular-shape biomass particles motion in turbulent flows is studied numerically and experimentally. Experiments are applied using different techniques (aerodynamic classifier, vibrating sieve and microscopic image analysis). Four different biomass fuels (at different shapes and sizes) are examined. Ten different models (7 irregular-shape models and 3 spherical models) are presented and validated against experiments. Several issues are investigated in the current study, including influence of particle size, particle moving orientation and particle shape. Additionally, influence of particles on the gas-phase is tested by considering the two-way coupling calculation. Results may draw the following points.  The key issue for modelling of irregular-shape particles motion in turbulent flow is not only the drag coefficient but also the particle-projected area.

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Fig. 20. Numerical simulation of model 1; captions are similar to those in Fig. 15.

Fig. 21. Numerical simulation of model 2; captions are similar to those in Fig. 15.

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 Irregular-shape particle moves longer distance in case of its fibre direction perpendicular to the flow and particle tends to follow the flow field; but in other orientation, particle moves shorter distance.  One-way and two-way coupling simulations are examined and results showed a tiny difference in our working conditions.  Small biomass particles are quickly accelerated and they tend to follow airflow; larger particles are slowly accelerated and then decelerated rapidly due to less response of particles to the air stream.  Early work in literatures showed that irregular-shape particle moves either normal or parallel to flow field, while current study confirmed that the particle orientation is mostly in between.  Flow field may possibly influence on the motion irregular-shape particles by orient them into a specific tendency.  Particle flying orientation is modelled by two different methods, stochastic and deterministic. Stochastic method did not show good agreement with the experiments, unlike the deterministic one.  A new shape factor is proposed and validated with a number of models. The correlation considers the influence of particle projected area, which is not considered in the early correlations in literature.  Most of irregular-shape particle models in literature showed discrepancies with the experiments. After implementing our new shape factor correlation, models showed better matching with the experimental data.  The new shape factor correlation could be used in wide range of irregular-shape models and even with the good agreement ones without menace.

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