Darong Tang,Junzhang Wu,Jinsong Zeng,*,Wenhua Gao,Liang Du

1 State Key Laboratory of Pulp and Paper Engineering,Plant Micro/Nano Fiber Research Center,South China University of Technology,Guangzhou 510640,China

2 China Tobacco Guangdong Industrial Co.Ltd.,Guangzhou 510385,China

Keywords:Cigarette Reverse engineering Computational fluid dynamics

ABSTRACT The three-dimensional(3D)model of cigarette was accurately constructed through reverse engineering as the research object of numerical simulation.The combustion process of cigarette was studied with computational fluid dynamics(CFD).Standard Laminar models with species transport approach were applied,and numerical simulation of the cigarette was analyzed with semi-implicit method for pressure-velocity coupling.The results showed that the model could predict velocity of cigarette smoke,the distributions of temperature and pressure at different times.In order to verify the correctness of model,it was found that the relationship between the velocity of smoke and pressure according to Darcy's law on z position(x=4 mm,y=0,0 mm≤z≤50.61 mm).

1.Introduction

Cigarette smoke is one of the most important sources of indoor air pollution.It contains thousands of chemical substances in the gas phase and particle phase,and 60 kinds of these materials have been proved or suspected to be carcinogenic to the human body[1].With the development of smoking and health research,improving the safety of smoking has gradually become the common goal for the tobacco industry.Shen et al.[2]investigated the influence of cut tobacco distribution in cigarette on the deliveries of ammonia and tar in mainstream cigarette smoke,the results showed that:the deliveries of ammonia and tar in mainstream cigarette smoke of Sample A(higher filling density at the lit end and lower at the filter end of cigarette)and Sample C(higher density at the filter end and lower at the lit end)reduced somewhat,and Sample C reduced more significantly.It may be due to the following reasons:The total mass of cigarette sample C involved in combustion is relatively reduced,and the higher density tobacco at the filter end has better filtration effect.Therefore,it is of great significance to study the combustion process of cigarette and to optimize the techniques for reducing cigarette tar and harmful materials.

Due to the characteristic complexity of smoke flow during the combustion process,the properties of smoke flow were analyzed by advanced CFD software[3-7],which enrich the theories of cigarette combustion process at the field of numerical simulation.Many documents reported constructing models to predict the combustion process of cigarette.Ali A.Rostami and Hajaligol[8]developed a 2D mathematical model of cigarette,and the diffusion process of CO and other gaseous smoke constituents through paper wrapper was analyzed.The results showed that the CO diffusion increases as the length of the cigarette,the paper permeability,or the external velocity of air increases.The model also confirmed that gases with larger diffusion coefficient diffuse out at a higher rate.Ali A.Rostami et al.[9]also developed a transient 2D model of cigarette smoldering process,and a variety of models have been incorporated for pyrolysis and oxidation as well as for heating transfer in porous media,including a two-temperature model for thermal nonequilibrium between gas and solid,and the rate of burn is in reasonable agreement with the experimental data.Yan et al.[10]simulated cigarette smoldering process with Fluent software.The temperature distributions at different times,the concentration distributions of O2,CO,CO2,and water vapor in the smoke were analyzed.The simulated and experimental values of maximum smoldering temperature were in the range of 900-1000 K,which indicated the validity of the model.Yu et al.[11]studied the radial diffusion and axial flow processes of cigarette smoke by using CFD with particle image velocimetry(PIV).The work found the increase of either the mean pore diameter of cigarette paper or the pressure at the suction end increased the percentage of CO in cigarette smoke diffused through the cigarette paper and the suction end.Eitzinger and Pirker[12]established a 3D mathematical model for the numerical simulation of freely chosen smoking regimes in contrast to previously published models.The model predicted pressure,flow velocity,temperature and gas concentrations inside and outside the cigarette.Saidi et al.[13]established a 3D model based on the principles of conservation mass,momentum and energy for geometry similar to a cigarette and successfully simulated the puff-smoldering cycles by using CFD.The simulation results showed that the velocity profiles,gas and solid temperatures,burn rates,profile and transport of gas species throughout the packed bed,and the flow of oxidation products in the mainstream and sidestream were in a good agreement with the existing experimental results for cigarettes.In sum,the model of cigarette that was reported in the literature is relatively one-sided,and the model is simply a porous zone which does not possess air flow channels among the cut tobacco.

This work aims to construct a 3D model of cigarette based on the above models using reverse engineering,which reflects the air flow channels.A scale model of cigarette is designed using the standard Laminar models with species transport approach,and the dynamic layer of dynamic mesh technique to analyze the combustion process of cigarette under ISO smoking regime.Velocity of cigarette smoke and the distributions of temperature and pressure in the actual three-dimensional tobacco flow channels were explored,which provided a reference for the study of the complex flow field of cigarette smoke.

2.Experimental and Validation

2.1.Experimental

Darcy's law[14]describes the relationship between the rate of fluid flow and the pressure drop in porous medium.Cigarette is a porous medium.The smoke flow velocity is so small that the smoke flow is under laminar flow,with the suction pressure produced by smoking,the smoke flow in cigarette accords with the law which is expressed as follows:

In which V is the flow velocity of smoke,k is the permeability of porous medium,μ is the viscosity of flow,and ?P is the pressure drop.

Darcy's law scheme of cigarette is shown in Fig.1,assuming that there is an infinite cigarette region in the front of the burning end,the smoke hardly flows,together with the surrounding air keeping uniformly stable at the infinite end,where the velocity of smoke V0is almost zero,the pressure P0is approximately atmospheric pressure,so the pressure drop between the burning end and the suction end of cigarette is equal to the pressure at the infinite end.

Table 1 lists the velocity and pressure of the suction end measured by an autosmoking machine[patent number:CN104764582A],this can be used as the pressure drop and velocity in the cigarette.Using Origin software for straight-line fitting as shown in Fig.2,V=-1087.27P,and the fitting coefficient R2=0.98894 is close to 1,it can be clearly seen that between velocity of the suction end and pressure the relations present direct ratio,so the results are in a reasonable agreement with Darcy's law.

2.2.Cigarette model

2.2.1.3D CT images of cigarette(without filter)

Cigarette with filter is complicated,in order to make it much simple,in this research the cigarette without filter is studied.A brand of cigarette in which the filter was manually removed was taken with a 61 μm resolution in a nano Voxel X-ray three-dimensional microscope(nanoVoxel2000,Sanying Precision Instruments Co.,Ltd.,China).As shown in Fig.3(a),the original image of cigarette was obtained by the 3D synthesis module in Avizo Fire 8.1 software.The tiny units that are less than the volumes of 106μm3were removed to obtain a 3D CT image of cigarette without filter,as shown in Fig.3(b).

Fig.1.Darcy's law scheme of cigarette.

Table 1 The experimental results

2.2.2.Establishment of cigarette sheet

In order to be able to clearly observe the structural information of cigarette,the cigarette is divided into a section of cigarette sheets optimized.In Fig.4,the radial binarization images were obtained by extracting the 3D CT image at intervals of 61 μm in Fig.3(b),and then the interval between the value images fits the size of 61 μm triangular faces that can get 84 STL images of cigarette sheets,as shown in Fig.5.

2.2.3.3D reconstruction of cigarette sheet

The cigarette sheet clearly shows the 3D flow channels in tobacco.However,the large amount of computation makes it very difficult to simulate it by directly computing the whole cigarette,so five cigarette sheets were chosen and imported to Geomagic Spark software,in which reverse engineering of 3D reconstruction for modeling was used[15-21],as shown in Fig.6.

2.2.4.Establishing a geometric model of the filter and dividing mesh

The geometric model was established in ICEM CFD 15.0 based on cigarette without filter.The length and diameter of the cigarette are 50.61 mm and 8 mm,respectively.The whole cigarette is composed of five cigarette sheets.The mesh information on the last radial binarization image of the first sheet was stretched to 12.5 mm in ICEM,and connected to the second sheet by use of interface.By that analogy,we can obtain the mesh model of the whole cigarette.The calculated mesh number of the cigarette was,715924.The geometric model and the mesh graph are shown in Fig.7,in which Z=0 stands for the burning end and Z=50.61 for the suction end.

2.3.Computational model

Fig.2.Velocity and pressure at suction end.

Fig.3.3D CT images of cigarette(without filter).

The combustion process of cigarette is transient and complicated,in which smoke particle number,particle diameter,flow velocity,temperature and pressure are constantly changing.In this study,the combustion process of cigarette was simplified with the following assumptions:

a)Cigarette tobacco is a porous medium with uniform pore size and constant porosity;

b)Smoke flowing through the cigarette is a laminar and homogeneous fluid.

Simulations are carried out in CFD code ANSYS 15.0 and the simulation was performed according to the ISO smoking regime,puff duration is 2 s,and puff interval is 60 s,a bell-shaped flow curve is obtained and shown in Fig.8.According to the Fig.7 and Fig.8,there are five times puffing and four smoldering process in the simulation.The computation domain spans from X=-4 mm to X=4 mm,from Y=0 mm to Y=8 mm,and from Z=0 mm to Z=50.61 mm,as shown in Fig.9.Velocity-inlet boundary was used at the burning end and pressureoutlet boundary was used at the suction end.The velocity and pressure varied with the times,so they were loaded using user defined functions(UDF).In order to make the calculation reach the reliable accuracy requirement,a non-steady 3D semi-implicit solver was used.The SIMPLE algorithm of the Fluent software was used for treating the pressure-velocity coupling,and the Second Order Upwind was selected for the momentum equation and the species content.The computational times are approximately four days when using a hexa-core 2.40-GHz CPU.Table 2 lists the simulation parameters for the CFD model,and the tobacco porosity is measured by an Automatic Mercury Porosimeter(Autopore 9510,Micromeritics Instrument Corp.).

2.4.Conservation equation

To simulate the flow of smoke in the cigarette and combustion process of cigarette,a species transport model is implemented in Fluent,which is a type of transport model.The species are subject to the general conservation equations.This mass conservation equation is expressed as:[22].

In which ρ is the physical density,is the velocity of the species,and Smis the dispersed phase attached to the continuous phase of the quality of the source term.As the smoke is a homogeneous fluid,the Sm=0.

The momentum conservation equation takes the form of[22]

Fig.4.Radial binarization images.

where

In which p is the phase of stress tensor in fluid,Γ is the stress tensor,ρis the gravity volume force andis the external volume force(interaction of the dispersed phase),μ is the molecular viscosity,I is the unit tensor,andconsiders the effect of volume expansion.

Fig.5.STL image of cigarette sheet.

The energy conservation equation is given as:[22]

where

In which E is the total energy of fluid micelle,including the internal energy,kinetic energy and potential energy,hiis the enthalpy for phase i,is the flow dispersion for phase i,and Shis the thermal of the volume source term.

2.5.Species transport equation

For the combustion process of cigarette,the smoke contains a variety of phases,so the simulation uses species transport approach.The species transport equation is expressed as follows:[23].

In which Yiis the mass fraction of speciesi,is the diffusion convection coefficient of species i,Riis the velocity of pure output of the combustion reaction,and Siis the velocity of additional output.

In which Di,mis the mass diffusivity coefficient for species i in the mixture,DT,iis the thermal diffusion coefficient,and T is the temperature of the mixture.

2.6.Validation

In the previous experiment,the smoke flowed in the cigarette according to Darcy’s law as measured by an autosmoking machine.To validate the correctness of the model,the longitudinal pressure and velocity(x=4 mm,y=0,1.324 mm≤z≤50.61 mm)at 1 s were read by Fluent software to establish the relationship between pressure and velocity under the ISO smoking regime.As shown in Fig.10,the fitting curve shows that the velocity and pressure present approximately direct ratio and the fitting coefficient R2=0.93361,V=-0.0614P-36.08043.Considering the complexity of the model and the simplification of the model during the simulation,in the before experiments,velocity of the suction end and pressure are in a reasonable agreement with Darcy's law.In order to further verify the validity of the simulation model,the simulation results are compared with the experimental values reported in the literature[24],and Wang had proved the relationship between pressure drop and puffing flow rate in cut tobacco of cigarette presents approximately direct ratio and is in agreement with Darcy's law.So it can be deemed that the smoke flowed in the cigarette according to Darcy's law which verifies the correctness of using reverse engineering and CFD to develop a 3D cigarette(without filter)model.

3.Results and Discussion

Under the ISO smoking regime,the combustion process of cigarette was simulated at different times,i.e.,t=1 s,t=40 s,t=63 s,t=101 s,t=125 s,t=162 s,t=187 s and t=217 s were selected to examine the flow field,temperature and pressure,respectively.

Fig.6.Reconstructed model of cigarette sheets.

3.1.Velocity distributions at different times

3.1.1.Three dimensional distributions of the velocity of smoke

Fig.7.Geometric model and mesh graph of cigarette.

In order to show the spatial distributions of the velocity of smoke in the cigarette,different times were selected for the velocity distributions of smoke at different Z(longitudinal)sections(Z=2 mm,8 mm,16 mm,24 mm,32 mm,40 mm,44 mm,48 mm).Fig.11 shows the simulation results.The velocity distributions of smoke at the different Z sections were similar that the velocity of smoke in the air area was obviously higher than that in the cut tobacco,and the velocity of smoke decreased from the central part to the peripheral part in the air area.As shown in Fig.11(a),the cigarette length was 49.286 mm at t=1 s in puffing combustion.The seven different Z sections were selected for the velocity distributions of smoke investigation.The smoke flowed throughout the cigarette,and the velocity of smoke in the air area was higher than that in the cut tobacco area.In Fig.11(b),the cigarette length was 44.99 mm at t=40 s in smoldering combustion,the eight different Z sections were selected.The smoke velocity had a significant decrease compared with the t=1 s(puffing combustion).The velocity of smoke decreased from the burning end to the suction end.The second,third and fourth cycles of the cigarette combustion process were shown from(c)to(h)in Fig.11.The velocity distributions of smoke were basically similar to the first cycle at the puffing and smoldering combustions.As the cigarette burned shorter,the smoke velocity became nearly equal at the burning and suction ends,and the flow of smoke reached a steady state.

3.1.2.The velocity distributions of smoke at longitudinal direction in puffing combustion

Fig.12 shows the velocity distributions of smoke in the longitudinal direction(x=4 mm,y=0,0 mm≤z≤50.61 mm)at different puffing times(t=1 s,63 s,125 s,187 s).Generally,the velocity of smoke distributions showed a rapidly decreasing trend near the burning end whereas it increased sharply near the suction end.The reasons were the effect of viscous resistance and inertial resistance of tobacco near the burning end and the suction pressure increasing near the suction end.As the cigarette burned shorter,the velocity of smoke gradually changed gentle in the middle area of cigarette.

Fig.8.Puff times-flow curve under ISO smoking regime.

Fig.9.Computational domain of the cigarette model.

3.2.The pressure distributions at different times

3.2.1.The pressure distributions at longitudinal section

The pressure distributions at three longitudinal sections(X=0.5 mm,4 mm,7.5 mm)at different times,i.e.,t=1 s,t=40 s,t=63 s,t=101 s,t=125 s,t=162 s,t=187 s and t=217 s,within the cigarette were shown in Fig.13.The internal pressure of cigarette decreased from the burning end to the suction end at the four puffing times(t=1 s,63 s,125 s,187 s),and the pressure drop gradually became smaller as the cigarette burned shorter.The internal pressure of the cigarette is close to zero at the four smoldering times(t=40 s,101 s,162 s,217 s),and pressure slowly decreased from the burning end to the suction end.In the initial combustion of t=1 s and t=40 s,the pressure distributions of the three different sections(X=0.5 mm,4 mm,7.5 mm)were similar.Furthermore,because of the air channel existing in the cut tobacco,and puffing playing a leading role near the suction end,a varying pressure line of the center of the middle section(X=4 mm)is clearly observed and marked with the ellipsecircle at the puffing combustion(t=1 s,63 s,125 s,187 s)in Fig.13(a),(c),(e),(g).It can be understood that due to the wall effect,the pressure decreased slowly in the sections near the wall region.However,the pressure distributions at the three sections were similar at the smoldering combustion(t=101 s,t=162 s,t=217 s).

Table 2 Simulation parameters for CFD model

Fig.10.Longitudinal pressure and velocity for simulation at 1 s.

Fig.11.The velocity distributions of smoke at different Z sections at different times.

Fig.11 (continued).

Fig.11 (continued).

Fig.12.The velocity distributions of smoke at location x=4 mm,y=0,0 mm≤z≤50.61 mm at different puffing times.

3.2.2.The pressure distributions in radial direction at puffing combustion

The results of pressure distributions in radial directions(0 mm≤x≤8 mm,y=0,z=26 mm(t=1s),32 mm(t=63s),38 mm(t=125s),45 mm(t=187s))at different puffing times(t=1 s,63 s,125 s,187 s)are shown in Fig.14.The pressure distributions in radial direction were basically consistent at different puffing times,and gradually became relatively flat with the cigarette further shortening.It was an important point at the center of the radial section that the pressure changed rapidly.The reason for this change is that there was a transition from the cut tobacco area to the air area at the center of the radial section,and the pressure drop in the tobacco parts was much greater than that in the air area.

3.3.The temperature distributions at different times

The temperature distributions in the longitudinal direction(x=4 mm,y=0,0 mm≤z≤50.61 mm)at different times were shown in Fig.15.The results of simulation agreed with the real combustion process,whether the puffing or smoldering combustion,the temperature was always up to about 1000-1100 K at the burning end.The temperature kept to be decreased until reaching indoor temperature at the longitudinal direction.As the cigarette shortened,the change of temperature gradually slowed down in the burning zone.Comparing the puffing with smoldering combustion of each cycle,it is clear that the temperature changes sharply during the puffing combustion.

Fig.13.The pressure distributions of different X sections(X=0.5 mm,4 mm,7.5 mm)at different times.

Fig.13 (continued).

Fig.13 (continued).

Fig.13 (continued).

Fig.14.Radial pressure distributions at different puffing times(t=1 s,63 s,125 s,187 s).

Fig.15.The temperature distributions in longitudinal direction(x=4 mm,y=0,0 mm≤z≤50.61 mm)at different times.

4.Conclusions

In this study,combined with the X-ray 3D microscope and 3D CAD software,reverse engineering was used to construct a 3D model of cigarette channel.Meanwhile the combustion process of cigarette under the ISO smoking regime was analyzed by the standard Laminar models with species transport approach.The model indicated that the smoke flowed in the cigarette according to Darcy's law which verifies the correctness of the model.The model predicted the velocity of smoke,pressure and temperature distributions in the combustion process of cigarette.The simulation results showed that the velocity of smoke in the air area was obviously higher than that in the cut tobacco area in the puffing and smoldering combustions;the flow of smoke reached a steady state with burned cigarette shorter.In the longitudinal direction,the internal pressure slowly decreased from the burning end to the suction end.Whether the puffing or smoldering combustion,the temperature was always up to about 1000-1100 K at the burning end and decreased until reaching indoor temperature.

Appendix A.UDF