Numerical Simulation of n-Heptane Spray Combustion in a Porous Medium Burner

ABSTRACT

A two-dimensional numerical simulation study is conducted to investigate the combustion process of n-heptane spray in a porous medium burner (PMB) based on the previous experimental work performed by this research group. In order to adapt the model for the conditions of different wall temperatures and different splash Mach numbers, the wall-impingement model in this study is based on the model by O’Rourke and Amsden and the interaction mechanism between the spray droplets and the wall is optimized through user-defined functions (UDFs). The effects of air inlet velocity, injected fuel quantity and preheating temperature on spray combustion are analyzed. The results show that the downstream velocity of the combustion flame increases when the inlet air velocity increases or the fuel injection rate decreases or the preheating temperature decreases. Under the same equivalence ratios, the flame propagation velocity increases as the increase of the dimensionless gas-oil joint effect parameter. The flame area also increases with the increase of inlet air velocity, but the rate of increase in the flame area gradually decreases as the reaction proceeds. An initial preheating temperature of 1060 K is conducive to the stable combustion of n-heptane spray for flame lengths less than 0.060 m.

KEYWORDS:

• Porous medium burner
• numerical simulation
• liquid fuel
• moving flame

Nomenclature

X length in the X direction (m)

Y length in the Y direction (m)

Q_f quantity of fuel injected (kg/s)

V_air inlet air velocity (m/s)

T preheating temperature (K)

$Y_i$ mass fraction of component i

$D_i$ diffusion coefficient of component i (m²/s)

$W_i$ molecular mass of component i (kg/kmol)

$v_i$ velocity vector of component i (m/s)

$v_p$ droplet velocity vector (m/s)

$v^{\prime }$ fluctuating gas flow velocity (m/s)

$C_D$ drag coefficient

$T_{wall}$ temperature of the PM wall (K)

$E$ splash Mach number

$V_{pn}^{\hspace{0.17em}}$ normal impact velocity of droplet (m/s)

$d_p$ droplet diameter (m)

$h_0$ thickness of the liquid film (m)

$T_{crit}$ critical wall temperature (K)

$T_{crit}^{\ast }$ 1.27

$T_{sat}$ saturation temperature of n-heptane (K)

T_max maximum flame temperature (K)

$y_s$ mass ratio of splashed droplets

Greek symbols

ԑ porosity of porous medium

${\rho }_g$ gas density (kg/m³)

${\rho }_p$ droplet density (kg/m³)

${\sigma }_p$ droplet surface tension (N/m)

${\delta }_{bl}$ thickness of the boundary layer (m)

φ equivalence ratio

${\omega }_i$ reaction rate of component i (kg/m²/s)

$\psi$ azimuth angle (°)

β axial to radial maximum velocity ratio

θ₁ dimensionless injected fuel quantity

θ₂ dimensionless inlet velocity

θ₃ dimensionless gas-oil joint effect parameter

Acknowledgments

This study was funded by the National Natural Science Foundation of China (Nos. 51576029 and 51476017).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [51476017,51576029].