CFD Investigation of Flame and Pressure Wave Propagation through Variable Concentration Methane-Air Mixtures in a Tube Closed at One End

ABSTRACT

CFD modeling of methane-air combustion and the subsequent flame and pressure wave propagations from the closed end of a detonation tube is presented, with a focus on propagation through variable concentration mixtures. A partially premixed combustion model that avoids the need to specify the flame speed is developed based upon the Flamelet Generated Manifold (FGM) model and needs no tuning to account for different methane concentrations. The numerical model is extensively validated using the experimental data collected from a large-scale detonation tube. The results show that the pressure wave propagation experiences three sequential stages: i) growth; ii) decoupling; and iii) decay. The peak overpressure is generated in the pressure wave growth stage in which the wave front transiently couples with the flame front, and the confined tube walls induce lateral wave reflections and force the flame front to transit from spherical to planar. Subsequently, the wave front starts decoupling from the flame front, with an almost constant global maximum pressure. After decoupling, the global maximum pressure drops because of the energy loss incurred through the wave propagation. The different methane concentrations introduced initially after the explosion chamber containing a stoichiometric mixture do not affect the peak overpressure or the pressure wave propagation but do affect the profile and propagation of the flame. Exponential acceleration of the flame propagation speed is found in the growth stage of pressure wave propagation, followed by the transition to a linear acceleration stage. For cases with the methane concentration becoming smaller than the stoichiometric concentration, the linear flame acceleration rate is smaller, with more pronounced flame stretching.

KEYWORDS:

• Flamelet Generated Manifold (FGM) model
• methane-air combustion
• deflagration
• wave propagation
• flame propagation

Acknowledgments

The authors wish to acknowledge the financial support by Australian Coal Association Low Emission Technologies Ltd (ACALET), Australian Department of Resources, Energy and Tourism and The University of Newcastle, Australia. This research/project was undertaken with the assistance of resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian Government.

Notation

Symbols

$c$	=	reaction progress variable, -
$c_{pi}$	=	ith species specific heat at constant pressure, J/(kg⋅K)
$c_{\mathrm{s}}$	=	local sound speed, m/s
$D_{\mathrm{e}\mathrm{f}\mathrm{f}}$	=	effective diffusivity coefficient, m2/s
$D_t$	=	turbulent diffusivity, m2/s
$f$	=	mixture fraction, -
$f^{\prime }{\left(s\right)}_{\mathrm{m}\mathrm{a}\mathrm{x}}$	=	maximum slope of temperature profile across the flame front, K/m
$h$	=	enthalpy, J
k	=	turbulence kinetic energy, m2/s2
$l_{\mathrm{f}}$	=	flame thickness, m
$M_{\mathrm{m}}$	=	reactant mass at the stoichiometric condition, kg
$p$	=	pressure, Pa
$P$	=	joint PDF of reaction-progress (c) and mixture fraction (f), -
$Pr$	=	Prandtl number, -
$Q$	=	heat released from stochiometric methane combustion, J
$r$	=	radial position inside DT, m
$R$	=	radius of DT, m
$s$	=	local position along the DT centreline, m
$S_c$	=	flamelet source term, 1/s
$S_{\mathrm{F}\mathrm{R}}$	=	Finite-Rate flamelet source term from the flamelet library, 1/s
$t$	=	time, s
$T$	=	temperature, K
$T_{\mathrm{c}}$	=	auto-ignition temperature of methane, K
$\tilde{\mathbf{u}}$	=	spatial density weighted velocity, m/s
$U$	=	velocity, m/s
$x$	=	mole fraction, -
$W$	=	molar mass, kg/mol
$Y$	=	mass fraction, -
${\tilde{Y}}_c$	=	Reynolds averaged un-normalized progress variable, -

Greek letters

${\alpha }_k$	=	constants, zero for reactants and unity for a few product species, -
$\gamma$	=	ratio of specific heat for methane, -
$\epsilon$	=	turbulence dissipation rate, m2/s3
$\mathrm{\Delta }p$	=	pressure drop, Pa
$\mathrm{\Delta }s$	=	distance between burnt and unburnt gases boundaries, m
$\mathrm{\Theta }$	=	gas thermal expansion coefficient, -
$\lambda$	=	thermal conductivity, W/(m⋅K)
${\mu }_t$	=	turbulent viscosity, kg/(m⋅s)
$\nu$	=	viscous diffusion rate (kinematic viscosity), m2/s
$\rho$	=	density, kg/m3
$\sigma$	=	scaled growth rate of flame acceleration, -
$\varphi$	=	relative humidity, -
${\chi }_c$	=	scalar dissipation rate, 1/s
${\chi }_{\mathrm{m}\mathrm{a}\mathrm{x}}$	=	prescribed maximum scalar dissipation within the premixed flamelet, 1/s
${\dot{\omega }}_c$	=	reaction rate of the progress variable c, mol/(s⋅m3)
${\dot{\omega }}_k$	=	molar production rate of species k, mol/(s⋅m3)

Subscripts or superscripts

b	=	burnt mixture
def	=	deflagration
eq	=	chemical equilibrium
f	=	flame
FT	=	flame tip
L	=	laminar
i	=	the ith species
u	=	unburnt mixture
sto	=	stoichiometric