Characteristic Chemical Time Scale Analysis of a Partial Oxidation

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Characteristic chemical time scale analysis of a partial oxidation flame in hot syngas coflow Xinyu Li, Zhenghua Dai, and Fuchen Wang Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b02490 • Publication Date (Web): 13 Feb 2017 Downloaded from http://pubs.acs.org on February 14, 2017

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Characteristic chemical time scale analysis of a partial oxidation flame in hot syngas coflow

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Xinyu Li, Zhenghua Dai*, Fuchen Wang*

4

Key Laboratory of Coal Gasification and Energy Chemical Engineering of Ministry of

5

Education, East China University of Science and Technology, Shanghai 200237, China

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KEYWORDS: Chemical time scale; Jacobian analysis; Partial oxidation; MILD

7

combustion

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Abstract: Characteristic chemical time scale analysis plays a key role in the

9

understanding of turbulence-chemistry interaction in turbulent combustion research, and

10

is also important basis for the selection or development of combustion models in

11

turbulent combustion modeling. A new method named Main Direction Identification

12

(MDID) was developed based on the modification of CTS-ID (Chemical time scale

13

identification) method to achieve the function of identifying the characteristic time scale.

14

Direction weight factor combined with mole fraction limit were used as a criterion in

15

MDID to determine the characteristic time scale. MDID was applied to study

16

characteristic chemical time scales of a CH4-O2 inverse diffusion flame in hot syngas

17

coflow, which is a model flame developed before to study the combustion process in

1

1

ACS Paragon Plus Environment

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partial oxidation reformers. Results show that chemical time scale given by the MDID

19

method is about 10-5s in combustion area and 10-2s in reforming area. The main reaction

20

pathway was also analyzed using MDID method. The new method was compared with

21

three existing methods published in previous studies, the Damköhler numbers given by

22

MDID are more consistent with the mild combustion nature of the flame compared with

23

other methods. Then the MDID method was evaluated on a conventional oxy-fuel type

24

high temperature flame to assess its flexibility to different reaction regimes. The time

25

scale variation accurately reflects the changes of reaction regimes, indicating that the

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MDID method performs well on reacting flows varying from fast reaction regime to slow

27

reaction regime. The effect of mole fraction limit on this method was also studied.

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1. Introduction

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Numerical simulation is an important tool in the studying of turbulent reacting process

30

in combustion devices such as gas turbines and gasifiers. In these devices, turbulent flow

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and complex reactions occur simultaneously and interact with each other. Multi-scale is

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an important feature of such combustion device, its flow and chemical timescales often

33

vary several orders of magnitude. This multiple time scale phenomenon makes the

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interaction between turbulence and reaction very complex and brings enormous

35

difficulties to the development of numerical models

1-3

. So it is critical for the selection

2


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and development of combustion models to have a deep insight into the interaction

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between turbulence and chemical reaction.

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The analysis of flow time scale and characteristic chemical time scale is an important

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way to understand the turbulence-chemistry interaction. According to the ratio of the two

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time scales, combustion processes can be divided into different regimes

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chemistry is fast compared to the eddy turnover time, the flame is in flamelet regime

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where the flame preserves a laminar flamelet shape within the smallest turbulent

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structures. Chemical reactions and turbulence mixing can be decoupled in numerical

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modeling 6-7. When the chemical time scale is much slower than the flow time scale, the

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overall reaction rate is limited by chemistry. In the case where chemical time scale and

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flow time scale are comparable, both turbulence and chemistry play a fundamental role 8

47

and the turbulence-chemistry interaction should be considered in the modeling. Chemical

48

time scale analysis is also an important basis for many chemistry reduction methods, e.g.

49

the Computational Singular Perturbation (CSP) method

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Dimensional Manifold (ILDM) method 10. Flow time scale usually can be represented by

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two characteristic time scales: the integral time scale = ⁄ and Kolmogorov time

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scale = ⁄ , where is the turbulent kinetic energy (m2·s-2), is the turbulent

53

dissipation rate (m2·s-3) and is the kinematic viscosity (m2·s-1).

9

4-5

. When the

and the Intrinsic Low

54

But the calculation of characteristic chemical time scale still lacks a unified method. In

55

premixed combustion systems, the characteristic chemical time scale is often defined as 3


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the ratio of flame thickness and laminar flame speed : ⁄

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is not suited for non-premixed and Moderate or Intense Low Oxygen Dilution (MILD)

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combustion systems. Such complicated reaction systems usually contain hundreds of

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elementary reactions and the calculation of characteristic chemical time scale of such

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systems remains an open question. For these complex systems, it is usually easy to

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calculate chemical time scales based on the Jacobian matrix analysis method

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substantial literature3, 12-13 exists on this issue. The Jacobian analysis pointed out that

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reciprocals of the eigenvalues of the Jacobian matrix of chemical source terms can be

64

regarded as chemical time scales of a reacting system. Such methods give multiple

65

chemical time scales of the system but cannot give a characteristic time scale. While in

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the modeling of combustion process, a definite characteristic chemical time scale is

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usually needed to calculate parameters like Damköhler (Da) number. This is very useful

68

for the choosing and improving of appropriate combustion models. For example, based

69

on the Da numbers which characterize the turbulence-chemistry interaction, it can be

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evaluated whether the fast reaction models can be used for the modeling of a target

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reacting system. The characteristic chemical time scale and Da number can also be

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introduced into Eddy Dissipation Model (EDC) to improve its performance as

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demonstrated by A. Parente et al.

74

time scale (MSTS) method based on Jacobian matrix analysis. This method performs

75

Jacobian analysis for the artificially selected main species of a reacting system and

14

. M. Rehm et al.

15

11

. But this definition

4

and

proposed a main species based

4


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regards the largest time scale as the characteristic chemical time scale. This method was

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also used by S.N.P. Vegendla

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Caudal et al.

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which can identify serval main characteristic time scales from all the time scales

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calculated by full Jacobian analysis. Principal Variable analysis (PVA) was introduced

81

into Jacobian analysis process by B.J. Isaac to calculate characteristic chemical time scale

82

18

83

Prufert 19 to calculate the characteristic chemical time scale of a partial oxidation flame.

17

16

to analyze the time scales in a high pressure gasifier. J.

came up with a chemical time scale identification (CTS-ID) method

. Recently a method called System Progress time scale (SPTS) was proposed by U.

84

However, further studies are still necessary because the reliability of these methods

85

have not been fully verified and sometimes big discrepancies exist between the results of

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these methods. In the present study a Main Direction Identification (MDID) method was

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developed based on CTS-ID method. And MDID method was further used to study the

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characteristic chemical time scales of a partial oxidation flame in hot syngas coflow. This

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partial oxidation flame is an inverse diffusion flame of CH4-O2 in hot syngas coflow and

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was developed to study the combustion process in non-catalytic partial oxidation

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reformer by the author 20. Previous analysis 20 had shown that the combustion area of this

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flame is in MILD combustion mode, while the chemical time scales and interactions

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between turbulence and chemistry have not been studied. This information is of crucial

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importance for the selection and development of proper combustion models for the

5


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simulation of partial oxidation process. The partial oxidation flame is also a good case for

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the assessment of different methods due to its multi reaction regime feature.

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In the following, a brief description of mathematical fundamentals of different methods

98

is given in Section 2. The partial oxidation flame and some computation details are

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presented in Section 3. In Section 4, chemical time scale results of the partial oxidation

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flame using MDID method and further analysis on reaction pathway and eigenvalue are

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first presented, then validation of the results and a comparison with other methods are

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given in Section 4.2. The flexibility of this new method to different reaction regimes is

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studied in Section 4.3 and Section 4.4 discusses the sensitive of results to a model

104

parameter in MDID method.

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2. Mathematical fundamentals

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2.1. Jacobian analysis process

107 108

Considering a reacting system containing K species and I elementary reactions at constant pressure and enthalpy. The chemical reaction system can be expressed as:

109

110

where z is the concentration vector of K species, S is the source terms induced by

111

chemical reactions. The chemical source term Sk of the kth species can be written as a

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summation of the production rates for all reactions involving the kth species:

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=

= ∑

6


(1)

(2)

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where is the stoichiometric coefficient for ith elementary reaction and qi is the ith

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elementary reaction rate which can be expressed as: = ∏%

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!

$ "#

− ' ∏%

!

$$ "#

(3)

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( where, and ' are the forward and reverse rate constant of the ith reaction, and

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(( and are the forward and reverse stoichiometric coefficients. These parameters can be

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calculated using chemical reaction mechanism files by the method given in 21.

120 121

Assuming that the derivative exists, the following equation can be obtained by taking the time derivative of Eq. (1)

)

122

-)

= * ∙ , * = -

(4)

123

where J is the Jacobian matrix of S. Jacobian matrix J is actually time dependent, but

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considering that only time scales are of interest, the Jacobian matrix can be assumed to be

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locally time independent

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assuming that all the eigenvalues are different, the following equation can be obtained:

22

. So by performing the eigen-decomposition on J and

* = ./.0

127 128

(5)

where P is the matrix of eigenvectors, / is the diagonal matrix of eigenvalues.

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The Jacobian matrix which can be regarded as rate constant matrix of the reacting

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system has a unit of s-1. So the reciprocals of its eigenvalues can be regarded as the

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chemical time scales of the system.

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2 = |4

#|

7


(6)

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It is worth noting that the eigenvalues and eigenvectors of J are either real or complex.

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Complex eigenvalue indicates an oscillatory chemical mode, with the real part represents

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the characteristic velocity of growth or decay and the imaginary part corresponds to the

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oscillation frequency. In this case, the complex eigenvalues and eigenvectors have to be

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transformed into real to make the physical meaning of a time scale analysis obvious. See

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17, 22-23

for details of this algebraic transformation.

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From equations (2) - (4), it can be seen that the components of J depend on z and the

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reaction rate parameters. This implies that the eigenvalues of J will also depend on z.

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Thus once the species space of a reacting system is known, the chemical time scales can

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be obtained by calculating the Jacobian matrix and its eigenvalues at this state point.

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However due to the complex structure of the dynamical system, J has various

144

eigenvalues. So multiple chemical time scales can be obtained using this method, but the

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characteristic time scale cannot be given by this method.

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2.2. Chemical Time Scales Identification method

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For a state point M of a reacting system, Jacobian matrix analysis can give chemical

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time scales associated to K system evolution directions. Among these directions, some

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are main directions while the others are minor. J. Caudal et al.

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Time Scales Identification (CTS-ID) method to identify the main directions. Assuming

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the system evolution direction at point M can be represented by chemical source term S

8


17

proposed a Chemical

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of the reacting system, the K projection coefficient sj can be obtained by projecting S on

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the real valued eigenvector V of the Jacobian matrix J:

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155 156 157 158 159

= ∑% 5 5 65

(7)

In fact the above derivation process is the same with CSP analysis, and the projection coefficient s can be seen as the mode vector f in CSP theory. In CTS-ID method, a normalized weight factor 75 was defined to measure the importance of the jth direction to chemical source term. 75 =

89: ;: 8

#∈@,A! ‖9# ;# ‖

(8)

160

According to the relevance of jth direction versus system evolution direction which is

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presented by S, 75 varies between 0 and 1. A value close to 1 indicates that this direction

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can be regarded as a main evolution direction of the system, a value close to zero means

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little relevance between this direction and the system main direction. 75 = 0.01 was

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used in CTS-ID method to identify the main directions.

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An index to identify the main chemical reaction pathway along each direction was also

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introduced in CTS-ID. The contribution of species i along direction j can be expressed as:

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F,5 = GHIJ5 K ∑A

;,:

#M@L;#,: L

(9)

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where 6,5 is the ith component of 65 , GHIJ5 K represents the sign of 5 . A positive

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sign of F,5 indicates that species i is produced in the jth direction while a negative sign

9


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means the opposite. If the weight factor of each direction is considered, then the index

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can be written as: ℎ,5 = F,5 75

172 173

(10)

2.3. Main direction identification method

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The method presented in section 2.2 can identify time scales associated with the several

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main evolution directions of the system, but the characteristic chemical time scale still

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cannot be determined. This study introduced a criterion to determine the characteristic

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time scale based on the above Jacobian analysis and CTS-ID process.

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The characteristic chemical time scale can be chosen as the time scale of the most

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relevant direction to the system evolution direction. An obvious and easy choice for the

180

criterion is choosing the direction with largest 75 ( 75 = 1) as the main direction of the

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system. But there are some questions with this choice. One is that it is hard to make a

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choice when the weight factors of several directions are all close to 1. The second is that

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the direction with the largest 75 does not necessarily represent the main direction of the

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reacting system. In the method described in section 2.2, the system evolution direction is

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represented by chemical source term S, while S is determined by both chemical reaction

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rate constant and reactant concentration [X] through multiplicative relation, as shown in

187

Eq. (1) and Eq. (2). Thus as long as the chemical reaction rate constant of one reaction

188

direction j is large enough, the corresponding projection coefficient component sj

189

obtained by Eq. (7) can be largest. So for the reaction direction with largest 75 , there is a 10


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case in which the chemical reaction constant is very large meanwhile the main reactant

191

concentrations are very small. Low reactant concentrations mean that only a small

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portion of the system is involved in this direction. In this situation it’s not appropriate to

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choose this direction as the main direction due to its low reactant concentrations.

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To resolve this problem, a minimum concentration limit [Xc] must be made if one

195

direction is to be chosen as the main direction. To facilitate comparison, mole fraction

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limit Xc instead of concentration limit [Xc] is used here. In combustion systems, the

197

differentiation phenomenon of species concentration is obvious. The mole fractions of

198

major species are usually much larger than those of intermediate species. So Xc =0.005 is

199

chosen here as the minimum limit for mole fraction. The results are not very sensitive to

200

this value in a near region as will be shown in Section 4.4. Assuming that u represents the

201

decreasing 75 order, .,O represent the mole fraction of reactants in increasing F,O

202

order, the criterion to identify the characteristic main direction can be expressed as: .O >

203

2 , & .RO

>

2

(11)

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If the mole fractions of first two main reactants of the largest weight factor direction

205

SP11 and SP21 are both larger than the limit Xc, this direction can be seen as the main

206

direction; while if the conditions are not met, the identification procedure Eq. (11) would

207

be performed to the remaining directions with the order of u (decreasing 75 ) until the

208

main direction is determined. This method is named as Main Direction Identification

209

(MDID) method in present study. 11


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While it is worth to note that Xc=0.005 is not suited for O2, because even a very low

211

mole fraction of O2 still play an important role in reactions. The limit for O2 is chosen as

212

the mole fraction when the combustion regime ends which is determined by eigenvalues

213

as shown later in Section 4.1.

214

2.4. Brief introduction of three existing methods

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2.4.1. PVA and MSTS method

216

The existence of high dimension in combustion system bring enormous difficulties to

217

the identification of characteristic chemical time scale. The Principal Variable Analysis

218

(PVA) method

219

using Principle Variable method, and selects the slowest time scale of the reduced system

220

as the characteristic time scale. The main process of the Principal Variable method is as

221

follow.

18

performs dimension reduction analysis on the high dimensional dataset

222

For a dataset D, consisting of n observations of Q variables, its sample covariance

223

matrix can be defined as S = 1⁄I − 1 TU T. The covariance matrix represents the

224

variance of the variables. Values close to one indicate strong correlations between

225

variables, whereas a value of zero indicates uncorrelated variables. Based on these

226

correlations, unimportant variables can be removed from the origin dataset using B2

227

method 24.

12


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Thus the original dataset D can be divided into two parts: the remained variables D(1)

229

and the removed variables D(2). So the sample covariance matrix S can also be expressed

230

as: Σ=W

231

232

ΣR X ΣRR

(12)

The partial covariance matrix of D(2) given D(1) can be defined as: 0 ΣR ΣRR, = ΣRR − ΣR Σ

233 234

Σ ΣR

(13)

The trace of ΣRR, was selected as the criterion of choosing q remained variables: 'Y2Z[\]],@ ^_

235

'Y2Z\

≤7

(14)

236

Left hand of above equation can be interpreted as the variance information loss

237

introduced by selecting q variables instead of origin dataset. In 18, a value of 0.01 was set

238

for 7.

239

Once the q main variables are obtained, q time scales can be get by performing

240

Jacobian analysis, and the largest time scale can be regarded as the characteristic

241

chemical time scale.

242

The main species based time scale (MSTS) method proposed by M. Rehm et al.

15

is

243

similar to the above PVA method. The difference is that MSTS method artificially selects

244

q variables as the main variables of a reacting system.

245

2.4.2. SPTS method

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The Jacobian matrix J of chemical reaction source S is actually the first partial

247

derivatives of S with respect to mass fraction Y. So considering from the point of

248

differential, for a system state M, the following formula holds:

249

ab

250

cd is the disturbance of mass fraction Y at point M. *cd can be regarded as the

251

velocity vector describing the velocity in which the system reacts on perturbations. So U.

252

Prufert 19 defined a time scale:

= *cd

(15)

e = ‖*cd ‖0

253

(16) )

254

cd can be selected as the direction of chemical source term S: cd = ‖)b ‖ . This system

255

progress time scale (SPTS) can be regarded as the time the system needs to react on

256

perturbations in the direction of linearized progress.

257

3. Partial oxidation flame

b

258

The characteristic chemical time scales of a CH4-O2 inverse diffusion flame in hot

259

syngas coflow is studied in this work. A detailed description of the configuration can be

260

found in

261

combustion process in partial oxidation reformer. The hot syngas coflow was used to

262

simulate the hot recirculated syngas in reformer. A schematic view of the configuration is

263

shown in Figure 1 and the boundary conditions are shown in Table 1. The oxygen inlet

264

has an inner diameter of d = 4 mm and a tube thickness of 1 mm. The fuel tube has an

265

inner diameter of df = 8 mm.

20

, only a brief description is given here. This flame was designed to study the

14


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Figure 1. Geometry of the flame configuration.

268

Table 1. Boundary conditions for the partial oxidation flame. Oxygen

Methane

Coflow

T(K)

300

300

1600

Velocity(m/s)

100

100

5.4

Species(mole fraction) 100%O2 100%CH4 56%H2+32%CO+12%H2O 269

To perform the chemical time scale analysis, CFD simulations were conducted first to

270

get the mass fraction, density and temperature data on each grid. Averaged data from

271

RANS method are widely used in the chemical time sale analysis studies 16, 18-19, 25-27. Due

272

to the present work focused on the time scale model development, the methods used for

273

producing input data were kept similar with other time scale analysis studies. In this

274

study, the CFD modeling was reproduced from our previous study 20. A 2D axisymmetric

275

structured grid containing 50855 cells was chosen after a grid sensitivity study. A

276

modified standard k-ε turbulence model and Eddy Dissipation Concept (EDC) model

277

were adopted to simulate the flame. DRM22 mechanism 28 which contains 24 species and

278

104 elementary reactions was chosen. Detailed boundary conditions and descriptions of

15


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the modeling effort can be found in 20. In the theory of EDC model, a computational cell

280

is divided into two parts: reacting fine structure and non-reacting surrounding area

281

Thus two kinds of mass fraction can be given by EDC model: averaged mass fraction and

282

fine scale mass fraction. The fine scale mass fraction is directly computed by chemical

283

reaction mechanism in the fine structure, while the cell averaged mass fraction is the

284

weighted average mass fraction of fine scale area and surrounding area

285

this fact, the fine scale mass fraction data was used in this work although only very little

286

deviation exists between the results of the two dataset.

30

29

.

. Considering

287

The chemical time scale analysis were performed at each grid point in the flow field

288

and the analysis in this work were carried out in MATLAB. Symbol calculation was used

289

in the derivation process of chemical source term and Jacobian matrix to reduce the errors

290

caused by numerical calculations.

291

4. Results and Discussions

292

4.1. Analysis of the partial oxidation flame using MDID method

293 294

Figure 2. Temperature profile of the CH4-O2 inverse diffusion flame in hot syngas

295

coflow.

16


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Figure 2 shows the temperature profile of the partial oxidation flame calculated using

297

the CFD model. The temperature is uniform and the peak temperature is about 1700K.

298

Previous study

299

combustion mode.

20

had shown that the combustion area of this flame is in MILD

300 301

Figure 3. Chemical time scales along the axis of the inverse diffusion flame.

302

Figure 3 shows the calculated characteristic chemical time scales along the flame axis.

303

Considering that the main concern here is time scales of reacting areas, the time scale

304

calculation is only performed for areas with a temperature above 900K to reduce the

305

calculation costs. As shown in Figure 3, characteristic time scale decreases before x=100d

306

(d=4mm is the diameter of oxygen channel) and reaches minimum at x=100d, then

307

increases and slowly converges to a constant value. This means that the MDID method

308

identified the existence of combustion area and reforming area. The trough refers to

309

combustion area and the slowly increasing area after x=160d refers to the reforming area. 17


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310

The characteristic chemical time scale given by MDID method is about 10-5-10-4s in

311

combustion area and 10-2s in reforming area.

312 313

314

Figure 4. Profiles of largest positive eigenvalues, temperature and HRR along the axis.

The signs of the eigenvalues of Jacobian matrix J indicate the explosive or decaying 12, 31-33

315

nature of the system in the analysis of kinetic systems

316

indicate a trend of the direction towards equilibrium, while positive eigenvalues are

317

referred to explosive modes. To enhance the physical understanding of the system, the

318

eigenvalues were further analyzed. Figure 4 shows the largest positive eigenvalue fgYh ,

319

the hear release rate HRR and the temperature profile along the axis. Positive eigenvalue

320

first appears at x=62.5d. The reaction pathway of the direction associated with this

321

eigenvalue is FR i jFk i lR → FR O i jFo O. Note that this formula only refers to a

322

reaction pathway, so the two sides are not balanced. The weight factor of this direction is

323

1. These mean that ignition occurs at this point. The corresponding temperature is 964K,

324

which is close to the auto-ignition temperature of the local mixture. The HRR also starts 18


. Negative eigenvalues

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to be positive from this point. The positive eigenvalue increases fast and reaches a

326

maximum at x=100d. Then the eigenvalue starts to decrease and approaches zero at

327

x=160d. So this direction lose their explosive nature at this point, indicating the end of

328

combustion area. The location of the end of combustion area given by eigenvalue

329

analysis agrees well with that given by the HRR and temperature. The HRR decreases to

330

zero at x=160d and the temperature starts to decrease after x=160d. After x=160d, all the

331

eigenvalues became negative, which means that the system evolves towards equilibrium.

332

The analysis of eigenvalues can be used to accurately identify the boundaries of

333

combustion area in partial oxidation flames.

334 335

Figure 5. Weights of leading reaction pathways and their corresponding time scales

336

(abscissa) and main components (blocks) at x=100d and x=250d, each bar corresponds to

337

a reaction pathway.

19


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338

Reaction pathway analysis of x=100d in combustion area and x=250d in reforming area

339

are shown in Figure 5. Only directions of the first six largest weight factors are given

340

here. For x=100d, the main reaction pathway is associated with the consumption of CH4,

341

H2 and O2 and the production of H2O, CO and CH3. The corresponding time scale is

342

10-5s. The weights of other reaction pathways can be ignored compared to the weight of

343

this pathway. This result shows that the combustion of CH4 and H2 is the main reaction at

344

x=100d and due to the lack of O2 in partial oxidation flame, CH4 is not completely

345

oxidized. Part of CH4 is oxidized into CO and part of CH4 decomposed into CH3 without

346

a further oxidation. At x=250d in reforming area, the main reaction pathway is associated

347

with the consumption of CO, H2O and the production of H2, CO2. This is a slow

348

reforming reaction with characteristic chemical time scale of 10-2s.

349

The discontinuity of the time scale near x=160d in Figure 3 is caused by oscillation

350

behavior of the local reacting system. As the oxygen decreases with x, the oxidation

351

reaction pathway becomes weaker and on the other hand the reforming pathway becomes

352

stronger. These two directions collapse into a complex conjugate pair at the end of

353

combustion area. This is a common phenomenon occurring at the intersection of two

354

stages for dynamic systems

355

factor than other directions near x=160d, was identified as the main direction and the time

356

scale was represented by the real part of its complex eigenvalues. The rapid decrease of

357

real part leads to large time scales near x=160d. After x=160d, reforming pathway was

32, 34

. This complex direction, which has a larger weight

20


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358

identified as main direction, and the characteristic time scale was also changed

359

accordingly.

360

4.2. Comparison with other methods

361

The present method is next compared with three existing methods which had been

362

employed in characteristic chemical time scale analysis: PVA, SPTS and MSTS. A brief

363

introduction of the three methods is given in Section 2.4. The CTS-ID method is not

364

involved because it gives multiple time scales at one point other than a single

365

characteristic time scale. The main species given by PVA method is H2, H2O2, CH2, CH4,

366

HCO and the main species chosen for MSTS method are CH4, O2, H2, CO, H2O, CO2. It

367

can be seen from Figure 6 that with the increase of x, all the four methods show similar

368

trend. The time scales decrease before x=100d and reach minimum at about x=100d, then

369

increase and stabilize near a constant value. All the methods identified the existence of

370

combustion area and reforming area and gave smaller time scales in combustion area,

371

larger values in reforming area. The time scales given by SPTS and MSTS are similar: in

372

combustion area the given time scales are 10-1s, in reforming area the time scales are

373

100s. While the time scales in combustion area given by PVA method are 10-3s and the

374

time scales in reforming area are 10-2s. Both the values are lower than the values given by

375

SPTS and MSTS. The Different choices of main specie between PVA and MSTS method

376

lead to the very different results. The time scales in reforming area given by MDID

21


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377

method are very similar to that of PVA, but the time scales in combustion area given by

378

MDID are much smaller than other methods, with an order of 10-4-10-5s.

379 380

Figure 6. Comparison of the characteristic time scales calculated by different methods.

381

No experimental work on the measuring of chemical time scale under MILD

382

combustion has been reported due to the difficulties in measurement. But many DNS

383

studies

384

comparable to the Kolmogorov flow time scale for MILD combustion, and the

385

corresponding Damköhler (Da) number defined as the ratio of Kolmogorov time scale

386

and chemical time scale Da = ⁄2 is of the order unity. So the Da number was

387

calculated to evaluate the results given by different methods. Figure 7 shows the Da

388

numbers on the flame axis calculated by different methods.

35-39

on MILD combustion have revealed that the chemical time scale 2 is

22


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389 390

Figure 7. Comparison of the Da numbers calculated by different methods.

391

Due to the formation of MILD combustion in this partial oxidation flame, the

392

combustion occur at a certain distance (about x =75d -125d) from the nozzle. In this

393

combustion area, the results given by the MDID method are very different from those of

394

the other three methods. The Da number given by MDID is of the order unity, indicating

395

that the flow time scale and chemical time scale is comparable and finite chemistry

396

should be considered in the modeling. However, Da numbers given by other three

397

methods are all much smaller than one which means that the flow time scale is much

398

smaller than chemical time scale and the flow is not affected by reactions in the

399

combustion area. This is unreasonable for a flame. The results of the new proposed

400

MDID method are more consistent with the nature of MILD combustion given by DNS

401

studies.

402

4.3. Flexibility of the MDID method to different reaction regimes 23


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403

The flexibility of MDID method to two different reaction regimes with Tr s 1 and

404

Tr ≪ 1 were studied in above sections, but fast reaction regime was not involved. When

405

the inverse diffusion type of the flame in Figure 1 changes to normal diffusion type, a

406

conventional high temperature flame including fast reactions can be obtained

407

also a common flame type in partial oxidation reformers. Figure 8 shows the temperature

408

profile of the partial oxidation flame in normal diffusion type. Since the O2 locates in the

409

outer channel of the burner, O2 reacts with the low velocity hot syngas immediately once

410

leaving the burner, and a high temperature flame is formed near the burner. The peak

411

temperature is about 3100K. To assess the flexibility of the MDID method to fast

412

reaction regime, MDID method was performed along the y=5mm line which penetrates

413

the high temperature area.

20

. This is

414 415

Figure 8. Temperature profile of the normal diffusion type flame in hot syngas coflow.

24


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Energy & Fuels

416 417

Figure 9. Characteristic chemical time scales and temperature along y=5mm line of the

418

normal diffusion case.

419 420

Figure 10. Da numbers along y=5mm line of the normal diffusion case.

421

The characteristic chemical time scales and corresponding Da numbers along the

422

y=5mm line are shown in Figure 9 and Figure 10. In the high temperature area near the

423

burner exit, 2 is very small with an order of 10-8s. With the increase of x, the

424

temperature decreases significantly due to the mixing of low temperature CH4, and 2 25


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425

increases to 10-5s accordingly. In this area, moderate reactions occur between methane

426

and low concentration oxygen which has not been completely consumed. The

427

temperature has a slight increase and 2 shows a decrease correspondingly. Further

428

downstream the oxygen is totally consumed and reforming reactions occupy a dominant

429

position. The time scales slowly increase from 10-5s to 10-2s. The two peaks of time scale

430

at x=25d and x=170d were caused by the oscillation behaviors during the transition of

431

different reaction regimes. The time scale and Da number variations show the existence

432

of three reaction regimes in the flame: fast reaction regime (Tr ≫ 1, moderate reaction

433

regime Tr s 1 and slow reaction regime Tr ≪ 1. The changes of chemical time

434

scales given by MDID method agree well with the changes of reaction regime. This

435

indicates the well flexibility of the MDID method to different reaction regimes.

436

The existence of moderate reaction regime in this normal diffusion type flame in hot

437

syngas coflow has not been observed in previous studies. This observation means that

438

even for this high temperature flame, combustion models based on fast reaction

439

assumption are not enough to accurately describe the temperature and species profiles,

440

turbulence-chemistry interaction must be considered in the modeling.

441

4.4. Effect of minimum mole fraction limit Xc

442

In this section the effect of minimum mole fraction limit Xc on the time scale

443

identification results is studied. First the results of an identification process without a

444

mole fraction limit Xc will be presented. This process identifies the time scale of the 26


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Energy & Fuels

445

direction with largest γj as the characteristic chemical time scale. The results are shown in

446

Figure 11. It can be seen that without Xc, the time scales become discontinuous and very

447

small time scales are identified in the post combustion range at about x=120d~200d. It is

448

unreasonable that the characteristic chemical time scales in post combustion area are

449

much smaller than those identified in combustion area. Compared with Figure 3 where

450

the Xc is considered, it can be concluded that the time scale results are much better

451

improved by introducing Xc.

452 453

Figure 11. Chemical time scales identified without Xc.

27


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454 455

Figure 12. Comparison of the chemical time scales obtained by different Xc.

456

However, not all the choices of the minimum mole fraction limit can lead to a good

457

result. The limit Xc=0.005 in MDID method was artificially chosen to distinguish the

458

major species and trace species. As a user input parameter, it may have an influence on

459

the results. So the sensitivity of time scale results on the value of Xc is studied in this part.

460

Since the role of Xc is to distinguish the major species and trace species, Xc should be

461

smaller than the lowest limit of major species and larger than the highest limit of trace

462

species. A reasonable range for Xc is 0.001~0.01. Figure 12 shows the time scales when

463

Xc varies inside of the range and outside of the range. When Xc varies inside of the range

464

(Xc=0.01 and 0.001), the time scale results given by different Xc agree perfectly; But

465

when Xc varies outside of the range, some outlier data points appear. For Xc=0.1, the data

466

points are abnormal in zone A, as shown in the figure. In Zone A, CH4 and O2 are the

467

first two main reactants, but due to the fact that mole fraction of CH4 is lower than the 28


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468

limit Xc =0.1 in this zone, the oxidation pathway is ignored by the algorithm and a less

469

important reaction pathway CO i FR l → jlR i FR is selected instead. For Xc=0.0005,

470

data points are abnormal in zone B. The mole fraction of CH3 in zone B is larger than the

471

limit Xc =0.0005, as a result the less important reaction pathway FR i jFo → H i jFk

472

is recognized as main pathway instead of the oxidation pathway. The fast time scale with

473

an order of 10-7s is given in zone B. So it can be found that both too high and too low

474

values of Xc will lead to bad results, and 0.001-0.01 is a reasonable range for Xc. The time

475

scale results are insensitive to the value of Xc if Xc is chosen in this specific range.

476

5. Conclusions

477

A characteristic chemical time scale identification method named MDID was

478

developed in the present study to analyze the characteristic chemical time scales of a

479

partial oxidation flame in hot syngas coflow. A criterion based on direction weight factor

480

and mole fraction limit was proposed to identify the characteristic time scale from the

481

numerous time scales obtained by full Jacobian analysis.

482

This method was first used to analyze the characteristic time scale of an inverse

483

diffusion flame of CH4-O2 in hot syngas coflow. Results show that the characteristic

484

chemical time scale is between 10-5s to 10-4s in combustion area, and 10-2s in reforming

485

area. The variations of characteristic time scale and obtained reaction pathway agree well

486

with the changes of reaction regimes in flame. The time scale results given by MDID

487

method were compared to other three existing methods: PVA method, SPTS method and 29


Energy & Fuels

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488

MSTS method. The calculated Da numbers given by MDID method agree better with the

489

MILD combustion nature of the flame than other methods, indicating that MDID

490

performs better in the analysis of the case flame. The flexibility of MDID method for

491

different reaction regimes were further tested on a normal diffusion type partial oxidation

492

flame including fast reaction regime. The variation of calculated characteristic time scale

493

agreed well with the changes of reaction regimes.

494

Results of this study indicate that turbulence-chemistry interaction must be considered

495

in the modeling of partial oxidation process in order to accurately predict the scalar

496

profiles. Combustion models based on fast reaction assumption are not sufficient for the

497

modeling of such systems. The detailed knowledge of characteristic chemical time scales

498

of partial oxidation flames can also be used for the modification of combustion models

499

for partial oxidation reformer to better describe the turbulence-chemistry interaction and

500

this will be the objective of future work.

501

AUTHOR INFORMATION

502

Corresponding Authors

503 504 505

*E-mail: [email protected] *E-mail: [email protected]

ACKNOWLEDGMENTS

30


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Energy & Fuels

506

This research was supported by the Science and Technology Commission of Shanghai

507

Municipality (No. 15DZ1200802) and the Coal-based Key Science and Technology

508

Program of Shanxi Province, China (No. MH2014-01).

509

NOMENCLATURE

510

MDID = Main Direction Identification

511

CTS-ID = Chemical time scale identification

512

CSP = Computational Singular Perturbation

513

ILDM = Intrinsic Low Dimensional Manifold

514

MILD = Moderate and Intense Low Oxygen Dilution

515

Da = Damköhler

516

EDC = Eddy Dissipation Model

517

MSTS = Main species based time scale

518

PVA = Principal Variable analysis

519

SPTS = System Progress time scale

520

RANS = Reynolds-Averaged Navier-Stokes

521

HRR = Heat release rate

522

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Characteristic Chemical Time Scale Analysis of a Partial Oxidation

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