5. An example of COSP application to the Virtual Smoking Machine

COSP has been successfully used to search for the optimum values of tar retention constants for cellulose acetate filter. An example has been used to illustrate the work COSP has done and its time efficiency.

The background

A typical cigarette consists of two parts: a tobacco column and a filter plug. The tobacco column is contained in wrapping paper, and the filter plug is wrapped by tipping paper.

During a puff, air is sucked into the cigarette at the burning tip of tobacco. The generated tar in the gas flow(smoke) will travel along the cigarette, some of the tar will be retained onto the filter, the rest will find their way into human body.

What the filter maker would like to know is:

1. the tar retention and gas flow inside a cigarette during a puff;
2. the effect of operating conditions on tar retention and gas flow.

A computer model was created by CHAM for the simulation of the cigarette. The following coefficients are employed in the model as follows:

Mdot = C1 * R2**C3 * (Tar1 - C2 * Tar2)

where Tar1 is the tar concentration in the gas phase near the solid phase surface; Tar2 is the tar concentration in the solid phase, R2 is the volume fraction of the solid phase; C1 is the mass transfer coefficient between gas and solid phase; C2 is the euqilibrium constant between the two phases; C3 is the geometry coefficient (nonlinear relationship between the solid surface and volume fraction).

Searching the above constants C1, C2 and C3 had to be adjusted manually by "trial-and-error", which is time-consuming and unsystematic.

In order to solve this problem, COSP is employed to search for the optimum values of the coefficients in a systematic and efficient way. Once the optimum values are obtained, they can be used for the prediction of pressure drop and tar retention of a new filter design. Thus, VSM can assist the design of filters which could enhance tar retention and have the desirable draw resistance.

Input details

Input data include:

• Constants to be optimised: C1, C2 and C3 and relevant input data are shown in the following table

Table 1: Data input for constants to be optimised

 C1 C2 C3 Initial value 0.05 1.E+3 2.0 Searching range 1.0E-2 ~ 1.0E+2 1.0E+1 ~ 1.0E+4 1.0 ~ 5.0
• Filter material: acetate cellulose and relevant input data are shown in the following table:

Table 2. Data input for cigarettes

 No. FLTLEN (mm) CIRCUM(mm) TOBLEN(mm) Mass (mg) 1 10 26.0 67 52.3 2 30 22.0 67 157.0 3 10 22.0 67 55.8 4 30 26.0 67 167.3 5 20 24.5 67 108.1

All the input data are specified in the COSP.INP file

• The operating condition is:

Bell-shaped flowrate profile, the highest flowrate being 30.0ml/s.
The tar retention is for one puff.
Tar concentration at the filter inlet is 0.05 kg/kg.

The operating conditions are specified in the q1 file

Output data

• Optimum value: C1= 4218.3; C2 =0.97 and C3= 1.99
• Objective Function is 3%
• Time consumed on Pentium III, 600MHz PC: 16.6 hours for 518 cycles

The following table shows the comparison of tar retention between CFD calculation and "experimental" results.

Table 3. Comparison of Tar retention between "experimental" results and calculation results

 No. FLTLEN (mm) CIRCUM(mm) Mass (mg) Tar retention(Experiments) Tar retention(Calculations) Error 1 10 26.0 52.3 0.703 0.697 0.8% 2 30 22.0 157.0 0.29 0.275 5.1% 3 10 22.0 55.8 0.371 0.374 0.8% 4 30 26.0 167.3 0.622 0.637 2.3% 5 20 24.5 108.1 0.498 0.517 3.8%

2D simulation

The above constants are employed for the 2D simulation of the cigarette with the data given above.

All the operating conditions are the same, but for 2D simulation, the porous wall for the wrapping paper and tipping paper is added.

Animated results

The animated results show the dependence of tar distribution, temperature and radial velocity with time.

Figure 1 Contour plot of radial velocity of gas phase

Figure 1 shows that, due to the porous structure of the wrapping paper of tobacco and the tipping paper of filter, a small amount of air will be sucked in through the paper. This is known as "the ventilation or air dilution" of cigarette smoke.

Figure 2 Contour plot of tar distribution in the gas phase.

The tar distribution in the gas phase shows the ventilation effect and at the mouth end, the gas-phase tar concentration near the tipping paper is ZERO.

Figure 3 Contour plot of tar distribution in solid phase

At the central line of the filter, the gas-phase tar concentration is the highest, thus there will be more tar retained on the solid phase. Therefore, the solid-phase tar concentration at the central line of the filter will be higher than at other location of the filter.

Figure 4 Contour plot of gas phase temperature

The temperature of gas phase will fall from 800 degree centigrade to 20 degree centigrade within 20mm behind the burning tip.

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