Numerical Simulation of the Burning Process in a King-Size Cigarette Based on Experimentally Derived Reaction Kinetics

Li, Qiaoling; Zheng, Quanxing; Deng, Xiaohua; Yu, Zhiqiang; Deng, Nan; Xing, Fei; Chen, Xin; Cai, Guohua; Wang, Chenlu; Yang, Renqiang; Ma, Pengfei; Li, Bin; Chen, Xiao Dong; Zhong, Hongxiang

doi:10.2478/cttr-2020-0014

Figures & Tables

Schematic diagram of tobacco pyrolysis and combustion reaction system.

The geometry of the computational domains.1) Tobacco rod; 2) Cigarette paper; 3) Filter rod; 4) External environment.

Approximated Gaussian peaks of five precursors at different heating rates.

Comparison between the experimental DTG curves and the fitted DTG curves of the tobacco pyrolysis reaction at different heating rates.

Comparison between the experimental DTG curves and the fitted DTG curves of char combustion at different oxygen concentrations.

Release amounts of “tar” and co at different reaction conditions.

Density fields of char in four cases during puffing.

Density fields of char at different times (case 3).

Permeability of the cigarette paper, char line and char density along the axis of the cigarette at different times (case 3).

Gas temperature fields of cigarette during puffing (case 3).

Comparison of experimental gas temperatures and predicted gas temperatures at different positions of a cigarette.

Flow velocity fields of cigarette during puffing (case 3).

“Tar” density fields during puffing (case 3).

CO density fields during puffing (case 3).

Released amounts of “tar” at the inlet and outlet of the filter rod and the filtration efficiency during puffing (case 3).

The puff-by-puff amounts of “tar” released in cases 3 and 5.

The puff-by-puff amounts of CO released in cases 3 and 5.

Kinetic parameters of char combustion_

W_O² range		0% ≤ W_O² ≤ 2%	2 %< W_O² ≤ 10%	10% < W_O² ≤ 23%

Parameters	Unit	W_O² = 1%, 2%	W_O² = 3%, 5%, 10%	W_O² = 15%, 20%
A_c	min⁻¹	1.48 × 10⁷	4.26 × 10⁷	8.30 × 10⁷
E_c	kJ·mol⁻¹	91.04	111.20	116.31
n_o	—	1.09	0.43	0.36
	R²	0.9441	0.9574	0.9537

NRMSE of the predicted gas temperatures and experimental gas temperatures for eight locations_

Location	22 mm	24 mm	26 mm	28 mm	30 mm	32 mm	34 mm	36 mm
NRMSE	16.0%	17.5%	11.0%	8.5%	13.9%	16.0%	15.8%	11.9%

Kinetic parameters of tobacco pyrolysis_

Parameters	Unit	R1	R2	R3	R4	R5
f_p,j	%	9.52	17.71	18.04	13.58	41.16
A_p,j	min⁻¹	1.47 × 10⁵	1.48 × 10⁸	1.82 × 10¹⁰	1.21 × 10¹³	0.4538
E_p,j	kJ·mol⁻¹	31.09	60.81	91.48	133.48	25.78
n_p,j	—	1.06	1.28	1.21	1.25	0.76
m_p,j	—	1.24	1.54	1.48	1.49	−0.04
R² = 0.9821

Mathematical relationships of “tar” and CO at different temperatures and oxygen mass fractions_

Temperature range	W_O² range	“Tar” (mg·g⁻¹)

423 K ≤ T ≤ 623 K	0% ≤ W_O² < 5%	Y₁ = −0.0049T² + 5.8838T−1617 (R² = 0.8990)
	5% ≤ W_O² < 15%	Y₁ = −0.0048T² + 5.7621T−1580 (R² = 0.9034)
	15% ≤ W_O² ≤ 23%	Y₁ = −0.0061T² + 7.1210T−1911 (R² = 0.9734)
623 K T ≤ 1273 K	0% ≤ W_O² ≤ 23%	160

Temperature range	W_O² range	CO (mg·g⁻¹)

423 K ≤ T ≤ 1273 K	0% ≤ W_O² < 5%	Y₂ = 0.2132T−89.19 (R² = 0.9575)
	5% ≤ W_O² < 15%	Y₂ = 0.2630T−107.32 (R² = 0.9608)
	15% ≤ W_O² ≤ 23%	Y₂ = 0.2516T−90.41 (R² = 0.9333)

The mathematical models of cigarette reported in the literatures_

Reference and year	Author(s)	Smoking conditions	Geometry	Model construction		Simulation contents

				Pyrolysis and char oxidation reaction kinetics	Transport system	Burning properties	Products
(1) 1963	Egerton et al.	Steady draw	1-D	—	√	Temperature	—
(2) 1966	Gugan	Smoldering	2-D	—	√	Combustion cone Temperature	—
(3) 1977	Baker	Smoldering	1-D	—	√	Heat release rate O₂ concentration	CO, CO₂
(4) 1978	Summerfield et al.	Steady draw	1-D	Using the kinetics parameters obtained by themselves (4)	√	Burning rate Temperature Pressure	—
(5,6,7) 1979–1981	Muramatsu et al.	Smoldering	1-D	Using the kinetics parameters obtained by themselves (5, 6)	√	Burn rate Temperature Density	—
(8) 2001	Miura et al.	Smoldering	1-D	—	√	Burning rate Temperature	—
(9) 2001	Yi et al.	Smoldering	2-D	Using the kinetics parameters obtained by Diblasi (10)	√	Temperature Solid density Char density O₂ concentration	Water
(11) 2002	Chen	Smoldering	1-D	Using the kinetics parameters obtained by themselves (11)	√	Temperature Density	—
(12) 2003	Rostami et al.	Smoldering	2-D	Using the kinetics parameters reported by Muramatsu et al. (5, 6)	√	Burning rate Temperature O₂ concentration	—
(13) 2004	Rostami et al.	Smoldering and steady draw	2-D	Using the kinetics parameters reported by Muramatsu et al. (5, 6)	√	Temperature O₂ concentration Pressure Flow velocity	—
(14) 2004	Saidi et al.	Puffing	3-D	Using the kinetics parameters for volatile species reported by Wojtowicz et al. (15)	√	Burning rate Temperature Flow velocity O₂ concentration	CO, CO₂ H₂O Nicotine
(16) 2005	Eitzinger et al.	Smoldering, puffing and steady draw	2-D	Using the kinetics parameters obtained by themselves (16)	√	Burning rate Temperature Flow velocity O₂ concentration	Combustion gas Water
(17) 2007	Saidi et al.	Puff-smoldering cycles	3-D	Using the kinetics parameters for volatile species reported by Wojtowicz et al. (15)	√	Burning rate Temperature Flow velocity O₂ concentration Char density	CO, CO₂ Volatile
(18) 2008	Saidi et al.	Puff-smoldering cycles	3-D	Using the kinetics parameters for volatile species reported by Wojtowicz et al. (15)	√	Burning rate Temperature Flow velocity Char density	CO, CO₂ H₂O

Parameters and values related to each domain_

Domain	Parameter	Definition	Unit	Value
1)	ρ_s0	Initial solid density	kg·m⁻³	740 (12)
	ϕ	Porosity	1	0.7
	C_p,s	Specific heat of solid	kJ·kg⁻¹·K⁻¹	1.043 (12)
	C_p,g	Specific heat of gas	kJ·kg⁻¹·K⁻¹	1.004 (12)
	k_s	Solid conductivity	W·m⁻¹·K⁻¹	0.316 (12)
	k_g	Gas conductivity	W·m⁻¹·K⁻¹	0.0242 (12)
	ɛ	Emissivity of tobacco	1	0.98 (12)
	d_pore	Pore diameter	m	5.75 × 10⁻⁴ (12)
	H_evaporation	Water evaporation heat	kJ·kg⁻¹	−2.2572 × 10³ (12)
	H_combustion	Char combustion heat	kJ·kg⁻¹	1.757 × 10⁴ (12)
	v	Flow velocity	m/s	0
	K_ut	Permeability of unburned tobacco	m²	5.6 × 10⁻¹⁰ (18)
	K_bt	Permeability of burned tobacco	m²	10⁵ (18)
2)	K_up	Permeability of unburned cigarette paper	m²	5 × 10⁻¹⁵
2)	K_bp	Permeability of burned cigarette paper	m²	10⁵ (18)
3)	d_p	Aerosol particle diameter	m	4.4 × 10⁻⁷ (19)
	d_f	Single fiber diameter	m	2.51 × 10⁻⁵ (19)
	D_t	Total denier of filter	g·(9000 m)⁻¹	35000
	D_s	Denier of per single fiber	g·(9000 m)⁻¹	3
	C_fiber	Crimping ratio of fibers	1	0.17
	S_filter	Cross-sectional area of filter rod	m²	4.899 × 10⁻⁵
	T_filter	Filter temperature	K	288
	K_filter	Permeability of filter	m²	2.5 × 10⁻¹⁰ (18)
4)	T	Ambient temperature	K	288
	P	Ambient gas pressure	kPa	101.3
	ρ_g0	Initial gas density	kg·m⁻³	1.225
	W_O²	Mass fraction of O₂	%	23
	W_N	Mass fraction of N₂	%	77

Comparison of the numerical and experimental results_

		Case 1	Case 2	Case 3	Case 4	Experimental
“Tar”	(mg/cig)	15.8	14.1	12.2	5.1	11.2
“Tar”	Relative deviation	41.1%	25.9%	8.9%	54.5%	—
CO	(mg/cig)	21.1	17.3	14.6	5.6	13.2
CO	Relative deviation	59.8%	31.1%	10.6%	57.6%	—

Numerical Simulation of the Burning Process in a King-Size Cigarette Based on Experimentally Derived Reaction Kinetics

Figures & Tables

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Kinetic parameters of char combustion_

NRMSE of the predicted gas temperatures and experimental gas temperatures for eight locations_

Kinetic parameters of tobacco pyrolysis_

Mathematical relationships of “tar” and CO at different temperatures and oxygen mass fractions_

The mathematical models of cigarette reported in the literatures_

Parameters and values related to each domain_

Comparison of the numerical and experimental results_

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