Chemical Explosive Mode Analysis for Local Reignition Scenarios in

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Chemical Explosive Mode Analysis for Local Reignition Scenarios in H2/N2 Turbulent Diffusion Flame Lei Wang, Yong Jiang, and Rong Qiu Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b03175 • Publication Date (Web): 16 Aug 2017 Downloaded from http://pubs.acs.org on August 21, 2017

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Chemical Explosive Mode Analysis for Local Reignition Scenarios in H2/N2 Turbulent Diffusion Flame Lei Wang, Yong Jiang * and Rong Qiu State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui, PR China KEYWORDS: Reignition; Extinction; Chemical explosive mode analysis; One-dimensional turbulence; Hydrogen syngas.

ABSTRACT: Local reignition scenarios in H2/N2 turbulent diffusion flame are investigated using one-dimensional turbulence (ODT) model and chemical explosive mode analysis (CEMA). Through analogy with the flame fronts in homogeneous ignition and laminar premixed flame, four reignition scenarios are distinguished and analyzed by CEMA. Results show that reignition scenario via premixed flame propagation corresponds to high temperature explosion index, and the reignition process is segmentally dominated by the reactions relating to the consumption and production of hydrogen radical. While reignition mode through independent flamelet corresponds to high radical explosion index, and the whole reignition process is dominated by the production reaction of hydrogen radical. When these two reignition processes are terminated by turbulent eddies, hybrid reignition process or reignition scenario through turbulent flame

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folding may occur, and turbulent folding mode corresponds to high dissipation rate and obvious temperature jump near the end of reignition process. In addition, statistical analysis shows that the premixed flame propagation mode have more effective to ignite the fluid parcel with low temperature, and the reignition scenario via independent flamelet is a quicker process.

INTRODUCTION As hydrogen and synthesis gas is a clean and efficient energy with a significantly reduced impact on the environment, it has been recognized as an attractive fuel in the future.1 Considering the safe operation of hydrogen and syngas fuel, the behaviors of local extinction and reignition should deserve attention. Flame extinction usually exists in the zones with high strain, and these regions may reignite when turbulent strain rates decrease. Reignition of extinction fluid parcels may occur through several possible modes, such as auto-ignition, premixed flame propagation, edge flame propagation and turbulent flame folding.2 Various experiments have been carried out to investigate the characteristics of auto-ignition and edge flame.3-5 There have also been many numerical studies on local extinction and reignition by using Direct Numerical Simulation (DNS),2, 6-8 Large Eddy Simulation (LES)9, 10 and one-dimensional turbulence (ODT) model.11, 12 Such as, Sripakagorn et al.7 performed DNS and Lagrangian flame element tracking technique to investigate reignition scenarios from temporal perspective. Garmory and Mastorakos10 performed LES-CMC to predict localized transient extinction and reignition events in piloted jet diffusion flames. Hewson and Kerstein11 investigated the local extinction and reignition with statistical strategy by using the ODT mode. In this work, the ODT mode is used to investigate the local reignition events from statistical and temporal perspective. Comparing with DNS and LES, the one-dimensional turbulence model, which solves unfiltered reaction-diffusion equations in one dimension with stochastically-


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modeled turbulent advection, may be treated as an intermediate role with the compromise for computational efficiency.13 In the ODT model, one or more velocity components are solved and applied to calculate the size and frequency distribution of the eddy events, enabling a mechanism for driving turbulence. As a standalone model, ODT has been applied to investigate various combustion issues.11-16 Remarkably, the ODT model can provide a fundamental understanding of extinction and reignition from spatio-temporal perspective12, and yield good agreement with state-space statistics obtained from DNS.13, 15 In addition, it also has been applied as a subgrid closure model in LES17 and RANS.18 In the numerical investigation, the extinction states and reignition scenarios are usually diagnosed by temperature7,

19

or some radicals20. These simple extinction criterions may be

unsuitable in high turbulent strain rate regions and unsteady cases.21, 22 In order to distinguish reignition scenarios more systematically, Chemical Explosive Mode Analysis (CEMA) and local Damköhler number are applied in detailed chemical kinetic systems. CEMA is based on the eigenvalue analysis of the chemical source terms, and is simple to perform. As an efficient diagnosis tool, CEMA has been used in diverse reacting flow simulations, such as turbulent lifted jet flame23, 24 and turbulent piloted diffusion flame.9 Past work of our group was focused on the diagnostic of extinction and reignition scenarios based on chemical explosive mode analysis.25, 26 In this work, the ODT model is used to capture local reignition phenomena from temporal perspective. Controlling chemistry of species and reactions for reignition scenarios are presented by CEMA, and the influences of eddy events for reignition processes are discussed. Meanwhile, some statistical characteristics of reignition modes are also investigated. METHODOLOGY


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One-dimensional turbulence model A detailed description of the ODT model for turbulent jet flame are given by Kerstein et al.14, 27

and Jiang et al.28, 29 In the ODT formulation, reactive-diffusive processes (solving governing

equations) and turbulent advection (modeling by eddy events) are addressed separately on a time resolved 1D domain. The governing equations formulated in Lagrangian reference frame can be expressed as

∂u 1 ∂ ∂u = (µ ) ∂t ρ ∂y ∂y

(1)

∂Yk 1 ∂ 1 =− (ρVkYk ) + Wkω&k ∂t ρ ∂y ρ

(2)

∂T 1 =− ∂t cp

N

∑ c pkYkVk k =1

∂T 1 ∂ ∂T 1 + (λ )− ∂y ρ c p ∂y ∂y ρcp

N

∑h W ω& k

k

(3)

k

k =1

where all the symbols have their usual meanings. The pressure is assumed to be constant in the simulation. The state equation, which can be used to determine the mixture density, is expressed as N

Yk k =1 Wk

p = ρ RuT ∑

(4)

where R u is the universal gas constant. In one dimension, mass conservation requires that ρ dy should be constant. Therefore, the dilatation treatment of the grid should be implemented at the end of each time step.12 The downstream spatial evolution (

x

direction) is interpreted by

temporal evolution using the following equations t

x(t ) = ∫ u (τ )dτ

(5)

0

+∞

u − u∞ = ∫ ρ (u − u∞ )2 dy −∞

∫

+∞

−∞

ρ(u − u∞ )dy

(6)


4

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where u and u∞ are bulk velocity and coflow velocity, respectively. As mentioned above, the turbulent advection can be modeled stochastically by eddy events, each involving the application of a triplet map. The triplet map is implemented to model the effects of a three-dimensional eddy with a one-dimensional rearrangement. This strategy can, to a certain degree, reflect the mechanism of rotational folding, flame curvature, flame-flame interactions and break-up flame structure.14 The triplet map can be represented as for  3( y − y0 )  2l − 3( y − y ) for  0 f ( y , y0 , l ) =  3( y − y0 ) − 2l for  y − y0

y0 ≤ y < y0 + l 3 y 0 + l 3 ≤ y < y 0 + 2l 3 y 0 + 2l 3 ≤ y < y 0 + l

(7)

otherwise

where y 0 and l are the position and size of the mapping eddy, respectively. The velocity is applied to calculate the size and frequency distribution of the string events, enabling a mechanism for driving turbulence. The eddy timescale method is used for large eddy suppression, which means that a stirring event with a turnover time longer than the elapsed simulation time should be prohibited in the simulation. Two model parameters, the so-called A and β , are identical to previous investigations ( A = 0.334, β = 1.45 ). The temporal discretization of the governing equations is based on splitting method. The diffusion term is integrated using a second-order explicit finite differencing scheme, while the source term is evaluated by using VODE30 integrator. Transport properties and the reaction process are calculated by the Chemkin II code.31 The results of our ODT code can reproduce the experiment values with good accuracy, and the details of validation is giving in our past work.28 Chemical explosive mode analysis For a general chemically reactive system, the conservation equations can be rewritten in the following form:


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Dy = ω(y) + s(y) Dt

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(8)

where ω (y ) and s(y) denote the chemical source term and the mixing source term, respectively.

y is the local state vector of the dependent variables, such as temperature and species concentrations. The full Jacobian matrix is comprised of the contributions from chemical source and mixing source. CEMA is an eigenvalue analysis of the chemical source Jacobian for a localized state. As elements and energy are conservative, the chemical Jacobian always involves

M +1 conservative modes which can be easily identified and excluded, where M is the number of participating elements.32 The real parts of the residual eigenvalues are assumed to be sorted in descending order without loss of generality, and the first eigenvalue is defined as λ e . The eigenmode corresponding to λ e is denoted as a chemical explosive mode (CEM) if its associated eigenvalue has a positive real part ( R e ( λ e ) > 0 ). The existence of chemical explosive mode means that local mixture tend to auto-ignite if it is put in an isolated environment (adiabatic and constant volume).24 And the transition of a CEM between explosive and non-explosive mode is strongly correlated with limit flame phenomena, such as ignition, extinction, and premixed flame front locations.24, 33 In order to quantify the normalized contribution of each variable (species and temperature) of the CEM, the vector of Explosion Index (EI) can be defined by

EI =

ae ⊗ beT

(9)

sum(| ae ⊗ beT |)

where a e and b e are the right and left eigenvectors of the eigenmode related to λ e , respectively.

⊗ and

denote element-wise multiplication and their absolute values, respectively. To

quantify the contribution of each reaction, the Participation Index (PI), which is defined in computational singular perturbation34 with ignoring the sign and error term, can be expressed as


6

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PI =

(be • S) ⊗ R

(10)

sum(| (be • S) ⊗ R |)

where S and R are the stoichiometric coefficient matrix and the vector of net rates, respectively. It should be noted that S includes a column associated with the heat release of each reaction, since temperature is a variable included in y . In order to analyze the reignition phenomena, a Damköhler number defined by chemical and mixed timescale is used. In this work, the local chemical timescale is evaluated by CEM time based on eigenvalue analysis, and the similar methods are also mentioned by Isaac et al.35 Since a turbulent diffusion flame is investigated, the reciprocal scalar dissipation rate at stoichiometric condition can be used as the mixing timescale. Therefore, the Damköhler number is defined as

Da =

− Re ( λe )

χ st

=

− Re ( λe )

(11)

2

2 DT ∇Z z = z

st

where Z and D T are the mixture fraction (in Bilger’s formula36) and the mixture local thermal diffusivity, respectively. The subscript s t denotes the stoichiometry condition. By this definition, which is also used by Lecoustre et al.,33 the Damköhler number of local mixture can be a negative or a positive value. When the CEM is present, the real part of λ e is positive and D a < 0 , otherwise D a > 0 . A small Damköhler number, regardless of the sign, means CEM is

much slower than the mixing process, which corresponds to a slowly reacting state. A large negative Damköhler number corresponds to a state where the reaction is in an explosive mode, while a large positive value indicates that the system is chemically approaching an equilibrium. Since D a spans several orders of magnitude and can have a negative value, the modified logarithm expression, which is a convenient way of representation, can be expressed as

f ( Da) = − sign(Re ( λe ))log10 (max(1,| Re ( λe ) / χst |))

(12)


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where sign() is the signum function. By this definition, the chemical explosive state (unstable state) can be described as f ( D a ) < 0 , while the stable burning state can be described as f ( D a ) > 0 . Furthermore, the slowly reacting state is denoted as f ( D a ) = 0 .

Table 1. H2/N2/O2 chemical mechanism k = ATbexp(-E/RT) A(cm, mol, s, K) b E(cal/mol) R1 H+O2=O+OH 3.55E+15 -0.4 16600.0 R2 O+H2=H+OH 5.08E+04 2.7 6290.0 R3 H2+OH=H2O+H 2.16E+08 1.5 3430.0 R4 O+H2O=OH+OH 2.97E+06 2.0 13400.0 R5 H2+M=H+H+Ma 4.58E+19 -1.4 104000.0 a R6 O+O+M=O2+M 6.16E+15 -0.5 0.0 4.71E+18 -1.0 0.0 R7 O+H+M=OH+Ma a R8 H+OH+M=H2O+M 3.80E+22 -2.0 0.0 k∞ 1.48E+12 0.6 0.0 R9 H+O2+M=HO2+Mb ko 6.37E+20 -1.72 520.0 R10 HO2+H=H2+O2 1.66E+13 0.0 820.0 R11 HO2+H=OH+OH 7.08E+13 0.0 300.0 3.25E+13 0.0 0.0 R12 HO2+O=O2+OH R13 HO2+OH=H2O+O2 2.89E+13 0.0 -500.0 c R14 HO2+HO2=H2O2+O2 4.20E+14 0.0 12000.0 1.30E+11 0.0 -1630.0 HO2+HO2=H2O2+O2 d R15 H2O2+M=OH+OH+M k∞ 2.95E+14 0.0 48400.0 1.20E+17 0.0 45500 ko 2.41E+13 0.0 3970.0 R16 H2O2+H=H2O+OH R17 H2O2+H=HO2+H2 4.82E+13 0.0 7950.0 R18 H2O2+O=OH+HO2 9.55E+06 2.0 3970.0 R19 H2O2+OH=HO2+H2Oc 1.00E+12 0.0 0.0 H2O2+OH=HO2+H2O 5.80E+14 0.0 9560.0 a Efficiency factor: ƐH2O=12 and ƐH2= 2.5. b Troe parameter: Fc=0.8. Efficiency factor: ƐH2O=11, ƐH2= 2 and ƐO2= 0.78. c R14 and R19 are expressed as the sum of the two rate expressions. d Troe parameter: Fc=0.5. Efficiency factor: ƐH2O=12 and ƐH2= 2.5. NO

Reaction

Computational configuration In this work, two hydrogen syngas turbulence diffusion flames (H3 and H5) are simulated using ODT model. The temperature and major species concentrations for two flames have been


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measured by Meier et al.,37 and the same configurations are used in the simulation. The burner inlet diameter ( D ) for fuel jet is 0.008 m, and the fuel composition is 50% H2 and 50% N2 by volume. The jet velocity ( u je t ) for H3 and H5 flame is 34.8 m/s and 21.7 m/s, respectively. The fuel jet Reynolds number is 10,000 and 6200, respectively. The inlet velocity of coflow (dry air) is fixed at 0.3 m/s. The grid size is set as 0.1 mm, since further refinements in the resolution do not alter the statistics of the computed variables. The above system is modeled using a detailed chemical mechanism38 which has 9 species and 19 reactions (Table 1). Thermochemical scalars at the inlet are initialized with a laminar strained flame by OPPDIF39 code. The inlet velocity profile at the fuel nozzle exit is obtained by fully developed turbulence. RESULTS AND DISCUSSION Flame front diagnosis

0.2

P = 1atm T0 = 1100K

-1

1.8

0.3

0.1 0.0

1.5

-0.1

1.2

-0.2 Thermal runaway

T H

H2 O2

0.6 0.3

Radical explosion

2.1 1.8

λe

0.3 0.2

P = 1atm T0 = 1100K

0.1 0.0

1.5

-0.1 1.2

-0.2 T H Thermal runaway

0.6 0.3

H2 O2

Radical explosion

0.0

0.0 60

Temp

0.9 Explosion Index

0.9

0.4 (b) PHI=1.2

-1

2.1

2.4

0.4

λe (µs )

λe

3

Temp

Temperature (10 K)

(a) PHI=0.8

λe (µs )

3

Temperature (10 K)

2.4

Explosion Index

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Energy & Fuels

70

80

90

60

70

80

90

Residence time (µs)

Residence time (µs)

Figure 1. Temperature, CEM timescale and explosion indices in auto-ignition of hydrogen–air mixtures at different equivalence ratios. First of all, CEMA is used to detect the scenarios of flame front in homogeneous ignition and laminar premixed flame. Figure 1 shows the temperature, CEM timescale and explosion indices in auto-ignition of hydrogen–air mixtures at different equivalence ratios. As mentioned above,


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Energy & Fuels

the zero-crossing of the real part of the CEM is strongly correlated to flame front. As shown in the figure, the ignition processes contain two stages. In the first stage (namely radical explosion), the ignition process is dominated by hydrogen radical, and the contribution of temperature is negligible. However, in the second stage (namely thermal runaway), the temperature is a remarkable controlling factor and the contribution of hydrogen radical declines. The two ignition stages can be divided at the point where the explosion index of temperature is larger than that of hydrogen radical. The similar results are also mentioned by Lu et al.23, 40 0.2

-1

1.2

0.0

0.8 -0.1 T H

Thermal runaway

0.6

0.0

0.8 -0.1

0.6

0.3

0.2 0.1

0.4 0.9

H2 O2

λe

1.2

Explosion Index

0.4 0.9

Temp

(b) PHI=1.2 2.0 P = 1atm T = 1100K 1.6 0

-1

3

0.1

1.6

T H

H2 O2

Thermal runaway

0.3

0.0 0.08

2.4

λe (µs )

λe

Temp

Temperature (10 K)

(a) PHI=0.8 2.0 P = 1atm T0= 1100K

λe (µs )

3

Temperature (10 K)

2.4

Explosion Index

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.0

0.10

0.12

0.14

0.08

X (cm)

0.10

0.12

0.14

X (cm)

Figure 2. Temperature, CEM timescale and explosion indices in 1D freely propagating laminar premixed flames of hydrogen–air mixtures at different equivalence ratios. In contrast with the homogeneous ignition, there is no radical explosion stage in onedimensional laminar premixed flame (Fig. 2). Since the CEM only exists in the region where the mixture is pre-ignition, the entire preheat zone is dominated by temperature, although the hydrogen radical still moderately participates in these processes. It means that the distinction of explosion index in ignition process is useful in diagnosing whether a flame front is controlled by auto-ignition or premixed flame propagation. As explosive mode is a chemical property of the mixture, this method can also be used to analyze flame fronts in turbulent flame.40


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Local extinction and reignition criterion The results of our ODT code can reproduce the experiment values with good accuracy. Figure 3 shows the conditional statistics for temperature and major species mass fractions of two simulated flames. It can be found that the means of oxygen and hydrogen mass fractions are in excellent agreement with the experimental data measured by Meier et al.37,

41

Although the

means of temperature are a little low predicted for both flames in the lean regions, there are no significant distinction in magnitude. The details of validation for ODT code though the comparison of H3 flame is giving in our past work.28 2.1

0.5

2.1

1.8

0.4

1.5 0.3 1.2 0.2

O2 H2(x10)

Temp

0.20

1.5 0.15 1.2 0.10 0.9

Y(O2) , Y(H2)

Temp

Y(O2) , Y(H2) 3 Temperature (10 K)

3

Temperature (10 K)

1.8

0.9

0.25

(b) X/D=40,H3 Flame

(a) X/D=20,H3 Flame

H2(x10)

O2

0.1

0.05

0.6

0.6

0.0

0.3 2.1

0.00

0.3 2.1

0.5

0.25

(d) X/D=40,H5 Flame

(c) X/D=20,H5Flame 1.8

Temp

1.8

0.4

0.20

0.3 1.2 0.2 0.9

O2

0.0 0.2

0.4

0.10 0.9

O2

H2(x10)

0.05

0.6

0.3 0.0

0.15 1.2

0.1

H2(x10)

0.6

1.5

Y(O2) , Y(H2)

3

1.5

Y(O2) , Y(H2) 3 Temperature (10 K)

Temp Temperature (10 K)

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Energy & Fuels

0.6

Mixture Fraction

0.3 0.0

0.00 0.1

0.2

0.3

0.4

Mixture Fraction

Figure 3. Conditional statistics for temperature and major species mass fractions. Symbols are measured values and curves are ODT results. To investigate the mechanism of the reignition scenarios in turbulent diffusion flame, the burning criterion should be defined at the beginning. As mentioned above, the local Damköhler number calculated by CEMA is applied as a diagnosis strategy. This method has been used and verified by Lecoustre et al.,33 and a comparison with the extinction diagnosis through critical


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temperature12 ( T c , Z = Z

st

< 1000 K

Page 12 of 28

) is shown here for qualitative analysis. Figure 4 shows the

scatter plots of temperature for two simulated flames. The stable burning state, chemical explosive state and slowly reacting state are presented in gray, red and blue, respectively. The stoichiometric zone ( 0.875Z st < Z < 1.125Z st ) is also marked in the Figure. As shown in Fig. 4c and 4f, most of gray points in the stoichiometric zone are above the dashed line, which means that there is no significant distinction of stable burning state diagnosed by two strategies in the far-field zones. However, the distinction between two diagnosis methods is remarkable in the near-field zones. As described in Fig. 4a and 4d, a large number of red points in stoichiometric zone are identified as stable burning state by the criterion of critical temperature. One significant reason is that the instantaneous strain may exceed the extinction limit, without the flame being extinguished in unsteady configuration.21, 22 And this influence may be significantly strengthened in high strain region of turbulent jet flame.

Figure 4. Scatter plots of temperature in H3 and H5 flames. Stable burning state, chemical explosive state and slowly reacting state are presented in gray, red and blue, respectively.


12

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Energy & Fuels

In addition, a quantitative comparison based on fully burning probability42 is also presented. Figure 5 shows the probability density function (PDF) and fully burning probability (FBP) for two flames. These statistical variables are calculated within a narrow band ( 2 ∆ ξ

= 0 .0 4

) of

mixture fraction centered on the location of maximum temperature. There are two ways to calculate FBP. One is based on threshold temperature ( T > T th ), and the other is based on Damköhler number ( f ( D a ) > 0 ). As shown in Fig. 5a, there is a skewing to high temperature region in H5 flame, which corresponds to more stable burning mixtures at the same axial position for the low Reynolds number configuration. To calculate FBP, threshold temperature is set to 1450K since this value is a good trade-off to detect extinction state in Fig. 5a. As described in Fig. 5b, the agreement between two methods is excellent in far-field region, while higher FBP based Damköhler number can be seen in the near-field region. This distinction is also attributed to high turbulent strain and unsteady effects. In contrast with the diagnostics method with threshold temperature, the strategy based on Damköhler number, involving all mixing and thermodynamic data, may provide more turbulence-chemistry information. In addition, it is also an effective method to quantify the contributions of reactions and species for local mixture. In order to investigate the temporal evaluation of complex turbulent combustion process, Lagrangian tracer strategy is applied in the ODT model. The transverse velocity of Lagrangian particles is idealized to be zero everywhere except at the regions with string events. In addition, the tracer particle should also have an instantaneous jump following the ODT fluid element due to the effect of triplet maps. As the dilatation treatment of the grid is implemented at the end of each time step, the corresponding transverse velocity of the tracer particle is also added in this process. The details of the particle-eddy interaction for ODT mode is described by Schmidt et al.43, 44


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Energy & Fuels

1.0

(a)

(b) X/D=05, H3 X/D=05, H5 X/D=10, H3 X/D=10, H5

0.09

flame flame flame flame

Based on temperature in H3 flame Based on Da in H3 flame Based on temperature in H5 flame Based on Da in H5 flame

0.8 Fully Burning Probability

Probability Density Function

0.12

0.06

0.03

0.00

0.6

0.4

0.2

0.0

1000

1200

1400

1600

1800

2000

2

4

6

8

Temperature (K)

10

12

14

X/D

Figure 5. Probability density function and fully burning probability within a narrow band in

1600

Temperature Variation

1200

#

Temp

t2

t5

2

t1

0

∆T=600K

800

4

t4

Da

∆t=1.4*tjet

400

Preheat Duration (explosive state)

-2

∆t=0.3*tjet

-4 (b)

1200

SDR

MF

t4

t3

t2

800

0.6

t5 t6

t1

400 0

-3 -1

0.3 0.0

8000

(c)

t1

6000

Heat Release Rate Normalized Thermal Diffusion

t2

t4

4000

0.1

t5 0.0

2000

-0.1

0 0

2

4

6

t / tjet,H3

8

f(Da)

(a) Particle 63

2000

Thermal Diffusion Mixture Fraction

-1

SDR (s )

Temperature (K)

mixture fraction.

HRR (J cm s )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 28

10

Figure 6. Temporal evolution of temperature, Da , mixture fraction, SDR, HRR and normalized thermal diffusion term for Lagrangian particle from the coflow in H3 flame ( t j e t

= D /u

je t

).

Figure 6 shows the temporal trajectories of temperature, Da , mixture fraction, scalar dissipation rate (SDR), hear release rate (HRR) and thermal diffusion term (normalized by the parameters of jet mixture) for Lagrangian particle. As mentioned above, a large positive


14

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Energy & Fuels

Damköhler number ( f ( D a ) > 0 ) corresponds to stable burning state, while a large negative Damköhler number ( f ( D a ) < 0 ) corresponds to unsteady explosive state. As shown in the figure, there are many oscillations of Da , due to the combined effect by mixing and reaction. Notably, when the trajectory of Da crosses the dashed line, the moment of this oscillation correlates to the state change of local mixture. For example, since the sign of f ( Da ) changes at t4 (Fig. 6a), it clearly shows that the state of the Lagrangian particle moves to an unstable region of phase space near the middle branch of the S-Curve. Meanwhile, as the state of the particle changes from unsteady state to stable burning at t2 and t5, the two moments can be recognized as the occurrence of local reignition. It should be noted that there are significant distinctions of the temperature variation, preheat duration (explosive state), scalar dissipation rate and thermal diffusion term between two reignition processes. These distinctions usually correspond to different reignition mechanisms which are analyzed by CEMA in below. Local Reignition scenarios In our previous work, two reignition scenarios (premixed flame propagation and auto-ignition) are defined by explosive index of CEMA.25 In this work, the controlling chemistry analysis based on CEMA is presented for further verification of these reignition mechanisms. Then the influences of turbulent eddy events for reignition processes are discussed, and other reignition modes are investigated. At last, some important characteristics of reignition processes are analyzed from statistical perspective.


15

Explosive state

0.6 0.9

T H

(b)

H2 O2

0.6 0.3 0.0 0.6

(c)

R09

0.4

R01 R08

R02 R09

R03 R11

0.2 0.0 2.5

2.6

2.7

2.8 2.9 t / tjet

3.0

3.1

3.2

Temp

(d)

0.2

λe

0.1

1.6

PHI=1.0 p=1atm T0=300K 0.0

1.2 0.8

-1

2.0

Page 16 of 28

λe (µs )

2.4

3

f (Da)

t1

0.8

Temperature (10 K)

Temperature variation ∆T=600K

3 2 1 Reignition, t2 0 -1 -2 -3 Da

Explosion Index

1.2 1.0

Temp

(a)

Participation Index

1.4

3

Explosion Index Participation Index

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Temperature (10 K)

Energy & Fuels

-0.1

0.4 0.6

T H

(e)

H2 O2

0.4 0.2 0.0

0.4

(f) R01 R08

0.2

R02 R09

R03 R11

0.0 0.09

0.10

0.11

0.12

0.13

X (cm)

Figure 7. Reignition scenario via premixed flame propagation. (a-c) Temporal evolution of temperature, Da , EI and PI for trace particle from t1 to t2 in H3 flame. (d-f) Temperature, λ e , EI and PI in 1D freely propagating laminar premixed flame of a stoichiometric H2/N2–air mixture. Figure 7 shows the temporal evolution of the temperature, Da , EI and PI for reignition particle from t1 to t2 in H3 flame. As shown in the figure, firstly, the temperature variation, which is defined as the difference value between the minimum temperature in the reignition process and the temperature at reignition moment, is large for this reignition scenario (about 600K). Secondly, the preheat duration, which is defined as the explosive state duration before reignition, is obviously longer than the jet time scale. And lastly, temperature with high explosion index is a dominant factor in the whole preheat process, although hydrogen radical still moderately participates (Fig. 7b). This is similar with typical premixed flame front (Fig. 7e), which also corresponds to high temperature explosion index when CEM is exist. To determine the dominant chemistry of this reignition scenario, the participation indices of main elementary reactions are also presented. These reactions can be divided into two categories:


16

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Energy & Fuels

the production of hydrogen radical (R2 and R3) and the consumption of hydrogen radical (R1, R9 and R11). R1 is the chain branching reaction increasing the amount of radicals in the radical pool, along with R2 and R3. While R9 is the main path for the production of HO2 radical which is less reactive and leads to the reduction of the reactivity of the system.45, 46 As shown in Fig. 7c, R9 is dominant at the preheat zone with low temperature, while the preheating process with high temperature is mainly controlled by R3. This feature is also similar with the ignition process of laminar premixed flame (Fig. 7f). Therefore, it can be recognized that the reignition of the fluid parcel is due to premixed flame propagation,2,

7

which occurs in a partially premixed mode

through a non-homogeneous mixture of varying stoichiometry and temperature. 2 2 To further verify this reignition mode, thermal diffusion term ( i p = DT ( ∂ T ∂y ) ), which

has been used to evaluate the effect of neighbouring flame elements and diagnose reignition scenarios by Sripakagorn et al.,7 is also analyzed (Fig. 6c). Instead of flame index, CEMA is used to define the burning state of the local mixture. As shown in Fig. 6c, positive diffusion term and unsteady burning state can be found in the premixed propagation process (from t1 to t2), and the similar results are also mentioned by Sripakagorn et al. In addition, this reignition scenario also corresponds to local maximum for HRR, small scalar dissipation rate and little variation in mixture fraction (Fig. 6b), which are coincident with the previous investigation in reignition mode via premixed flame propagation.2 In contrast, Fig. 8 shows another reignition mechanism which is called as independent flamelet. As shown in the figure, firstly, there is little variation of temperature in the entire reignition process of the fluid parcel (Fig. 8a). Secondly, the preheat duration (from t4 to t5) for this reignition mode is obviously shorter than the jet time scale. And lastly, the hydrogen radical with high explosion index dominates the mainly ignition process, and the transient thermal


17

Energy & Fuels

runaway zone can also be found near the reignition moment (Fig. 8b). This is similar with the homogeneous ignition (Fig. 8e), which is controlled by hydrogen radical with a relatively thin

Reignition, t5

Explosive state duration, ∆t=0.3*tjet,H3

0 -2

1.3

0.6

Thermal runaway

0.3

Participation Index

0.0 0.6

(c) R01 R08

0.4

R02 R09

R03 R11

0.2 0.0 9.0

9.1 t / tjet,H3

9.2

(d)

2.4

9.3

Temp

λe

T H

H2 O2

0.4 0.3 0.2 0.1 0.0 -0.1 -0.2

PHI=1.0 P=1atm T0=1100K

2.0 1.6 1.2 0.8

H2 O2

Explosion Index

T H

(b)

2.8

-1

Temperature variation,∆T=20K

f (Da)

2

λe (µs )

Da

3

Temp

Burning, t4

0.9 Explosion Index

(a)

Temperature (10 K)

1.4

3

Temperature (10 K)

thermal runaway region near the very end of the preheating process.

Participation Index

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 28

(e)

0.6

Thermal runaway

0.4 0.2 0.0 0.6

(f) 0.4

R01 R08

R02 R09

R03 R11

0.2 0.0 60

70 80 Residence time (µs)

90

Figure 8. Reignition scenario via independent flamelet. (a-c) Temporal evolution of temperature,

Da , EI and PI for Lagrangian particle from t4 to t5 in H3 Flame. (d-f) Temperature, λ e , EI and PI in auto-ignition of a stoichiometric H2/N2–air mixture. For dominant chemistry of this reignition mode, R3 is the dominant reaction in the whole reignition process, although R1 and R2 still moderately participates in the explosion region (Fig. 8c). This characteristic is also similar with the process of auto-ignition which is shown in Fig. 8f. Therefore, we can recognize that the reignition of the fluid parcel is due to the properties of independent flame element, and this reignition scenario can be called as independent flamelet7 or auto-ignition2, 47. In addition, this reignition process corresponds to negligible thermal diffusion term and unsteady burning state (Fig. 6c), which are coincident with the results of Sripakagorn et al.7 In contrast with premixed flame propagation, four remarkable features can be found in the reignition scenario via independent flamelet: high radical explosion index, complete control by


18

Page 19 of 28

R3, small temperature variation and rapid reignition process. The last two characteristics of

50 Temp

Da

Reignition,t7

2 0 -2

0.6 H2

H

O2

0.3 0.0 3.15

3.20

3.25

3.30

3.35

3.40

Position

3.45

1.10 1.05

Stirring event in ODT

1.00 0.95

0 1.5

0.90 Burning,t8

1.2

Reignition,t9 Temp Da Turbulent flame folding through eddy event

0.9

2 0 -2

0.6 Explosion Index

0.4 T

SDR

50

Turbulent flame folding through eddy event

0.8

#

(b)particle141

100

-1.16

1.2

3.10

150

Temp (10 K)

Temp (103K)

0 1.6

-1.12

200

Y/D

Stirring event in ODT

Y/D

100

-1.08

f (Da)

Position

3

150

SDR

#

(a)particle56

f (Da)

SDR (s-1)

200

SDR (s-1)

independent flamelet mode are also mentioned in the previous investigation.7

Explosion Index

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.9

T H

H2 O2

0.6 0.3 0.0 4.04 4.06 4.08 4.10 4.12 4.14 4.16 4.18 4.20 t / tjet,H3

t / tjet,H3

Figure 9. Reignition scenario via turbulent flame folding. (a-b) Temporal evolution of scalar dissipation rate, position, temperature, Damköhler number and EI for Lagrangian particles in H3 flame. The shadow regions correspond to stirring events. In addition, due to turbulent effects, there may be some eddy events terminating the current reignition scenario of fluid parcel. Figure 9 shows the temporal evolution of two Lagrangian particles which encounter eddy events in the reignition processes. As shown in the figure, before the occurrence of stirring event in the ODT domain, the dominant factor of the reignition process is temperature (Fig. 9a) or H radical (Fig. 9b). As analyzed above, the reignition process corresponds to premixed flame propagation and independent flamelet, respectively. Then, these processes are terminated by stirring events which can be reflected by the change of positions in the ODT domain. After that, the local scalar dissipation rates increase and the stable burning states appear in a very short time. We attribute this reignition scenario occurring by turbulence folding burning sections onto non-burning ones, and this important reignition mechanism is


19

Energy & Fuels

called as turbulence flame folding which is also mentioned by Lignell et al.2 and Hawkes et al.8 In contrast with two reignition scenarios mentioned above, reignition mechanism through turbulence folding always corresponds to high dissipation rate and obvious temperature jump near the very end of ignition process.

0

1.0 String eddies

0.9

-2

0.8 Position

T

0.96

H

Premixed mode

0.6

Auto-ignition mode

0.92 0.90

0.3

0.88 0.0 3.65

0.86 3.70

3.75

3.80

3.85

Temp

#

(b) Particle 81

Da

2

1.2 String eddies

1.0

0

0.8 -2

0.6 1.0

0.94 Y/D

0.9

f (Da)

1.1

f (Da)

2

0.8

Position

T

-0.7

H

Premixed mode

Premixed mode

-0.8

0.6 -0.9

0.4

Premixed mode

-1.0

0.2 0.0 1.4

Y/D

Da

3

Temp

Explosive Index

#

Temperature (10 K)

1.4 (a) Particle 115

3

Temperature (10 K)

1.2

Explosive Index

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 28

1.6

1.8

t / tjet,H3

2.0

2.2

2.4

2.6

2.8

3.0

3.2

-1.1 3.4

t / tjet,H3

Figure 10. Hybrid reignition process induced by string events in ODT. (a-b) Temporal evolution of temperature, Damköhler number, position and EI for Lagrangian particles in H3 flame. The shadow regions correspond to stirring events. However, not all of eddy events in ODT can induce the occurrence of reignition phenomena. Figure 10 shows the temporal evolution of two Lagrangian particles which also encounter eddy events in reignition processes. As shown in the figure, reignition mode via premixed flame propagation can be found in the early stage, due to high temperature explosive index. After that, the reignition processes are terminated by eddy events. However, compared with turbulent flame folding mechanism, the unsteady states of the fluid parcels are maintained, and the preheating stages have to carry on with another reignition process. The subsequent reignition mode may be the same or different with the anterior one, which is determined by the current thermochemistry state of mixture. This mode is a hybrid scenario which contains two or more basic reignition processes.


20

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Energy & Fuels

In contrast with the distinction of pre-ignition processes, the dominant factors of post-ignition period are similar for reignition scenarios. Figure 11 shows the EI and PI of the post-ignition points after local reignition. As shown in the figure, the temperature is the dominant factor for all reignition scenarios (Fig. 11a). Meanwhile, the active radicals (such as H and OH) are consumed rapidly, and chain-termination reaction R8 is dominant in the post-ignition regions (Fig. 11b). The reason may be that the most remarkable characteristic is temperature rise in the post-ignition period.

Figure 11. EI and PI of post-ignition points after local reignition. (Small values are ignored.) Statistical analysis In this work, some features of reignition scenarios are also analyzed from statistical perspective. To calculate conditional probability distribution, 300 and 600 realizations of ODT are performed for H3 and H5 flame, respectively. About 40,000 reignition processes are analyzed for each flame. As shown in Fig. 12a and 12b, the probabilities of all reignition


21

Energy & Fuels

scenarios and reignition events affected by eddies (turbulent folding and hybrid mode) are presented respectively. These probabilities are calculated by the number of reignition events, which occur near a certain axial position, in all trace particles. As described in these subfigures, both of two conditional probabilities in H3 flame are larger than that in H5, and this can be attributed to high turbulent strains and more eddy events in high Reynolds number configuration. 0.12

0.12 (a)

0.10

(b)

H3 flame, All reignition events H5 flame, All reignition events

0.08 Probability

Probability

H3 flame, reignition events affected by eddies H5 flame, reignition events affected by eddies

0.10

0.08 0.06 0.04

0.06 0.04

0.02

0.02

0.00

0.00 2

0.16

4

X/D

6

8

10

2

H3 flame, Dominated by independent flamelet H3 flame, Dominated by premixed flame propagation H3 flame, Dominated by turbulent flame folding H5 flame, Dominated by independent flamelet H5 flame, Dominated by premixed flame propagation H5 flame, Dominated by turbulent flame folding

(c)

0.14 0.12 0.10 0.08 0.06

4

0.5

X/D

6

8

10

H3 flame, Dominated by independent flamelet H3 flame, Dominated by premixed flame propagation H3 flame, Dominated by turbulent flame folding H5 flame, Dominated by independent flamelet H5 flame, Dominated by premixed flame propagation H5 flame, Dominated by turbulent flame folding

(d) 0.4 Probability

Probability

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 28

0.3

0.2

0.04 0.1 0.02 0.00 0

200

400

600

800

Temperature variation (K)

1000

1200

0.0 0.0

0.2

0.4

0.6

0.8

-3

Preheat duration (10 s)

Figure 12. Conditional probabilities of all reignition events (a), reignition events affected by eddies (b), temperature variation (c) and preheat duration (d) in ODT. However, the statistical features of temperature variation (Fig. 12c) and preheat duration (Fig. 12d) in the reignition processes are similar for two flames. Since hybrid reignition process is a composite mode, it is classified into other scenarios and the dominant reignition mechanism is judged by the means of explosive and participation index in the whole reignition process. As shown in Fig. 12c, reignition mode dominated by premixed flame propagation has a higher


22

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Energy & Fuels

temperature variation (500K~900K) corresponding to the peak probability, which means premixed flame propagation mode have more effective to ignite the fluid parcel with low temperature. As described in Fig. 12d, reignition scenario dominated by independent flamelet has a small preheat duration corresponding to great possibility, which means that independent flamelet mode is a quicker reignition process. In contrast with first two reignition scenarios, the probability distribution of temperature variation for turbulent flame folding scenario is more flat. Meanwhile, the probability of preheat duration is distributed between independent flamelet and premixed flame propagation mode. The reason may be that flame folding mentioned in this work is a subsequent process of the other two reignition scenarios, and the location of turbulent eddy in the ODT model, proposed by Kerstein et al.,14, 27 is a uniform distribution. CONCLUSION In this work, the one-dimensional turbulence (ODT) model is performed in H2/N2 turbulent diffusion flames with detailed chemistry. Based on chemical explosive mode analysis (CEMA), flame fronts diagnosis, burning state analysis and reignition scenario definition are presented. Firstly, flame fronts in homogeneous ignition and laminar premixed flame are analyzed by CEMA. The distinction of Explosion Index can be used to identify flame fronts scenarios. As explosive mode is a chemical property of the mixture, this method can also be used in turbulent flame. Secondly, Damköhler number based on CEMA is used as a diagnostic method of burning state. Results show that the stable burning state can be described by a large positive Damköhler number. Meanwhile, local reignition events are presented by Lagrangian tracer strategy from temporal perspective.


23

Energy & Fuels

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Page 24 of 28

Then, four reignition scenarios are analyzed by CEMA. Results show that reignition scenario through premixed flame propagation corresponds to high temperature explosion index, large temperature variation and small dissipation rate, and the pre-ignition process of this reignition scenario is dominated by reaction R9 and R3 segmentally. While reignition mode through independent flamelet corresponds to high radical explosion index, small temperature variation and rapid reignition process, and the whole pre-ignition process is dominated by reaction R3. When these two reignition processes are terminated by turbulent eddies, hybrid reignition process or reignition scenario via turbulent flame folding may occur. The turbulent folding mode corresponds to high dissipation rate and obvious temperature jump near the end of reignition process. In addition, the dominant factors of post-ignition are similar, since the temperature rise is the most remarkable feature in post-ignition regions. And lastly, there are more reignition events in high Reynolds number configuration, while the probability distribution of temperature variation and preheat duration are similar for both flames. The statistical analysis shows that the premixed flame propagation mode have more effective to ignite the fluid parcel with low temperature, and the reignition scenario via independent flamelet is a quicker process. AUTHOR INFORMATION Corresponding author: Jiang Yong. E-mail: [email protected]. Tel: +86 551 63607827. Notes: The authors declare no competing financial interest. ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (No. 51576183) and the Fundamental Research Funds for the Central Universities (No.


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Energy & Fuels

WK2320000033 and No. WK2320000035), for which the authors would like to express their gratitude.

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(39) Lutz, A. E.; Kee, R. J.; Grcar, J. F.; Rupley, F. M. OPPDIF: A Fortran program for computing opposed-flow diffusion flames; Sandia National Laboratories Report: SAND96-8243, 1996. (40) Lu, T. F.; Yoo, C. S.; Chen, J. H.; Law, C. K. Analysis of a turbulent lifted hydrogen/air jet flame from direct numerical simulation with computational singular perturbation, 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Jan 7 - 10, 2008. (41) Dataset of H3 and H5 flame. Available at http://www.dlr.de/vt/desktopdefault.aspx/tabid3067/4635_read-6718/ (42) Sevault, A.; Dunn, M.; Barlow, R. S.; Ditaranto, M., Combust. Flame 2012, 159, 33423352. (43) Schmidt, J. R. Stochastic models for the prediction of individual particle trajectories in one dimensional turbulence flows. Ph.D. thesis, University of Arizona, Salt Lake City, 2004. (44) Schmidt, J. R.; Wendt, J. O. L.; Kerstein, A. R., J. Stat. Phys. 2009, 137, 233-257. (45) Kreutz, T. G.; Law, C. K., Combust. Flame 1996, 104, 157-175. (46) Mir Najafizadeh, S. M.; Sadeghi, M. T.; Sotudeh-Gharebagh, R., Int. J. Hydrogen Energy 2013, 38, 2510-2522. (47) Chen, J. H.; Hawkes, E. R.; Sankaran, R.; Mason, S. D.; Im, H. G., Combust. Flame 2006, 145, 128-144.


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