Computational fluid dynamic modeling of a Fluid ...

Computational fluid dynamic modeling of a Fluid catalytic cracking atomizer V. Abdolkarimi1 , F.Hormozi1* , A.J. Jolodar2, M.Taghizadeh3 1

Chemical Engineering Department , University of Semnan , Semnan , Iran 2

Research Institute of Petroleum Industry (RIPI), Tehran, Iran

3

Chemical Engineering Department ,Babol University of Technology ,Babol, Iran *

Corresponding author. Tel.: +98 231 3320295; fax: +98 231 3340063. E-mail address: [email protected]

Abstract A new two-phase atomizer of fluid catalytic cracking (FCC) process studied experimentally recently, is now modeled in three dimension in lagrangian frame work by Computational Fluid Dynamic (CFD) method. Special emphasis was placed on the study of the liquid atomization. This atomizer tested quantitatively in air-water cold system using particle dynamic analyzer (PDA). Linearized Instability Sheet Atomization (LISA model) was employed to simulate the water atomization process. The effects of different distances from nozzle outlet on droplet size and velocity distribution in downward spray are studied. Predictions of droplet diameters, trajectories and velocities are presented and compared with relevant experimental results and found them in a good agreement. Key words: CFD , Atomization , Two fluid nozzle, LISA model, Droplet size

1.

Introduction

Fluid catalytic cracking is a process used to change the oil heavy like vacuum gas-oil into light and more valuable products (petrol). This process is performed in the riser that the powder catalyst pours from the regenerator on the atomized feed. To achieve an impact surface of catalyst, one should atomize the feed using a two-phase atomizer. This process causes efficiency, selectivity and properties of FCC products to increase. In addition, the uniform feed atomization causes the increase of the initial catalytic cracking reaction of catalyst-hydrocarbon and the decrease of the decomposition of catalyst-products Theologos et al. (1999). The uniform distribution of feed in FCC riser is followed by the increase of desirable products (petrol) and decrease of undesirable products (coke and dry gas) Johnson(1994), Dahlstrom(1996), Abul-Hamayel(2002). For designing such atomizer, the proper distribution of droplet size in low pressure is of much importance Miller et al.(2000). One can optimize the different parts of atomizer by means of experimental designing method (Taguchi) based on the mean droplets size produced, Garcia et al.(1995). As the catalyst in FCC process encounters with the feed in different distances of the feed injection in riser

reactor, the effect of distance on size and velocity distribution of spray droplets is important on designing the efficient atomizers. CFD models provide valuable information on how possible improvements affect overall performance in a relatively cost-effective manner. prototype atomizer models must be tested at testing facilities before commissioning, which is an expensive process. CFD offers a cost-effective alternative to experiments, but the accuracy of the model results must first be assured. As Oberkampf and Trucano (2002) proposed, this can be accomplished by two means: verification and validation. Verification involves ensuring that the algebraic and differential equations of the model have been accurately solved, while validation implies the verification of the numerical code, reaching the correct solution. Furthermore, it is also necessary to determine whether the correct model has been employed, in other words, whether the physical models used to represent the physical processes were the right ones. To illustrate the effectiveness of CFD in the spray application, a atomization of water by means of new designed nozzle is studied in this paper. for validating the modeling results the experimental results presented by Jolodar et al. (2005) was used which provide a complete experimental database for atomizing of water under controlled conditions.

Information dealing with the effect of the gas flow field on the trajectory of individual droplets of various sizes is critical for the understanding of the dynamics of spray which is accomplished by the effect of continuous phase turbulence on the dispersion of droplets. In this article special attention is given to spray formation and droplet size and velocity distribution and their comparison with experimental data. The construction of a computational model involves the input of working conditions, simplifications, mesh generation , turbulence and atomization models, boundary conditions, including: thermal conduction, viscosity and surface tension of droplet and the selection of the algorithm of solution. 2.

Atomizer design and construction

The two-phase atomizer is designed as three following Sections (Figure 1) (a) Primary atomization (b) Hard mixing (c) Final atomization The primary atomization section is consisted of two concentric tubes; along the internal tube there are some holes to mix liquid feed and atomizer gas. The liquid feed (water or vacuum gas-oil) and the atomizer gas (air or steam) enter into internal tube and annular space, respectively and mix together through the holes existing on the internal tube. Then the two-phase mixture enters to the hard mixing section, which is consisted of a cylindrical spiral (d) surrounded by a connecting tube. This spiral will produce a homogeneous mixture by the circulatory movement and hard mixing at the opening of the orifice. Finally, the homogeneous mixture will be atomized to a solid conical spray after passing the circular orifice. characterization of optimized nozzle presented in Table 1.

Table1 Characterization of optimized nozzle (Jolodar et al. 2005) Factors

Optimum level

Length of distribution tube Number of holes of distribution tube Holes diameter of distribution tube Length of connecting tube Length of spiral Orifice shape

14 cm 15 0.75mm 8cm 8cm with cone

Orifice hole diameter

1mm

Orifice hole depth

5mm

Pressure of mixture

30psig

Water flow rate

6.5l/h

Air flow rate

3.

205.95l/h

Experimental set-up

Flow diagram of the experimental system is shown in Figure 2. Water is pumped by pump P1 from tank T1. In order to eliminate the pump vibrations a knock out drum is used. Flow rate and pressure of the entering water is read by FI1 and PI1 and is controlled by valve V1. The entering air to the system after passing the regulator PIC and valve V2 is measured by FI2 and PI2. To prevent the recycle in air and water lines we used check valves CV1 and CV2 after PI1 and PI2, respectively. The pressure of air and water mixture in primary atomization section is measured by PI3 before entering to the hard mixing section. For measuring the size and velocity of droplets, the particle dynamical analyzer (PDA, Dantec dynamics, Denmark) was used, which can measure the diameter and velocity of the spherical particles simultaneously in gas and liquid media, Haugen(1990).

Figure 1. Sketch of pressure swirl atomizer (Jolodar et al. 2005).

This system can measure the diameter of spherical particles in the range of 0.5 μm to few millimeters. also the maximum velocity of the particles measured is 500 m/s. The simultaneous measurement of diameter and velocity of the particles makes it possible to interrelate these quantities. This system is based on Phase Doppler Anemometry, which is the developed model of Laser Doppler Anemometry Durst(1997). In this system after producing laser beam, it divides into two beams by equal intensities through a Bragg cell. These two beams after passing through transmitting optics pass each other in the transmitter lens focal length. The receiving optic receives the lights reflected by the contacting droplets and sends them to photo detector and signal processor, respectively. Then the processed data is transmitted to the computer and will be analyzed by “BSA FLOW” software (Jolodar et al. 2005). This apparatus makes the simultaneous measurement of the velocity and diameter of the particles possible in any surface of spray. The measurement of the particles’ velocity is based on the change of frequency between “source light” and “received light”, while the measurement of the particles’ diameter is based on the phase differences of the reflected lights received by two

detectors. This phase difference has a direct relation with particle’s diameters. A traverse is planned to interchange the atomizer in cylindrical, spherical and Cartesian coordinates in three X, Y and Z directions with an accuracy of one-tenth millimeter. 4.

Computational model

CFD modeling involves three main steps: (1) Creating the model geometry and grid. (2) Defining the appropriate physical models and (3) Defining the boundary and operating conditions. The governing conservation equations of mass, momentum and energy and physical models involved in the process are discretized over control volumes and solved by finite volume method. Special emphasis is placed on the study of the liquid atomization process and hence the geometry consists of the orifice and a cylindrical space of radius 5cm and 20cm length beneath the orifice, is modeled. Table 2 shows the operating conditions used in the model that includes air and water flow rates around relevant experimental values for a meaningful comparison.

Figure 2. Schematic view of experimental apparatus (Jolodar et al. 2005).

Table2 Operating conditions applied in the model

(

101325

pa

Air temperature

298

k

Air mass flow rate

3.51e -4

kg/s

water density

998

kg/m3

water mass flow rate

2.7e -3

kg/s

water temperature

298

k

orifice pressure

165000

pa

orifice diameter

1

mm

orifice depth

5

mm

Spray angle

60

deg

4.1. Governing equations

∂ρ + ∇. ρU = S m     (1) ∂t ∂ ρU + ∇ ⋅ ρU U = −∇p + ∇ ⋅τ + ρ g + S M   ∂t         (2)  ∂ (ρE ) + ∇ ⋅ U (ρE + p ) = ∂t ∇.⎛⎜ k eff ∇T − ∑ j h j J j + ⎛⎜τ eff .U ⎞⎟ ⎞⎟ + S h   (3) ⎝ ⎠⎠ ⎝

)

)

(

2

p

u E = h− +   ρ 2

 (4)

 

Realizable k–e model was employed for turbulence prediction of gas phase as it predicts the spreading rate of both planar and round jets more accurately.  The term "realizable'' means that the model satisfies certain mathematical constraints on the Reynolds stresses, consistent with the physics of turbulent flows. The Reynolds stress tensor for the gas phase is given by eq. (5) and its accompanying equations (6) to (12).

)

(

τ ′g′ = −2 / 3 ρ g k g + ρ g μ t , g ∇.U g I + ⎛ ⎝

T

⎞ ⎠

ρ g μ t , g ⎜ ∇.U g + ∇.U g ⎟

(

)

⎡⎛ μ t,g ∂ ρ g k g + ∇. ρ g k g U g = ∇ ⎢⎜⎜ μ + σk ∂t ⎢⎣⎝

(

)

)

⎛

εg

⎝

kg + υgε g

ε g ⎜⎜ ρ g C1 S − ρ g C 2

 

 

  ξ ⎤

(5) ⎤ ⎞ ⎟∇ k g ⎥ + ⎟ ⎥⎦ ⎠

Gk ,g − ρ g ε g + S k

(6)

⎤ ⎞ ⎟∇ ε g ⎥ + ⎟ ⎥⎦ ⎠

⎞ ⎟+S ε ⎟ ⎠

 

 

(7)

⎡   C1 = max ⎢0.43, ξ + 5 ⎥⎦ ⎣ kg ξ =S    

 

 

(8)

 

 

(9)

S = 2 Eij Eij  

 

 

(10)

  

               (11)

 

 

εg

 

C2 = 1.9, σ ε g = 1.2, σ k g = 1

The gas flow equations are solved in the Eulerian frame work that could be found in well known texts such as reference V. Ranade(2002). The conservation of mass, momentum and energy are eq. (1), eq. (2) and eq. (3) respectively. The interaction between discrete (water droplets) and gas phases is introduced by the source term (S) of each equation.

( ) ( ) (

)

(

⎡⎛ μt,g ∂ ρ g ε g + ∇. ρ g ε g U g = ∇ ⎢⎜⎜ μ + ∂t σk ⎢⎣⎝

Operating pressure

μ t = ρC μ

k

2

  

ε

(12)

A Lagrangian approach was employed to calculate the movement of the droplets, eq. (13).

du p dt

(

gx ρ p − ρ

= FD +

ρp

)+ F

x

   

(13)

The drag force imposed on the droplet is given by eqs. (14) to (17).

FD =

18 μ C D Re (u − u p )   ρ p d 2p 24

C D = C D , sphere (1 + 2 .632 y )   

 

(14)

 

(15)

Re > 1000 ⎧0.424 ⎪   CD,sphere = ⎨ 24 ⎛ 1 2 / 3 ⎞ ⎪ Re ⎜1 + 6 Re ⎟ Re ≤ 1000 ⎠ ⎩ ⎝

Re =

(16)

ρd p u − u p

      (17) μ In eq. (15) y is the droplet torsion and is given by eqs. (18) to (22) as a function of time. y (t ) = We c + e

⎡( y 0 − We c ) cos (ω t ) +

⎤ ⎥ ⎢ 1 ⎛⎜ dy 0 + y 0 − We c ⎞⎟ sin (ω t )⎥ ⎟ ⎢ ω ⎜ dt ⎥ td ⎠ ⎣ ⎝ ⎦

− (t / t d ) ⎢

 

 

 

(18)

C C Wec = F K We   Cb

 

 

(19)

1 Cd μl =     td 2 ρl r 2

 

 

(20)

 

 

(21)

 

 

ω2 =

CKσ

ρl r

3

−

1   td

C K = 8, C d = 5, C F = 1 / 3, C b = 0.5  

(22)

The dispersion of droplets due to turbulence in the fluid phase can be predicted using the stochastic tracking model (random walk) which includes the effect of instantaneous turbulent velocity fluctuation, u ′(t ) on the droplet trajectories as follows:

u = u + u ′(t )    

 

 

(23)

u ′, v′, w′ = ς u ′2  

 

 

(24)

u ′2 = 2 k / 3         (25) By substitution of eq. (23) in the trajectory equation (13) it is included the instantaneous value of the fluctuating gas flow velocity to predict the dispersion of the particles due to turbulence. In the equation (24) ς is a normally distributed random number, and the remainder of the righthand side is the local RMS value of the velocity fluctuations. The instantaneous value of the fluctuating velocity is kept constant over the eddy life time. The characteristic lifetime of the eddy is defined by eq. (26) .

τ e = −TL log(r ) TL ≈ 0.15

(26)

k

        (27) ε Where TL is the lagrangian integral time scale and r a uniform random number between 0 and 1. The particle eddy crossing time is defined by eq. (28). ⎡ ⎛ ⎞⎤ Le ⎟⎥ t crosss = −τ ln ⎢1 − ⎜     (28) ⎢ ⎜ τ u − u p ⎟⎥ ⎠⎦ ⎣ ⎝ 4d p ρ p        (29) τ = 3ρ g C D U r Where τ is the droplet relaxation time, Le is the eddy length scale. The droplet is assumed to interact with the fluid phase eddy over a time step which is the smaller of the eddy lifetime and the eddy crossing time. A new value of the instantaneous velocity is obtained by applying a new value of ς in eq. (24) at the end of each time step.

mixing core into the swirl chamber.  The swirling liquid pushes against the walls and if the liquid pressure is sufficiently high, a high angular velocity is attained and an hallow air-cored vortex is created. The swirling liquid then flows through the outlet of the swirl chamber and spreads out of the orifice under the action of both axial and radial forces, forming a tulip-shaped or conical sheet beneath the orifice. The sheet subsequently disintegrates into droplets. The liquid-air interaction, liquid surface tension and viscous forces are the primary factors governing the liquid breakup process. The spray cone angle may range from 30° to almost 180°, depending on the relative magnitude of the tangential and axial velocity components at the nozzle exit, and hence can be controlled by adjusting these variables. The droplet size is a function of liquid pressure, gas-liquid flow rate ratio and swirl chamber dimensions Huimin Liu(2000). The transition from internal injector flow to fully-developed spray can be divided into three steps: film formation, sheet breakup, and atomization. The pressure-swirl atomizer model is called the Linearized Instability Sheet Atomization (LISA) model of Schmidt et al.(1999). The LISA model is divided into two stages:   film formation and sheet breakup into atomized droplets.  The mathematical analysis assumes that KelvinHelmholtz waves grow on the sheet and eventually break the liquid into ligaments. It is then assumed that the ligaments break up into droplets due to their instability. Once the liquid droplets are formed, the spray evolution is determined by drag, collision, coalescence, and secondary breakup.  A sketch of how this process is thought to occur is shown in Figure 3.

4.2. Atomizer model For most practical applications, such as liquidfuel combustion in gas turbines, oil furnaces, and direct-injection spark-ignition engines, a wider spray cone angle is desired. To achieve a wide spray cone, a simplex, i.e. a pressure-swirl atomizer can be used Huimin Liu(2000). A pressure-swirl atomizer consists of a converging conical swirl chamber with a small orifice at the vertex(Figure 1). Liquid is accelerated through a spiral hard

Figure 3. Spray formation steps in pressure-swirl atomizer model Collazo(2009). 4.2.1.

Film formation

The centrifugal motion of the liquid within the injector orifice creates an air core surrounded by a

liquid film (Figure 3). The thickness of this film, t, is related to the liquid mass flow rate by eq. (30).

(

m& = πρ ut d inj − t

) 

    (30) u ,is the axial component of velocity at the injector exit. This quantity depends on internal details of the injector and is difficult to calculate from first principles. Instead, the approach of Han et al. (1997) is used. The total velocity is assumed to be related to the injector pressure by eq. (31). 2 Δp (31) U = kv ρl

where ⎡ 4m& k v = max ⎢0.7, 2 d ρ 0 l cos θ ⎣⎢ u = U cos θ

ρl ⎤

⎥ 2Δp ⎦⎥

(37)

oh = We l / Re l

(38)

(33)

ρ U 2h Uh , Re l = We l = l σ υl r0 h0 h= ⎛θ ⎞ r0 + Lb sin ⎜ ⎟ ⎝2⎠

Sheet breakup and atomization

η = η 0 e ikx +ωt

(34) Where η 0 is the initial wave amplitude, k = 2π / λ is the wave number, and ω = ω r + iω i is the complex growth rate. The most unstable disturbance has the largest value of ω r , denoted here by Ω , and is assumed to be responsible for sheet breakup. From reference [16], the real component of growth rate, ω r , is related to the wave number ,k, given by eq. (35). 1 ωr = − 2υ l k 2 tanh (kh ) + tanh (kh ) + Q

{

⎡ σk 3 ⎤ ⎫⎪ tanh (kh) − Q U k − [tanh(kh) + Q]⎢− QU 2 k 2 + ⎥⎬ ρl ⎦⎥ ⎪ ⎣⎢ ⎭ 2

2

π

(36) ks Where k s is the wave number corresponding to the maximum growth rate. The breakup from ligaments to droplets is assumed to behave according to Weber's analysis for capillary instability(1931). The initial droplet diameter is given by eqs. (37) to (40).

(32)

The pressure-swirl atomizer model includes the effects of the surrounding gas, liquid viscosity, and surface tension on the breakup of the liquid sheet. Details of the theoretical development of the model are given in Senecal et al. (1999) and are only briefly presented here. The model assumes that a two-dimensional, viscous, incompressible liquid sheet of thickness 2h moves with velocity U through a quiescent, inviscid, incompressible gas medium. a spectrum of infinitesimal wavy disturbances are imposed on the initially steady motion. The spectrum of disturbances results in fluctuating velocities and pressures for both the liquid and the gas. The amplitude of these disturbances is given by eq. (34).

4υl2 k 4

dL =

d 0 = 1.88 d L (1 + 3oh )1 / 6

The tangential component of velocity ( w = U sin θ ) is assumed to be equal to the radial velocity component of the liquid sheet downstream of the nozzle exit. 4.2.2.

When the liquid film is broken down a ligament of section diameter d L given by eq. (36) is produced (Figure 3).

2 2

(35)

(39) (40)

Lb is the ligament length and related to the maximum growth rate, Ω , by eq. (41). U ⎛η ⎞ (41) Lb = Uτ = ln ⎜⎜ b ⎟⎟ Ω ⎝ η0 ⎠ the maximum growth rate is found by numerically maximizing eq. (35) as a function of k. 4.3. Droplet collision model

The algorithm of O'Rourke (1981) is applied for droplet collision modeling. the O'Rourke's method is a stochastic estimate of collisions. This method makes the assumption that two particles may collide only if they are located in the same continuous-phase cell. The probability of collision of two droplets is derived from the point of view of the larger droplet, called the collector droplet and identified below with the number 1. The smaller droplet is identified in the following derivation with the number 2. The calculation is in the frame of reference of the larger droplet so that the velocity of the collector droplet is zero. The collector undergoes a mean expected number of collisions given by:

n 2π (r1 + r2 )2 v rel Δt (42) V The probability distribution of the number of collisions that the collector experiences follows a Position distribution. n=

n

n (43) n! Once it is determined that two droplets collide, the outcome of the collision must be determined. In general, the outcome tends to be coalescence if the P (n ) = e − n

droplets collide head-on, and bouncing if the collision is more oblique. In the reference frame being used here, the probability of coalescence can be related to the offset of the collector droplet center and the trajectory of the smaller droplet. The critical offset is a function of the collisional Weber number and the relative radii of the collector and the smaller droplet.

⎛ 2. 4 f ⎞ bcrit = (r1 + r2 ) min ⎜1, ⎟ ⎝ We ⎠ ⎛r f ⎜⎜ 1 ⎝ r2

⎞ ⎛ r1 ⎟⎟ = ⎜⎜ ⎠ ⎝ r2

3

⎞ ⎛r ⎟⎟ − 2.4⎜⎜ 1 ⎠ ⎝ r2

(44)

2

⎞ ⎛r ⎟⎟ + 2.7⎜⎜ 1 ⎠ ⎝ r2

⎞ ⎟⎟ ⎠

(45)

The value of the collision parameter b is determined as : b = (r1 + r2 ) Y

(46)

Y is a random number between 0 and 1. The calculated value of b is compared to bcrit , and if b < bcrit , the result of the collision is coalescence. It is assumed that some fraction of the kinetic energy of the droplets is lost to viscous dissipation and angular momentum generation. This fraction is related to b, the collision offset parameter. Using assumed forms for the energy loss, O'Rourke derived the following expression for the new velocity: m v + m 2 v 2 + m 2 (v1 − v 2 ) ⎛ b − bcrit ⎞ ⎜ ⎟ v1′ = 1 1 ⎜ r + r −b ⎟ m1 + m 2 crit ⎠ ⎝ 1 2 (47)

The new droplet is given the same properties as the original droplet (i.e., temperature, material, position, etc.) with the exception of radius. 4.5. Algorithm of solution

The discrete phase trajectory is solved coupled with continuous phase flow field. The effect of droplets on the gas phase is introduced by the source terms of continuous phase equations. The algorithm of coupled two phase calculation depicted in Figure 4 consists of following steps: 1. Solve the continuous phase flow field (prior to introduction of the discrete phase). 2. Introduce the discrete phase by calculating the particle trajectories for each discrete phase injection. 3. Recalculate the continuous phase flow, using the interphase exchange of momentum, heat, and mass determined during the previous droplet calculation. 4. Recalculate the discrete phase trajectories in the modified continuous phase flow field. 5. Repeat the previous two steps until the droplets travel the specified number of steps or exit from calculating domain.

Continuous phase flow field calculation

Droplet trajectory calculation 

4.4. Droplet breakup model

The wave breakup model of Reitz (1987) , which considers the breakup of the droplets to be induced by the relative velocity between the gas and liquid phases, was used. The model assumes that the time of breakup and the resulting droplet size are related to the fastest-growing KelvinHelmholtz instability. Ω , and the corresponding wavelength, Λ ,are given by Reitz. ⎛ ρ a3 ⎞ 0.34 + 0.38We12.5 Ω⎜ 1 ⎟ = (48) ⎜ σ ⎟ (1 + oh ) 1 + 1.4Ta 0.6 ⎝ ⎠

(

(

)

)(

1 + 0.45oh 0.5 1 + 0.4Ta 0.7 Λ = 9.02 0 .6 a 1 + 0.87We1.67

(

2

)

)

(49)

In the wave model, breakup of droplet is calculated by assuming that the radius of the newly-formed droplets is proportional to the wavelength of the fastest-growing unstable surface wave on the original droplet. r = 0.61Λ (50)

Update continuous phase source terms 

Figure 4. Coupled discrete phase calculations 5.

Results and discussion

Droplet size and velocity distributions are obtained in different distances from nozzle tip i.e (80, 140, 200mm) through the cylindrical space beneath the nozzle orifice. The experimental values and the relevant CFD results are compared and discussed hereinafter. The solid line represents the experimental results and dots represent the results of the modeling. Figure 6 represents the radial evolution of the mean diameter at different distances. The results have been obtained over 50 points on the center line of each cross-section in the y direction (Figure 5), though the droplets placed on different radiuses in each cross-section and are not placed on whole of the 50 points,

Figure 5. sketch of calculation points on the circle radius of conical section. (as shown in Figure.8). The mean diameter of droplets at each point in the spray cross-section is calculated by eq. (51). Nj

(D10 ) j

=

∑ Di i =1

Nj

(51)

in which ‘j’ is the measured points in the spray’s cross-section and ‘Di’ the samples diameter in each point of surface and ‘Nj’ the total numbers of sampled droplets in point j. The measurements give a minimum droplet size at the spray axis and an increase in size towards the edges of the spray. As is shown in Figure 6, the agreement between measurement and calculations is reasonably good. The droplets nearest to the axis for axial distance of 80mm, represent the main difference between simulation and experiments. A possible reason could be the difficulty of measuring the smaller droplets with the laser apparatus employed. At the distances of 140 and 200mm the dispersion of droplet diameters increase with increase in the radial position due to vortex flow of the surrounding air (Figure 5) which mixes droplets with different diameters together. The results

based on mean diameter at each section and comparison with experimental results are shown in Table 3. Figures 7 shows that as the spray cone section is set farther from nozzle orifice, the droplet mean diameter increases. Table 3 Mean diameter of droplets in different distances from the tip of optimized nozzle in downward condition Distance(mm)

Mean diameter (µm) Simulated

Experimental

Relative difference%

80

18.23

24.2

24.7

140

19.86

19.92

0.3

200

22.12

25

11.5

Figure. 8 shows the predicted number density at each cross-section. The number density distribution is defined by dividing the number of droplets in each interval by the total number of droplets accommodated on the circle radius of cone section (Figure5).As seen the droplet number concentration is high at the region near the axis of the spray, which is due to existence of air-cored vortex in the pressure swirl atomizer.

Figure.9 shows the radial distribution of the droplet mean velocity. At the center of the spray cone the droplet velocity is high and reduces towards the edge of the spray. A relatively uniform velocity distribution of droplets in spray is observed. Mean velocity of droplets at each interval in the spray cross-section is calculated by eq. (52). Nj

∑ vi

i =1

simulation

40

19.5

8.4

140

12.2

12.8

4.7

200

7.55

10.7

29.4

experimental

simulation

200

300

Z (mm)

Figure 7. Variation of mean diameter with distance. 20 10

80mm

0.25

0

5

10

15

20

z=140mm

25 20 15

140mm

200mm

0.2

25

30 Mean diameter(µm)

100

z=80mm

30

experimental

30 25 20 15 10 5 0 0

0

0.15 0.1 0.05

10 5

0

0

0 0

5

10

15

40 Mean diameter(µm)

Experimental

21.14

(52)

Nj

In eq.(52) the parameters are defined similar to eq.(51). The results based on mean velocity at each section and comparison with experimental results are shown in Table 4. Figures 10 shows that as the spray cone section is set farther from nozzle orifice, the droplet mean velocity decreases.

Mean diameter(µm)

Simulated

Relative difference%

80

Mean diameter (µm)

j

=

Mean velocity (m/s)

Distance(mm)

Number density

v

Table 4 Mean velocity of droplets in different distances from the tip of optimized nozzle in downward condition

20

25

z=200mm

30 20 10 0 0

5

10

15

20

r(mm)

Figure 6. Droplet mean diameter in radial coordinate.

25

5

10

15

20

25

r(mm)

Figure 8. Number density distribution in radial coordinate.

30

35

simulation

experimental

Mean velocity(m/s)

40

6.

z=80mm

30 20 10 0 0

5

10

Mean velocity(m/s)

20 15

z=140mm

10 5

Conclusion

The simulation results of a FCC atomizer was presented, and it has been compared with some previously published experimental data. From a modeling point of view, the main hypotheses of simplifications, geometric model, discretization and physical models, seem to be correct, as they predict the main parameters of the system with acceptable validity. For the modeling of liquid atomization, the LISA model employed and its coupling with the CFD calculations of the droplet’s trajectories proved to be valid in terms of size and velocity distribution inside the specified volume beneath the orifice. Also it is seen that the vortex flow of surrounding air is responsible for droplet size scattering near the edge of spray. In short, this paper discussed the possibilities of CFD modeling to predict the behavior of a real FCC atomizer. In addition, the importance of reliable experimental data for validating the models has been highlighted.

0

Mean velocity (m/s)

0

10

20

15 z=200mm

10 5

The authors thank Mohsen Rezaeian at the Amir Kabir University of Technology, Iran, and Joaquín Collazo at the university of Vigo, spain, for their navigations through modeling of the FCC atomizer. Nomenclature

0 0

10

a b

20 r(mm)

Figure 9. Droplet mean velocity distribution in radial coordinate. simulation

experimental

25 Mean diameter(µm)

Acknowledgement

20

cylindrical liquid jet radius (m) collision parameter (m) drag coefficient

CD d0

most probable initial droplet diameter (m)

d inj

nozzle outer diameter (m)

dL

ligaments diameter (m)

E ij

strain rate component( s −1 )

FD Gk

drag force (N). generation of turbulence due to the mean −1 −3

velocity Gradients ( kgm s

15

gx

10 5 0 0

100

200

300

Z(mm)

Figure 10. Variation of mean velocity with distance.

gravitational acceleration ( ms −1

).

−2

)

−1

h h

enthalpy ( Jkg K ) sheet half thickness at break-up (m)

Jj

diffusion flux of species j ( kgm

Ks

wave number corresponding to the maximum

−2 −1

s

)

( ).

growth rate Ω m

−1

−1

k eff

wave number ( m ) effective conductivity due to the turbulence

kv

( wm −1 k −1 ) velocity coefficient of the nozzle

k

k

kinetic energy per unit mass ( m 2 s −2 )

k

Lb

thermal conductivity ( wm −1 k −1 ) length where the ligaments are formed (m)

m&

liquid mass flow rate ( kgs

n

mean number of collisions Ohnesorge number pressure (Pa) nozzle operating pressure (Pa) droplet radius(m) radial distance from center line to the mid-line of the liquid sheet (m) source term

Oh p

Δp r

r0 S S T t t

td TL U

−1

strain rate tensor( s −1 ) local temperature (K) time (s) liquid film thickness (m) characteristic time scale (s) lagrangian time scale (s) total velocity ( ms −1 )

r u

velocity vector ( ms −1 )

u

velocity magnitude ( ms −1 )

up

particle velocity ( ms −1 )

u′ Wec

velocity fluctuations ( ms −1 ) collisional Weber number droplet torsion

y

)

,

Greek letters rate of dissipation of the turbulence kinetic

ε

η ηb η0 θ μ μt

energy ( m 2 s −3 ) wave amplitude of liquid film disturbances (m) critical wave amplitude of liquid film disturbances (m) initial wave amplitude of liquid film disturbances (m) spray half angle (degrees) gas dynamic viscosity (pa.s) gas turbulent viscosity (pa.s)

ν νl

gas kinematic viscosity ( m 2 s −1 )

ρ

gas density ( kgm

ρl σk σε τ τ τe ω ωr

liquid kinematic viscosity ( m 2 s −1 ) −3

liquid density ( kgm

) −3

)

turbulent Prandtl number turbulent Prandtl number liquid sheet break-up time (s) −1 −1

viscous stress tensor ( kgm s eddy life time (s) complex growth rate real growth rate

Abul-Hamayel, M.A, Effect of feedstocks on high-severity fluid catalytic cracking, Chem. Eng. Technol. 25 (1) (2002) 65–70. Collazo, J., J. Porteiro , D. Patiٌo, J.L. Miguez, E. Granada, J. Moran, Simulation and experimental validation of a methanol burner, Fuel 88 (2009) 326–334. Dahlstrom, B.F., K. Ham, M.E. Becker, T.P. Hum, Feed injection, riser-termination system replaced in fast-track revamp, Oil Gas J. 94(31) (1996). Durst, F., G.Brenn, T.-H. Xu, A review of the development and characteristics of planar phase-Doppler anemometry,Meas. Sci. Technol.8 (11) (1997) 1203–1221. Garcia, A., D. Phillips, Principles of experimental design and analysis, Chapman & Hall, 1995. Han, Z., S. Perrish, P. V. Farrell, and R. D. Reitz. Modeling Atomization Processes of Pressure-Swirl Hollow-Cone Fuel Sprays. Atomization and Sprays, 7(6):663-684, Nov.Dec.1997. Haugen, P.,Particle sizing and velocity measurements using Laser Doppler technique,in: Ninth Symposium of the American Meteorological Society on Turbulence and Diffusion, Roskilde, Denmark,1990. Huimin Liu, Science and Engineering of Droplet Fundamentals and Applications, Noyes publication Park Ridge, New Jersey, U.S.A. Copyright © 2000 by Noyes Publications. JebraieliJolodar A.,,M.M.Akbarnejad ,M.Taghizadeh

)

( )

−1 Ω maximum growth rate of disturbances m   Literature cited

M.Ahmadi Marvast Laser-based flow measurement in Performance assessment of FCC atomizer, Chemical Engineering Journal 108 (2005) 109–115. Johnson, D.L, A.A. Avidan, New nozzle improves FCC Feed atomization, unit yield patterns, Oil Gas J. 92 (43) (1994). Miller, R., Y.-L. Yang, E. Gbordzoe, New development in FCC feed injection and stripping technologies, in: NPRA Annual Meeting, Convention Center, San Antonio, Texas, 2000. Oberkampf WL, Trucano TG. Verification and validation in computational fluid dynamics. Prog Aerosp Sci 2002;38:209–72. O'Rourke. P.J., Collective Drop Effects on Vaporizing Liquid Sprays. PhD thesis, Princeton University, Princeton,New Jersey, 1981. Ranade, Vivek V., Computational Flow Modeling for Chemical Reactor Engineering Copyright 2002 by ACADEMIC PRESS. Reitz. R.D., Mechanisms of Atomization Processes in HighPressure Vaporizing Sprays. Atomization and SprayTechnology, 3:309-337, 1987. Schmidt,D.P.,I. Nouar,P. K.Senecal,C. J.Rutland,J. K.Martin, and R. D.Reitz. Pressure-Swirl Atomization in the Near Field. SAE Paper 01-0496, SAE, 1999. Senecal, P.K., D. P. Schmidt, I. Nouar, C. J. Rutland, and R. D. Reitz. Modeling High Speed Viscous Liquid Sheet Atomization. International Journal of Multiphase Flow, 25 (1999), pp. 1073–1097. Theologos, K.N., A.I. Lygeros, N.C. Markatos, Feedstock atomization effects on FCC riser reactors selectivity, Chem. Eng. Sci. 54 (22)(1999) 5617–5925. Weber. C., Zum Zerfall eines Flüssigkeitsstrahles. ZAMM, 11:136-154, 1931.