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LES of flame acceleration and DDT in small-scale channels
Accepted Manuscript LES of flame acceleration and DDT in small-scale channels Yongyao Zhao, Cheng Wang, Yong Bi PII:
S0950-4230(17)30158-4
DOI:
10.1016/j.jlp.2017.02.011
Reference:
JLPP 3420
To appear in:
Journal of Loss Prevention in the Process Industries
Received Date: 30 October 2016 Revised Date:
15 February 2017
Accepted Date: 15 February 2017
Please cite this article as: Zhao, Y., Wang, C., Bi, Y., LES of flame acceleration and DDT in small-scale channels, Journal of Loss Prevention in the Process Industries (2017), doi: 10.1016/j.jlp.2017.02.011. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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LES of flame acceleration and DDT in
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small-scale channels
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Yongyao Zhao1, Cheng Wang1*, Yong Bi1
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E-mail: [email protected] 1
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology,
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Beijing 100081, China
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Abstract Large eddy simulation (LES) has been performed to investigate the process of flame
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acceleration (FA) and deflagration-to-detonation transition (DDT) in a small-scale channel
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filled with methane-oxygen mixture. A transport model for sub-grid kinetic energy was used
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to enclose the sub-grid fluxes while the sub-grid scale combustion was modelled by the
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artificially thickened flame (ATF) model. A fifth-order Weighted Essential Non-oscillatory
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(WENO) finite difference scheme was used to discretize the advection term of the governing
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equations. The results showed that the interaction of the flame with the flow and the pressure
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wave ahead led to the flame acceleration. The overdriven detonation led by the local
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explosion formed and the flame propagated upstream which then coupled with the precursor
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shock wave. A retonation wave propagating downstream was further observed. The
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experimental results substantiate the validation of the calculation and further identified the
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DDT mechanism.
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Keywords: large eddy simulation, WENO, flame acceleration, DDT
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Introduction Most gaseous explosions usually start from electrical spark or autoignition, which lead to
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the transition to detonation. In order to prevent accidental explosions in the production and
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control the detonation initiation in the propulsion system, it is necessary to investigate the
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mechanism of DDT. Ciccarellia & Dorofeev,(2008); Liberman et al., (2010); Ivanov et al.,
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(2011); Kagan & Sivashinsky, (2003); Oran & Gamezo, (2007); Thomas et al., (2010); Valiev
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et al., (2009); Nie et al. (2014, 2015); Wang et al., (2016) have already conducted various
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studies on the general initiation of DDT. However, detailed mechanism of FA and DDT
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remain one of the major unresolved problems in combustion science, hence need for further
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research
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Micro-scale combustions have attracted more attention since several studies on simulations
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and experiments on the process of DDT in the micro-scale channel have been conducted. Wu
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et al. (2007, 2011) analyzed the effects of tube diameter and equivalence ratio on the flame
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propagation of ethylene-oxygen mixtures, and observed several reaction propagation
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scenarios including DDT/C–J detonation, oscillating flame, steady deflagration, galloping
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detonation and quenching flame. Liberman et al. (2010) investigated the flame acceleration in
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channels, and observed that the flame propagation exhibits three distinct stages: (1) the flame
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accelerates exponentially producing shock waves far ahead from the flame, (2) the flame
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acceleration decreases and shocks are formed directly on the flame surface, and (3) the final
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third stage of the actual transition to a detonation. Li et al. (2016) also conducted a DDT study
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in the macro-scale tube, and noticed that the boundary layer plays more important role in the
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flame acceleration in the narrow channel and further has an influence on the DDT distance.
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Manzhalei et al. (1998) studied the near-limiting propagation of detonation waves in a
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capillary tube filled with acetylene-oxygen mixture. The momentum and the heat losses
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caused by the wall friction as well as the heat of conduction led to a different propagation
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modes of the flame. Kuznetsov et al. (2005) studied the effect of initial pressure on the run-up
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distance to DDT in a smooth tube with a stoichiometric hydrogen-oxygen mixture, found the
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dependence to be close to the inverse proportionality. The mechanism of DDT through 2D
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and 3D simulations using detailed chemistry reactions were investigated by Liberman et al.,
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2010 and Ivanov et al., 2011. They found that, the mechanism of DDT is entirely determined
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by the features of the flame acceleration in tubes with no-slip walls. Moreover, FA and DDT
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simulations of 3D Navier-Stokes equation with detailed chemical reaction mechanism. They
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obtained “numerical schlieren” and “numerical shadowgraph” which clarify the meaning of
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the experimental schlieren and shadow photos. Han et al. (2017) studied numerically the
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integrated mechanistic behavior of flame acceleration and DDT in micro- and macro-channels
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by DNS. The pressure wave and flow field play an important role in the combustion
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dynamics. However, the simulation of DDT and detonation in the combustible mixtures is a
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formidable task for direct numerical simulation (DNS) (Han et al. 2015; Wang et al., 2013).
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LES method is a good choice to study the flame acceleration (FA) and DDT. Xiao et al.
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(2012) undertook both experimental and numerical studies on the formation of a premixed
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hydrogen/air tulip flame in a closed channel and discussed the evolution of flame structure.
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They claimed the appearance of adverse pressure gradients resulted in reverse flow in the
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unburned gas, which caused the onset of the tulip or a distorted tulip flame. Johansen &
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Ciccarelli (2009) simulated the flame propagation in a closed channel with an obstacle using
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large eddy simulation with the dynamic Smagorinskye-Lilly subgrid model and the Boger
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flame surface density combustion model. They found that flame velocity showed oscillations
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which were as a result of the acceleration and deceleration of the unburned gas flow through
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obstacles. The flame–vortex interaction was investigated by Sarli et al. (2009) using LES
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model coupled to the power-law and flame-wrinkling model, and they found that the
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interaction intensified the rate of flame propagation and the pressure rise. Shin et al. (2008)
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examined the effect of turbulence on the highly unstable detonation by using Monotone
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Integrated Large Eddy Simulation (MILES), and compared the results from inviscid Euler
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equations, Reynolds Averaged Navier-Stokes (RANS) equations, and MILES. They found all
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approaches are capable of capturing the highly unstable detonation wave, but show distinctive
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differences in FFT analysis of highly unstable detonation. Yu & Navarroe-Martinez (2014)
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used a flame thickening approach to capture DDT with relatively coarse meshes, and assessed
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the capabilities of ATF to capture DDT. Emami et al. (2015) also used LES to study the DDT
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in an obstructed channel containing premixed stoichiometric hydrogen-air mixture. They
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studied the effect of grid resolution on the formation of hot spots and the occurrence of DDT,
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and verified the accuracy of the results in predicting the DDT. They claimed that the flame-
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vortex interaction with the folding and wrinkling flame were the main mechanism of the
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flame acceleration in the slow flame regime. Robert et al. (2015) presented a first LES study
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addressing different scenarios for knock and super-knock observed in a spark ignition (SI)
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engine. LES showed that the pressure waves generated by one or a couple of autoignition
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spots were strong enough to induce locally a strong fresh gases temperature increase leading
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itself to a substantial decrease of the autoignition delay. From the above discussions on the
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various articles, it could be observed that only few researches focused on the complete
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process of DDT by applying LES. Hence this present study seeks to apply the large eddy simulation (LES) methodology to
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investigate the FA and the methane-oxygen DDT in the channel with no-slip and adiabatic
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walls. Further validation of the numerical simulation results was compared with the experiments.
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Governing equations
A spatial filter based on local grid size has been applied to the compressible Navier-Stokes
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equations for mass, momentum, total energy, and mass fraction of a reactant to obtain the
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governing equations for LES. The resulting LES equations are obtained by applying Favre
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averaging, which is defined by °f = ρ f / ρ , where the over line indicates volume average. The
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volume average for flow variable f is given by: f ( x) =
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∂ ρ ∂ ρ u°i + =0 ∂t ∂xi
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(1)
The governing equations are as following:
∂ ρ u°i ∂ ∂ ∂ + ( ρ u°° (τ ij ) − (τ ijsgs ) i u i + Pδ ij ) = ∂t ∂x j ∂x j ∂x j
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∫ f ( x′)F ( x − x′) dx′
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(2)
(3)
° ∂ ∂ qi ∂ρ E ∂ ° + P )u%i ) = ∂ (u%% + (( ρ E − H isgs i τ ij ) − ∂t ∂xi ∂xi ∂xi ∂xi
(4)
∂ ρY° ∂ °% ∂ ∂Y° ∂ sgs ξω& + ρYu i = ( ρ Fξ Di )− ϕi + ∂t ∂xi ∂xi ∂xi ∂xi F
(5)
υ ∂k sgs ∂ u° ∂ ρ k sgs ∂ ∂ + ( ρ u°i k sgs ) = (ρ t ) − τ ijsgs ( i ) − C e ρ ( k ) 3 2 ∆ ∂t ∂xi ∂ xi pr ∂xi ∂x j
P = ρ RT°
(6)
(7)
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where; ρ , u i , P , τ , E , q , Y , and ω& denote density, velocity, pressure, stress, total energy,
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energy diffusion vector, mass fraction and reaction rate, respectively. Several terms in the
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LES equations require closure, such as the sub-grid stress τ ijsgs , the unclosed term Hi , the sub-
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grid diffusion of specie mass ϕi . Here, a closure scheme based on a transport model for the
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sub-grid kinetic energy k sgs is used to close the momentum, energy and mass fraction sub-
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grid fluxes, shown as function (6), which is solved along with the LES equations. The three
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terms at the right hand of function (6) are the sub-grid kinetic energy diffusion, production,
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and dissipation, respectively. The unresolved momentum fluxes are expressed according to
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the Boussinesq assumption. The enthalpy fluxes and mass fraction sub-grid fluxes are
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modeled through a simple gradient assumption. The sub-grid stress, energy flux and specie
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mass fraction are closed as follows:
sgs
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sgs
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τ ijsgs = − 2 ρυ t ( s° s° ij − ij δ ij ) +
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H isgs = − ρ
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ϕisgs = − ρ
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υt ∂% h prt ∂xi
υt ∂Y
Sct ∂xi
2 ρ k sgsδ ij 3
(8)
(9)
(10)
Where, υt = Cυ (k sgs )1/2 ∆ , h denote total enthalpy, and h = E + P / ρ . Constants 0.067 and 0.916
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are employed for model coefficients Cυ and Ce , prt and Sct are valued as 1.0. The chemical
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source term is closed as
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ω&= A ρ Y°exp ( −
Ea ) RT
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The thickened-flame (TF) model (Durand & Polifke, 2007; Colin, 2000) is used in the
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combustion closed model. In the TF model, the flame front is artificially thickened to be
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resolved on LES mesh, which is simply achieved by decreasing the pre-exponential factor of
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the chemical Arrhenius law whereas enhancing the molecular diffusion by a factor F. The
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response of the thickened-flame to turbulence is considered by incorporating an efficiency
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function (Charlette et al., 2002) in the governing equations. In this present work, the
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thickening factor defined as F = N ∆ / δ , N is the grid number in the flame front, ∆ is the cell
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size and δ is the thickness of laminar flame. The efficiency function ξ is Power-Law Flame-
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Wrinkling Model (De & Acharya 2008). These parameters of the system are summarized in
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Table 1. They are chosen to model the stoichiometric methane-oxygen mixture. The numerical
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methods used are the 5thorder WENO scheme for convective terms, the 6thorder central
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difference for viscosity terms and the 3rd-order TVD Runge-Kutta method for time
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discretization (Wang et al., 2016; Han et al. 2015, 2017).
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Experimental apparatus The experimental setup is shown in Fig. 1 and it is well discussed in our recent article
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(Wang & Hu, 2016). It consists of a constant volume combustion vessel, a gas mixing system,
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a high-speed photography system, a high-voltage ignition system, and a data acquisition
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system. The combustion vessel is a horizontal explosion channel, with a transparent quartz
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glass on one side. The channel is closed at both ends with a square cross section of 20 mm ×
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20 mm, and the length is 1.5 m, which was filled with premixed methane–oxygen, shown as
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Fig. 1. The initial pressure in the channel was 33 kPa, and the initial temperature was also
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chosen to be 298 K. The ignition position was located at the left end of the channel. The spark
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igniter, pressure recorder, temperature recorder and high-speed video camera were controlled
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by the synchronization system.
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Results and discussions
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In our study, two-dimensional channel was used. The computational domain was 20 mm×
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1.5 m filled with stoichiometric methane-oxygen premixed gas. The boundary was a solid
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reflecting and no-slip wall. To ignite the mixture in the simulation, a circular region of hot
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burned material was placed at the left end of the channel while a small perturbation was
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further added to the burnt region. Initial velocity, temperature and pressure of 0.0 m/s, 298 K
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and 33 KPa, respectively were considered in the unreacted mixture. The validity of the
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numerical method and the tested convergence of the solutions with different mesh sizes (1,
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0.5, 0.2, 0.1 mm) were verified as shown in Fig. 2. When the grid resolution was 1.0 mm, the
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solution differs significantly from that obtained with the refine mesh, and the flame
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propagates faster than that of the experiment. As the mesh become finer, the results tend to
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converge. The results obtained with the grid resolutions of 0.2 and 0.1 mm were almost the
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same, and the position of the flame tip change with time, agree with the experimental results
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before DDT occurs.
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The flame tip speed obtained from the numerical calculation was also compared with the
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experimental results, as shown in Fig. 3. The overall trend of the curves was roughly the same.
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experimental results, there was a long acceleration period of the flame before an abrupt
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increase appears with the value of 2500 m/s at x~0.77 m which indicate the occurrence of
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DDT. The velocity further decays to 2300 m/s. In the numerical simulation, at the first stage,
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the flame accelerates exponentially with a rapid augmentation of the flame surface area as
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shown in Fig. 3. This phenomenon has been explained theoretically and confirmed by DNS
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and experimental studies by Liberman et al. (2011). During the second stage, the rate of flame
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acceleration decreases. It was noticed that, at a mesh size of 1 mm, the calculated flame
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velocity was larger than the experimental values before DDT occurs. While, with the finer
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mesh, the flame velocity tends to be close to the experimental values before DDT. The DDT
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run-up distance was slightly longer than that of the experimental result. This was because the
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simulation used 2D, while 3D was used for the experiment. Ivanov et al., (2013) observed that
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the flame velocity in 3D case is larger than that in 2D case, and the time of DDT is shorter in
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3D case compared to 2D due to extra dimension. In the stage of DDT, the flame velocity had a
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sharp increase, reaching the maximum value, and then decays to a steady value.
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Fig. 4 shows the process of flame acceleration and DDT for both the experiment and
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numerical results. Fig. 4a presents a high-speed image of the experiment while Fig. 4b shows
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the numerical results of temperature contours. After ignition, the initial laminar flame kernel
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expands, and then the flame gradually spreads to the right end of the channel, showing a
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fingerlike appearance. In this stage, the brightness of the flame surface was brighter, and then
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becomes dim along with the flame surface changing. As the flame propagates, a suddenly
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white light near the flame front appears, which means local explosion occurs. As shown in Fig.
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3, the flame velocity reaches the maximum value after a while. These explosions initiate the
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process of DDT, and the detonation front continue to propagate upstream while a retonation
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wave moves downstream. The white light gradually fill the channel, and the detonation and
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retonation propagation process are shown by the red lines. Similar to the experimental results,
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numerical results show the processes of flame acceleration, DDT, and the resulting detonation
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propagation can be seen from the temperature contours shown in Fig. 4b.
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Fig. 5 shows the temperature and pressure profiles in the flame front along the channel at a
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selected time interval. As the flame propagates forward, the thermal expansion of hot products
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induces the unburned gas to flow ahead of the flame. In this process, pressure waves are
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produced constantly. This lead to a small heating of the gas which is less than 500 K in the
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unburned material ahead of the flame, until the pressure is strong enough for DDT occur. Due
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forms, leading to the development of high flame speed. As time elapsed the shock waves are
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coalesced, merged, amplified and hence creating a layer of compressed and heated unreacted
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gas – which is the preheat zone (Liberman et al. 2009). This leads to more unburned mixture
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with higher density and temperature entering the flame front. Eventually, the flame front
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coincides with the leading shock, leading to the flame propagating as detonation waves.
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Fig. 6 shows the time-distance trajectory of the flame tip and the leading shock according to
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the numerical results. As the flame propagates to the right, it acts as a piston producing
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compression waves in the unreacted gas, which steepens into the shock waves far ahead of the
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flame front. The leading shock stands in front of the flame front, presenting a typical two
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waves and three regions structure. The distance between them is about two times of the
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channel width, which is less than Ivanov’s result (2013), five to seven times of the channel
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width. This might be as a result of too large calculating area used in the study with regards to
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the 2D model. The distance between them gradually decreases which tends to zero at about
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x=0.74 m at t~1.4ms. The flame accelerates constantly and becomes faster at t~1.4ms,
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corresponding to the velocity increase fast as shown in Fig. 3. Consequently, the flame
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catches up with and couples the leading shock, which leads to the overdriven detonation.
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The flame acceleration is not only related to pressure waves, but also to the flow field
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around flame front. After ignition of the flame kernel, initially, the weak compression waves
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move away and produces flow ahead of the flame with the velocity, approximately u = (Θ−1)U f ,
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Θ = ρu ρb ≈ 10 , where ρu and ρb indicate the density ratio of the unburned and burned gas,
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respectively (Zeldovich et al. 1985). Fig. 7 shows the flow field near the flame front at
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t=0.727 ms and 0.86 ms. The figure shows the velocity contours and the corresponding
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longitudinal velocity profiles (right part) in the cross section A and B. Owing to the wall
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friction, the flow velocity vanishes at the channel walls, and has maximal value at the center
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of the channel which exceeds 100 m/s. The flame surface is stretched gradually, which results
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in more fresh fuel being consumed. Higher burning velocity results in an enhancement of the
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flow velocity ahead of the flame, which in turn gives rise to a larger gradient field and boosts
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flame stretching. As the flame is stretched in the velocity field ahead of the flame front, a
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positive feedback coupling is established between the upstream flow and the burning velocity
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(Ivanov et al., 2013). Whiles it was realized that the flow velocity was dropping to zero at the
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channel walls, the flow ahead of the flame was uniform in the bulk. This is because, the time
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velocity profiles (i.e. the Poiseuille flow) (Kuznetsov et al., 2010). According to Zeldovich
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(1985), the estimated time of formation of a parabolic velocity profile in the upstream flow
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given as t = D 2 / υ , is similar to the magnitude obtained in (Liberman et al., 2009), i is larger
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than 10 s for the channel with width 20 mm. However, the duration of the whole process of
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DDT is in the range of 1 ms, which is shorter than the time required for the formation of a
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parabolic velocity profile in the upstream flow by many orders of magnitude.
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The streamlines near the flame front are drawn at some time instants, as shown in Fig. 8. It
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has been found that, upto the time of DDT, the flow ahead of the flame remains laminar, and
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only becomes unparalleled behind the flame surface. At t=1.31 and 1.39 ms, all the
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streamlines vanish in front of the flame, and this is because pressure waves steepen into shock
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waves in front of which there is no disturbance.
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The pressure and temperature distributions are presented in Fig. 9 in the process of DDT.
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The leading shock is located on the right side of the flame, and the preheating zone forms
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ahead of the flame front at t=1.31 ms (see Fig. 9a). The unburned mixtures were compressed
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and heated in the preheating zone by the increasing pressure. As a result, a larger amount of
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mixture enters the reaction zone, which enhance the reaction rate. These effects lead to
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stronger temperature and pressure gradient as a feedback. Under such interactive circumstance,
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it causes the formation of a shock wave directly ahead of the reaction zone, and these
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conditions lead to the coupling of the shock and the reaction zone, which results in the
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transition to detonation (Ivanov et al., 2011). Fig. 9b shows the change process of pressure
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contours. At t=1.35 ms, there was a high-pressure zone between the flame front and the wall.
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Then, a strong circular pressure wave could be seen caused by local explosion, triggering the
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transition from deflagration to detonation. Finally, the flame coupled with the leading shock,
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leading to the flame propagate as detonation waves.
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Fig. 10 shows the occurrence of local explosion and its process of development. When
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t=1.383 ms, there appears a local explosion near the wall that causes local pressure rises
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rapidly. The explosion waves propagate in the channel forming reverse detonation wave and
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transverse wave at t=1.39 ms. At the same time, this explosion wave propagates forward,
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catches up with the flame and collides with the precursor shock, triggering another stronger
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local explosion at t=1.396ms. Finally, a strong overdriven detonation forms, the flame
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coupling with the precursor shock propagates upstream, and another stronger reverse
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detonation wave propagates downstream, see Fig. 10 at t=1.401 and 1.405 ms.
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4. Conclusions LES method has been used to investigate the flame acceleration and DDT in small scale
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channels. The artificially thickened flame approach was adopted since the mesh scale is
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greater than the thickness of the flame. The comparisons of experimental and numerical
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results show that, applied method in this study is more effective and can capture the typical
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characteristic of flame acceleration and DDT.
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The flame velocity initially increase rapidly as a result of the stretching of the flame front
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within the boundary layer. The interaction between the flame and the flow field around the
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flame front establishes a positive feedback mechanism, promoting the flame propagation.
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Though the channel width is 20mm, the Poiseuille flow is not formed in front of the flame up
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to the time of DDT occurs, and the flow was always laminar.
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The fast acceleration of the flame is due to its coupling with the shock wave formed at the
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flame front. As the pressure increases, the leading shock is close to the flame front, and the
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preheating zone appears ahead of the flame, increasing the chemical reaction rate. Finally, the
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shock-wave complex near the wall becomes severe, which causes local explosion, and then
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triggers the process of DDT. Then, there appear retention waves propagating backward with
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detonation wave propagating forward.
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Acknowledgements
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This research is supported by the National Natural Science Foundation of China under grants
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11325209 and 11521062.
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Ivanov, M. F., Kiverin, A. D., Yakovenko, I. S., & Liberman, M. A. (2013). Hydrogen–oxygen flame
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Johansen, C. T., & Ciccarelli, G. (2009). Visualization of the unburned gas flow field ahead of an accelerating flame in an obstructed square channel. Combust. Flame, 156(2), 405-416.
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Khokhlov, A. M., Oran, E. S., & Thomas, G. O. (1999). Numerical simulation of deflagration-to-
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detonation transition: The role of shock-flame interactions in turbulent flames. Combust. Flame,
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Knudsen E., Pitsch H. (2008). A dynamic model for the turbulent burning velocity for large eddy simulation of premixed combustion. Combust. Flame, 154: 740. Li, J., Zhang, P., Yuan, L., Pan, Z., & Zhu, Y. (2016). Flame propagation and detonation initiation distance of ethylene/oxygen in narrow gap. Appl. Therm. Eng., 110, 1274–1282. Liberman, M. A., Ivanov, M. F., Kiverin, A. D., Kuznetsov, M. S., Chukalovsky, A. A., &
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Rakhimova, T. V. (2010). Deflagration-to-detonation transition in highly reactive combustible
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mixtures. Acta Astronautica, 67(7-8), 688-701.
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Liberman, M. A., Kuznetsov, M., Ivanov, A., & Matsukov, I. (2009). Formation of the preheated zone
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ahead of a propagating flame and the mechanism underlying the deflagration-to-detonation
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transition. Physics Letters A, 373(5), 501-510.
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Nie B, He X, Wang C, Lu H, Xue F., (2015). Computational method of the propagation velocity of
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methane explosion flame based on correlation coefficient of images. Combust. Sci. Technol.,
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Nie B, He X, Zhang C, Li X, Li H. (2014). Temperature measurement of gas explosion flame based on the radiation thermometry. Int. J. Thermal Sci., 78:132-144.
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Oran, E. S., & Gamezo, V. N. (2007). Origins of the deflagration-to-detonation transition in gas-phase combustion. Combust. Flame, 148(1–2), 4-47.
Poinsot, T., & Veynante, D. (2005). Theoretical and numerical combustion (2nd ed.). R.T. Edwards.
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Robert, A., Richard, S., Colin, O., & Poinsot, T. (2015). Les study of deflagration to detonation
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mechanisms in a downsized spark ignition engine. Combust. Flame, 162(7), 2788-2807. Sarli V. Di, Benedetto A. Di, Russo G., Jarvis S., Long E. J., Hargrave G. K., (2009). Large Eddy
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Simulation and PIV Measurements of Unsteady Premixed Flames Accelerated by Obstacles. Flow
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Turbul. Combust., 83(2):227-250.
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Shin J., Cho D., Won S. and Choi J. (2008). Large Eddy Simulation of a Highly Unstable Detonation
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Wave. 46th AIAA Aerospace Sciences Meeting and Exhibit 7 - 10 January 2008, Reno, Nevada.
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Thomas, G., Oakley, G., & Bambrey, R. (2010). An experimental study of flame acceleration and
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deflagration to detonation transition in representative process piping. Process Saf. Environ., 88(2),
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Valiev, D. M., Bychkov, V., Akkerman, V., & Eriksson, L. (2009). Different stages of flame
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acceleration from slow burning to Chapman-Jouguet deflagration. Physical Review E,
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80(0363173).
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scale pipeline. Transactions of Beijing Institute of Technology, 8, 784-788. Wang C., Shu CW., Han W., Ning J. (2013). High resolution WENO simulation of 3D detonation
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Wang C., Hu BB, (2016). Experimental study on the explosive flame propagation of CH4-O2 in small
waves. Combust Flame. 160, 447–462.
Wang C.， Zhao Y.， Han W., Large eddy Simulation of Flame Acceleration and Transition from Deflagration to Detonation. 25th ICDERS August 2 – 7, 2015 Leeds, UK.
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Wang C.， Zhao Y.，Zhang B. (2016). Numerical simulation of flame acceleration and deflagration-todetonation transition of ethylene in channels. J. Loss Prevent. Proc., 43:120-126. Wu, M. H., Burke, M. P., Son, S. F., & Yetter, R. A. (2007). Flame acceleration and the transition to
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detonation of stoichiometric ethylene/oxygen in microscale tubes. Proc. Combust. Inst., 31(2),
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2429-2436.
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Xiao H, Shen X, Sun J. (2012). Experimental study and three dimensional simulation of premixed
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mixtures. Proc. Combust. Inst. 33:2287-93.
hydrogen/air flame propagation in a closed duct. Int. J. Hydrog. Energy, 37: 11466-73. Yu, S., & Navarro-Martinez, S. (2014). Modelling of deflagration to detonation transition using flame thickening. Proc. Combust.Inst., 35(2), 1955–1961. Zbikowski M., Makarov D., Molkov V. (2008). LES model of large scale hydrogen–air planar
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Wu M, Wang C. (2011). Reaction propagation modes in millimeter-scale tubes for ethylene/oxygen
detonations: Verification by the ZND theory. Int. J. Hydrog. Energy, 33(18): 4884-4892. Zeldovich YaB, Barenblatt GI, Librovich VB, Makhviladze GM. (1985). Mathematical theory of
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combustion and explosion. New York: Consultants Bureau.
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Figure captions
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Table 1 Physical parameters of the model system.
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Fig. 1. Sketch of experimental apparatus: (1) pure methane, (2) pure oxygen, (3) gas mixing device, (4)
ignition electrode, (5) horizontal channel, (6) high-speed video camera, (7) pressure and
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temperature recorder, (8) data recorder, (9) synchronization controller, (10) spark igniter.
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Fig. 2. Comparison of the flame tip position-time evolution between experimental and numerical
results computed for different mesh, △x= 1, 0.5, 0.2 and 0.1 mm.
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Fig. 3. Flame tip velocity against distance along the channel for experimental and numerical results.
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Fig. 4. Flame acceleration and DDT occurs: (a) high speed video of experiment; (b) time interval of
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temperature contours of numerical results, △=0.5 mm.
Fig. 5. Evolution of temperature and pressure profiles corresponding to leading point along the
channel, time instants are from t=0.727 ms to 1.546 ms.
Fig. 6. Change of distance between the flame tip and the leading shock
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Fig. 7. Flow field ahead of the flame front at t=0.727 ms (A) and 0.86 ms (B) and corresponding velocity
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profile along the channel in the cross A and B.
Fig. 8. Flame structure and streamlines around the flame front at different times, t=0.86, 1.21, 1.31, 1.39ms
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Fig. 9. Temperature and pressure contours at different times for transition to detonation: (a) the
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temperature, and (b) the pressure.
Fig. 10. Pressure contours for local explosion and DDT.
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Table 1 Physical parameters of the model system Notations
Values
Initial pressure
P0
33 KPa
Initial temperature
T0
Initial density
ρ0
Polytropic exponent
γ
Molecular weight
M
Preexponential factor
A
Chemical energy release Activation energy 411
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Parameter
298 k
1.19 kg/m3 1.15
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0.027 kg/mol
1.21×1010 m3/Kg/s
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q
60 RT0/M
Ea
69 RT0
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Fig. 1. Sketch of experimental apparatus: (1) pure methane, (2) pure oxygen, (3) gas mixing device,
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(4) ignition electrode, (5) horizontal channel, (6) high-speed video camera, (7) pressure and
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temperature recorder, (8) data recorder, (9) synchronization controller, (10) spark igniter.
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Fig. 2. Comparison of the flame tip position-time evolution between experimental and numerical
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results computed for different mesh, △x= 1, 0.5, 0.2 and 0.1 mm.
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Utip(m/s)
2000 1500
Experimental
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△=1 mm
△=0.2 mm
0 0
0.5
1
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x(m)
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1.5
Fig. 3. Flame tip velocity against distance along the channel for experimental and numerical results.
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Local explosion
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(a)
(b)
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Fig. 4: Flame acceleration and DDT occurs: (a) high speed video of experiment; (b) time interval of temperature contours of numerical results, △=0.5 mm.
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30 T p
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T(K)
3000
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1000
0
447
0.6 x(m)
0.8
5
1
channel, time instants are from t=0.727 ms to 1.546 ms.
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0.4
10
Fig. 5. Evolution of temperature and pressure profiles corresponding to leading point along the
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p(bar)
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0.8
x(m)
0.6
Leading shock
0.4
Flame tip
0 1
1.1
1.3
1.4
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0.2
1.5
1.6
Fig. 6. Change of distance between the flame tip and the leading shock.
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100 0 305
u(m/s)
80
0.05
0.1
x(m)
0.15
60
40
0.2
A
20
0
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0.005
0.01 y(m)
0.015
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B
u(m/s)
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0.08
0.12
0.16 x(m)
0.01 y(m)
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corresponding velocity profile along the channel in the cross A and B.
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0.005
0.015
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Fig. 7 Flow field ahead of the flame front (red line) at t=0.727 ms (A) and 0.86 ms (B) and
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0
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0.2
100
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Fig 8 Flame structure and streamlines around the flame front at different times, t=0.86, 1.21, 1.31, 1.39 ms.
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Fig. 9: Temperature and pressure contours at different times for transition to detonation: (a) the temperature, and (b) the pressure.
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Fig. 10: Pressure contours for local explosion and DDT.
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Highlights
Yongyao Zhao, Cheng Wang*, Yong Bi E-mail: [email protected]
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LES of flame acceleration and DDT in small-scale channels
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(1) FA and DDT in small-scale channels are investigated with LES and experimental method.
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(2) The interaction of the flame with the flow field and the pressure wave is the main mechanism for flame acceleration.
(3) The flow ahead of the flame always keeps laminar up to the time of DDT occurs. (4) Local explosion triggers the DDT and causes the retonation wave propagates
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downstream.
S0950-4230(17)30158-4
DOI:
10.1016/j.jlp.2017.02.011
Reference:
JLPP 3420
To appear in:
Journal of Loss Prevention in the Process Industries
Received Date: 30 October 2016 Revised Date:
15 February 2017
Accepted Date: 15 February 2017
Please cite this article as: Zhao, Y., Wang, C., Bi, Y., LES of flame acceleration and DDT in small-scale channels, Journal of Loss Prevention in the Process Industries (2017), doi: 10.1016/j.jlp.2017.02.011. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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LES of flame acceleration and DDT in
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small-scale channels
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Yongyao Zhao1, Cheng Wang1*, Yong Bi1
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E-mail: [email protected] 1
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology,
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Beijing 100081, China
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Abstract Large eddy simulation (LES) has been performed to investigate the process of flame
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acceleration (FA) and deflagration-to-detonation transition (DDT) in a small-scale channel
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filled with methane-oxygen mixture. A transport model for sub-grid kinetic energy was used
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to enclose the sub-grid fluxes while the sub-grid scale combustion was modelled by the
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artificially thickened flame (ATF) model. A fifth-order Weighted Essential Non-oscillatory
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(WENO) finite difference scheme was used to discretize the advection term of the governing
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equations. The results showed that the interaction of the flame with the flow and the pressure
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wave ahead led to the flame acceleration. The overdriven detonation led by the local
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explosion formed and the flame propagated upstream which then coupled with the precursor
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shock wave. A retonation wave propagating downstream was further observed. The
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experimental results substantiate the validation of the calculation and further identified the
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DDT mechanism.
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Keywords: large eddy simulation, WENO, flame acceleration, DDT
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Introduction Most gaseous explosions usually start from electrical spark or autoignition, which lead to
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the transition to detonation. In order to prevent accidental explosions in the production and
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control the detonation initiation in the propulsion system, it is necessary to investigate the
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mechanism of DDT. Ciccarellia & Dorofeev,(2008); Liberman et al., (2010); Ivanov et al.,
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(2011); Kagan & Sivashinsky, (2003); Oran & Gamezo, (2007); Thomas et al., (2010); Valiev
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et al., (2009); Nie et al. (2014, 2015); Wang et al., (2016) have already conducted various
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studies on the general initiation of DDT. However, detailed mechanism of FA and DDT
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remain one of the major unresolved problems in combustion science, hence need for further
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research
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Micro-scale combustions have attracted more attention since several studies on simulations
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and experiments on the process of DDT in the micro-scale channel have been conducted. Wu
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et al. (2007, 2011) analyzed the effects of tube diameter and equivalence ratio on the flame
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propagation of ethylene-oxygen mixtures, and observed several reaction propagation
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scenarios including DDT/C–J detonation, oscillating flame, steady deflagration, galloping
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detonation and quenching flame. Liberman et al. (2010) investigated the flame acceleration in
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channels, and observed that the flame propagation exhibits three distinct stages: (1) the flame
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accelerates exponentially producing shock waves far ahead from the flame, (2) the flame
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acceleration decreases and shocks are formed directly on the flame surface, and (3) the final
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third stage of the actual transition to a detonation. Li et al. (2016) also conducted a DDT study
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in the macro-scale tube, and noticed that the boundary layer plays more important role in the
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flame acceleration in the narrow channel and further has an influence on the DDT distance.
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Manzhalei et al. (1998) studied the near-limiting propagation of detonation waves in a
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capillary tube filled with acetylene-oxygen mixture. The momentum and the heat losses
52
caused by the wall friction as well as the heat of conduction led to a different propagation
53
modes of the flame. Kuznetsov et al. (2005) studied the effect of initial pressure on the run-up
54
distance to DDT in a smooth tube with a stoichiometric hydrogen-oxygen mixture, found the
55
dependence to be close to the inverse proportionality. The mechanism of DDT through 2D
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and 3D simulations using detailed chemistry reactions were investigated by Liberman et al.,
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2010 and Ivanov et al., 2011. They found that, the mechanism of DDT is entirely determined
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by the features of the flame acceleration in tubes with no-slip walls. Moreover, FA and DDT
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simulations of 3D Navier-Stokes equation with detailed chemical reaction mechanism. They
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obtained “numerical schlieren” and “numerical shadowgraph” which clarify the meaning of
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the experimental schlieren and shadow photos. Han et al. (2017) studied numerically the
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integrated mechanistic behavior of flame acceleration and DDT in micro- and macro-channels
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by DNS. The pressure wave and flow field play an important role in the combustion
65
dynamics. However, the simulation of DDT and detonation in the combustible mixtures is a
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formidable task for direct numerical simulation (DNS) (Han et al. 2015; Wang et al., 2013).
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LES method is a good choice to study the flame acceleration (FA) and DDT. Xiao et al.
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(2012) undertook both experimental and numerical studies on the formation of a premixed
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hydrogen/air tulip flame in a closed channel and discussed the evolution of flame structure.
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They claimed the appearance of adverse pressure gradients resulted in reverse flow in the
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unburned gas, which caused the onset of the tulip or a distorted tulip flame. Johansen &
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Ciccarelli (2009) simulated the flame propagation in a closed channel with an obstacle using
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large eddy simulation with the dynamic Smagorinskye-Lilly subgrid model and the Boger
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flame surface density combustion model. They found that flame velocity showed oscillations
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which were as a result of the acceleration and deceleration of the unburned gas flow through
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obstacles. The flame–vortex interaction was investigated by Sarli et al. (2009) using LES
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model coupled to the power-law and flame-wrinkling model, and they found that the
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interaction intensified the rate of flame propagation and the pressure rise. Shin et al. (2008)
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examined the effect of turbulence on the highly unstable detonation by using Monotone
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Integrated Large Eddy Simulation (MILES), and compared the results from inviscid Euler
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equations, Reynolds Averaged Navier-Stokes (RANS) equations, and MILES. They found all
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approaches are capable of capturing the highly unstable detonation wave, but show distinctive
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differences in FFT analysis of highly unstable detonation. Yu & Navarroe-Martinez (2014)
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used a flame thickening approach to capture DDT with relatively coarse meshes, and assessed
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the capabilities of ATF to capture DDT. Emami et al. (2015) also used LES to study the DDT
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in an obstructed channel containing premixed stoichiometric hydrogen-air mixture. They
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studied the effect of grid resolution on the formation of hot spots and the occurrence of DDT,
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and verified the accuracy of the results in predicting the DDT. They claimed that the flame-
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vortex interaction with the folding and wrinkling flame were the main mechanism of the
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flame acceleration in the slow flame regime. Robert et al. (2015) presented a first LES study
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addressing different scenarios for knock and super-knock observed in a spark ignition (SI)
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engine. LES showed that the pressure waves generated by one or a couple of autoignition
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spots were strong enough to induce locally a strong fresh gases temperature increase leading
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itself to a substantial decrease of the autoignition delay. From the above discussions on the
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various articles, it could be observed that only few researches focused on the complete
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process of DDT by applying LES. Hence this present study seeks to apply the large eddy simulation (LES) methodology to
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investigate the FA and the methane-oxygen DDT in the channel with no-slip and adiabatic
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walls. Further validation of the numerical simulation results was compared with the experiments.
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Governing equations
A spatial filter based on local grid size has been applied to the compressible Navier-Stokes
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equations for mass, momentum, total energy, and mass fraction of a reactant to obtain the
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governing equations for LES. The resulting LES equations are obtained by applying Favre
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averaging, which is defined by °f = ρ f / ρ , where the over line indicates volume average. The
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volume average for flow variable f is given by: f ( x) =
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∂ ρ ∂ ρ u°i + =0 ∂t ∂xi
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(1)
The governing equations are as following:
∂ ρ u°i ∂ ∂ ∂ + ( ρ u°° (τ ij ) − (τ ijsgs ) i u i + Pδ ij ) = ∂t ∂x j ∂x j ∂x j
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∫ f ( x′)F ( x − x′) dx′
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(2)
(3)
° ∂ ∂ qi ∂ρ E ∂ ° + P )u%i ) = ∂ (u%% + (( ρ E − H isgs i τ ij ) − ∂t ∂xi ∂xi ∂xi ∂xi
(4)
∂ ρY° ∂ °% ∂ ∂Y° ∂ sgs ξω& + ρYu i = ( ρ Fξ Di )− ϕi + ∂t ∂xi ∂xi ∂xi ∂xi F
(5)
υ ∂k sgs ∂ u° ∂ ρ k sgs ∂ ∂ + ( ρ u°i k sgs ) = (ρ t ) − τ ijsgs ( i ) − C e ρ ( k ) 3 2 ∆ ∂t ∂xi ∂ xi pr ∂xi ∂x j
P = ρ RT°
(6)
(7)
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where; ρ , u i , P , τ , E , q , Y , and ω& denote density, velocity, pressure, stress, total energy,
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energy diffusion vector, mass fraction and reaction rate, respectively. Several terms in the
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LES equations require closure, such as the sub-grid stress τ ijsgs , the unclosed term Hi , the sub-
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grid diffusion of specie mass ϕi . Here, a closure scheme based on a transport model for the
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sub-grid kinetic energy k sgs is used to close the momentum, energy and mass fraction sub-
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grid fluxes, shown as function (6), which is solved along with the LES equations. The three
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terms at the right hand of function (6) are the sub-grid kinetic energy diffusion, production,
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and dissipation, respectively. The unresolved momentum fluxes are expressed according to
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the Boussinesq assumption. The enthalpy fluxes and mass fraction sub-grid fluxes are
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modeled through a simple gradient assumption. The sub-grid stress, energy flux and specie
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mass fraction are closed as follows:
sgs
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τ ijsgs = − 2 ρυ t ( s° s° ij − ij δ ij ) +
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H isgs = − ρ
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ϕisgs = − ρ
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υt ∂% h prt ∂xi
υt ∂Y
Sct ∂xi
2 ρ k sgsδ ij 3
(8)
(9)
(10)
Where, υt = Cυ (k sgs )1/2 ∆ , h denote total enthalpy, and h = E + P / ρ . Constants 0.067 and 0.916
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are employed for model coefficients Cυ and Ce , prt and Sct are valued as 1.0. The chemical
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source term is closed as
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ω&= A ρ Y°exp ( −
Ea ) RT
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The thickened-flame (TF) model (Durand & Polifke, 2007; Colin, 2000) is used in the
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combustion closed model. In the TF model, the flame front is artificially thickened to be
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resolved on LES mesh, which is simply achieved by decreasing the pre-exponential factor of
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the chemical Arrhenius law whereas enhancing the molecular diffusion by a factor F. The
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response of the thickened-flame to turbulence is considered by incorporating an efficiency
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function (Charlette et al., 2002) in the governing equations. In this present work, the
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thickening factor defined as F = N ∆ / δ , N is the grid number in the flame front, ∆ is the cell
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size and δ is the thickness of laminar flame. The efficiency function ξ is Power-Law Flame-
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Wrinkling Model (De & Acharya 2008). These parameters of the system are summarized in
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Table 1. They are chosen to model the stoichiometric methane-oxygen mixture. The numerical
143
methods used are the 5thorder WENO scheme for convective terms, the 6thorder central
144
difference for viscosity terms and the 3rd-order TVD Runge-Kutta method for time
145
discretization (Wang et al., 2016; Han et al. 2015, 2017).
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Experimental apparatus The experimental setup is shown in Fig. 1 and it is well discussed in our recent article
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(Wang & Hu, 2016). It consists of a constant volume combustion vessel, a gas mixing system,
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a high-speed photography system, a high-voltage ignition system, and a data acquisition
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system. The combustion vessel is a horizontal explosion channel, with a transparent quartz
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glass on one side. The channel is closed at both ends with a square cross section of 20 mm ×
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20 mm, and the length is 1.5 m, which was filled with premixed methane–oxygen, shown as
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Fig. 1. The initial pressure in the channel was 33 kPa, and the initial temperature was also
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chosen to be 298 K. The ignition position was located at the left end of the channel. The spark
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igniter, pressure recorder, temperature recorder and high-speed video camera were controlled
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by the synchronization system.
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Results and discussions
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In our study, two-dimensional channel was used. The computational domain was 20 mm×
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1.5 m filled with stoichiometric methane-oxygen premixed gas. The boundary was a solid
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reflecting and no-slip wall. To ignite the mixture in the simulation, a circular region of hot
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burned material was placed at the left end of the channel while a small perturbation was
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further added to the burnt region. Initial velocity, temperature and pressure of 0.0 m/s, 298 K
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and 33 KPa, respectively were considered in the unreacted mixture. The validity of the
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numerical method and the tested convergence of the solutions with different mesh sizes (1,
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0.5, 0.2, 0.1 mm) were verified as shown in Fig. 2. When the grid resolution was 1.0 mm, the
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solution differs significantly from that obtained with the refine mesh, and the flame
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propagates faster than that of the experiment. As the mesh become finer, the results tend to
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converge. The results obtained with the grid resolutions of 0.2 and 0.1 mm were almost the
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same, and the position of the flame tip change with time, agree with the experimental results
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before DDT occurs.
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The flame tip speed obtained from the numerical calculation was also compared with the
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experimental results, as shown in Fig. 3. The overall trend of the curves was roughly the same.
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experimental results, there was a long acceleration period of the flame before an abrupt
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increase appears with the value of 2500 m/s at x~0.77 m which indicate the occurrence of
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DDT. The velocity further decays to 2300 m/s. In the numerical simulation, at the first stage,
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the flame accelerates exponentially with a rapid augmentation of the flame surface area as
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shown in Fig. 3. This phenomenon has been explained theoretically and confirmed by DNS
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and experimental studies by Liberman et al. (2011). During the second stage, the rate of flame
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acceleration decreases. It was noticed that, at a mesh size of 1 mm, the calculated flame
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velocity was larger than the experimental values before DDT occurs. While, with the finer
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mesh, the flame velocity tends to be close to the experimental values before DDT. The DDT
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run-up distance was slightly longer than that of the experimental result. This was because the
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simulation used 2D, while 3D was used for the experiment. Ivanov et al., (2013) observed that
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the flame velocity in 3D case is larger than that in 2D case, and the time of DDT is shorter in
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3D case compared to 2D due to extra dimension. In the stage of DDT, the flame velocity had a
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sharp increase, reaching the maximum value, and then decays to a steady value.
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Fig. 4 shows the process of flame acceleration and DDT for both the experiment and
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numerical results. Fig. 4a presents a high-speed image of the experiment while Fig. 4b shows
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the numerical results of temperature contours. After ignition, the initial laminar flame kernel
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expands, and then the flame gradually spreads to the right end of the channel, showing a
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fingerlike appearance. In this stage, the brightness of the flame surface was brighter, and then
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becomes dim along with the flame surface changing. As the flame propagates, a suddenly
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white light near the flame front appears, which means local explosion occurs. As shown in Fig.
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3, the flame velocity reaches the maximum value after a while. These explosions initiate the
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process of DDT, and the detonation front continue to propagate upstream while a retonation
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wave moves downstream. The white light gradually fill the channel, and the detonation and
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retonation propagation process are shown by the red lines. Similar to the experimental results,
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numerical results show the processes of flame acceleration, DDT, and the resulting detonation
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propagation can be seen from the temperature contours shown in Fig. 4b.
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Fig. 5 shows the temperature and pressure profiles in the flame front along the channel at a
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selected time interval. As the flame propagates forward, the thermal expansion of hot products
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induces the unburned gas to flow ahead of the flame. In this process, pressure waves are
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produced constantly. This lead to a small heating of the gas which is less than 500 K in the
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unburned material ahead of the flame, until the pressure is strong enough for DDT occur. Due
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forms, leading to the development of high flame speed. As time elapsed the shock waves are
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coalesced, merged, amplified and hence creating a layer of compressed and heated unreacted
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gas – which is the preheat zone (Liberman et al. 2009). This leads to more unburned mixture
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with higher density and temperature entering the flame front. Eventually, the flame front
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coincides with the leading shock, leading to the flame propagating as detonation waves.
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Fig. 6 shows the time-distance trajectory of the flame tip and the leading shock according to
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the numerical results. As the flame propagates to the right, it acts as a piston producing
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compression waves in the unreacted gas, which steepens into the shock waves far ahead of the
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flame front. The leading shock stands in front of the flame front, presenting a typical two
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waves and three regions structure. The distance between them is about two times of the
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channel width, which is less than Ivanov’s result (2013), five to seven times of the channel
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width. This might be as a result of too large calculating area used in the study with regards to
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the 2D model. The distance between them gradually decreases which tends to zero at about
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x=0.74 m at t~1.4ms. The flame accelerates constantly and becomes faster at t~1.4ms,
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corresponding to the velocity increase fast as shown in Fig. 3. Consequently, the flame
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catches up with and couples the leading shock, which leads to the overdriven detonation.
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The flame acceleration is not only related to pressure waves, but also to the flow field
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around flame front. After ignition of the flame kernel, initially, the weak compression waves
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move away and produces flow ahead of the flame with the velocity, approximately u = (Θ−1)U f ,
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Θ = ρu ρb ≈ 10 , where ρu and ρb indicate the density ratio of the unburned and burned gas,
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respectively (Zeldovich et al. 1985). Fig. 7 shows the flow field near the flame front at
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t=0.727 ms and 0.86 ms. The figure shows the velocity contours and the corresponding
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longitudinal velocity profiles (right part) in the cross section A and B. Owing to the wall
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friction, the flow velocity vanishes at the channel walls, and has maximal value at the center
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of the channel which exceeds 100 m/s. The flame surface is stretched gradually, which results
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in more fresh fuel being consumed. Higher burning velocity results in an enhancement of the
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flow velocity ahead of the flame, which in turn gives rise to a larger gradient field and boosts
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flame stretching. As the flame is stretched in the velocity field ahead of the flame front, a
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positive feedback coupling is established between the upstream flow and the burning velocity
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(Ivanov et al., 2013). Whiles it was realized that the flow velocity was dropping to zero at the
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channel walls, the flow ahead of the flame was uniform in the bulk. This is because, the time
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velocity profiles (i.e. the Poiseuille flow) (Kuznetsov et al., 2010). According to Zeldovich
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(1985), the estimated time of formation of a parabolic velocity profile in the upstream flow
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given as t = D 2 / υ , is similar to the magnitude obtained in (Liberman et al., 2009), i is larger
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than 10 s for the channel with width 20 mm. However, the duration of the whole process of
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DDT is in the range of 1 ms, which is shorter than the time required for the formation of a
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parabolic velocity profile in the upstream flow by many orders of magnitude.
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The streamlines near the flame front are drawn at some time instants, as shown in Fig. 8. It
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has been found that, upto the time of DDT, the flow ahead of the flame remains laminar, and
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only becomes unparalleled behind the flame surface. At t=1.31 and 1.39 ms, all the
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streamlines vanish in front of the flame, and this is because pressure waves steepen into shock
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waves in front of which there is no disturbance.
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The pressure and temperature distributions are presented in Fig. 9 in the process of DDT.
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The leading shock is located on the right side of the flame, and the preheating zone forms
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ahead of the flame front at t=1.31 ms (see Fig. 9a). The unburned mixtures were compressed
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and heated in the preheating zone by the increasing pressure. As a result, a larger amount of
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mixture enters the reaction zone, which enhance the reaction rate. These effects lead to
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stronger temperature and pressure gradient as a feedback. Under such interactive circumstance,
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it causes the formation of a shock wave directly ahead of the reaction zone, and these
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conditions lead to the coupling of the shock and the reaction zone, which results in the
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transition to detonation (Ivanov et al., 2011). Fig. 9b shows the change process of pressure
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contours. At t=1.35 ms, there was a high-pressure zone between the flame front and the wall.
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Then, a strong circular pressure wave could be seen caused by local explosion, triggering the
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transition from deflagration to detonation. Finally, the flame coupled with the leading shock,
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leading to the flame propagate as detonation waves.
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Fig. 10 shows the occurrence of local explosion and its process of development. When
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t=1.383 ms, there appears a local explosion near the wall that causes local pressure rises
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rapidly. The explosion waves propagate in the channel forming reverse detonation wave and
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transverse wave at t=1.39 ms. At the same time, this explosion wave propagates forward,
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catches up with the flame and collides with the precursor shock, triggering another stronger
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local explosion at t=1.396ms. Finally, a strong overdriven detonation forms, the flame
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coupling with the precursor shock propagates upstream, and another stronger reverse
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detonation wave propagates downstream, see Fig. 10 at t=1.401 and 1.405 ms.
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4. Conclusions LES method has been used to investigate the flame acceleration and DDT in small scale
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channels. The artificially thickened flame approach was adopted since the mesh scale is
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greater than the thickness of the flame. The comparisons of experimental and numerical
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results show that, applied method in this study is more effective and can capture the typical
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characteristic of flame acceleration and DDT.
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The flame velocity initially increase rapidly as a result of the stretching of the flame front
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within the boundary layer. The interaction between the flame and the flow field around the
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flame front establishes a positive feedback mechanism, promoting the flame propagation.
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Though the channel width is 20mm, the Poiseuille flow is not formed in front of the flame up
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to the time of DDT occurs, and the flow was always laminar.
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The fast acceleration of the flame is due to its coupling with the shock wave formed at the
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flame front. As the pressure increases, the leading shock is close to the flame front, and the
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preheating zone appears ahead of the flame, increasing the chemical reaction rate. Finally, the
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shock-wave complex near the wall becomes severe, which causes local explosion, and then
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triggers the process of DDT. Then, there appear retention waves propagating backward with
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detonation wave propagating forward.
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Acknowledgements
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This research is supported by the National Natural Science Foundation of China under grants
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11325209 and 11521062.
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hydrogen/air flame propagation in a closed duct. Int. J. Hydrog. Energy, 37: 11466-73. Yu, S., & Navarro-Martinez, S. (2014). Modelling of deflagration to detonation transition using flame thickening. Proc. Combust.Inst., 35(2), 1955–1961. Zbikowski M., Makarov D., Molkov V. (2008). LES model of large scale hydrogen–air planar
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detonations: Verification by the ZND theory. Int. J. Hydrog. Energy, 33(18): 4884-4892. Zeldovich YaB, Barenblatt GI, Librovich VB, Makhviladze GM. (1985). Mathematical theory of
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Figure captions
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Table 1 Physical parameters of the model system.
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Fig. 1. Sketch of experimental apparatus: (1) pure methane, (2) pure oxygen, (3) gas mixing device, (4)
ignition electrode, (5) horizontal channel, (6) high-speed video camera, (7) pressure and
390
temperature recorder, (8) data recorder, (9) synchronization controller, (10) spark igniter.
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Fig. 2. Comparison of the flame tip position-time evolution between experimental and numerical
results computed for different mesh, △x= 1, 0.5, 0.2 and 0.1 mm.
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Fig. 3. Flame tip velocity against distance along the channel for experimental and numerical results.
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Fig. 4. Flame acceleration and DDT occurs: (a) high speed video of experiment; (b) time interval of
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temperature contours of numerical results, △=0.5 mm.
Fig. 5. Evolution of temperature and pressure profiles corresponding to leading point along the
channel, time instants are from t=0.727 ms to 1.546 ms.
Fig. 6. Change of distance between the flame tip and the leading shock
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Fig. 7. Flow field ahead of the flame front at t=0.727 ms (A) and 0.86 ms (B) and corresponding velocity
400
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profile along the channel in the cross A and B.
Fig. 8. Flame structure and streamlines around the flame front at different times, t=0.86, 1.21, 1.31, 1.39ms
402
Fig. 9. Temperature and pressure contours at different times for transition to detonation: (a) the
404 405 406 407 408
temperature, and (b) the pressure.
Fig. 10. Pressure contours for local explosion and DDT.
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Table 1 Physical parameters of the model system Notations
Values
Initial pressure
P0
33 KPa
Initial temperature
T0
Initial density
ρ0
Polytropic exponent
γ
Molecular weight
M
Preexponential factor
A
Chemical energy release Activation energy 411
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Parameter
298 k
1.19 kg/m3 1.15
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0.027 kg/mol
1.21×1010 m3/Kg/s
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q
60 RT0/M
Ea
69 RT0
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Fig. 1. Sketch of experimental apparatus: (1) pure methane, (2) pure oxygen, (3) gas mixing device,
415
(4) ignition electrode, (5) horizontal channel, (6) high-speed video camera, (7) pressure and
416
temperature recorder, (8) data recorder, (9) synchronization controller, (10) spark igniter.
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Fig. 2. Comparison of the flame tip position-time evolution between experimental and numerical
425
results computed for different mesh, △x= 1, 0.5, 0.2 and 0.1 mm.
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Utip(m/s)
2000 1500
Experimental
1000
△=1 mm
△=0.2 mm
0 0
0.5
1
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500
1.5
Fig. 3. Flame tip velocity against distance along the channel for experimental and numerical results.
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Local explosion
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(b)
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Fig. 4: Flame acceleration and DDT occurs: (a) high speed video of experiment; (b) time interval of temperature contours of numerical results, △=0.5 mm.
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30 T p
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T(K)
3000
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15
1000
0
447
0.6 x(m)
0.8
5
1
channel, time instants are from t=0.727 ms to 1.546 ms.
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0.4
10
Fig. 5. Evolution of temperature and pressure profiles corresponding to leading point along the
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20
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1
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0.8
x(m)
0.6
Leading shock
0.4
Flame tip
0 1
1.1
1.3
1.4
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450 451
1.2
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0.2
1.5
1.6
Fig. 6. Change of distance between the flame tip and the leading shock.
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100 0 305
u(m/s)
80
0.05
0.1
x(m)
0.15
60
40
0.2
A
20
0
456
0.005
0.01 y(m)
0.015
0.02
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B
u(m/s)
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0.08
0.12
0.16 x(m)
0.01 y(m)
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corresponding velocity profile along the channel in the cross A and B.
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0.005
0.015
0.02
Fig. 7 Flow field ahead of the flame front (red line) at t=0.727 ms (A) and 0.86 ms (B) and
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0
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0.2
100
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Fig 8 Flame structure and streamlines around the flame front at different times, t=0.86, 1.21, 1.31, 1.39 ms.
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Fig. 9: Temperature and pressure contours at different times for transition to detonation: (a) the temperature, and (b) the pressure.
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Fig. 10: Pressure contours for local explosion and DDT.
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Highlights
Yongyao Zhao, Cheng Wang*, Yong Bi E-mail: [email protected]
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LES of flame acceleration and DDT in small-scale channels
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(1) FA and DDT in small-scale channels are investigated with LES and experimental method.
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(2) The interaction of the flame with the flow field and the pressure wave is the main mechanism for flame acceleration.
(3) The flow ahead of the flame always keeps laminar up to the time of DDT occurs. (4) Local explosion triggers the DDT and causes the retonation wave propagates
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downstream.