Optimal swirl number and equivalence ratio for minimizing the soot and NO emissions in turbulent methane combustion

Abstract

The simultaneous effect of the swirl number (SN) and equivalence ratio on NO and soot emissions in turbulent methane–air combustion was numerically investigated. The realizable k-ε model has been applied for modeling turbulence and eddy dissipation (ED) and probability density function (PDF) models were adopted for chemical reaction. The general gradient diffusion hypothesis (GGDH), high order algebraic model (HOGGDH), and simple eddy diffusivity model have been applied for modeling the turbulent heat flux (THF) vector. The Brooke–Moss model has been employed to predict the soot particle quantities. Comparing the results of the different numerical models (PDF and EDM with algebraic THF) with available experimental data indicated that employing the second-order models significantly leads to the modification of predicting temperature distribution in EDM. However, due to the effect of the PDF model on soot modeling, the PDF model provides more accurate results. The numerical simulations have been performed for various SNs (SN = 0–1.33) and equivalence ratios (0.125–0.75). In all of equivalence ratios the flame temperature and pollutants emission (NO and soot) were strongly affected by the SN. Also, the SN has different effects on NO and soot emission. Finally, for each of NO and soot emission, a correlation relative to effective combustion factors such as SN and equivalence ratio was presented. It is found that by increasing the equivalence ratio, the NO emission increases with a power of 2.3, and soot emission decreases with a power of 8.7.

Keywords:

• Equivalence ratio
• NO emission
• soot formation
• swirl number
• turbulent combustion

Nomenclature
$\overline{{\mathrm{ }u}_i^{\mathrm{\prime }}{\mathrm{T}}^{\prime }}$	=	components of turbulent heat flux vector
$\overline{{\mathrm{ }u}_i^{\mathrm{\prime }}{\mathrm{Y}}^{\prime }}$	=	components of turbulent mass flux vector
$\overline{{\mathrm{ }u}_i^{\mathrm{\prime }}{u}_j^{\mathrm{\prime }}}$	=	components of Reynolds stress tensor
$C_{\theta }$	=	model coefficient
$D_{n,m}$	=	diffusion coefficient, species n in ambient m
$M_{\omega ,\mathcal{R}}$	=	reactant molecular weight
$M_{\omega ,j}$	=	production molecular weight
$\dot{m}$	=	mass flow rate (kg/s)
$R_n$	=	species production/consumption rate
$S_h$	=	heat source term
$c_p$	=	heat capacity
$k_{b,r}$	=	reverse reaction rate coefficient
$k_{f,r}$	=	forward reaction rate coefficient
$u_i,u_j$	=	velocity vector components
D	=	diameter of combustor
d	=	fuel nuzzle diameter
f	=	mixture fraction
k	=	turbulent kinetic energy
L	=	length of the cylindrical volume
$P$	=	pressure
R	=	radius
t	=	time
T	=	temperature
Y	=	mass fraction

Greek symbols
${\delta }_{ij}$	=	Kronecker symbol
${\epsilon }_H$	=	heat eddy diffusivity
${\epsilon }_M$	=	momentum eddy diffusivity
${\upsilon }_t$	=	turbulent kinematic viscosity
${\vartheta }_{n,r}^{\prime }$	=	stoichiometric coefficient, for reactant species ‘n’ in reaction ‘i'
${\vartheta }_{n,r}^{″}$	=	stoichiometric coefficient, for product species ‘n’ in reaction ‘i'
$\mathrm{\epsilon }$	=	dissipation rate of the turbulent kinetic energy
$\tau$	=	turbulent time scale
$\mu$	=	dynamic molecular viscosity
$\rho$	=	density
Φ	=	equivalence ratio

Subscript
i,j	=
J	=
$\mathcal{R}$	=	reactant
t	=	turbulent
Prt	=	turbulent Prandtl number
${Sc}_{t,m}$	=	turbulent Schmidt number
EDM	=	eddy dissipation model
PDF	=	probability density function
GGDH	=	generalized gradient diffusion hypothesis
HOGGDH	=	high order generalized gradient diffusion hypothesis
SED	=	simple eddy diffusivity
UDF	=	user define function
SN	=	swirl number

Other symbols
∼	=	Favre average
¯	=	Reynolds average