Effect of Tube Size on Flame and Pressure Wave Propagation in a Tube Closed at One End: A Numerical Study

ABSTRACT

Deflagration of fire and explosion caused by ignition of a methane-air mixture is a major safety concern in industrial settings, such as the mining and petrochemical industries. The aim of this study is to investigate numerically the effect of tube size on the flame and pressure wave propagations for methane-air deflagration in a tube closed at one end. A partially premixed combustion model that avoids the need to specify the flame speed is deployed based upon the Flamelet Generated Manifold (FGM) model. Good agreement is achieved between the predicted results and the benchmark experimental data collected using a large-scale detonation tube (L/D = 66). Subsequently, the explosion behaviour immediately after the ignition of methane-air mixtures and the propagation characteristics of the flame front and pressure wave through the tube are examined, covering a broad range of L/D, that is from 26 to 526, in which the diameter is changed and the length is kept fixed. The results show that the pressure wave propagates significantly faster in narrower tubes and hence decouples from the flame front shortly after ignition, which in turn results in a low overpressure at the flame front. Moreover, abrupt changes in gas properties are observed in narrow tubes with L/D ≥ 132. The peak overpressure increases as the tube diameter increases; however, the local maximum pressure decreases substantially in large tubes when approaching the tube vent but remains almost constant throughout in the narrow tubes. Similarly, the flame propagates faster in narrower tubes. A correlation that estimates the distance the flame propagates in the exponential acceleration stage is proposed as a function of tube size and time. Deviations of less than 7% are obtained when comparing the predicted results using the correlation against the experimental data. The results provide local information that aids the theoretical interpretation of experimental observations and the understanding of the fuel combustion and explosion phenomena in different sized tubes.

KEYWORDS:

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

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, 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.

• A combustion model that avoids the need to specifying the flame speed is validated.

• Global maximum pressure is found at the flame front in narrow tubes.

• Local maximum pressure decreases in large tubes when approaching the tube vent.

• Abrupt changes in gas properties are observed in narrow tubes.

• A correlation predicting the flame propagation distance after ignition is proposed.

Notation

Symbols

$A=$	=	Constant, m/s
$B=$	=	Constant, 1/s
$c=$	=	Reaction progress variable, -
$c_p=$	=	Mixture specific heat, J/(kg⋅K)
$c_{\mathrm{s}}=$	=	Local sound speed, m/s
$D_{\mathrm{e}\mathrm{f}\mathrm{f}}=$	=	Effective diffusion coefficient, kg/(m⋅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
$k=$	=	Thermal conductivity, W/(m⋅K)
$L=$	=	Tube length, m
$L_{\mathrm{f}}=$	=	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, -
$\dot{q}=$	=	Energy generation rate from methane-air combustion, W
$Q=$	=	Total energy liberated from the reaction per unit volume, Pa
$r=$	=	Radial position inside DT, m
$R=$	=	Radius of DT, m
$Re=$	=	Reynolds number, 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
${\tilde{u}}_i=$	=	Spatial density weighted velocity in the ith direction, m/s
$U=$	=	Velocity, m/s
$Y=$	=	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, -
$\mathrm{\Delta }p=$	=	Pressure drop, Pa
$\mathrm{\Delta }s=$	=	Distance between burnt and unburnt gases boundaries, m
$\epsilon =$	=	Turbulence dissipation rate, m2/s3
$\mathrm{\Theta }=$	=	Gas thermal expansion factor, -
$k=$	=	Turbulence kinetic energy, m2/s2
${\lambda }_{\mathrm{f}}=$	=	Flame thickness, m
$\nu =$	=	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 CC, mol/(s⋅m3)
${\dot{\omega }}_k=$	=	Molar production rate of species k, mol/(s⋅m3)

Subscripts or superscripts

$\mathrm{e}\mathrm{q}=$	=	Chemical equilibrium
$\mathrm{f}=$	=	Flame
$\mathrm{F}\mathrm{F}=$	=	Flame front
$\mathrm{L}=$	=	Laminar
$\mathrm{k}=$	=	The kth species
$\mathrm{s}\mathrm{t}\mathrm{o}=$	=	Stoichiometric
$\mathrm{u}=$	=	Unburnt mixture