lable at ScienceDirect

Applied Thermal Engineering 31 (2011) 188e193

Contents lists avai

Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Optimization of vane mist eliminators

Elhame Narimani, Shahrokh Shahhoseini*

Simulation and Control Research Laboratory, School of Chemical Engineering, Iran University of Science and Technology, P.O. Box 16765-163, Tehran, Iran

a r t i c l e i n f o

Article history:Received 9 November 2009Accepted 31 August 2010Available online 21 September 2010

Keywords:Mist eliminatorsCFDSeparation efficiencyVaneResponse surface method

* Corresponding author. Tel.: þ98 21 77240540-270E-mail address: shahrokh@iust.ac.ir (S. Shahhosein

1359-4311/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.applthermaleng.2010.08.031

a b s t r a c t

Vane mist eliminators are among the most effective devices to separate liquid droplets from a gas flow.Separation efficiency of these devices is largely dependent on the gas velocity, vane spacing and vaneturning angles. In this study the efficiency of this type of mist eliminator has been investigated, usingcomputational fluid dynamic (CFD). In addition, a prediction model of the separation efficiency wasobtained based on the response surface methodology. The simulation results showed that there wasa conceivable dependency of separation efficiency on the gas velocity and geometrical parameters ofvanes. The optimal values of these parameters were determined in order to achieve the maximumseparation efficiency.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Since gas liquid content could upset or damage the equipments,it is sometimes necessary to remove small quantities of liquid dropsfrom the gas streams. Vane mist eliminators are the devices thatcan effectively remove entrained liquid from a gas flow, usually byinertial impingement. In these eliminators, the wavy vanes (zigzagshaped plates) cause the gas to move in a zigzag manner betweenthem as shown in Fig. 1. The liquid drops cannot follow thesechanges in the direction due to their higher inertia. Thus theyimpinge and adhere on to the solid surfaces.

When the amount of the liquid is sufficiently high, it formsa film, which drains away under the gravity. In the case of verticalvane units, where the gas flows upwards, this drainage is counter-current to the gas flow. If the gas flows horizontally through theunit the drainage is perpendicular to the gas flow [1]. The separa-tion efficiency was investigated by Claes and De Bruyne [2].Recently, some researchers have conducted several studies in orderto improve the performance of demisters [1e9]. Numerical andexperimental behavior of the droplet in the gas flow has beenstudied by A.I.Josang [9].

Response surface methodology (RSM) applies a set of statisticaland mathematical techniques that are useful for designing, devel-oping, improving and optimizing the process under study. RSM haswidely been used in the field of chemical engineering to study theyield or output of a system [10]. In this study the optimizationanalysis of demisters in wet flue gas desulphurization has been

1.i).

All rights reserved.

performed by researchers [11]. Since they ignored film breakup,their results showed that the higher velocity caused the moreseparation efficiency. However, in real practice higher air velocityalso leads tomore film breakup causing lower separation efficiency.In this research, film breakup has also been included into theprocess model. Consequently, it was possible to find the optimalconditions of a system of multistage vanes.

2. CFD simulation

CFD simulation is a suitable technique to study the hydrody-namics, involved in the separation of the droplets from the gas flow.Most of the liquid droplets can be separated from the gas flow inthe first vane stage. However, due to some droplet producingphenomena in this process some new fine droplets can be found atthe outlet of the separator. It is desirable to find out the possiblemechanisms for this secondary droplet generation and considertheir effects on the performance of the separator. The mechanismscan be classified into four groups representing the origin of the newdroplets as given below.

1) Dropletedroplet interaction2) Droplet breakup3) Splashing of impinging droplet4) Re-entrainment from liquid film

Among the above mechanisms for secondary droplet generationthe breakup of the droplets by their impingement on the liquid filmand re-entrainment from the liquid film are more likely to occur.The constant Weber number model was applied to take film

Fig. 1. Fluid flow in between the vanes of a mist eliminator.

Table 1The re-entrainment limit for constant We number model [9].

Fate of ligament

We > 1.2 Re-entrainmentWe < 1.2 Unchanged

E. Narimani, S. Shahhoseini / Applied Thermal Engineering 31 (2011) 188e193 189

breakup into the account [9]. In this model the breakup of thedroplets caused by re-entrainment from liquid film can be esti-mated based on the following equation.

We ¼ rgugDl

3mg(1)

where, Dl is as shown in Fig. 2.This equation was used to explain the re-entrainment from

a ligament on the deposited water. The ligament can be createdfrom a droplet impact or shear. The size of the ligament wasassumed to be the same as that of the hitting droplet. The size of thedroplet was used to determine whether re-entrainment occurs ornot. A Weber number threshold is then required. The value of thecritical We number applied in this study was the same as thatreported in the literature, which gives Wecritical ¼ 1.2 [9].

Wecritical is the maximum stable droplet size in a turbulentstream. Table 1 shows a summary for the re-entrainment limit inthe particle tracking routine.

In the conditions of this study, the Weber number of the drop-lets was in the range of 4e7, in which film breakup occurs.

The normal distribution of droplet diameter can be determinedusing RosineRammler correlation to produce droplets with theaverage diameter of 60 mm. If the size distribution is of the Rosin-eRammler type, the mass fraction of the droplets for which thediameter is greater than d can be calculated as below.

Fig. 2. An impinging droplet causes waves on the surface that may lead to torn theligaments off [9].

Yd ¼ e�ðd=dÞn

(2)

Where, d is the mean diameter and equal to 60 mm. The minimaldiameter is 10 mm and the maximum one is 110 mm. n is the spreadparameter. It was calculated to be 4.2, using the followingequation.

n ¼ Lnð�LnYdÞLn

�d=d

� (3)

In this work EulerianeLagrangian approach was applied. Thedroplets were supposed to be the discrete phase and the air wasassumed to be the continuous phase.

2.1. Discrete phase model

The trajectory of a discrete phase particle was predicted byintegrating the force balance on the particle, which is written ina Lagrangian reference frame. This force balance equates theparticle inertia with the forces acting on the particle and can bewritten (for the x direction) as [1]:

dupdt

¼ FD�u� up

�þ gx�rp � r

�rp

þ Fx (4)

where, u is the fluid phase velocity, up is the particle velocity, m isthe molecular viscosity of the fluid, r is the fluid density, rp is thedensity of the particle and dp is the particle diameter. Re is therelative Reynolds number, which is defined as [11]:

Re ¼ rdp��up � u

��m

(5)

where Fx is an additional acceleration (force/unit particle mass)term, FD (u � up) is the drag force per unit particle mass and FD canbe calculated as below [11].

FD ¼ 18mrpd2p

CDRe24

(6)

The drag coefficient, CD, can be computed as follows [9].

CD ¼ 24Resph

�1þ b1Re

b2sph

�þ b3Resphb4 þ Resph

(7)

b1 ¼ exp�2:3288�6:4581fþ 2:4486f2

�b2 ¼ 0:0964þ 0:5565fb3 ¼ exp

�4:905�13:8944fþ18:4222f2 �10:2599f3

�b4 ¼ exp

�1:4681þ 12:2584f�20:7322f2 þ15:8855f3

� (8)

where, 4 is the shape factor and defined as:

f ¼ sS

(9)

Table 2Operating conditions and fluid property [12].

Item Flow Flow pattern P, Pa T �C rg, kg m�3 rd, kg m�3 mg, Pa S�1 md, Pa S�1 s N m�1

Experiment condition Air water Dispersed flow 0.1Eþ06 20 1.2 9.98Eþ02 1.8E-05 9.98E-04 7.3E-01

Fig. 3. A comparison between simulated and experimental efficiencies.

E. Narimani, S. Shahhoseini / Applied Thermal Engineering 31 (2011) 188e193190

where, s is the surface area of a sphere having the same volume asthe particle and S is the actual surface area of the particle. TheReynolds number Resph was computed where the sphere diameterwas equal to s. In this study f ¼ 1.

2.2. Continuous phase model

Navier-stokes and Ke3 equations of continuous phase aredescribed as:

vuvx

þ vv

vy¼ 0 (10)

vuvt

þ uvuvx

þ vvuvy

¼ Fx � vpvx

þ 1Re

"v2uvx2

þ v2uvy2

#(11)

vv

vtþ u

vv

vxþ v

vv

vy¼ Fx � vp

vyþ 1Re

"v2v

vx2þ v2v

vy2

#(12)

v

vtðrkÞ þ v

vxj

�rkuj

� ¼ v

vxj

"�mþ mt

sk

�vkvxj

#þ m

vuivxj

"vuivxj

þ vujvxi

#� r3

(13)

v

vtðr3Þþ v

vxkðr3ukÞ¼

v

vxk

�mþmt

s3

�v3

vxk

þC13

kmvuivxj

"vuivxj

þvujvxi

#

�C2r32

k(14)

where, Cm ¼ 0.09, C1 ¼ 1.44, C2 ¼ 1.92, sk ¼ 1.0, s3 ¼ 1.3 and mt isturbulent velocity.

Calculated as [11]:

mt ¼ Cmrk2

3(15)

The number of droplet breakups (breakup parcels) directly dependson the air velocity. A leaner equation was proposed to model thisrelationship as given below.

Breakup parcels ¼ A� V þ B (16)

where, A and B are the model parameters and their values weredetermined by fitting the equation into the experimental data. Thevalues of A and Bwere computed as 1.4163 and 5.4124 respectively.

2.3. Simulation assumptions

In this simulation the following presumptions are assumed:

1. The width of the vanes is big enough to suppose the flow is twodimensional.

2. The number of the stages is increased when the vane turningangle decreases in order to keep the vane length constant.

3. The flow in between the vanes is incompressible.

2.4. Boundary conditions

The inlet boundary condition of the gas phase was that the inletvelocity of liquid droplets was assumed to be equal to the gas inletvelocity. The outlet condition was that outlet pressure was equal tothe atmospheric pressure. In this study, the gas flow with liquiddroplets between the vanes was simulated, where gas velocity andwetness fraction were 3e5 m/s and 0.089, respectively. The simu-lation results were compared with some reported experimentaldata, reported in the literature [12]. Then this vane plates weresimulated with three different vane angles and three vane spacing.In these cases the separating efficiency was computed using CFDsimulations. In the next stage, the response surface method wasemployed to find the optimal conditions of the vane, using theseCFD simulation results of separating efficiencies. The operatingconditions and fluid properties used in these simulations aresummarized in Table 2.

It is assumed that the droplets with a given diameter of Ddi wereinjected at the inlet and it is possible to find some droplets at theoutlet with a diameter equal to or smaller than Ddi. Thus, theseparating efficiency of a droplet can be calculated as follows [11].

h ¼

Xni¼1

ðmihdiÞ

Xni¼1

mi

(17)

hdi ¼yixi

(18)

2.5. Model validation

The separation efficiency simulations were performed fordifferent velocities between 3 and 9 m/s, where a ¼ 120 andD ¼ 20 mm. Fig. 3 shows good agreement between the predictedseparation efficiency and corresponding experiment data [12]. Itindicates that the higher air velocities lead to the greater separationefficiencies. The reason is, increasing the gas velocity would bringmore inertial force leading to more rapid changes in the movingdirection of the droplets, causing to the impingement of moredroplets into the vane wall.

Table 3Low and high levels of the factors.

Independent variables Coded levels

�1 0 1

v (m/s) 3 4 5D (mm) 20 30 40a (�) 60 90 120

Table 5The relation between vane spacing, separation efficiency and pressure drop.

D (mm) h DP (Pa)

20 8.62E-01 4.34E-0230 6.8E-01 2.07E-0240 6.33E-01 7.5-03

E. Narimani, S. Shahhoseini / Applied Thermal Engineering 31 (2011) 188e193 191

2.6. Response surface method

The response surface method was applied to find the optimalconditions of a vane mist eliminator in terms of gas velocity, vanespacing and vane turning angle in order to maximize separationefficiency. The response surface method fits a polynomial, as givenin equation (19), into the experimental data and then employs thepolynomial to find the optimal conditions [11].

Y ¼ bo þXki¼1

biiXi þXki¼1

biXi þXi<j

bijXiXj þ eðX1;X2.;XkÞ (19)

where, Y is the response, k is a variable, e is the error and bi, bi and bijare the unknown parameters in the second order polynomialmodel. Modeling and experimental errors are two sources of error(e) in equation (19). Since in this study CFD data are used instead ofexperimental data the error (e) is only due to the weakness of fit. Athree-factor, three-level central composite face-centered design(CCF) was used to determine the optimal factors of separationefficiency.

Three independent variables were selected to be gas velocity(x1), vane spacing (x2) and vane angle (x3). A total of 15 differentcombinations (including one replicate of centre point that wassigned the coded value of 0) were chosen in random orderaccording to a CCF configuration for the three factors. Several CFDsimulations were carried out to inspect how the parameters affectthe vane separation efficiency. The coded values of independentvariables were found from the following equation.

x1 ¼ X1 � X1

1=2ðX1H � X1LÞ¼ X1 � 4

1(20)

x2 ¼ X2 � X2

1=2ðX2H � X2LÞ¼ X2 � 30

10(21)

x3 ¼ X3 � X3

1=2ðX3H � X3LÞ¼ X3 � 90

30(22)

Table 4Central composite face-centered design with three independent variables (codedvariables).

RUN x1 x2 x3

1 �1 �1 �12 þ1 �1 �13 �1 þ1 �14 þ1 þ1 �15 �1 �1 þ16 þ1 �1 þ17 �1 þ1 þ18 þ1 þ1 þ19 �1 0 010 þ1 0 011 0 �1 012 0 þ1 013 0 0 �114 0 0 þ115 0 0 0

Each independent coded variable had 3 levels of�1, 0 andþ1. InTable 3 high and low levels of these three factors are presented.Table 4 shows the values that were used for the central compositeface-centered (CCF) design.

3. Results and discussion

The results of Table 5 show the relations among vane spacing,separation efficiency and pressure drop. They were producedwhere vane angle and air velocity were 120� and 3 m/s, respec-tively. This table indicates declining vane spacing raises vaneseparation efficiency. It also implies that the lower vane spacinggives the higher pressure drop. Therefore, the highest desirablepressure drop is first to be determined then the lowest corre-sponding vane spacing can be used as a constraint of theoptimization.

Table 6 shows three values for each parameter (gas velocity,vane spacing and vane angle) and corresponding values of sepa-ration efficiency from CFD simulation results. The coefficients ofequation (19) were calculated by applying multiple regressions.Tables 7 and 8 show these coefficients for the uncoded and codedfactors. The uncoded second order model was obtained as follows.

Y ¼ 1:036�0:122X1þ0:0037X2þ0:00286X3þ0:0136X21

þ0:0000167X22 �0:0000132X2

3 þ0:000175X1X2

þ0:000283X1X3�0:0000950X2X3 (23)

R2 is the coefficient of multiple determinations and measuresthe proportion of the variation in the data point Yi, which isexplained by the regressionmodel. Ra2 is used to balance the cost ofusing a model with more parameters against the increase in R2. Inthis study R2 is 99.18% and Ra2 is 97.7%.

Ra ¼ ðn� 1ÞR2 � Kn� 1� K

Ra2 < R2(24)

where, k is the number of regression parameters in the model and nis the number of data points.

Table 6CFD simulation results for separation efficiency.

RUN X1 X2 X3 Y*10

1 3 20 60 9.412 5 20 60 9.653 3 40 60 9.354 5 40 60 9.555 3 20 120 9.126 5 20 120 9.597 3 40 120 7.818 5 40 120 8.469 3 30 90 9.1310 5 30 90 9.3311 4 20 90 9.3812 4 40 90 8.8413 4 30 60 9.3214 4 30 120 8.6315 4 30 90 9.05

Table 7Estimated regression coefficients and corresponding separation efficiencies foruncoded factors.

Term Coefficient Standard error T statistic P level

Constant 1.036 8.327E-02 12.442 0.0X1 �0.122 0.039 �3.123 0.026X2 3.709E-03 3.118E-03 1.189 0.287X3 2.860E-03 1.039E-03 2.751 0.040X1X2 1.750E-04 2.656E-04 0.658 0.539X1X3 2.833E-04 8.855E-05 3.199 0.024X2X3 �9.500e-05 8.855E-06 �10.728 0.000X1X1 1.366E-02 4.686E-03 2.917 0.033X2X2 1.666E-05 4.686E-05 0.356 0.736X3X3 �1.315E-05 5.206E-06 �2.525 0.053

Table 8Estimated regression coefficients and corresponding separation efficiencies forcoded factors.

Term Coefficient Standard error T statistic P level

Constant 0.908 4.039E-03 224.943 0.0x1 0.016 2.376E-03 7.407 0.000x2 �0.031 2.376E-03 �13.215 0.0000x3 �0.037 2.376E-03 �15.446 0.0000x1x2 1.749E-03 2.656E-03 0.659 0.539x1x3 8.49E-03 2.657E-03 3.199 0.024x2x3 �0.0285 2.657E-03 �10.728 0.000x1x1 1.367E-02 4.686E-03 2.917 0.033x2x2 1.667E-03 4.686E-03 0.356 0.736x3x3 �1.183E-02 4.686E-03 �2.526 0.053

E. Narimani, S. Shahhoseini / Applied Thermal Engineering 31 (2011) 188e193192

The coded factors are dimensionless variables. The coefficientsof equation (19) for coded factors were estimated by the means ofa least squares method. The coded second order model wasobtained as follows.

Y ¼ 0:908þ0:0176x1�0:0314x2�0:0367x3þ0:0137x21þ0:00167x22�0:0118x23þ0:00175x1x2þ0:00849x1x3�0:0285x2x3 (25)

Given the values of vane spacing, vane angle and air velocity,vane efficiency can be calculated from equation (25). Each of theseparameters has a dual effect on the performance of the separator.Vane spacing is a crucial variable to keep high separation efficiencyand maintain the demister system stable. On one hand, too smallvane spacing leads to too much pressure drop and energyconsumption for pumping the gas. On the other hand, if the vanespacing is too large, the separation efficiency drops due to the largemoving area of the droplets. A large value of air velocity leads toa high inertial force that in turn causes rapid changes in the movingdirection of the droplets, forcing them to crash harder into the vanewalls and resulting in high separation efficiency. However, higherair velocities cause more significant liquid film breakup leading toless separation efficiency. A small vane angle results in a largecentrifugal force of the droplets at the bends of the vanes, whichresults in more separation efficiency. Whereas, too small vaneangles means there would be less chance for the droplets to movearound the bend walls leading to less separation rate. The CFDsimulation results revealed that if vane angle is smaller than itsoptimal value the gas flow cannot move well inside the bends,causing a low separation rate.

4. Conclusions

In this study the separation efficiency of liquid droplet by wavplate separators was simulated and compared with the experi-mental data. It was assumed that liquid droplet breakup by

impingement of liquid filmwas the most important mechanism forthe generation of the secondary droplets under the operatingconditions. Since CFD simulation results were in good agreementwith the experimental data, the CFD results were applied in orderto investigate the influence of gas velocity, vane spacing and vaneturning angle on the separation efficiency based on a responsesurface method. This investigation resulted in a mathematicalmodel that in turn was employed to find the optimal conditions formaximum separation efficiency of the demisters. The resultsrevealed that in the 20 mm of vane spacing the highest separationefficiency could be achieved when the air velocity and vane anglewere 5 m/s and 60�, respectively.

Nomenclature

a Vane angle, �(degree)CD Drag coefficient, DimensionlessDl Ligament diameter, mmD Vane spacing, mmdp Particle diameter, mmDdi Diameter of ith droplet with d diameter, mmDP Pressure dropt, Pad Mean diameter, nmFx Additional acceleration, Force Unit partical massFD Drag force, Force. Unit partical massmi Mass of droplets with yi mass fraction, kgmg Gas viscosity, Pa s�1

m Molecular viscosity, Pa s�1

n Spread parameter, DimensionlessRe Relative Reynolds number, Dimensionlessrp Droplet density, Kg m�3

rg Gas density, Kg m�3

r Fluid density, Kg m�3

rd Droplet density, Kg m�3

S Surface Area, m2

u Air velocity, m s�1

up Particle velocity, m s�1

ug Gas flow velocity, m s�1

y Air velocity, m s�1

We Weber number, DimensionlessWeC Critical Weber number, DimensionlessXi Dimensionless variables, DimensionlessXi uncoded variables, -Xi Mean value of uncoded variables, -XiH The high level of the ith factor, -XiL The low level of the ith factor, -xi Coded variable, Dimensionlessxi Mass fraction of injected droplets, DimensionlessY Response, Dimensionlessyi Mass fraction of separated droplets, Dimensionlessh Vane separation efficiency, Dimensionlesss Surface tension, N.m-14 Shape factor, Dimensionless

References

[1] C. Galletti, E. Brunazzi, L. Tognotti, A numerical model for gas flow and dropletmotion in wave-plate mist eliminators with drainage channels, Chem. Eng.Sci. 63 (23) (2008) 5639e5652.

[2] J. Claes, R. De Bruyne, Demisting with metal fibre webs and felts, Filtr. Sep. 13(5) (1976) 494e501.

[3] Y. Wang, P.W. James, Calculation of wave-plate demister efficiencies usingnumerical simulation of the flow field and droplet motion, Chem. Eng. Res. 76(48) (1998) 980e985.

[4] R. Rahimi, D. Abbaspour, Determination of Pressure Drop in mesh misteliminator by CFD, Chem. Eng. Process 47 (10) (2007) 1504e1508.

E. Narimani, S. Shahhoseini / Applied Thermal Engineering 31 (2011) 188e193 193

[5] P.W. James, B.J. Azzopardi, Y. Wang, J.P. Hughes, A model for liquid film flowand separation in a wave-plate mist eliminator, Chem. Eng. Res. Design 83 (5)(2005) 469e477.

[6] A. Brigadeau, Modeling and Numerical Investigation of High PressureGaseLiquid Separation, Ph.D. thesis, Norwegian University of Science andTechnology, 2007, pp. 201e211.

[7] S. Lim, Q.L. Zhou, T.M. Xu, S.E. Hui, A study of the type selection of misteliminators with the help of P�v�dcr method, J. Eng. Thermal Energy Power19 (2004) 575e578.

[8] L. Yang, S.H. Wang, X.M. Wang, Study on characteristics of a sulfur removaldemister, China, J. Power Eng. 25 (2005) 289e292.

[9] A.I. Josang, Numerical and Experimental Studies of Droplet Gas Flow,Ph.D. thesis, Dept. of Technology, Telemark University college, 2002,pp. 96e115.

[10] K. Hinkelmann, O. Kempthorne, Introduction to experimental design, in: ,Design and Analysis of Experiments, vol. 1. John Wiley and Sons, New York,2008, pp. 87e94.

[11] J. Zhao, B. Jin, Z. Zhong, Study of the separation efficiency of a demister vanewith response surface methodology, J. Hazard. Mater. 147 (2) (2007)363e369.

[12] L. Jia, H. Suyi, W. Xiamo, Numerical study of steamewater separators withwave-type vanes, China, J. Chem. Eng. 15 (4) (2007) 492e498.