Swirling gas–solid flow through pneumatic conveying dryer

Powder Technology 235 (2013) 500–515

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Swirling gas–solid flow through pneumatic conveying dryer K.A. Ibrahim a, Mofreh H. Hamed b, c, W.A. El-Askary a, Samy M. El-Behery a,⁎ a b c

Faculty of Engineering, Menoufiya University, Shebin El-kom, Egypt Faculty of Engineering, Kafrelsheikh University, Kafrelsheikh, Egypt Faculty of Engineering, Islamic University in Madinah, Madinah, Saudi Arabia

a r t i c l e

i n f o

Article history: Received 2 July 2012 Received in revised form 10 October 2012 Accepted 13 October 2012 Available online 23 October 2012 Keywords: Swirl Eulerian–Lagrangin Gas–solid Pneumatic dryer Heat and mass transfer 4-way coupling

a b s t r a c t Numerical and experimental investigations of swirling pneumatic conveying dryer are performed. In the numerical study, the Eulerian–Lagrangian model is used to simulate the two-phases. The gas phase is simulated based on Reynolds Averaged Navier–Stokes equations (RANS) employing four turbulence models, namely: standard k–ε model, RNG-based k–ε model, extended k–ε model and low-Reynolds number k–ε model. Meanwhile 3-dimensional particle tracking procedure is used for the solid phase. The model takes into account the lift and drag forces and the effect of particle rotation as well as the particles dispersion by turbulence effect. The effects of inter-particles collisions and turbulence modulation by the solid particles, i.e. four-way coupling, are also included in the model. The experimental study is carried out on a pilot scale vertical pneumatic transport system. The swirl is imparted to the flow by axially rotating pipe of the same diameter as the drying pipe. Crushed limestone of different sizes is used to represent the solid phase. Measurements of pressure and temperature distributions along the dryer are performed at different inlet conditions. Comparisons between present model predictions and experimental results show a good agreement. The results indicate that the RNG-based k–ε model gives better results compared with other tested turbulence models. In addition, it is found that the pressure drop of swirling flow is higher than that of non-swirling one and the swirl enhances the drying process. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Drying is defined as a process of moisture removal due to simultaneous heat and mass transfer by hot gas stream or other sources. It is an essential operation in the chemical, food, agricultural, ceramic, polymers and plastic, pulp and paper, pharmaceutical and wood processing industries. One of the most widely used drying systems is the pneumatic dryer and is also known as flash dryer, which can be characterized as continues-convective dryer [1]. The axial flow pneumatic dryer was extensively studied by many researchers [2–10]. Generally, the gas–solid flows through pneumatic conveying dryer can be modeled using either Eulerian–Eulerian or Eulerian–Lagrangian approach. Description of these models can be found in the comprehensive reviews by Gouesbet and Berlemont [11], Enwald et al. [12] and Balachandar and Eaton [13]. The accuracy of two-phase flow models depends on the level of the accuracy of single phase flow model, especially turbulence modeling. Unfortunately, there is no universal turbulence model that can be applied to all flow categories. Most of turbulence studies are case-by-case validations to

⁎ Corresponding author. E-mail address: [email protected] (S.M. El-Behery). 0032-5910/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.powtec.2012.10.032

select the most appropriated turbulence model for a particular case (see for example Marzouk and Huckaby [14], El-Behery et al. [15], El-Behery and Hamed [16], Balabel et al. [17], Balabel and El-Askary [18], Ng and Tan [19]). Li and Tomita [20,21] investigated numerically and experimentally the swirling gas solid flow in vertical pneumatic conveying. They found that the solids concentration is higher near the pipe wall in the swirling flow and the axial and tangential gas velocity is increased nearby the pipe wall due to the presence of particles. Swirling gas– solid flow through vertical sudden expansion pipe was numerically investigated by Marzouk and Huckaby [14]. They tested three versions of the k–ε turbulence models namely: standard, RNG and realizable k–ε turbulence model. They found that the best predictions were obtained when the standard k–ε was utilized. Large eddy simulation of swirling particle-laden flow in a model axisymmetric combustor was performed by Oefelein et al. [22]. They compared the predicted results with published experimental data and a good agreement was obtained. Zuo and Bulck [23] investigated numerically the effect of swirl on oil droplet evaporation using hot gas stream. They found that the swirl enhances the mixing between fuel and gas stream and evaporation process is enhanced as a result. A critical review of previous work reveals that the swirling pneumatic conveying dryer has not been studied. Therefore, the aim of the current paper is to study numerically and experimentally the

K.A. Ibrahim et al. / Powder Technology 235 (2013) 500–515

Nomenclature English symbols Cp Specific heat [J/kg∙K] D Pipe diameter [m] Dv Diffusion coefficient [m 2/s] dp Particle diameter [μm] Hfg Latent heat of vaporization [J/kg] h Enthalpy [J/kg] hh Heat transfer coefficient [W/m 2∙K] hm Mass transfer coefficient [m/s] M Molecular weight [kg/kmol] mo Mass flow rate [kg/s] m Mole fraction [−] Nu Nusselt number [−] Pr Prandtl number [−] Prt Turbulent Prandtl number [−] r Radial coordinate [m] Re Reynolds number [−] Ro Rossby number [−] Sc Schmidt number [−] Sh Sherwood number [−] T Temperature [K] t Time [s] U Time average velocity [m/s] u Instantaneous velocity [m/s] u` Fluctuating velocity [m/s] X Solid water content [kgwater/kgsolid] x Axial coordinate [m] Y Water vapor mass fraction [kgwater/kgair] y Normal distance from the pipe wall [m]

Greek symbols α Gas void fraction [−] β Solids void fraction [−] δ Porosity [−] ε Turbulent kinetic energy dissipation rate [m 2/s 3] λ Thermal conductivity [W/m∙K] μ Viscosity [kg/m∙s] μt Turbulent viscosity [kg/m ∙s] ρ Density [kg/m 3] ℜ Universal gas constant [J/kmol ∙K] τw Shear stress at wall [N/m 2] Ω Pipe angular velocity [1/s] ω Angular velocity [1/s] Subscripts Ave Average cr Critical da Dry air g Gas H2O Water vapor in Inlet m Mean p Particle s Solid/suspension v vapor w Wall/water wb Wet bulb

501

performance of pneumatic conveying dryer under the effect of swirl. An Eulerian–Lagrangian model including three-dimensional particle tracking is employed in the present study. The model takes into account the effects of particle–particle and particle–wall collisions, turbulence modulation and turbulence dispersion as well as the effect of lift forces and particle rotation. 2. Mathematical model The Eulerian–Lagrangian model is used to simulate the two-phases. The gas phase is simulated based on Reynolds Averaged Navier–Stokes equations (RANS) with different k–ε models, while particle tracking procedure is used for the solid phase. To provide a reasonable solution for engineering objectives some simplifying assumptions are made. 2.1. Model assumptions 1. The flow model is for a 2-D/axisymmetric duct. 2. In the particle tracking procedure the particles are spherical. 3. The particles are rigid during particle–particle and particle–wall collisions. 4. The gas phase is assumed as an ideal gas-mixture of air and water vapor. 5. Heat and mass transfer occurs between the gas phase and individual particles (i.e., heat and mass transfer between particles themselves is ignored). 2.2. Fluid flow modeling The gas flow calculations are based on the Reynolds averaged Navier–Stokes (RANS) equations in connection with four turbulence models namely standard k–ε model of Launder and Spalding [24], RNG based k–ε model of Eghlimi et al. [25], Low-Re k–ε model of Launder and Sharma [26] and high-Re k–ε model of Chen and Kim [27]. The RNG k–ε model was derived using a rigorous statistical technique (renormalization group theory), which accounts for the effect of swirl on turbulence and provides an analytical formula for turbulent Prandtl numbers. The RNG provides an analytically derived formula for the effective eddy viscosity. This formula accounts for low-Reynolds number effects and has also an additional term in its dissipation rate equation (the rate of strain, R) that significantly improves the accuracy for rapidly strained flow. For the dissipation rate equation of Chen and Kim model, two time scales are included to allow the dissipation rate to respond to the mean strain more effectively than that of the standard k–ε model. This treatment is the major improvement of this k–ε model for complex turbulent flow problems. The time scales included in the model are: the production range time scale, k/G, and the dissipation rate time scale, k/ε. This model is hereafter referred to as extended k–ε model. The general form of the elliptic differential equations governing axisymmetric, swirling, turbulent, steady, compressible and nonisothermal two-phase flow is:

 ∂ ∂φ 1∂ ∂φ φ αρg U g φ−αΓ φ þ αρg rV g φ−αΓ φ r ¼ Sφ þ SP r ∂r ∂x ∂x ∂r

ð1Þ

φ

where, Sφ and SP are source terms of gas and dispersed phases, respectively. The gas source term and exchange coefficient, ΓФ are summarized in Table 1 for the dependent variable ϕ while the constants of the turbulence models are given in [15]. The effective and eddy viscosities are calculated as follows: − Standard k–ε model, low-Re k–ε model and the extended k–ε model

μ eff ¼ μ g þ μ t

;

μ t ¼ Cμ f μ ρ

k2 ε

ð2Þ

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Table 1 Governing equations of the gas phase. Conservation of

φ

Γφ

Sφ

Mass

1

0.0

0.0

Axial momentum

Ug

μeff


  → ∂U ∂ ∂ − ∂αp þ ∂x αμ eff ∂xg − 23 ∇:V g αrμ eff þ 1r ∂r ∂x

∂V g ∂x



Radial momentum

Vg

μeff


 
 ∂U g ∂V g 2 → ∂αp ∂ 1∂ þ − ∇:V g þ αμ eff αμ eff r r ∂r 3 ∂r ∂r ∂r ∂x W 2g 2 αμ e → Vg þ ∇:V g −2αμ eff 2 þ ρg 3 r r r

Tangential momentum

Wg

μeff

−

Energy Equation

Tg

μg Pr

Turbulent kinetic energy

k

μ eff σk

α(G − ρε − D)

Dissipation rate

ε

μ eff σε

α kε ðC ε1 f 1 G−C ε2 f 2 ρε Þ þ C 3 ρG k −αρg R þ αE

Water vapor mass fraction

Y H2 O

μt ρDv þ Sc t

0.0

The damping function, fμ is calculated from for the low-Re k–ε model as follows   2 f μ ¼ exp −3:4=ð1 þ Rt =50Þ

ð3Þ

where fμ =1 for other models and Rt =ρgk2/μgε is the turbulent Reynolds number.

 ∂μ V þ ρg rg þ 1r ∂reff W g 2  3   ∂ αρg U g U 2g þ V 2g þ W 2g 6 7 ∂x − 2C1pg 6   7 4 1∂ 5 rαρg V g U 2g þ V 2g þ W 2g þ r ∂r

μt þ Pr t

μ eff r2

2

g

and angular velocities are calculated from the equations of motion as reported in [31] through, →

dX p → ¼ up dt

mp

" μ eff ¼ μ g



ð7Þ

→

− RNG based k–ε model sffiffiffiffiffiffiffiffiffiffiffi #2 C μ ρg k pffiffiffi 1þ μg ε

−

→ → → du p → ¼ F D þ F LS F LR þ F g dt

ð8Þ

→

; μ t ¼ μ eff −μ g

ð4Þ

The Prandtl number, σk and σε in the RNG bases k–ε model are calculated as,      λ−1:3939 0:6321  λ þ 2:3939 0:3679 μg     þ ¼ λ −1:3939 λ þ 2:3939 μ o o eff

!2

dω p → ¼T dt

ð9Þ

 → → 3 T ¼ πμdp 0:5∇  U g −ω p

→

ð10Þ

→

ð5Þ

where, λ is an inverse Prandtl number (i.e., σk =σε = 1/λ) with λo = 1. The rate of strain R for RNG based k–ε model is expressed as given in [25]. The low-Re k–ε model is the only model used here which uses the damping functions and the extra source terms D and E (see Table 1). These source terms and damping functions are calculated as given in [26]. To account for the increase of turbulent Prandtl number near the wall, the expression given by Kays [28] is used as follows: 1 μ μ ¼ 0:5882 þ 0:228 t −0:0441 t Prt μg μg

Ip


 μg  1− exp −5:165 ð6Þ μt

2.3. Particulate phase modeling The solid phase is simulated using the Lagrangian approach, whereby thousands of computational particles ‘parcels’ are traced through the flowfield in each coupled iteration. After each given time step the new position of the parcels and the new transitional

→ →

and particle vewhere, X p is the particle position vector,ug ; u p are the gas → → locity vectors, ω p is the particle angular velocity vector, T is the torque acting on the particle, Ip =0.1mpdp2 is the particle moment of inertia and → →

→

→

mp is the particle mass, F D ; F LS ;FLR and F g are the components of the force arising from drag, slip-shear lift, Magnus lift due to particle rotation and gravity, respectively, and calculated as given by El-Behery et al. [15]. The temperature of each particle is calculated along its trajectory by integrating the following energy balance equation, mp C pp

  o dT p 2 d ¼ hh πdp T g −T p − m d H fg dt

ð11Þ

In order to solve the forgoing equations (i.e. Eqs. (7)–(11)); the instantaneous gas velocity components at the particle's location are needed. The mean velocities are interpolated from neighboring grid points, while the fluctuating components are generated using the Stochastic Separated Flow model (SSF) given by [29]. This model assumes that the turbulent flow is characterized as a series of eddies, and the particles interact with these turbulent eddies. Each eddy is associated with a fluctuating velocity, a lifetime and a characteristic length. A normally distributed random number, ζ, with zero mean and unity variance is generated to calculate the fluctuating component. More details of the model can be found in [29].

K.A. Ibrahim et al. / Powder Technology 235 (2013) 500–515

a. Two-Dimensional characteristics.

503

b. Three- Dimensional characteristics.

Fig. 1. Representation of particle–particle collision.

particle Reynolds number, Rep, and Schmidt number, Sc, which is equivalent to Prandtl number, Pr, and they are defined as:

2.4. Mass transfer model The mass transfer in the present model is based on the two-stage drying process. In the first stage, the solid surface can be considered to be fully wetted and the resistance to the mass transfer is located in the gas side. The second drying stage period starts when the particulate surface becomes no longer wetted and evaporation must occur from within the pores and dry porous crust starts formation around the wet core. The mass transfer model is described in details by El-Behery et al. [6]. 2.5. Heat transfer coefficient The convective heat transfer coefficient, hh, is calculated from Nusselt number, Nu, which is expressed as a function of Reynolds number, Rep and Prandtl number, Pr, which are defined as: hdp ; Nu ¼ λg

Rep ¼

→ →    ρg dp ug −u p  μg

;

Pr ¼

μ g C pg λg

ð12Þ

Various empirical correlations can be used to calculate the heat transfer coefficient. In our previous studies [2,6] six popular correlations had been tested against experimental data. It was found that the correlation proposed by Baeyens et al. [1] produces better results than the other tested correlations. This correlation reads: Nu ¼ 0:15Rep

ð13Þ

Sh ¼

hm dp ; Dv

Sc ¼

μg ρg D v

ð14Þ

2.7. Coupling between the two phases The particles occupy the computational cell and reduce the gas volume fraction. They also exert interaction forces on the surrounding gas phase. Thus, the two phases are coupled through the gas volume fraction φ and through the total source/sink term, SP that accounts for the momentum, heat and mass exchange between continuous and dispersed phases. The void fractions of dispersed phase, β and gas phase, α are calculated respectively using trajectory method as depicted in [30] by: Nk Δt k V k V Cell traj

β¼∑

;

α ¼ 1−β

ð15Þ

where, Nk is the number of actual particles in the computational particle ‘parcel’ (k), Vk is the volume of the particle, Vcell is the volume of computational cell and ∑ means summing over all trajectory passing through traj

the computational cell. The source terms of dispersed phase in the gas equations are taken as given by El-Behery et al. [6]: 2.8. Particle–particle and particle–wall collisions

2.6. Mass transfer coefficient In analogy to the heat transfer coefficient, hh, the mass transfer coefficient, hm, is calculated from Sherwood number, Sh, which is equivalent to Nusselt number, Nu. It is often expressed as a function of the

In the present study the representative particles are traced one by one. Therefore, it is necessary to create a colliding partner numerically at each time, as shown in Fig. 1. The characteristics of the virtual particle, P0, like diameter, transitional and angular velocities are the mean values of the cell enclosing the real particle. Afterwards, the collision

Fig. 2. Problem definition and the computational domain in the axisymmetric numerical simulation.

504

K.A. Ibrahim et al. / Powder Technology 235 (2013) 500–515

probability Pc, i.e. the probability that the particle undergoes a collision in the current time step, is calculated as proposed by Oesterlé and Petitjean [32] by, →



−npo ðdp þdp0 Þ v p −v p0 Δt L

P c ¼ 1−e

→

ð16Þ

At each time the occurrence of collision is assumed to take place if the probability of collision, Pc is greater than a randomly generated number, Ψ, from a uniformly distributed interval [0, 1]. In two-

a. Axial velocity 1.5

U/Uave

1.2

0.9

2.9. Supplementary equations

0.6

Experimental Numerical

0.3

0.0 0.0

dimensional simulations (non-swirling), the position of the virtual particle is chosen randomly by generating a collision angle, α, from a uniformly distributed interval [−π/2, π/2], as shown in Fig. 1a. For 3-D simulations (swirling), the origin of the local coordinates is translated to the particle center, and then the coordinates are rotated to align the z-axis with the relative velocity vector. The position of the virtual particle is chosen by generating two angles α and β form the uniformly distributed intervals [−π/2, π/2] and [−π, π], respectively, as shown in Fig. 1b. Finally, reverse rotation and translation are carried out to obtain the position of the virtual particle P0 in the local coordinates. The post-collision velocities are calculated in the present study using the hard sphere model as described by Crowe et al. [30]. Besides the velocity gradient, the particle–wall is a further source of particle spin. The particle trajectory after impact with the wall is greatly affected by the wall morphology. As a result of the surface roughness, the particle generally hits a local surface slightly inclined to the flow direction by a small angle. The virtual-wall model developed by Sommerfeld [33] is adopted to calculate the roughness contribution angle.

0.2

0.4

0.6

0.8

1.0

In order to solve the above set of equations several supplementary equations, definitions and empirical correlations are required. These were presented by El-Behery et al. [6]. It should be noted that both the gas and solid phases are mixtures and hence their thermodynamic properties are calculated using the mixture theory.

r/R

b. Tangential velocity 0.0

a. x/D = 9.0 1.5 -0.3

-0.6

U/U ave

W/Uave

1.2

-0.9

0.9

Experimental Extended k- ε Low Re k- ε Standard k- ε RNG k- ε

0.6 0.3

-1.2 0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.0

r/R

0.2

0.4

0.6

0.8

1.0

0.6

0.8

1.0

r/R

c. Turbulent kinetic energy

b. x/D = 14.0

0.003

1.5 1.2

0.002 2

U/U ave

k/U ave

0.9 0.6

0.001 0.3

0.000 0.0

0.0 0.0 0.2

0.4

0.6

0.8

1.0

0.2

0.4

r/R

r/R Fig. 3. Inlet profiles at x/D = 4.0 adopted from Rocklage-Marliani et al. [38].

Fig. 4. Comparisons between predicted axial velocity profiles using different turbulence models and experimental data of Rocklage-Marliani et al. [38].

K.A. Ibrahim et al. / Powder Technology 235 (2013) 500–515

a. x/D = 6.5

b. x/D = 9.0

0.0

0.0

Experimental Extended k-ε Low Re k- ε Standard k- ε RNG k-ε

-0.3

W/Uave

W/Uave

-0.3

-0.6

-0.9

-1.2 0.0

-0.6

-0.9

0.2

0.4

0.6

0.8

-1.2 0.0

1.0

0.2

0.4

r/R

0.6

0.8

1.0

0.6

0.8

1.0

r/R

c. x/D = 11.5

d. x/D = 14.0

-0.3

-0.3

W/Uave

0.0

W/Uave

0.0

-0.6

-0.6

-0.9

-1.2 0.0

505

-0.9

0.2

0.4

0.6

0.8

1.0

-1.2 0.0

r/R

0.2

0.4

r/R

Fig. 5. Comparisons between predicted tangential velocity profiles using different turbulence models and experimental data of Rocklage-Marliani et al. [38].

2.10. Boundary conditions In the present study, there are four types of boundary conditions. At inlet, the gas velocity, temperature, mass fraction of water vapor and turbulent kinetic energy and its dissipation rate are specified. In compressible flow computations, the gas mass flow rate is specified at inlet instead of the gas velocity. The inlet velocity profile is assumed to be uniform and the turbulent kinetic energy and its dissipation rate are calculated by: 2

3=4

kin ¼ 0:04U in ; εin ¼ C μ

3=2

kin 0:03D

ð17Þ

At outlet the gradient of all variables in the flow direction is set to zero, except the axial gas velocity which is corrected to satisfy the overall mass balance. At the wall, the no-slip boundary conditions are imposed for the momentum equation, while for the energy equation; adiabatic wall boundary condition is considered. At the centerline, the symmetric boundary conditions are applied. 2.11. Solution procedure Finite volume discretizations using the hybrid scheme for all variables, expect the density which is interpolated using the first order upwind scheme, are applied. The iterative solution based on the SIMPLE algorithm of Patankar [34] is used for the solution of the gas phase with an extended technique to compressible flow according to Karki [35]. The equations of motion of each particle along with its temperature equation are integrated using fourth order Runge–Kutta method. The FORTRAN code used in the present study was developed and

validated by El-Behery et al. [6,15,31,36,37]. In the present study the code is extended to axisymmetric swirling gas–solid flow by including the tangential momentum equation and three-dimensional particle tracking. The solution procedure can be found elsewhere, see for example El-Behery et al. [6,15,31,36,37]. 2.12. Evaluation of turbulence models performance The accuracy of swirling pneumatic conveying prediction depends on the level of accuracy of single phase predictions. An important issue in the swirling flow prediction is the turbulence modeling. Therefore, an evaluation of the turbulence models presented previously is carried out in this section. The experimental data of Rocklage-Marliani et al. [38] are used to assess the performance of the selected models. The experimental test section is a pipe of diameter 100 mm and length of 1500 mm. the Reynolds number based on the pipe diameter, D and the average axial velocity, Uave is 2.8× 105. The swirl strength is characterized by Rossby number, Ro which is defined as: Ro ¼

ΩD 2U ave

ð18Þ

where Ω is the angular velocity of swirl generator (rotating honeycomb). The value of Rossby number in this test case is 1. The rotating honeycomb will not be modeled in the present study. Instead, the measured axial and tangential velocity profiles as well as the turbulent kinetic energy at x/D = 4.0 will serve as inlet boundary condition in the present study. Therefore, the computational domain extends from x/ D = 4.0 to x/D = 15.0. The physical problem definition and computational domain are shown in Fig. 2, while Fig. 3 shows the inlet profiles

K.A. Ibrahim et al. / Powder Technology 235 (2013) 500–515

(8) driven by an AC motor (9) through a venturi contraction. This venturi is placed at the entrance of the transport tube aiming to reduce both the gas flow rate deviated through the feeder and the length of the acceleration region of the transport tube. The screw feeder has a pipe type construction with minimum gaps between screw and pipe. This ensures that no void space for material accumulation and the material moves ahead positively. The particles are conveyed pneumatically through the test section (10) which is an insulated galvanized iron pipe of 4.5 m long and internal diameter of 8.1 cm. Arrangement has been made to make the first 0.55 m (6.79D) of the pipe can be rotated about the pipe axis to induce swirling motion to the flow. The rotational speed can be controlled by adjusting the driving motor speed. This swirl generator is selected because of its lower pressure drop (no flow obstructions) and hence low pressure drop and minimum particles break-up. In addition, it is easy to be implemented in any numerical code. The main drawback of this type of swirl generator is the low induced swirl due to the low viscosity of air. After being pneumatically transported, the particles are separated from the air by means of a cyclone (11) and returned to another reservoir. The entire test rig is thermally insulated to minimize the heat losses.

3.1. Static pressure measurements The static pressure along the tube is measured at 10 points distributed uniformly along the stationary pipe using inclined multi-tube water manometer (12). The tubes of the manometer are connected to pressure taps distributed along the drying duct. These pressure taps have an internal diameter of 1 mm and drilled normally to the pipe wall. Pressure drop profiles for continuous steady flow of air alone are measured for Reynolds

a. x/D = 9.0 0.006

Experimental Extended k- ε Low Re k- ε Standard k- ε RNG k- ε

0.004 2

of axial and tangential velocities and turbulent kinetic energy at x/D = 4.0. A computational grid of 220 × 130 in the axial and radial directions, respectively, is employed based on grid-dependence study. The predicted axial velocity profiles at x/D = 9.0 and 14.0 are compared with experimental data in Fig. 4. It can be seen from this figure that all the tested turbulence models predicts the axial velocity fairly good at x/D = 9.0 and the best agreement is obtained when the RNG k–ε model is used. The figure indicates also that all models except the RNG k–ε model predict the axial velocity near the pipe wall with good agreement and under-predict it near the pipe center. The RNG k–ε model shows an opposite trend. Thus, it predicts the velocity very well near the pipe center and under-predicts it near the pipe wall. The comparisons between predicted tangential velocity profiles at different axial locations and experimental data are shown in Fig. 5. In general, two regions for the tangential velocity can be identified from this figure. The first one is the forced vortex region near the pipe center, while the other is the free vortex region near the pipe wall. It can be seen that all the tested turbulence models predict the tangential velocity profiles fairly good in the forced vortex region up to x/D = 11.5. Downstream this position, only the RNG k–ε model gives fairly acceptable results. For the free vortex region near the pipe wall, all the tested turbulence models failed to predict the correct decay of the tangential velocity. However, the RNG k–ε model gives the closest agreement to the experimental data. Fig. 6 shows comparisons between predicted turbulent kinetic energy and experimental data of Rocklage-Marliani et al. [38]. The figure indicates that all the tested models fail to predict the decay of turbulent kinetic energy with axial distance. The turbulent kinetic energy dissipation rate, ε is needed at inlet as a boundary condition. However, this quantity is not measured by Rocklage-Marliani et al. [38]. Therefore, the dissipation rate of turbulent kinetic energy is calculated based on the turbulent kinetic energy and pipe diameter as given by Eq. (17). As a test, the turbulence length scale is changed from 0.01D to 0.1D and no noticeable change in the turbulent kinetic energy at the measuring stations is obtained. Therefore, the shortage of these models may be attributed to their linear nature. Generally, the best prediction is obtained by the RNG k–ε model. This model is used in the present study for swirling flow simulations.

k/Uave

506

0.002

0.000 0.0

0.2

0.4

0.6

0.8

1.0

0.6

0.8

1.0

r/R

b. x/D = 14.0 0.006

0.004 2

The experimental apparatus and the instruments required to perform the experimental measurements are illustrated in Fig. 7. The air is supplied to the test rig from of two electrically driven compressors (1) through two interconnected air reservoirs (2) of capacities 1.57 and 7.16 m 3. Each compressor delivers a maximum flow rate of 880 Nm3/h. The maximum operating pressure for both compressors is 8 bars. A flow control valve (3) is integrated at the line inlet in order to regulate the air flow rate which is measured by a calibrated orifice meter (4). The pressure drop across the orifice plate is measured by a mercury U-tube manometer (5). Air volume flow rate is determined from reading of pressure drop across the orifice plate and the mass flow rate is then calculated on multiplying with the density upstream of the orifice. The air density is obtained from perfect gas law, based on the measurements of air pressure and temperature at a distance 60 cm upstream of the orifice plate. The air is then directed to the insulated heating chamber (6). The heating chamber is a parallel piped box 50× 50× 100 cm, made of 5 mm thick steel sheets, and occupied by four electrical heaters each of 4600 W capacity. In order to achieve better heat transfer rate to the air, the chamber interior is divided into three passages. This increases the air residence time and the total surface area. In addition, baffle plates are introduced along the air passages to increase the heat transfer surface area. The temperature at the exit of the heating chamber is maintained at the desired temperature by means of a relay temperature controller. Particles are stored in a reservoir (7) and introduced into the transport tube by a screw feeder

k/Uave

3. Experimental setup and measurements

0.002

0.000 0.0

0.2

0.4

r/R Fig. 6. Comparisons between predicted turbulent kinetic energy profiles using different turbulence models and experimental data of Rocklage-Marliani et al. [38].

K.A. Ibrahim et al. / Powder Technology 235 (2013) 500–515

507

Fig. 7. Schematic view of the experimental apparatus.

number in a range between 5×104 and 2×105 and it is found to conform closely to the friction factor correlation reported by White [39]. 3.2. Temperature measurements The axial profiles of air temperature along the test section are measured by nine thermocouples (J-type) (13). To minimize direct heat transfer from flowing particles to the thermocouple, the thermocouples are installed in the conveying pipe through copper tube with

its upper half removed. The thermocouples and the copper tubes are protruding 4 mm into the conveying pipe (i.e. the gas temperature is measured at r/R = 0.9). The solids temperature is measured at six positions by sampling probes connected to micro-cyclones and calorimeters (14). The sampling probe is constructed from 6 mm diameter stainless steel tube and they are bent downward and located at the pipe center. The micro-cyclones have the same design features of the main cyclone with a scale of one-tenth. The extracted solids are collected in the calorimeters and

Fig. 8. Size distribution of crushed limestone solid particles.

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Fig. 9. Specific heat capacity of crushed limestone solid particles.

their temperature is measured using thermocouples (J-type) (15) installed in the bottom of the calorimeters and protruded 5 mm inside it. All thermocouples are connected to Master-K PLC module which in turn connected to a PC (16). All thermocouples are calibrated and their calibration equations are programmed using KGL version 3.66 [40]. The measured temperatures are monitored and stored, in tables and graphs, using DAQFactory Version 5.34 [41] every 0.1 sec.

3.3. Solids water content measurements To measure the solids water content, the solid particles collected in the calorimeters are weighed and dried in a temperature controlled electrical oven. The mass of solid samples are measured every 1 h until the sample weight is unchanged. The mass of water present in the sample is the difference between the mass of sample before drying, mwet and its mass after drying, mdry. The solids water content, X is then calculated as:

X¼

mwet −mdry mdry

ð19Þ Fig. 10. Used wall boundary conditions for tangential velocity.

3.4. Measurement of inlet air water content

3.5. Solids properties measurements

Humidity ratio of air or air water content is the ratio between actual mass of water vapor present in moist air to the mass of dry air. The air water content is measured in the present study by measuring the dry and wet bulb temperatures of the air upstream of the orifice meter. The psychrometric relations reported in [42] are used to calculate the air water content, W H2 O .

The solid particles used in the present study are crushed limestone. The particle size, particle density, porosity, critical water content, and specific heat are measured as presented in the following subsections.

Table 2 Uncertainties in the measured parameters. Parameter

Uncertainty

Temperature, T Pressure, p Solids density, ρs Upstream gas density, ρu Air mass flow rate, mo g Solids mass flow rate, mo s Solids water content, X Air water content, W H2 O

±0.05 °C ±0.0098 kPa ±4.27% ±0.022 kg/m3 ±0.0084 kg/s ±3.336 × 10−5 kg/s ±0.00897 kgwater/kgdry solid ±2.642 × 10−4 kgwater vapor/kgdry air

3.5.1. Particle size Large quantity of crushed limestone is sieved over a set of ASTM E11 standard sieves and the material retained on each sieve is collected and weighed. The solid particles in a given size range are well mixed and stored in plastic containers. The cumulative particle size distribution is then determined for each size range and fitted to Rosin–Rammler equation which is given by:   n  Y d ¼ 1− exp − dp =d p

ð20Þ

The mean diameter, d p and the exponent, n which gives the best fit are given in Ref. [26] for each size range. Fig. 8 shows the measured size distribution combined with the best fit equation.

K.A. Ibrahim et al. / Powder Technology 235 (2013) 500–515

0.1

0.0

0.0

-0.1

-0.1

-0.2

-0.2

Wg /UAve

b. x/D = 25.0

0.1

Wg /UAve

a. x/D = 6.75

-0.3 Single Phase

-0.4

-

d p= 412

-0.5

-

d p= 927

-0.6

μm

-0.4

-0.6

-

d p= 1636 μ m

-0.7 0.2

0.4

0.6

0.8

-0.8 0.0

1.0

r/R

c. x/D = 40.0

0.1

0.0

0.0

-0.1

-0.1

-0.2

-0.2

-0.3 -0.4

-0.6

-0.6

-0.7

-0.7 0.4

0.6

0.8

1.0

0.6

0.8

1.0

0.6

0.8

1.0

r/R

-0.4 -0.5

0.2

0.4

-0.3

-0.5

-0.8 0.0

0.2

d. x/D = 52.0

0.1

Wg /UAve

Wg /UAve

-0.3

-0.5

μm

-0.7 -0.8 0.0

509

-0.8 0.0

0.2

0.4

r/R

r/R

Fig. 11. Effect of particles diameter on the tangential velocity of the gas phase (mo s ¼ 0:053kg=s, Re = 7.2 × 104).

3.5.2. Particle density The particles used in the present work are porous. Therefore, there are two densities describing the particles namely: the density of solid material from which the particle is constituted, ρs and the apparent density, ρsa (i.e., including the volume of the pores). The solid density is measured by suspending a known mass of solids in a known volume of water. The water/particles suspension is heated to 60 °C for about 5 h in order to fill the particles' pores with water. The volume of solids is then determined as the difference between water/solids and water volumes. The apparent density is measured by suspending a known mass of solid particles in a molten wax of known volume. The bubbles are allowed to escape and the wax is allowed to solidify. The volume of the particles including the volume of pores is then determined as the difference between wax/particles and wax volumes. The solid density and the apparent density of the particles are found to be 2714 and 2143 kg/m 3, respectively. 3.5.3. Porosity and critical water content The porosity of solid particles, δ is defined as the ratio between pores' volume and the particle volume including the pores. From definition, the porosity can be calculated by: δ ¼ 1−ρsa =ρs

volume of pores. Therefore, the critical water content can be calculated by:
X cr ¼ ρw

1 1 − ρsa ρs

 ð22Þ

3.5.4. Specific heat The specific heat of solid particles, Cps is measured experimentally by heating a known mass of solid particles and putting it in a known mass of cold water contained in insulated glass calorimeter. The temperature of water/calorimeter/solids is recorded until steady state is reached. The specific heat of solid particles is determined by simple heat balance (heat gained = heat lost):       C ps ms T h −T f ¼ C pc mc T f −T c þ C pw mm T f −T c |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl} heat lost f rom particles

heat gained by calorimeter

ð23Þ

heat gained by water

ð21Þ

The critical solid water content is the water content at which the particles surface becomes no longer wetted. If we assumed that all pores are filled with water, then the volume of water equals the

In the above equation subscripts h, c and f stand for hot, cold and final, respectively. The experiment is repeated twenty times and the results are averaged, as shown in Fig. 9. The average specific heat of crushed limestone particles, Cps is found to be 0.8815 ± 0.0513 kJ/kgK.

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3.6. Experimental procedure The compressors are switched on to charge the air reservoirs. After the air reservoirs being fully charged, the flow control valve is adjusted to the desired flow rate and the electrical heaters are switched on. The air temperatures along the conveying pipe are monitored. Once the steady state temperature is reached, a large mass of solid particles are stored in the feeding reservoir and the electrical motor which drives the screw feeder is switched on to feed the solid particles at a constant rate. The steady state temperature for single-phase (air) flow showed that the temperature difference between two points at x/D = 6.97 and 49.53 is less than 0.4 °C in all tests. This indicates that the heat loss from the system is insignificant. Once the steady state conditions are reached again, the pressure and temperature upstream of the orifice meter are recorded along with the pressure drop across the orifice plate. The air temperature as well as the static pressure along the pipe is also recorded. After about 2 to 3 min, a considerable amount of solid particles is collected in the calorimeters and retained on the thermocouples connected to their bottoms. The readings of these thermocouples are registered. These temperatures are assumed to be the same as the solid temperature at the pipe center. The solid water content is obtained by drying the collected solids in an electrical oven and following the sequence given in Section 3.3. The measurements are repeated three times for the same flow conditions and the results are averaged. The maximum deviation from the mean value is less than ±7%, which insures the repeatability of the experimental test. 3.7. Experimental uncertainty The most common sources of errors in the measured parameters are found in the pressure drop across orifice meter, upstream pressure and temperature, and solid mass. These parameters have direct effect on the accuracy of air and solid water content, and air and solid mass flow

a. dp = 416 µm

b. dp = 931.5 µm

rates. The uncertainty analysis is carried out according to Kline and McClintock method, reported in [43]. Values of uncertainty in the measured parameters are shown in Table 2. 4. Results and discussions The grid used in the present work is non uniform in the radial direction. Thus, the grid is very fine near the pipe wall and gradually expanded to the pipe centerline. A 135 × 380 computational grid is selected based on grid independence study at Re= 7.2× 104. Furthermore, the number of computational parcels and the time step used in the integration of Eqs. (7)–(11) are selected to insure independent results. Due to the polydisperse nature of the used particles, the total mass flow rate is divided into ten monodisperse groups each contains 10% of the total mass flow rate. In the present numerical simulation, a fixed particle size is considered for each group. The particles sizes of these groups are given in Ref. [26]. As indicated previously, the swirl is imparted to the flow by axially rotating pipe of length 6.79 D. The rotational speed is measured using a tachometer, which reads 2973 rpm. At a Reynolds number of 7.2 × 104, this rotational speed corresponds to a Rossby number of 0.98. The wall boundary conditions for the tangential velocity are implemented in the present numerical code as given in Fig. 10. Tangential velocity profiles for the gas phase are shown at different axial locations in Fig. 11 for different particles sizes. Generally, it can be seen from this figure that the tangential velocity is greater in two-phase flow than that in single phase flow at all axial positions. Near the exit of rotating pipe (x/D=6.75), the tangential velocity has its greatest value near the pipe wall. In addition, the swirl velocity increases as the particles size decreases. This can be explained as; the finest particles respond rapidly to the swirl motion and hence transfer large tangential momentum to the gas phase. As the flow progresses downstream the rotating pipe, the small particles lose their tangential momentum faster than the larger ones. Therefore, the tangential velocity for the gas phase increases as the particle size increases. This behavior of solid particles can be explained by

c. dp = 1642 µm

Fig. 12. Effect of particle diameter on the particles trajectories (Re = 7.2 × 104, mo s ¼ 0:053 kg=s, Ro = 0.97).

K.A. Ibrahim et al. / Powder Technology 235 (2013) 500–515

examining the 3-D solid trajectories, shown in Fig. 12. This figure shows the effect of particle diameter on the particles trajectories. It can be seen from this figure that the smaller particles respond rapidly to the swirl motion, while the larger ones attain larger spiral motion in the downstream section of the pipe. The effect of swirl on the pressure drop is shown in Fig. 13 for different particle diameters. It can be seen from this figure that the pressure drop is increased due to swirl motion. Also as Reynolds number increases the pressure drop for swirling approaches that of non swirling flow. This can be attributed to the fact that the swirl intensity

decreases as Reynolds number is increased at constant rotation speed of the pipe. It can also be seen that the model under-predicts the pressure drop in the swirling flow cases. This may be due to the effect of the three-dimensional nature of swirling flow. The effect of swirl on the axial distribution of gas phase temperature is shown in Fig. 14 for different particles diameters. The swirl motion causes the particles to move in spiral path which increases

a. d p = 412 μm 355

a. d p = 412 μm

350

250

Exp.

Num.

340

T g (K)

ΔP/Δ L (Pa/m)

Exp. Non-Swirling Swirling

345

Num.

Non-Swirling Swirling

200

511

150

335 330 325

100

320 315

50 310 0

0

5E+4

1E+5

1.5E+5

2E+5

0

10

20

b. d p = 927 μm

Re

30

40

50

60

40

50

60

40

50

60

x/D

355

b. d p = 927 μm

350

250

345 340

T g (K)

ΔP/Δ L (Pa/m)

200

150

335 330 325 320

100

315 310

50

0

5E+4

1E+5

1.5E+5

2E+5

Re

0

10

20

30

x/D

c. d p = 1636μm 355

c. d p = 1636 μm

350

250

340

200

T g (K)

ΔP/Δ L (Pa/m)

345

150

335 330 325 320

100 315 310 50

0

5E+4

1E+5

1.5E+5

2E+5

0

10

20

30

x/D

Re Fig. 13. Effect of swirl on the pressure drop (mo s ¼ 0:053 kg=s, Ω = 311.46 rad/s).

Fig. 14. Effect of swirl on the gas phase temperature for different particles diameters (Re = 7.2 × 104, mo s ¼ 0:053 kg=s, Ro = 0.97, Tg,in = 353 K).

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K.A. Ibrahim et al. / Powder Technology 235 (2013) 500–515

the particles residence time. As a result, the heat transfer rate increases and gas temperature decreases, as shown in Fig. 14. The effect of swirl on the solid water content is presented in Fig. 15 for different sizes of solid particles. This figure shows that the effect of swirl on the solid water content is similar to that of the gas temperature. Thus, the swirl motion decreases solid water content. This can be attributed to the increased mass transfer rate due to swirl. In addition, the figure indicates that the solid water content

at pipe exit is decreased by 17.74%, 25% and 20.46% for tested average particles sizes of 412, 927 and 1636 μm, respectively. The effect of swirl on the solid temperature is shown in Fig. 16 for different particles diameters. The figure indicates that the solid temperature is slightly decreased due to the swirl motion. To explain this behavior, the effect of swirl on the heat transfer budget is examined. It

a. d p = 412 μm 320

a. d p = 412 μm

Exp. Exp.

Num.

Non-Swirling Swirling

0.14

Num.

Non-Swirling Swirling 315

0.12

Tp (K)

X s (kg water /kg dry solids )

0.16

0.10

310 0.08 0.06 305 0.04

0

10

20

30

40

50

60

x/D

b. d p = 927 μm

0

10

20

30

40

50

60

40

50

60

40

50

60

x/D

b. d p = 927 μm 320

0.14 315 0.12

Tp (K)

X s (kg water /kg dry solids )

0.16

0.10

310 0.08 0.06 0.04 0

305 10

20

30

40

50

60

x/D

10

20

30

x/D

c. d p = 1636 μm

c. d p = 1636μm

320

0.16 0.14

315

0.12

Tp (K)

X s (kg water /kg dry solids )

0

0.10 0.08

310

0.06 0.04

0

10

20

30

40

50

60

x/D Fig. 15. Effect of swirl on the solid phase water content for different particles diameters (Re = 7.2 × 104, mo s ¼ 0:053 kg=s, Ro = 0.97, Tg,in = 353 K,).

305

0

10

20

30

x/D Fig. 16. Effect of swirl on the solid phase temperature for different particles diameters (Re = 7.2 × 104, mo s ¼ 0:053 kg=s, Tg,in = 353 K).

K.A. Ibrahim et al. / Powder Technology 235 (2013) 500–515

513

Fig. 17. Effect of swirl on the gas phase temperature contours at different particles diameters (Re = 7.2 × 104, Tg,in = 353 K, mo s ¼ 0:053 kg=s).

Fig. 18. Effect of Reynolds number on the axial distribution of swirl number for gas phase (d p ¼ 412 μm, mo s ¼ 0:053 kg=s, Ω = 311.46 rad/s).

Fig. 19. Effect of Reynolds number on the percentage decrease in the outlet solid water content due to swirl (Tg,in = 353 K, mo s ¼ 0:053 kg=s, Ω = 311.46 rad/s).

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K.A. Ibrahim et al. / Powder Technology 235 (2013) 500–515

was found that both of the convective and evaporative heats are increased due to swirl. However, the rate of increase in evaporative heat is apparently greater than that of the convective heat which causes a slight decrease in the solid temperature in swirling flow. It was shown previously in [31] that the lift forces move the particles toward the pipe center in non-swirling flow. In contrast, in swirling flow the centrifugal force causes the particles to migrate towards the pipe wall. Therefore, the solids concentration is higher near the pipe center in non-swirling flow and near the pipe wall in swirling flow. The effect of this particle motion mechanism on the gas phase temperature distribution is presented in Fig. 17. It can be seen from this figure that the gas temperature is low near the pipe center in non-swirling flow and near the pipe wall in swirling flow. The solids concentration plays a substantial role in such cases. The figure also shows that the axial temperature gradient increases as the particle size decreases. This is apparently due to the increased heat transfer area as the particle size decreases. The degree of swirl (swirl strength) is characterized by a nondimensional swirl number (S), which represents the axial flux of tangential momentum divided by the axial flux of the axial momentum [38]. Thus,

The effect of particle diameter on the percentage decrease in the solid water content due to swirl at pipe outlet, ΔXout is shown in Fig. 19 at different Reynolds number. It was previously indicated that the smaller particles respond rapidly to the swirl motion while the larger particles reserve their spiral motion longer. Therefore, the particle diameter is a controlling parameter in swirl pneumatic dryers. Thus, at a certain Reynolds number, the percentage decrease in solid water content increases with the increase in particle diameter up to certain particle diameter and then decreases. Fig. 19 shows also that the transition particle diameter (the particle diameter at which the percentage decrease in solid water content at outlet starts to decrease) decreases as the Reynolds number increases. In addition, the percentage decrease in outlet solid water content decreases as the Reynolds number increases. This may be, probably, due to the decrease in particle residence time as the Reynolds number increases. This can, however, be explained by examining the particles trajectories shown in Fig. 20 at different Reynolds numbers. The figure indicates that, as the Reynolds number increases the particles move in straighter paths and thus, the particles residence time decreases as a result. 5. Conclusions

R

2

2π∫ ρUWr dr S¼

0 R

ð43Þ 2

2π∫ ρU Rrdr 0

The effect of Reynolds number on the axial distribution of swirl number for the gas phases is shown in Fig. 18. The figure indicates that the swirl number decreases as Reynolds number increases. This can be attributed to the increase in axial momentum flux as Reynolds number increases.

a. Re = 7.2×104

b. Re = 1.1×105

Swirling gas–solid two-phase flow through pneumatic conveying dryer was investigated numerically and experimentally. The four-way coupling Eulerian–Lagrangian approach was employed to simulate the process under consideration. The effect of heat, mass and momentum exchange between the two phases was considered. In addition, four different turbulence models were tested in this study. The experimental study was carried out in a pilot scale pneumatic conveying dryer using crushed limestone with different sizes. The swirl was imparted to the flow by axially rotating pipe element. Comparisons between predicted results and published data for axial and tangential velocities as

c. Re = 7.2×105

Fig. 20. Effect of Reynolds number on the particles trajectories (dp = 416 μm, Ω = 311.46 rad/s).

K.A. Ibrahim et al. / Powder Technology 235 (2013) 500–515

well as turbulent kinetic energy showed that the RNG based k–ε model performs better than the other turbulence models. The following main points are concluded: 1. The smaller particles respond rapidly to the swirl flow than the larger one while the larger particles attain their spiral motion in the downstream part of the pipe. 2. As the Reynolds number increases the particles moves in a straighter path. 3. The presence of swirl enhances the drying process. 4. The gas temperature decreases and the drying rate increases due to swirl. 5. The pressure drop in swirling flow is larger than that of non-swirling flow. 6. The gas temperature is higher at the pipe center in swirling flow and near the pipe wall in non-swirling flow. References [1] J. Baeyens, D.V. Gauwbergen, I. Vinckier, Pneumatic drying: the use of large-scale data in a design procedure, Powder Technology 83 (1995) 139–148. [2] S.M. El-Behery, W.A. El-Askary, K.A. Ibrahim, M.H. Hamed, Porous particles drying in a vertical upward pneumatic conveying dryer, International Journal of Aerospace and Mechanical Engineering 5 (2011) 110–125. [3] M. Mezhericher, A. Levy, I. Borde, Three-dimensional modelling of pneumatic drying process, Powder Technology 203 (2010) 371–383. [4] T.J. Jamaleddine, M.B. Ray, Numerical simulation of pneumatic dryer using computational fluid dynamics, Industrial and Engineering Chemistry Research 49 (2010) 5900–5910. [5] T.J. Jamaleddine, M.B. Ray, Drying of sludge in a pneumatic dryer using computational fluid dynamics, Drying Technology 29 (2011) 308–322. [6] S.M. El-Behery, W.A. El-Askary, K.A. Ibrahim, M.H. Hamed, Numerical simulation of heat and mass transfer in pneumatic conveying dryer, Computers & Fluids 68 (2012) 159–167. [7] A.H. Pelegrina, G.H. Crapiste, Modelling the pneumatic drying of food particles, Journal of Food Engineering 48 (2001) 301–310. [8] C.P. Narimatsu, M.C. Ferreira, J.T. Freire, Drying of coarse particles in a vertical pneumatic conveyor, Drying Technology 25 (2007) 291–302. [9] B. Saravanan, N. Balsubramaniam, C. Srinivasakannan, Drying kinetics in a vertical gas–solid system, Chemical Engineering Science 30 (2007) 176–183. [10] I.C. Kemp, D.E. Oakley, R.E. Bahu, Computational fluid dynamics modelling of vertical pneumatic conveying dryers, Powder Technology 65 (1991) 477–484. [11] G. Gouesbet, A. Berlemont, Eulerian and Lagrangian approaches for predicting the behaviour of discrete particles in turbulent flows, Progress in Energy and Combustion Science 25 (1998) 133–159. [12] H. Enwald, E. Peirano, A.-E. Almstedt, Eulerian two-phase flow theory applied to fluidization, International Journal of Multiphase Flow 22 (Suppl.) (1996) 21–66. [13] S. Balachandar, J.K. Eaton, Turbulent dispersed multiphase flow, Annual Review of Fluid Mechanics 42 (2010) 111–133. [14] O.A. Marzouk, E.D. Huckaby, Effects of turbulence modeling and parcel approach on dispersed two-phase swirling flow, in: Proceedings of the World Congress on Engineering and Computer Science, Oct. 20-22, 2009, San Francisco, USA, 2009. [15] S.M. El-Behery, M.H. Hamed, M.A. El-Kadi, K.A. Ibrahim, CFD prediction of air-solid flow in 180o curved duct, Powder Technology 191 (2009) 130–142. [16] S.M. El-Behery, M.H. Hamed, A comparative study of turbulence models performance for turbulent flow in a plane asymmetric diffuser, Computers & Fluids 44 (2011) 248–257. [17] A. Balabel, A. Hegab, M. Nasr, S.M. El-Behery, Assessment of turbulence modeling for gas flow in two-dimensional convergent-divergent rocket nozzle, Applied Mathematical Modelling 35 (2011) 3408–3422.

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