An improved CFD model of gas flow and particle interception in a fiber material☆

Zhiwei Sun ,Jianhui Wen *,Xiao Luo ,Wen Du Zhiwu Liang ,*,Kaiyun Fu

1 Technology Center of China Tobacco Hunan Industrial Co.,Ltd.,Changsha 410007,China

2 Joint International Center for CO2 Capture and Storage(iCCS),Hunan Provincial Key Laboratory for Cost-effective Utilization of Fossil Fuel Aimed at Reducing CO2 Emissions,College of Chemistry and Chemical Engineering,Hunan University,Changsha 410082,China

1.Introduction

Modeling of the smoke flow and the interception distribution of harmful ingredients in a filter is a huge challenge.It is very difficult to establish a real filter model due to its complex microstructures,even though various simplifications can be made.The problem becomes even more complicated when a variety of smoke components pass through the filter,due to the different characteristics of aerosols and their different interactions with filter materials.However,ignoring the temperature change in the filter for it is very small in the first suction[1],the numerical simulation research of filter can be divided into two aspects: flow field distribution and harmful ingredients filtration efficiency.

Many researchers conducted early related research about the velocity,pressure and other physical parameters in the filter material or other fiber material by using fluid mechanics analytical methods.Saidiet al.[2,3]developed a three-dimensional CFD model of single cigarette suction,which included the distribution of the smoke velocity,pressure throughout the filter during puff by puff suction,and the mass flow rate through the ventilation dilution area around the paper and the combustion wire.Jaganathanet al.[4]described a novel procedure for modeling fluid flow through the real microstructure of a fibrous material by using the DVI(Digital volumetric imaging)method and CFD method.This model could predict the permeability of fibrous materials well.Besides,he obtained the velocity and pressure distribution in the fibrous media.Xuetal.[5]investigated the pressure drop in a wider speed range in fiber filter media by comparing the VBA(Visual Basic for Applications)program and CFD method.The results showed that the pressure drop and mean velocity of the fluid were no longer a linear relationship while the mean velocity of the fluid was large than 0.3 m·s?1.

Some researchers carried out research on the interception efficiency,interception discipline and interception mechanism of particle in fiber material and then proposed the fiber filtering dynamics model.Keithet al.[6,7]carried out his research about the mechanism of filtering of smoke in a filter,and the results showed that there were three ways for smoke particle to collect in a filter,which include interception,inertial impaction,and diffusion.Albrecht studied the movement of the aerosol particle flowing past a single cylindrical fiber,and developed the Albrecht particle inertia theory[8].Davis[9]banded the three mechanisms together and utilized a formula to express it,therefore,a new fiber filtration theory for an isolated cylindrical fiber was established.On the basis of this,researchers proposed the overall fiber efficiency theoretical model[10–13].

Based on the flow theory and particle interception theory,it became possible to develop the smoke flow and particle interception in a filter.So far,there are two directions to build the model,i.e.macroscopic method and microscopic method,respectively.Microscopic method was mainly based on the combination of imaging technology with computer technology to generate a real fiber model,and then used the DPM(Discrete Phase Model)model in Fluent or DEM(Discrete Element Method)model combined with Fluent to simulate the particle filtering in filter media.Hosseini and Vahedi Tafreshi[14,15]built 2D and 3D real fibrous filter media by using C++subroutines,and simulated the particle filtration by using the DPM of the Fluent,and obtained the pressure drop in fibrous filter.Qianet al.[16]simulated the gas–solid flow characteristic within the fibrous media by using the CFD–DEM coupled method,and then studied the influences of the fiber structure and particle properties on particle deposition and agglomeration characteristics in the filtration process.Although this method could generate relatively the true structure of the fiber filter,now it could only build a micrometer-scale model of the fibrous filter because of the limitation of computing ability.In order to study the performance of the whole fiber filter,researchers considered the establishment of a whole range of fiber filters from a macroperspective.The macroscopic method mainly established the whole fiber filtering medium model based on the theory of porous media,then UDF that describes the kinds of particle filtering mechanisms in filter fibrous media was added to the Fluent default conservation equation as source terms for simulation.The significant advantage of this method was that it could well simulate the fiber filters in the whole size range and a variety of filtering mechanisms could be flexibly and accurately described by UDF.Therefore,it was quite valuable and practical for the qualitative research of the influences of fiber medium structure and performance parameters which affect the efficiency of the particle filter.By using the porous model and a volume averaging method,Wenet al.[17]simulated the smoke flow and particle interception in a cellulose acetate filter.Although it built the numerical model of the whole scale of the filter,the deviations were still big and the method to calculate the source term was not given.In addition,the filtering models developed by these researchers could only apply to a cylindrical fiber.Recently,by solving the equivalent diameter of cellulose acetate fibers(Y-shaped fibers)and estimating the effective hydrodynamic particle diameter,Duet al.[18]improved the cylinder-shaped single fiber filtration model and proposed the Y-shaped single fiber model for calculating the filtration efficiency of a cigarette filter.

In this work,an improved CFD model of gas flow and particle interception in fiber material which fiber size is Y-shape was developed.A porous medium model was used to build the model of the whole size of the fiber filter medium.A mixture model was adopted.The Y-shape fiber filtering model theory was applied and then the algorithm of particle interception in the whole size of fiber filter medium was calculated.Taking filter and nicotine particle as research subjects,the smoke flow and the interception of nicotine in the filter within the 2.0 s puff duration at different suction model were then simulated by using Fluent software.By solving the momentum equations,the velocity and pressure distribution in the filter could be obtained.By solving the mass equations,the volume fraction distribution of nicotine aerosol in the filter was obtained as well,and the filtration efficiency of the filter could be calculated.Finally,we compared the nicotine particle filtration efficiency between Fluent simulation results and experimental results,as well as the model prediction in the literature to validate our model.

2.Theory

2.1.Pressure drop of smoke fl ow

Since the Reynolds number for a smoke flow through a cellulose acetate filter at 40°C(313 K)is usually larger than 0.33[5],the pressure drop is no longer a linear relationship with the mean smoke velocity and but can be expressed as the Forchheimer equation[19]:

where Δp,ρ,ν,L,and μ are the pressure drop, fluid density, fluid velocity,length of thfilter,and viscosity of flow respectively.The permeability of porous medium,k,is available for many types of fiber and its reciprocal δ which is usually called the “viscous parameter”can be calculated by various methods[20].The Forchheimer coefficient,β,can be calculated from the modified formula by Lee and Yang[21].Besides,the Reynolds number of the smoke flow is much less than the critical Reynolds number 50[22],which indicates that the flow is laminar.

2.2.Filtration mechanism of nicotine particle in a filter

The filter consists of cellulose acetate and its filtration can be regarded as the results of composite filtering by multiple single fibers[23].The single fiber filtration model,in which the single fiber is regarded as an isolated cylinder that is perpendicular to the flow direction and in finitely long,mainly has three mechanisms for the filtration of aerosol particle:direct interception,inertial impaction,deposition and diffusion.Single fiber filtration equations in consideration of interference of the neighbor fibers were utilized for the calculation of the contribution of diffusion and interception to smoke filtration efficiency[11].The filtration due to inertial impaction can be calculated by Yeh's equation[13]equation.The interpretation of the three mechanisms can be seen in following equations:

(a).Diffusional deposition

The filtration efficiency due to diffusion can be calculated by Eq.(2)[12]:

Diffusion,interception and impaction work simultaneously during filtration.The combined single fiber efficiency ηScan be calculated by the products of penetration ratio as Eq.(5):

The overall filtration efficiency of a filter η0can be calculated from the single fiber efficiency by Eq.(6)[11]:

The filter fibers in this work are not cylindrical but Y-shaped.According to Du's model[18],the effective diameterdfof a filter fiber is applied in this simulation.It can be calculated by Eq.(7)

where:Ris the radius of the single Y type fiber outline,it can be showed in Fig.1.

Fig.1.Approximation of the shape and diameter of the fiber.

The solid fraction α of the filter is calculated using the fiber diameterdf.

where:

C=crimping ratio of fibers;

Df=total denier of filter;

Ds=denier per single fiber;

For the 3.0Y32000 filter of sample 1,Ris 15 μm,Cis 17%,Sfiberis 45.1 mm2,dfis 25.1μm and α is0.138.For the 3.0Y35000 filter of sample 2,α is 0.150,whiledfis again 25.1 μm.

For the particle sizedp,Duet al.proposed a new method for the estimation of the effective particle size of the cigarette smoke utilizing the difference of the filtration efficiency of the filters under ISO and HCI smoking regimes.According to his research,the estimated particle diameterdpwas 0.44 μm[18].

3.Computational Fluid Dynamics Model Descriptions

3.1.Model assumptions

Based on the characteristics of smoke passing through the fiber filter,the following assumptions for the computational fluid dynamics model have been made in this study:

(1)smoke is incompressible as it passes through the filter;

(2)the nicotine particles are stable when the smoke flows through the filter;meanwhile the change of the diameter of nicotine and the mass transfer between smoke phase and nicotine phase are neglected;

(3)the change of smoke temperature in the filter and the heat exchange between smoke and air outside are neglected;

(4)the changes of efficiency of nicotine particle during the whole smoking process were assumed to be insignificant with puff numbers increasing.

3.2.Multiphase model

Fluent multiphase model include VOF model,mixture model and Eulerian model.The VOF model can model two or more immiscible fluids by solving a single set of momentum equations and tracking the volume fraction of each of the fluids throughout,in this research,the air and nicotine particles are miscible.The mixture model and the Eulerian model are appropriate for flows in which the phases mix or separate.If there is a wide distribution of the dispersed phases,the mixture model may be preferable.If the dispersed phases are concentrated just in portions of the domain,the Eulerian model may be preferable.In this research,the nicotine particles are widely distributed in smoke,so the mixture model is adopted.

The mixture model is a simplified multiphase model that can be used to model multiphase flows where the phases move at different velocities,but assume local equilibrium over short spatial length scales.The mixture model can modelnphases( fluid or particulate)by solving the momentum,continuity,and energy equations for the mixture,the volume fraction equations for the secondary phases,and algebraic expressions for the relative velocities[24].Here,we define air in smoke as phasepand nicotine particle in smoke as phaseq.

3.3.Conservation equations

3.3.1.Mass conservation equations

The continuity equation for phasepis:

where ωp,ρp,andvpare the volume fraction,the density,the velocity of phaseprespectively,and ε=1?α.

For phaseq,neglecting the mass transfer between phasepand phaseq,the continuity equation for phaseqis

where ωq,ρq,andvqare the volume fraction,the density,the velocity of phaseqrespectively.Sqis the source term of phaseq.

The quality of the source term presents the increasing or decreasing quality of phaseqper unit time and per unit volume,with the unit of kg·m?3·s?1.The quality,which cannot be calculated directly by the default equations in Fluent,should be negative because the quality of nicotine particle is decreasing as it flows through the filter.The solution is to have added the quality of source term to reflect the phenomenon that nicotine particles are filtered by the filter(Fig.2).

The expression of quality of nicotine source term can be computed as follows.

where ω0is the initial volume fraction of nicotine.

3.3.2.Conservation of momentum for each phase

The forces on the single nicotine particle in filter during movement mainly include drag force,pressure gradient force,virtual mass force,Bassett force,Saffman lift force,Magnus force and gravity.In this study,the major force on the single nicotine particle is drag force because the diameter of nicotine particle is very small and the concentration can be disregarded due to the assumption of in finite dilution.Besides this,other forces,which are very small in magnitude compared to the drag force,can be neglected[25,26].The momentum equation for the mixture can be obtained by summing the individual momentum equations for all phases.It can be expressed as:

wherenis the number of phases,ωiis the volume fraction of phasei,Fis the additional resistance term producing by the porous media,andvmis the mass-averaged velocity:

The momentum of the smoke particle generates attenuation in the effect of viscous resistance and inertial resistance while flowing though the filter.In the porous medium model of Fluent,a negative momentum source term is added to the momentum conservation equation to denote the momentum attenuation,and the expression of additional resistance term as follows:

3.4.Geometric model of filter and boundary conditions

The filters used in this simulation are reported in literature[18].Their specifications are listed in Table 1.

A two-dimensional of the filter of sample 1 was developed using GAMBIT,and then the mesh grids were set with boundary conditions and a fluid field was shown in Fig.3.TheXdirection was the direction of smoke flow and Y direction was the direction of filter radius.Moreover,X=0 mm is the tobacco side andX=28 mm is the suction side.The grids were set to be more intensive near the boundary layer in order to eliminate the boundary effect.

Fig.2.The solving schemes of the quality of the source term.

(1)Inlet conditions

Table 1Specifications of cigarette samples

The inlet boundary condition was set to be velocity inlet type.The velocity UDF(User Defined Function)was used to express the variation of the smoke speed.In this research,the sine function was applied to describe the velocity changing with time in the process of one suction,and the expressions,which the relationships are shown in Fig.4,arev=0.61sin(πt/2)andv=0.96sin(πt/2)for ISO suction model and HCI suction model,respectively.As well,the initial volume fraction of nicotine particle is set to be 0.0103%,which is provided by the Technology Center,China Tobacco Hunan Industrial Co.,Ltd.,Changsha.

(2)Outlet conditions

The outlet boundary condition was set to be pressure outlet,and its expression isp= ?(δμνL+b1ρν2L).

(3)Wall conditions

The no-slip condition of flow was set to be the wall.

(4)Flow area

Fluid boundary type is used.The flow area is simplified as a porous medium,and the porosity is 0.862,the inertial resistance coefficient is 38860 and the viscous resistance coefficient is 1.329×109.

3.5.Numerical solutions

To ensure that the simulated results presented in this paper are independent of mesh density,this research studied several kinds of tetrahedral meshes,with cell sizes of 4 mm,2 mm,1 mm,0.8 mm,0.6 mm,and 0.4 mm.When the cell sizes are under 2 mm(1 mm,0.8 mm,0.6 mm,0.4 mm),the change of the pressure drop in the whole filter in ISO average velocity(ν =0.38 m·s?1)is tiny,ranging from?366 Pa to?364 Pa.Therefore,the cell size with 0.4 mm is sufficient,and results in a mesh composed of 2656 elements.

The Laminar model is used in this work.A second order upwind scheme is used for momentum and volume fraction and turbulent kinetic energy,respectively.The UDF program is applied to express inlet velocity because of the time variation of inlet velocity,and so is the outlet pressure set.Mass sources are also included to describe the nicotine particle filtration in the filter.In this work,the 2D computational fluid dynamics code,Fluent 6.3,was used to solve the momentum and mass equations.The pressure and velocity coupling was done through the continuity equation by use of the SIMPLEC algorithm.An explicit formulation was considered for time discretization[27].

Fig.4.The relationship of the smoke speed changing with time in ISO model and HCI model.

4.Results and Discussion

In this section,the simulation results were compared with the experimental data from Duet al.,as well as his model predictions[18].

4.1.Flow field distribution

In the ISO suction model,the time in one suction is 2 s and the suction capacity is 35 ml.The case of the smoke flow and the nicotine particle entrapment within 2 s suction time was simulated,and then several representative moments were selected to study the flow field variation including velocity and pressure and the nicotine particle volume fraction distribution in the filter.

Fig.5.Contour of the velocity magnitude of mixture(smoke)(t=0.1 s).

Fig.6.Scatter plot of the velocity magnitude of mixture(smoke)(t=0.43 s).

4.1.1.Velocity

This research simulated the smoke flow in the filter by using the UDF program to describe the velocity,as the speed is changing with time.For simplifying the research,the velocity at time 0.1 s and at time 0.43 s(when the velocity is equal to the average velocity of ISO model,namely,ν =0.38 m·s?1)was studied.Fig.5 showed the contour of mixture(smoke)velocity magnitude at time 0.1 s.From the picture,it can be seen that the mixture(smoke)velocity close to the suction side is zero this is because the mixture(smoke)does not penetrate the whole filter at the beginning of the puffing process.Fig.6 showed the mixture(smoke)velocity magnitude along the filter centerline.It can be seen from Fig.6 that the mixture velocity magnitude increased instantaneously once it entranced the filter due to the effective cross section of the filter becoming small.In addition,the mixture velocity magnitude pro file along the filter centerline almost stays at same value because of the tiny changes of the total pressure in the filter during the rest of the time.This phenomenon is also reported in the Saidiet al.[2]research.Figs.7 and 8 show the contour of the mixture(smoke)velocity and its magnifying picture for velocity field close to wall respectively.It can be understood that due to the wall effect,the velocity of the mixture(smoke)in the near wall region is descending sharply to zero toward the wall surface.

4.1.2.Pressure

The contour of the pressure in the filter at two different moments(t=0.43 s andt=1.0 s,which correspond to ISO model average velocity and the maximum velocity respectively)within the whole puffing process is obtained through this simulation method and is shown in Figs.9 and 10.From Fig.9,we can see that the static pressure slowly reduces from the tobacco side to the suction side.The pressure drop increases in the filter along with the increase of the smoke velocity as seen by comparing Figs.9 and 10.The relationship between pressure drop and smoke velocity in the filter is presented in Fig.11.It can be seen from the picture that the relationship between the pressure drop and smoke velocity is approximately linear when the smoke velocity is low.As the smoke velocity increases,the pressure drop nonlinearly increases with the velocity increasing.This is because the smoke flow is influenced by the viscous resistance and inertial resistance.The viscosity resistance is linearly correlated to the flow velocity,while the inertial resistance is related to the square of the flow velocity.Therefore,the pressure drop increases linearly with the increase of the flow velocity when the flow velocity is small because the inertial resistance is very small and the fluid is mainly affected by the viscous resistance.With the increase of flow velocity,the pressure drop and velocity were a quadratic relationship because the inertial resistance gradually dominated.As the initial resistance is taken into consideration in this research,the simulation results can more truly mirror the pressure drop in the filter especially in relatively high smoke speed.

Fig.7.Contour of the velocity magnitude of mixture(smoke)(t=0.43 s).

4.1.3.Concentration

Fig.8.Magnifying contour of the velocity magnitude of mixture(smoke)near wall(t=0.43 s).

Fig.9.Contour of the pressure distribution at t=0.43 s.

Fig.10.Contour of the pressure distribution at t=1.0 s.

The nicotine particle volume fraction pro file at two different moments(t=0.1 s andt=0.43 s)are shown in Figs.12 and 13 respectively.As is shown in Fig.12,the nicotine particle volume fraction nearby the outlet of the filter is zero at the beginning of the puffing process,because the smoke velocity is very low and the smoke or the nicotine particles do not penetrate through the filter,this phenomenon can be also reflected by the contour of smoke velocity at time 0.1 s.As seen in Fig.13,the nicotine volume particle fractions in the filter diminish gradually from the tobacco side to suction side,because the nicotine particles are intercepted by the filter.The comparison of Du's model prediction and Fluent simulated results of the nicotine particle filtering efficiency changing with time in filter is shown in Fig.14.It is seen from the Fluent simulated results that the smoke does not move through the filter at the initial phase of pumping,and the nicotine particle filtering efficiency is 100%,while the nicotine particle filtering efficiency of the Du's model prediction decreases sharply from 100%to about 40%.At the end of pumping,the nicotine particle filtering efficiency of Du's model prediction turn to 100%instantaneously.However,it changes more slowly in the Fluent simulated results.The results of the two models are almost same on the rest of time.Connecting with the practical situation,the Fluent simulated results more correspond to the process that the nicotine particles are intercepted by the filter during the whole pumping process comparing to Du's model prediction.Finally,the filtration efficiency of the nicotine particle of sample 1 computed in ISO model is 39.7%.

Fig.11.The pressure drop in the whole filter changing with smoke axial velocity.

4.2.The validation of the CFD model of nicotine particle filtering in a filter

To validate the CFD model of nicotine particle filtering in a filter,the efficiency of nicotine particle capture according to the Fluent simulated results and Du's model prediction as well as measured by experiment is discussed including different thickness and porosity of filter under different suction models.For simplifying the research,an estimated dynamic diameter of nicotine particle is adopted in order to limit the complexity introduced by the diameter distribution of smoke particle.

Fig.12.Nicotine volume fraction distribution pro file at 0.1 s.

Fig.13.Nicotine volume fraction distribution pro file at 0.43 s.

Fig.14.Du's model prediction and Fluent simulated results of the nicotine particle filtering efficiency changing with time in filter.

4.2.1.Comparisons of nicotine filtration efficiency in different filter thickness by three methods

Figs.15 and 16 shows the comparison of the nicotine particle filtration efficiency of sample 1 that have different filter lengths under the ISO or HCI model by three methods:Du's model prediction,Fluent simulated results,and experimental results.From the two figures,we can draw the conclusion that the longer the filter,the higher the efficiency of the nicotine particle filtration.Besides,the increase of the nicotine particle filtration efficiency decreases over time because the nicotine concentration decreases with the increase of the filter length.However,this trend is not obvious,the possible reason is that the nicotine particle concentration is very low and the filter is not long enough.Moreover,the nicotine entrapment model from Fluent simulated results was in good agreement with that from the experimental results,and the total filtering efficiency of the nicotine of the Fluent simulated results is bigger than that of Du's model prediction whether under the ISO model or HCI model.This is because the filtering efficiency of the nicotine particle of Fluent simulated results at the beginning period is bigger than that of Du's model prediction.

Fig.15.Nicotine filtration efficiencies of sample 1 having different filter lengths under ISO smoking.

Fig.16.Nicotine filtration efficiencies of sample 1 having different filter lengths under HCI smoking.

4.2.2.Comparison of nicotine filtration efficiency in different filter porosity by three methods

The nicotine particle efficiency of sample 1 and sample 2 are tested by Du's model prediction,Fluent simulated results,and experimental results are also listed in the table for the comparison.As is shown in Table 2,the nicotine entrapment models from the simulated results are in good agreement with that of experimental results,and their relative error is less than 5%.It can also be seen from the table that the nicotine particle efficiency whether the ISO model or HCI model of Fluent simulated results is large than that of Du's model prediction.

5.Conclusions

An improved CFD model of gas flow and particle interception in fiber material which fiber size is Y-shape was developed based on porous medium model and mixture model.The algorithm of particle interception in the whole size of fibrous medium successfully simulated the filtering process and computed the filtration efficiency.The variation of speed under different suction models was described as the UDF program,which reflected well the real single smoke situation and precisely predicted the nicotine particle filtration efficiency at both the beginning and the end of the smoke process.The smoke velocity pro files and pressure pro files,as well as nicotine particle volume fraction pro file at different velocity were obtained,and finally,the nicotine particle filtration efficiency under the ISO model was computed.The simulation results were in good agreement with that from the experimental results and more close to reality comparing with the model predicted results in the literature.Besides,the relative deviation of this improved CFD model was lesser than the previous CFD model.In the present work,only the nicotine particles were taken as the marker,but this model can be also used to simulate the flow and interception of other harmful components alone or together on this basis.

Nomenclature

Across-sectional area of filter,mm2

Ccrimping ratio of fibers

CuCunningham correction factor

Dparticle diffusion coefficient

Dsdenier per single fiber

Dttotal denier of filter

dffiber diameter,μm

dpnicotine particle diameter,μm

GRatio between particle diameter and fiber diameter

KBBoltzmann constant,J·K?1

KuKuwabara hydrodynamic factor

kcoefficient of permeability

Llength of the filter,mm

PePeclet number

StkStokes number

Ttemperature,K

vfluid velocity,m·s?1

vdrdrift velocity,m·s?1

vmmixture velocity,m·s?1

α solid fraction of filter

β inertial resistance coefficient

δ viscous resistance coefficient

ε porosity of filter

λ mean free path length of gas molecules,m

μ viscosity of fluid,Pa·s?1

μmviscosity of mixture,Pa·s?1

ρ fluid density,kg·m?3

ρmmixture density,kg·m?3

ω volume fraction

Table 2Nicotine particle efficiency by three different methods of sample 1 and sample 2 under ISO model or HCI model

Acknowledgments

The authors greatly appreciate Wilfred Olson and Raphael Idem for their great contribution to help me correct any grammar mistakes and insightful inputs to the research work.

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