Using Sensitivity Analysis and Gradual Evaluation of Ignition Delay

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Using Sensitivity analysis and Gradual Evaluation of Ignition Delay Error to Produce Accurate Low Cost Skeletal Mechanisms for Oxidation of Hydrocarbon Fuels under High Temperature Conditions Alireza Shakeri, Karim Mazaheri, and Mohammad Owliya Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b01671 • Publication Date (Web): 25 Aug 2017 Downloaded from http://pubs.acs.org on August 26, 2017

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Using Sensitivity analysis and Gradual Evaluation of Ignition Delay Error to Produce Accurate Low Cost Skeletal Mechanisms for Oxidation of Hydrocarbon Fuels under High Temperature Conditions Alireza Shakeri1*, Karim Mazaheri1 , Mohammad Owliya2 1 Center of Excellence of Aerospace Systems, Sharif University 2 Mapna

of Technology, Tehran, Azadi Avenue, Iran

Turbine Co, Karaj, Fardis Roud, Iran

Abstract Three dimensional thermo-hydrodynamic analysis of gas turbine combustion chambers is of great importance in power generation industry to achieve higher efficiency and less emissions. However, usage of comprehensive full detailed mechanisms in these simulation algorithms is prohibited because of their huge CPU time and memory space requirements. Many reduction approaches are available in the literature to remedy this problem. Here a new approach is presented to reduce large detailed or skeletal mechanisms of oxidation of hydrocarbon fuels to a low cost skeletal mechanism. The method involves an integrated procedure including a Sensitivity Analysis (SA) and a procedure of Gradual Evaluation of Ignition Error (GEIE). The sensitivity analysis identifies reactions which are less effective on the flame temperature (Tf) and also those less effective to determine the NO concentration (XNO). Using GEIE procedure also gives the less effective reactions to determine the ignition delay time (߬௜௚௡ ). In this process three cut-off limits (COL) are selected for Tf, XNO, and߬௜௚௡ . The procedure is validated and examined for two different hydrocarbon fuels, i.e., methane and kerosene. The detailed mechanism of GRI-3.0 is used for methane, to produce a low-cost skeletal mechanism containing 118 reactions and 39 species. Similarly a validated skeletal mechanism for kerosene including 382-reactions and 106-species is used to generate a low-cost skeletal mechanism including only 180-reaction and 79-species. The accuracy of the obtained skeletal mechanisms was investigated to predict the ignition delay and the flame temperature for a range of inlet temperatures (T0) of 1000-1800 K, combustion pressures (pc) of 1.0-30.0 atm, and equivalence ratios (ɸ) of 0.5-2.0 using a homogeneous IGNITION model. In addition, the applicability of the produced mechanisms to predict the oxidation parameters such as flame temperature, velocity of burnt gas, concentration of the main fuel species, some minor radicals and other selected species are investigated and validated for both skeletal mechanisms using homogeneous models of PSR and PREMIXED over a range of different T0’s (300-1800 K) and pc‘s (1.0-30.0 atm) and ɸ‘s (0.5-2.0). Comparisons show that the two new skeletal mechanisms have a good agreement with similar known base mechanisms but offer a significant gain in terms of computational cost. Keywords: Detailed Mechanism, Skeletal Mechanism, Sensitivity Analysis, Ignition Delay Time, Flame Temperature, NO Concentration.

1 *

Corresponding author. Tel.: +9802166164614, Fax: +9802166044006-6 ACS Paragon E-mail address: [email protected]

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1. Introduction Nowadays, with the growth of computers speed and capacity, using more accurate chemical mechanisms for simulation of hydrocarbon fuels oxidation is of prime interest for industry and researchers. Three dimensional thermo-hydrodynamic analysis of gas turbine combustion chambers is of great importance in power generation industry to achieve higher efficiency and less emissions. However, usage of comprehensive full detailed mechanisms in these simulation algorithms is prohibited because of their huge CPU time and memory space requirements. Using accurate detailed mechanisms is still impractical for most real industrial applications, e.g., gas turbine combustors. Due to the high computational cost, use of detailed mechanisms to predict combustion features in multi-dimensional simulations have limitations and researchers often seek extraction of simplified mechanisms with a much less number of reactions and species [1-2]. There are many proposals for reduction of detailed mechanisms to less expensive reduced mechanisms. This has resulted in introduction of many different mechanisms with different levels of details and comprehensiveness. Selection of insignificant mechanisms or missing the significant reactions will result in non-accurate or even erroneous results. Furthermore, mechanisms which are realistically large and comprehensive include a very large number of huge equations, and these equations have very different time scales, resulting in a stiff system of equations, and the time and space complexity of computations become intolerable for almost all industrial applications. This problem is more severe as the hydrocarbon fuel molecule gets larger, since the number of involved species and reactions grows exponentially with the molecule size. Unfortunately almost all liquid fuels used in engines include very large molecules. In fact even 1D simulations of these systems of equations are very expensive. Literature review shows that all reduction schemes fall into five major categories, i.e., global multi-step, lumping, time scale analysis, stiffness reduction and skeletal reduction [3]. Of course different reduced mechanisms are designed using different criteria and therefore are appropriate for different applications. The main validation process for a new proposed full or detailed mechanism is to compare between the computed parameters and the experimental data [4-6]. However, to validate a newly proposed reduced mechanism, the main procedure is to compare its performance with its parent mechanism, although researchers usually use other validated detailed or skeletal computational models as well to assess the accuracy and performance of the newly designed reduced mechanisms [7-8]. Global multi-step chemical mechanisms for methane combustion are recently reviewed by Mazaheri et al. and a new combined algorithm has been proposed for optimizing the reaction rate parameters [9]. Despite low computational cost of such mechanisms in computational fluid dynamic simulations, these schemes usually show low relative accuracy in comparison with the detailed mechanisms and they may be useful only in prediction of some selected macroscopic combustion properties e.g., pollutant emissions. The lumping procedure includes combining similar species and reaction pathways to reduce the number of variables. This is especially effective for large hydrocarbon fuel molecules which typically consist of a large number of isomers with similar thermal and transport properties, or many species with similar diffusivities. These can be grouped to substantially reduce the number of species [10-12]. Many researches are devoted to construct more accurate reduced mechanisms by means of time-scale analysis [13-18]. Here fast chemical processes recognized by quasi steady state (QSS) species or partial equilibrium (PE) reactions are

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substituted by algebraic equations, and the number of independent processes is dwindled. Main procedures applied in this regard are QSS approximation [19], PE approximation [20], rate controlled constrained equilibrium (RCCE) [21], intrinsic low dimensional manifold (ILDM) [22] and computational singular perturbation (CSP) [23]. Despite higher accuracy of such mechanisms in comparison with the global multi-step mechanisms, still these reduced mechanisms suffer from lack of accuracy in simulation of many combustion parameters, especially in prediction of the ignition delay time [13-18]. Methods in the fourth category, i.e., stiffness reduction, are mostly similar to time-step analysis, e.g., QSSA [19], PEA [20], ILDM [22], and CSP [23]. In these methods, to find the stiff Jacobian matrix, semi-implicit splitting schemes are frequently used. Interest on skeletal reduction of full mechanisms in combustion simulations has grown steadily by increase in the computational power [14, 24]. The resulting mechanism include only elementary reactions, and is a subset of the parent detailed mechanism. The main advantage of the skeletal mechanism is that its time complexity is quite low, and it’s a good strategy for any reduction procedure for a large detailed mechanism to be preprocessed by a skeletal mechanism to make the size of the mechanism affordable for more time consuming reduction methods. Extracting skeletal mechanisms for a specified range of operating conditions is achieved by either the removal of unimportant reactions or the removal of unimportant species, which is more involved because of complex couplings. Those methods which eliminate unimportant species include: CSP [14,23, 25], level of importance (LOI) [26-27], connectivity method [28], directed relation graph [29- 31], directed relation graph with error propagation [32], path flux analysis [33-34], DRG-aided sensitivity analysis [35], DRGEP with sensitivity analysis [36], Iterative screening and structure analysis [37], and DRG with ISSA [7]. The main task here is to find strong couplings, and DRG and its derivatives are shown to be the fastest algorithms for this purpose, although their use in species reduction shall be with enough care to avoid deletion of species with complex couplings with main species. So far, many methods have been proposed for removal of unimportant reactions, the most oldest of them are: sensitivity analysis [43-44], principal component analysis (PCA) [17-18], computational singular perturbation (CSP) [14, 24], and detailed reduction [42]. In practice people usually use a series of reduction algorithms in sequence to find a more appropriate model with a less computational cost. As an example, to predict the ignition delay time, recently a 34-species skeletal mechanism has been derived for kerosene using a combined procedure including; sensitivity analysis (SA) and Chemical Explosive Mode Analysis (CEMA) [8]. To find a more effective reduction procedure further to the above methods, many novel techniques are introduced as genetic and other optimization algorithms [38-41], artificial neural network [45], self-organizing map [46], graph theory [29, 32] and tabulation [47]. These extensive researches and procedures show the practical importance and the multidisciplinary nature of the reduction problem. Since we are mostly interested to improve combustion analysis of industrial gas turbine combustors, in this article we are focused on two fuels widely used in gas turbines, i.e., methane and kerosene. Kerosene is a widely used fuel in gas turbines, and does not have a unique composition. It is a mixture of different compounds and full modeling of combustion of all components is impractical. Instead, here we use models based on surrogate of three compounds [7] to mimic jet-fuel behavior. Also, we use different mixtures to examine generality to simulate combustion of our results. Of course different reduced mechanisms are designed using different criteria and therefore are appropriate for different applications. However, for accurate analysis of hydrocarbon fuels oxidation, including ignition and extinction, which are very important in many


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applications, the most important combustion parameters are flame temperature, species concentrations, and ignition delay time. In this article, a two-step integrated procedure is introduced to reduce a detailed or skeletal mechanism to a lower order mechanism and is implemented for many practical conditions. In the first step sensitivity analysis of all reactions with respect to the flame temperature and NO concentrations are performed, and based on predefined cut-off limits non-significant reactions are determined. In the second step, a new approach called Gradual Evaluation of Ignition Error (GEIE) is used to identify less effective reactions on ignition delay time based on a predefined cut-off limit. The main contribution of this procedure is introduction of an exhaustive search in all elementary reactions with simultaneous using of three criteria, i.e., flame temperature, NO concentration, and ignition delay time. The other important contribution is using sensitivity analysis for the first two criteria, while we use zero dimensional model simulations for the third one. We show that this smart integration could significantly reduce recent well-built skeletal mechanisms as [7] without significant increase in relative errors. To show applicability of this method, two well-known mechanisms widely used in analysis of gas turbine combustors, i.e., the detailed mechanism of GRI-3.0 [48] for methane oxidation and skeletal mechanism of Wang [7] for kerosene are used to generate two new low cost skeletal mechanisms. Different 0D and 1D reactor models are used to fully examine the accuracy of these two skeletal mechanisms in prediction of combustion properties in a wide range of operating conditions, in comparison with their parent detailed or skeletal mechanisms. In section 2, we will present basis of the proposed methodology and apply it to produce two skeletal mechanisms for methane and kerosene. Then we will validate both of these reduced models under different combustion conditions. In the third and fourth sections, we use a set of homogenous reactor models to examine performance of the generated M1 and K1 skeletal mechanisms in a very wide range of combustion conditions, and are compared with the parent mechanism.

2. Methodology of Mechanism Reduction 2.1.

General Description

To design new reduced mechanisms from detailed or skeletal mechanisms many different methods are proposed which are reviewed in the introduction. Here a new approach is presented which simultaneously uses three different criteria, i.e., the flame temperature, the ignition delay time, and NO concentration, to eliminate less significant reactions for simulation of oxidation of hydrocarbon fuels oxidation under high temperature conditions. The approach combines Sensitivity Analysis (SA) together with a procedure called Gradual Evaluation of Ignition delay Error (GEIE), used to minimize the error propagation in prediction of ignition delay time. The main motivation to use sensitivity analysis is its extensive usage in design of skeletal mechanisms by elimination of less significant reactions, both in simple procedures like [28, 44, 49] and also in more complex procedures [35, 37, 50] for design of skeletal mechanisms. The reason to select three specific different parameters for reduction procedure, i.e., flame temperature, ignition delay time, and also NO concentration, is their critical importance for most industries applications. An advantage of this procedure is that these criteria are simultaneously considered, and the procedure results in a fairly optimum


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skeletal mechanism, based on selected threshold values for all of them. We will see that the procedure is easily implemented, is applicable to all detailed or skeletal mechanisms, and results in a fairly optimum skeletal mechanism. Although the time complexity of this procedure is more than some of the other similar methods, since this is performed only once to design a new skeletal mechanism, this higher computational cost is not important. The main computational cost is due to the CPU time used in two or three dimensional simulations, in which the skeletal mechanisms designed by the new procedure is certainly much more efficient than alternative mechanisms. Sensitivity analysis for oxidation of methane and kerosene with respect to the flame temperature and NO concentration shows that normalized sensitivity factors of different reactions covers a wide range of five levels of order of magnitude (from 10-3 to 10+1). The reactions corresponding to the first two levels of the order of magnitude of normalized sensitivity factors may be removed only if the elimination of such reactions does not make the ignition delay error more than the predefined cut-off limit of 3%. Details of this procedure follows.

2.2.

Basic Definitions

Here, we make a few definitions which are later used in description of the reduction procedure. NSF: Normalized sensitivity factor is defined for each reaction with respect to a specific parameter, e.g., flame temperature or NO concentration, based on equation 1. IER: Ineffective reactions are those with a sensitivity factor respect to a specific combustion feature computed by the IGNITION model of CHEMKIN to be about zero. For instance, IERXNO includes those reactions that based on IGNITION model have almost no impact on concentration of NO. LER: Less effective reactions are reactions with values of NSF below a threshold value selected by ourselves. The calculated NSFs for both flame temperature and NO concentration for all reactions may be classified to two groups based on their order of magnitude. The first lower two orders of magnitude are designated “less effective”. Here we have set this threshold value equal to 10-1, i.e., if NSF lays between 10-3 and 10-1 the reaction is classified as a less effective reaction. ILER: It is the onion of IER and LER sets of reactions. COL: Cut-off limits are the threshold values used for different NSFs with respect to major combustion parameters, i.e., flame temperature, NO concentration and ignition delay time, to distinguish ineffective reactions and removing those reactions from our list of effective reactions. If three effectiveness criteria of a reaction are simultaneously examined and all of them are small enough, then that reaction is totally removed from list of reactions. For flame temperature and NO concentration if the reaction belongs to IER or LER, it is considered below the COL. For ignition delay time, we use a homogeneous zero dimensional simulation model and assign a maximum acceptable relative error in computation of ignition delay, preset here to 3% as the COL. A higher value will increase the number of acceptable reactions. The GEIE approach is used to apply this preset value with respect to the base mechanism, to limit the error propagation.


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2.3.

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Sensitivity Analysis

Sensitivity analysis can be performed using the base mechanism to identify the effectiveness of each reaction on flame temperature and concentration of pollutant emissions (i.e., NO). Normalized sensitivity factors (NSF) is calculated by:

NSFυ = here

∂ lnυ , υ = Tf or X NO ∂ lnαi

(1)

αi is the pre-exponential factor of the ith reaction.

2.4.

Gradual Evaluation of Ignition Error (GEIE)

In this procedure, all reactions are examined in an exhaustive search one by one. In each iteration, only one reaction is temporarily removed and the ignition delay of the remaining set of reactions is computed based on zero dimensional IGNITION model of CHEMKIN. Then, it is compared with the base mechanism ignition delay as shown in equation 2. If this relative error is less than the cut-off limit for ignition delay time (COLτign), the reaction is considered to be less effective for ignition delay. The value of COLτign is selected based on the level of desired accuracy of the final reduced mechanism, and is optionally selected here equal to 3%. Obviously selecting a higher value for COLτign results in higher errors in off design conditions. This GEIE approach guarantees to partially limit the error propagation for ignition delay time. The flowchart of this approach is illustrated in figure 1. Note that no reaction is removed at this stage, and only the less effective reactions are recognized.

%COL τ ign =

τ i , base − τ i , skl × 100 τ i , base

(2)

Start Get data (base mechanism, operating conditions) Calculate τign,base Construct skeletal mechanism by eliminating reaction i Calculate τign,skl

i=i+1 N

Check. COL of τign,skl

N

Y Add reaction I to the list of effective reactions


i=NR

Y

End

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Fig 1. Flow chart of the GEIE approach

2.5.

Description of The Whole Algorithm

The whole algorithm is illustrated in figure 2. NR is the number of reactions included in the base mechanism. Start Get data (base mechanism, operating condition) Sensitivity analysis w.r.t. Tf and XNO using IGNITION model Sorting NSFTf and NSFXNO in order of magnitude groups Identifying ILERTf and ILERXNO Identifying LERτign using GEIE approach i=1

Y

Does reaction i belong to the common set of ILERT, ILERXNO, LERτ

Remove reaction i N i=NR

N

N i=i+1

Y End

Fig 2. Flow chart for reduction of a detailed or skeletal mechanism to obtain a skeletal mechanism.

The algorithm may be described as follows: •

The reference operating conditions are assigned.

•

For each reaction of the base mechanism, NSFTf and NSFXNO are determined.

•

It is determined if each reaction belongs to IERTf and IERXNO (or LER).

•

Using GEIE if any reaction has an ignition delay relative error less than the COL is labeled as a less effective reaction LERτ.

•

Any reaction included in (IER or LER) Tf and (IER or LER) XNO and LERτign is removed from the base mechanism.

This procedure is applied to two base mechanisms: •

The detailed mechanism of GRI-3.0[48] for oxidation of methane with 325 reactions and 53 species, which resulted in a skeletal mechanism called here M1, with 118 reactions and 39 species.


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•

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The skeletal mechanism of Wang [7] for oxidation of kerosene with 382 reactions and 106 species, which resulted in a skeletal mechanism called here K1, with 180 reactions and 79 species.

Now we will study validity of these two mechanisms under different combustion conditions.

2.6.

Applying The Procedure to Different Base Mechanisms

We apply the proposed procedure to the methane fuel. The basis or reference combustion condition for this reduction procedure is: T0=1500 K, ɸ=1.0, and P=1.0 atm. The detailed mechanism of GRI-3.0 for oxidation of methane (with 325 reactions and 53 species) is used, which resulted in a skeletal mechanism called here M1, with 118 reactions and 39 species. Table 1 shows all reactions removed in the procedure. Among the removed reactions, there are several sub-mechanisms which lead to discard the following less effective species: C2H2, CH2OH, CH2CO, C3H7, CH3OH, NH2, CH3CHO, C2H, NO2, HCNN, HCNO, NH3, HCCON, and HOCN. Removed reactions with their corresponding species are presented in table 1. We will show that the elimination of 207 reactions from the GRI-3.0 mechanism under high temperature leads to negligible error for prediction of ignition delay time, concentration of NO, and flame temperature. To show the generality of the proposed approach for other hydrocarbon fuels, the procedure is also applied for kerosene. The reference condition for this reduction procedure is: T0=1500 K, ɸ=1.0, and P=1.0 atm. We use the skeletal mechanism introduced by Wang [7] (with 382 reactions and 106 species) and reduce it to a skeletal mechanism called here K1, with 180 reactions and 79 species. Table 2 shows all reactions removed in the procedure. The proposed procedure has resulted in removal of 27 species of the skeletal mechanism of Wang as follows: C5H813, CH3HCO, IC4H5, CH3CO, PHHCO, MEALL, PHCO, C5H913, CC9H17C, TC3H5, IC4H3, CPD, BPHC3H6, SC3H5, SCH2, CPHC3H6, DC8H17, APHC3H6, STYREN, C5H7, C4H73, C5H5O13, BPHPROPY, C6H1115, C6H1112, C5H4OH, and C2H4O2H. Sub mechanism related to these species which are removed from the skeletal mechanism are shown in table 2. Also a number of reactions are removed which do not contribute in removal of any specific species from the reference mechanism. We will show that discarding of the above-described reactions (202) together with the relevant species (27) leads to small accuracy deterioration. Removal of such less effective reactions from the reference mechanism for combustion under high temperature conditions, results in a fast computation of the net rate of creation of species. One observes in table 2 that removal of most submechanism has significantly reduced the number of reactions. In fact two of them include 11 reactions, and each of the remaining 1, 2, 2, 4, 4, 4, 2, and 5 sub-mechanisms respectively include 11, 10, 8, 7, 6, 5, 4, 3, and 2 reactions.


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Table 1. Eliminated reactions with their corresponding species from the GRI-3.0 mechanism for high temperature methane-air combustion. C2H2 O+C2H2 O+C2H2 O+C2H2 H+C2H(+M) H+C2H2(+M) H+C2H3 OH+C2H2 OH+C2H2 OH+C2H2 OH+C2H2 OH+C2H3 C+CH3 CH+CH2 CH+HCCO CH2 C2H+H2 C2H4(+M) HCCO CH2+CH2 C2H3+O2 O+C3H8 H+C3H8 OH+C3H8 C3H7+H2O2 CH3+C3H8 CH3+C2H4(+M) O+C3H7 H+C3H7(+M) H+C3H7 OH+C3H7 HO2+C3H7 HO2+C3H7 CH3+C3H7

=> C3H7

CH2OH H+HCCO OH+C2H CO+CH2 C2H2(+M) C2H3(+M) H2+C2H2 H+CH2CO H+HCCOH C2H+H2O CH3+CO H2O+C2H2 H+C2H2 H+C2H2 CO+C2H2 H2+C2H2 H+C2H2 H2+C2H2(+M) 2CO+C2H2 2H+C2H2 HO2+C2H2

=> => => => => =>

O+C2H3 O+CH2CO O+CH2CO H+CH2CO H+CH2CO H+HCCOH OH+C2H2 OH+CH2CO CH+CH2O CH2+CO(+M) H+CH2CO(+M) H+CH2CHO OH+CH2CHO

O+C2H O+C2H2 H+C2H(+M) OH+C2H OH+C2H2 C+CH2 C2H+O2 C2H+H2

HCNN(+M) CO+H+N2 HCN+NO O+HCO+N2 H+HCO+N2 CH2+N2

CH2+NO CH2(S)+NO HCNO+H HCNO+H HCNO+H HCCO+NO

NH2+O NH2+O NH2+H NH2+OH HCN+OH HNCO+H HNCO+OH HCNO+H NH3+H NH3+OH NH3+O

CH+CO OH+C2H C2H2(+M) H+HCCO C2H+H2O H+C2H HCO+CO H+C2H2

HO2+NO NO+O+M NO2+O NO2+H CN+NO2 NCO+NO2

H+HCNO H+HCNO H+HNCO OH+HCN NH2+CO HCNO+CO

NH3+H NH3+OH NH3+O

HCN+OH HOCN+H

OH+NH H+HNO NH+H2 NH+H2O NH2+CO NH2+CO NH2+CO2 NH2+CO NH2+H2 NH2+H2O NH2+OH

NO2+OH NO2+M NO+O2 NO+OH NCO+NO N2O+CO2

NH3

HOCN H+CH2CO H+HCCOH

H+CH2CO OH+HCCO CH2+CO2 HCCO+H2 CH3+CO H+CH2CO H+CH2CO HCCO+H2O H+CH2CO CH2CO(+M) CH2CHO(+M) CH2CO+H2 H2O+CH2CO

NO2

HCNO

NH2 OH+CH2OH OH+CH3 CH3OH(+M) CH3OH(+M) CH2OH+H2 CH3O+H2 CH3OH(+M) CH2OH+H2O CH3O+H2O CH3OH(+M) CH2OH+CH4 CH3O+CH4

C2H H+CH3CHO OH+CH2CHO OH+CH3+CO HO2+CH3+CO CH2CHO+H2 CH3+H2+CO CH3+H2O+CO CH3+H2O2+CO CH3+CH4+CO

HCCOH H+HCCOH OH+C2H2

O+CH3OH O+CH3OH H+CH2OH(+M) H+CH3O(+M) H+CH3OH H+CH3OH OH+CH3(+M) OH+CH3OH OH+CH3OH CH2(S)+H2O(+M) CH3+CH3OH CH3+CH3OH

HCNN CH+N2(+M) HCNN+O HCNN+O HCNN+O2 HCNN+OH HCNN+H

CH2CO OH+CH2O OH+CH2OH CH2OH(+M) CH3OH(+M) H2+CH2O OH+CH3 CH2(S)+H2O H+CH2OH CH2OH+H2 H2O+CH2O CH2OH+H2O CH2OH+CH4 HO2+CH2O HCO+CH2OH C2H5+CH2OH

CH3OH OH+C3H7 C3H7+H2 C3H7+H2O HO2+C3H8 C3H7+CH4 C3H7(+M) C2H5+CH2O C3H8(+M) CH3+C2H5 C2H5+CH2OH O2+C3H8 OH+C2H5+CH2O 2C2H5

CH3CHO O+C2H5 O+CH3CHO O+CH3CHO O2+CH3CHO H+CH3CHO H+CH3CHO OH+CH3CHO HO2+CH3CHO CH3+CH3CHO

O+CH2OH O+CH3OH H+CH2O(+M) H+CH2OH(+M) H+CH2OH H+CH2OH H+CH2OH H+CH3O H+CH3OH OH+CH2OH OH+CH3OH CH3+CH3OH CH2OH+O2 OH+CH2CHO OH+C3H7

HOCN+H H+HNCO


NH2+H2 NH2+H2O NH2+OH

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Table 2. Eliminated reactions with their relevant species from the Wang mechanism under high temperature kerosene-air combustion. C5H913 NC4H5 IC4H5 C5H813 C5H813 C5H813 C5H813 C5H813 C5H813 C5H813 C5H813 C4H6 C4H6 C4H6 C4H6 IC4H5 CH3HCO CH3HCO CH3HCO CH3HCO CH3HCO CH3CO TC3H5 C4H8 C4H8 C4H8 C4H8 MEALL MEALL MEALL C5H813 AC5H10 AC5H10 C5H913 C5H913 CC9H17C C5H913 C5H5 CPD CPD CPD C5H7 C3H6 C3H6 SC3H5 SC3H5 C2H2

+ + + + + + + + + + + + + + + + + + + + + + + + + +

CH3 CH3 O2 OH OH O O H H OH HO2 OH O CH3 O2 HO2 OH H O2 CH3 M O2 O O2 OH H

+ + + + +

O2 AC3H5 OH O2 OH

+ + + + +

O2 H(+M) O2 OH H

+ +

OH CH3

+ +

O2 CH3

PHC3H7 PHC3H7 PHC3H7 CPHC3H6

+ + +

OH O2 PHCH2

PHC3H7 PHC3H7 PHC3H7 APHC3H6 C5H813 C5H813 C5H7 C3H6 C3H6 TC3H5

+ + +

H OH CH3

+ +

H OH

+ +

OH H

C5H5 C5H5O13

+

HO2

C6H1112 C6H1115 C5H5 C5H5O13

+

HO2

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = => => = = = = = = = = = =

C5H813 + H C5H813 C5H813 ACROL + CH3HCO CH3HCO + AC3H5 CH2O + MEALL ACROL + C2H4 CH2O + C4H6 C5H7 + H2 AC3H5 + C2H4 C5H7 + H2O IC4H5 + H2O2 IC4H5 + H2O IC4H5 + OH IC4H5 + CH4 C2H3CO + CH2O CH3CO + H2O2 CH3CO + H2O CH3CO + H2 CH3CO + HO2 CH3CO + CH4 CH3 + CO+M CH3CO + CH2O C2H5 + CH3CO MEALL + HO2 MEALL + H2O MEALL + H2 C4H6 + H C4H6 + HO2 C4H6 + C3H6 CH2O + MEALL C5H913 + HO2 C5H913 + H2O C4H6 + H3 C5H813 + H 2C2H4 + C5H913 CH2O +ACROL+CH3 CPD(+M) C5H5 + HO2 C5H5 + H2O C5H5 + H2 CPD + H SC3H5 + H2O SC3H5 + CH4 PC3H4 + H CH3HCO + HCO SC3H5

237 238 239 240 241 242 243 244 245 246 247 159 161 162 165 166 94 95 96 97 98 99 119 149 143 145 150 153 154 155 242 234 235 236 237 343 363 188 194 195 196 248 105 114 116 117 382

C2H5 CH3HCO CH3HCO CH3HCO CH3HCO CH3HCO CH3HCO SC3H5 C4H8 C5H813 C5H813 IC4H5 IC4H5 IC4H5 IC4H5 IC4H5(+M) PHCH2O PHCH2 PHHCO PHHCO PHHCO PHHCO PHHCO PHHCO PHHCO PHHCO PHHCO PHHCO PHHCO PHHCO PHCO CYC9H18 CYC9H18 CYC9H18 CYC9H18 CYC9H18 CC9H17C PHC3H7 PHC3H7 PHC3H7 BPHC3H6 BPHC3H6 SCH2 SCH2 SCH2 SCH2 HCCO

= = = =

CPHC3H6 CPHC3H6 CPHC3H6 STYREN

+ + + +

H2O HO2 TOLUEN CH3

354 355 356 357

DC8H17 DC8H17 AC8H17 AC8H17

= = = = = = = = = =

APHC3H6 APHC3H6 APHC3H6 PHCH2 C5H7 C5H7 CPD TC3H5 TC3H5 AC3H5

+ + + + + + + + +

H2 H2O CH4 C2H4 H2 H2O H H2O H2

344 345 346 347 344 345 346 344 345 346

C6H5 STYREN BPHPROPY CPHC3H6 C4H73 C4H73 CYC9H18 TC3H5 TC3H5 PC3H4

= =

C5H5O13 NC4H5

+ +

OH CO

185 191

= =

C6H1115 AC3H5 = =

C5H5O13 NC4H5

+ +

OH CO

C2H4

+

+

O

+ + + + + + + + + + + + +

HO2 OH H O2 CH3 O2 O O2 OH O HO2 CH2O CH3

+

O

+ + + + +

O2 HO2 OH H CH3

+ + + + +

O2 HO2 OH H CH3

+ + + + +

O2 HO2 OH H CH3

+ + +

OH AC3H5 PHCH2

+ + + + +

M C2H2 H2O CO2 H

= = = = = = = = = = = => = = = = = = = = = = = = = = = = = = = = = = = = => = = = = = = = = = =

CH3HCO + CH3 + CH3CO + CH3CO + CH3CO + CH3CO + CH3CO + CH3HCO + CH3HCO + ACROL + CH3HCO + CH2CO + CH2CO+C2H3+ C4H6 + C5H813 C4H4 + PHHCO + PHHCO + PHCO + PHCO + PHCO + PHCO + PHCO + PHCO + PHCO + PHCO + PHCO + PHCO + PHCO + PHCO + C6H5 + CC9H17C + CC9H17C + CC9H17C + CC9H17C + CC9H17C + 2C2H4 + BPHC3H6 + BPHC3H6 + BPHC3H6 + C6H5 + BPHPROPY CH2 + C3H3 + CH2 + CH2O + SCH2 +

= = = =

= = + = => =

STYREN C6H6 STYREN STYREN C2H4 C4H6 NC3H7 CH3CO CH2CO TC3H5

C6H1116 C6H1112

= =

C6H1112 C6H1115

307 308

BPHC3H6 BPHPROPY

= =

BPHPROPY STYREN

307 308

C5H5 C5H4OH

HO2

=>

+

C2H4

C2H5 NC3H7 DC8H17 DC8H17

=> C2H4 + O2 + O + H

+

C2H4O2H


OH

= = = =

= =

C5H4OH C5H4O

H HCO H2O2 H2O H2 HO2 CH4 HCO C2H4 CH3HCO AC3H5 C2H3 OH HCO H(+M) H H H HO2 H2O2 H2O H2 CH4 H HO2 H2O2 H2O H2 CH4 CO HO2 H2O2 H2O H2 CH4 C5H913 H2O C3H6 TOLUEN TOLUEN M H H2O CO CO

+ +

+ + + + + + + + +

56 93 94 95 96 97 98 117 148 240 241 167 168 172 239 375 220 221 223 224 225 226 227 228 223 224 225 226 227 228 229 311 315 320 327 331 343 348 349 350 351 352 38 39 40 41 89

AC6H12 AC5H10

258 259 261 262

H C2H2 CH3 CH3 C2H3 H C4H73 CH2O CH3

204 231 253 257 344 345 346 344 345 346 306 307

+

352 353

CH3 + +

H H

307 308

Page 11 of 31

2.7.

Validation of the Procedure Under Different Combustion Conditions

Here we study validity and accuracy of M1 skeletal mechanism under a fairly wide range of operational conditions. Variations of the relative error for flame temperature, ignition delay time, and NO concentration for simulation M1 skeletal mechanism by IGNITION model of CHEMKIN are illustrated in figures 3-4. For M1 skeletal mechanism, the relative error for flame temperature and ignition delay time for similar operational conditions are given in figure 4, and computed concentration of NO is shown in figure 5. Summary of results are illustrated in table 3. The relative error for flame temperature is less than 0.1%, and for delay time is often less than 2%.The relative error of NO concentration is also often less than, 1.25%.

2

5

0.5

3

0 2

-0.5 -1

1 -1.5

0.5

0.75

1

1.25

0

1.5

1

2

0

0

-1

-2

-2 1500

1550

1600

Equivalence ratio

1650

1700

-4 1800

1750

Inlet temperature(K) 2

Methane-air combustion P=10.0 atm,T0=1800 K

2

8

0

0

-2

-8

1

1.5

2

Relative error for flame temperature(%)

(c)

-4 0.5

2

16

Relative error for ignition delay time(%)

4

(d)

Methane-air combustion φ=1, T0=1800 K

1

1

0

0

-1

-1


-2

4


4 1


1.5

2 (b) Methane-air combustion P=1 atm, φ=1.0

Methane-air combustion P=1.0 atm, T0=1500 K



(a)


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

-16

Equivalence ratio

-2

0

5

10

15

20

25

-2 30

Pressure(atm)

Fig 3. Relative errors for flame temperature and ignition delay time for skeletal mechanism of M1 methane under different conditions. The variable parameter is: a) ɸ (P=1atm and T=1500K) b) Inlet temperature (P=1atm and ɸ=1) c) ɸ (P=10atm, and T=1800K) d) pressure (ɸ=1.0 and T=1800K).


Energy & Fuels

16

2 Methane-air combustion P=1.0 atm, T0=1500 K

(b) Methane-air combustion P=1atm,φ=1

Relative error for NO concentration(%)

Relative error for NO concentration

(a)

8

0

-8

-16

0.5

0.75

1

1.25

1

0

-1

-2 1500

1.5

1550

Equivalence ratio

1650

1700

1750

1800

2 Methane-air combustion P=10 atm, T0=1800 K

(d)


(c)

1

0

-1

-2

1600

Inlet temperature(K)

2


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 12 of 31

0.5

1

1.5

1

0

-1

-2

2

Methane-air combustion φ=1, T0=1800 K

5

10

Equivalence ratio

15

20

25

30

Pressure(atm)

Fig 4. Relative errors for NO concentration for skeletal mechanism of methane under different conditions. The variable parameter is: a) ɸ (P=1atm and T=1500K) b) Inlet temperature (P=1atm and ɸ=1) c) ɸ (P=10atm, and T=1800K) d) pressure (ɸ=1.0 and T=1800K).

Cases

Table 3. Summary of relative errors for simulation of M1 methane ignition by IGNITION Inlet Pressure Equivalence Relative error Relative error Relative error temperature [atm] ratio of Tf of τign of XNO [K]

a

1500

1.0

0.5-1.5

0.1

1.6

9.5

b

1500-1800

1.0

1.0

0.05

1.2

1.2

c

1800

10.0

0.5-2.0

0.8

6.4

1.2

d

1800

1-30

1.0

0.05

0.02

0.8

Comparisons between errors under different conditions show that the maximum relative error is usually below 2%. Therefore to predict flame temperature, NO concentration and ignition delay time, the M1 skeletal mechanisms follow the base mechanism with a much less number of reactions, which will lead to a significant faster computational performance in 3D CFD computations. Now we study the validity and accuracy of K1 skeletal mechanism under a fairly wide range of operational conditions. Variations of the relative error for flame temperature and ignition delay time for simulation of K1 skeletal mechanism by IGNITION model of CHEMKIN are illustrated in figure 5.


Page 13 of 31

Figure 5a (condition a) shows that for atmospheric pressure, inlet temperature of 1500 K, and equivalence ratio in the range of 0.5-2.0, the maximum relative error of 2.1% for flame temperature and 8% for ignition delay time is achieved. Under atmospheric pressure, stoichiometric equivalence ratio, and inlet temperature in the range of 1500-1800 K (condition b) almost similar relative errors are observed (figure 5b). Under pressure of 10 atm, inlet temperature of 1800 K, and equivalence ratio in the range of 0.5-2.0 (condition c) the relative errors of flame temperature and delay time are respectively less than 0.4% and 7.2%. Similarly under conditions of stoichiometric equivalence ratio, inlet temperature of 1800 K , and pressure in the range of 1-30 atm, the relative error for flame temperature and ignition delay time are again less than, respectively, 1.25% and 7.5%. Summary of these results are illustrated in table 4.

8

4

2

0

1

-4

16

1

1.25

-8 1.5

3

12

2

8

1

4

0 1500

1550

Equivalence ratio

16

12

0

8

-1

4

1

1.5

2


1


Kerosene-air combustion P=10.0 atm, T0=1800 K

0.5

1650

1700

1750

0 1800

2

16 (d)

-2

1600


2 (c)

Kerosene-air combustion P=1.0 atm, φ=1.0

0

Kerosene-air combustion φ=1.0, Τ0=1800 Κ

1

8

0

0

-1

-8

-2

0

5

10

15

20

25

30


0.75


3

0 0.5

4 (b)

Kerosene-air combustion P=1.0 atm, T0=1500 K



(a)


4


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

-16

Pressure(atm)

Equivalence ratio

Fig 5. Relative errors for flame temperature and ignition delay time for skeletal mechanism of K1 under different operational conditions. The variable parameter is: a) ɸ (P=1atm and T=1500K) b) Inlet temperature (P=1atm and ɸ=1) c) ɸ (P=10atm, and T=1800K) d) pressure (ɸ=1.0 and T=1800K).

Cases

Table 4. Summary of relative errors for simulation of K1 kerosene combustion parameters by IGNITION Inlet temperature [K] Pressure [atm] Equivalence ratio Relative error of Tf Relative error of τign

a

1500

1.0

0.5-1.5

2.1

8.0

b

1500-1800

1.0

1.0

2.0

7.0

c

1800

10.0

0.5-2.0

0.4

7.2

d

1800

1-30

1.0

1.25

7.5

Since we have used the IGNITION model, reactions most sensitive to the ignition delay time are remained. The base operational conditions for performing the reduction process (the design condition) are selected as ɸ=1, P=1 atm, and T0=1500 K. As the operational condition is moved from the design condition, the error in prediction of the ignition delay time is


Energy & Fuels

increased. Comparisons between errors under different conditions show that the maximum relative error for ignition delay time is below 8% under the worst off-design conditions (ɸ=0.5, 2.0, T0=1800 K) very far from the base operational conditions. Therefore to predict t the flame temperature and ignition delay time, the K1 skeletal mechanisms follow the base mechanism with a much less number of reactions, which will lead to a significant faster computational performance in 3D CFD computations.

3. Applicability of The Obtained Skeletal Mechanism M1 3.1.

Performance of M1 at Reference Combustion Condition

The validation of the M1 skeletal mechanism is done in comparison with the detailed GRI-3.0 mechanism under the reference high temperature operating condition: T0=1500 K, P=1.0 atm, ɸ=1.0. Three different configurations including IGNITION [51], PSR [52], and PREMIXED [53] of CHEMKIN software are used for simulations. First we use the IGNITION reactor model of CHEMKIN to examine the temporal performance of the M1 mechanism. In Figure 6, the temporal variation of the flame temperature, concentration of major fuel species, minor radicals and other selected species are compared with the detailed GRI-3.0 mechanism under the reference operating conditions. Results show that M1 follows very closely GRI-3 full mechanism. 100

2800 P=1.0 atm, T0=1500 K, φ=1.0 CH4-air combustion

CH4

2400

2200

2000

1800

10

-2

10

-3

Line: GRI-3.0 Symbol: Skeletal

0

0.5

1

1.5

+

CO +

+ +

+

+

NO

+ + + +

10

+

-4

CH3

+

+

+ + +

C2H4

+

C2H6

10-5

+ +

+

10

-7

10

-8

+ + + + +

CO2 Lines: GRI-3.0 Symbols: Skeletal

+

2

+ + + + + + + + + + + + + +

+

10-6

1600

1400

P=1.0 atm, T0=1500 K, φ=1.0 CH4-air combustion

10-1

Species mole fraction

Flame temperature(K)

2600

+

0

0.5

1

1.5

2

Time(Sec)

Time(ms) (a)

(b)

0

10


-1

10

0

O2

+ + + + + + + + + + H+ + + +

-2


10 CH2O

10-3

+ + +

10-4 + +

10-5

+

OH

-6

10

+

+

+

+ + +

+ +

+

+


10

10


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 31

+

+

O

+

-2

H2O

10

+ + + + + + + + + + + + + +

+

-4

+

+

+

+

+ + + + H2

+ +

+

+

+

+ +

+

+

C2H5

+

10

-6

10

-8

+ +

+

-7

10

+

+

+ +

Lines: GRI-3.0 Symbols: Skeletal


-8 +

10

10

-9

10

0.5

1

1.5

2

-10

0

0.5

1

Time(Sec)

Time(ms)

(c)

(d)


1.5

2

Page 15 of 31

Fig 6. (a) Temperature, (b) major fuel species, (c) minor radicals, and (d) other selected species versus time based on IGNITION model using the skeletal mechanism (M1) compared with the GRI-3.0 detailed mechanism, T0=1500 K, P=1.0 atm, ɸ=1.0.

The ignition delay time may be defined as the time during which the initial temperature of reactants reaches to the adiabatic flame temperature of final products. Therefore, one expects to see a rapid change in the temperature near the end of the ignition delay time period as shown in figure 6. This is consequently accompanied with a sharp change in species concentrations. Next we use the PSR model of CHEMKIN software [52] to study performance of the M1 in a homogenous reactor under the reference combustion conditions. Figure 7 shows variations of the flame temperature, concentration of the major fuel species, the minor radicals and other selected species with respect to a range of inlet temperatures, for different equivalence ratios ranged 0.5-2.0. All results are compared with results of the full GRI-3.0 mechanism. 2900

10

P=1.0 atm, φ=1.0 CH4-air combustion

P=1.0 atm, φ=1 CH4-air combustion

0

CO2

2800

10

-2

10

-4

10

-6

10

-8

CO



NO

2700

2600

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

CH3

+-

+-

+-

CH4 +-

+-

+-

+-

+-

-10

10

C2H6

2500 -12

10 Lines: GRI-3.0 Symbols: Skeletal

2400 900

1200

1500


1800

10-14 900

1200

1500

1800


Inlet temperature(K) (a)

(b) 100

10-1 P=1.0 atm, φ=1.0 CH4-air combustion

10-2 +

+

+

+

H+

+

+


OH +

+

+

+

+

+

+

+

+

+

+

+


O


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

10-3

10-4

10-5

H2O -1

10

CH2O O2

-6

10


H2

10

900


-2

-7

1200

1500

10

1800

900

1200

1500

1800


Inlet temperature(K) (c)

(d)

Fig 7. Variations of (a) temperature, (b)major fuel species, (c) minor radicals and (d)other selected species versus inlet temperature using PSR model for the M1 skeletal mechanism compared with the GRI-3.0 detailed mechanism, T0=900-1800 K, P=1.0 atm, ɸ=1.0.

To study the applicability of the M1 mechanism in homogeneous simulations that include transport effects, the PREMIXED model of CHEMKIN software [53], is used. Figure 8 shows the spatial variation of mass density and axial velocity, concentration of major fuel species, minor radicals and other selected species, and they are compared with the detailed GRI3.0 mechanism. The agreement between the detailed and the skeletal M1 schemes is excellent.


Energy & Fuels

1.4

3

100

2.5

10-1



1.2

0.8 1.5 0.6 1

CO2 CO

10-2


2

Axial velocity(m/s)

Mass density(kg/m3)

1

CH4 + + + +

+

-3

10

+

C2H6

+ +

+

+

+

+ + + +

+ +

-4

10

+

+ + +

+ + + +

-5

10

0.4

CH3

NO +

+

+

+

0.5

0.2

0

0

0.05

0.1

10

C2H4


+

-7

10

0 0.2

0.15

+

-6

Lines: GRI-3.0 Sumbols: Skeletal

+

0.06

0.08

0.1

0.12

0.14

Distance(cm)

Distance(cm) (a)

(b)

-2

101

10


+

+

+

+ + + + +

+ 0

O

+ + + +

-3

10

CH2O

H2O -1

10


+ + + + +

H + + + +

-4

10

+ + + + + + + + +

10-5 OH


10

+ +


-2

10

+

+

+

+

+ + + + + + + + + + + + + + + H2 + +

+

+

+

+

10

10-4 C2H5

-5

+ +

O2 +

-3 +

10

-6

10


+ +


-7

-6

10 0.02

0.04

0.06

0.08

0.1

10

0.12

0

0.05

Distance(cm)

0.1

0.15

0.2

Distance(cm)

(c)

(d)

Fig 8. Spatial variation of (a) mass density and axial velocity, (b)major fuel species, (c)minor radicals and (d) other selected species in PREMIXED model predicted by the M1 skeletal mechanism and compared with the GRI-3.0 detailed mechanism, T0=300 K, P=1.0 atm, ɸ=1.0.

3.2.

Performance of M1 at Different Combustion Condition

In this section, effects of different inlet temperatures, different equivalence ratios and different pressures on the combustion characteristics of methane oxidation, including ignition delay time, flame temperature, gas velocity, concentration of major species, and minor radicals are examined under different operating conditions. Figure 9 shows the ignition delay time based on the inlet temperature in the range of 1500-1800 K, equivalence ratios in the range of 0.5-2.0, and the pressures of 1.0, 15.0, and 30.0 atm. 10-2

10

-3

T0=1600 K CH4-air combustion


1.0 atm

Ignition delay time(Sec)


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 16 of 31

-3

10

15.0 atm

10-4

30.0 atm

1.0 atm

10-4 15.0 atm

30.0 atm


Lines: GRI-3.0 Symbols: Skeletal -5

10

0.5

1

1.5

10

2

-5

0.5

1

Equivalence ratio

1.5

Equivalence ratio


2

Page 17 of 31

(a)

(b)

-3

-3

10

10 T0=1700 K CH4-air combustion




1.0 atm

-4

10

15.0 atm 30.0 atm

10-5

1.0 atm

10-4

15.0 atm

10-5

30.0 atm



0.5

1

1.5

10

2

0.5

1

Equivalence ratio

1.5

2

Equivalence ratio

(c)

(d)

Fig 9. Ignition delay time versus equivalence ratio computed by IGNITION model by the M1 skeletal mechanism and compared with the GRI-3.0 detailed mechanism, T0=1500-1800 K, P=1.0, 15.0, 30.0 atm, ɸ=0.5, 1.0, 1.5, 2.0.

Figure 10 shows the temporal variations of the flame temperature, concentration of major fuel species, minor radicals and other selected species. Simulations are performed by IGNITION model of CHEMKIN. Results are compared with the detailed GRI-3.0 mechanism under different operating conditions, and again one observes excellent agreement between them.

101

2600 P=1.0 atm, T0=1500 K, φ=0.5 CH4-air combustion

10


0

2400

CH4

-1

2200

2000

1800

1600


10

-2

+ + + + + + + +

10

-3

10-4 10-5 10

-6

10

-7

0

0.5

1

1.5

2

10

-8

* + + *+ *+ +

0

*

2E-05


0.0001


100

-3

O2


CH2O

-5

OH

H O

-6

10-1

-2

H2O

10

H2 -3

10

C2H5

-4

10

10-7

10

8E-05

(b)

10-4

10

6E-05

101

-1

10-2

10

4E-05

Time(Sec)

(a)

10

NO


Time(ms) 10

CO

+ + + + + + + * * * * * +* * * * +* * * *+ * *+ + CH3 * *+ + * + * + * + C2H4 * + * + * + * + C2H6 + * + * * +

* +

1400

CO2

+ +



10


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



-8

-5

0

5E-06

1E-05

1.5E-05

2E-05

2.5E-05

10

3E-05

0

2E-06

Time(Sec)

4E-06

6E-06

8E-06

1E-05

Time(Sec)

(c) (d) Fig 10. Temporal variations of (a) temperature, (b) major fuel species, (c) minor radicals and (d) other selected species using IGNITION model predicted by the M1 skeletal mechanism and compared with the GRI-3.0 detailed mechanism, T0=1500-1800 K, P=1.0, 10.0, 20.0, 30.0 atm, ɸ=0.5, 1.0, 1.5, 2.0.


Energy & Fuels

To examine performance of the M1 mechanism under different combustion conditions in a homogenous reactor, the PSR model of CHEMKIN is used. Figure 11 shows variations of the flame temperature, major fuel species, minor radicals and other selected species versus inlet temperature in the range of inlet temperature of 300-1800 K, equivalence ratio of 0.5, 1.0, 1.5, 2.0 and pressures of 1.0, 10.0, 20.0, 30.0 (atm.). To examine how the new M1 mechanism behaves in full CFD computations, the spatial variations of the M1 model in the homogenous PREMIXED model of CHEMKIN is used. Figure 12 shows the spatial variations of mass density and axial velocity, concentration of major fuel species, minor radicals and other selected species and also compares the results with the basis detailed GRI-3.0 mechanism. It is easily observed that a very close agreement is achieved for all cases.

101

2600 P=1.0 atm, φ=0.5 CH4-air combustion

100


2400 CO2

-1



10

2200

2000

1800

10-2

CO

NO

-3

10

10-4 + + + - - - + + + + - - CH4 - +- +- + + - - +- + + - - +- + CH3 - +- +- + - +- +- + - +- ++- +- +- + +- +- -6 + -5

10

1600

10



-7

1400 300

600

900

1200

1500

10

1800

300

600


900

(a)

+

+

+

+

+

+

+

1500

1800

(b) 100

P=20.0 atm, φ=1.5 CH4-air combustion +

1200


100 +

+

+

+

+

+

+

H2O +

+

P=30.0 atm, φ=2.0 CH4-air combustion +

+

+

+

10-1

-1

10

H2O


H2


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 31

-2

10

H -3

OH

10

O2

-4

10

-2

10

H -3

OH

10

-4

10

O2

O -5

-5

10

10



-6

10

800

1000

1200

1400

1600

1800


10 1400

1500

1600

1700

1800


(c)

(d)

Fig 11. Variations of (a) flame temperature, (b) major fuel species, (c) minor radicals and (d) other selected species versus inlet temperature using PSR model simulated by the M1 skeletal mechanism and compared with the GRI-3.0 detailed mechanism, T0=300-1800 K, P=1.0, 10.0, 20.0, 30.0 atm, ɸ=0.5, 1.0, 1.5, 2.0.


Page 19 of 31

1.4

100

25



15 0.8 10 0.6


1

-2

10

-3


0.2

0

0.1

0.2

0.3

0.4

0.5

10-5 0.04

0 0.7

0.6

CO

- *+ *- * *+ - + * + * + * +* + +* * + +* CH3 + * +* +* + * C2H4 +* * * + + * + * * C2H6 + * + + +*

10-4

5

0.4

10

CO2

CH4

10-1

20

Axial velocity(cm/s)

3

Mass density(kg/m )

1.2

*+

0.05

0.06

0.07

(a) 101 P=20.0 atm, T0=300 K, φ=1.5 CH4-air combustion

10

0


H2O

H2O

-1

10


H2

10-2 -3

10

10-4

0.08

(b)

1

10

100

NO Lines: GRI-3.0 Symbols: Skeletal

Distance(cm)

Distance(cm)


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

O2 Lines: GRI-3.0 Symbols: Skeletal

H

+

+ + + + +

+

+

+

+

+

+

+

+

OH

+

10-5

+ + + +

-6

10

+ +

10-7

O

10

-1

10

-2

H2

10-4 10

-5

10

-6

10

+

O2

10-3

-7

H + + + + + + + + + + +


+

-8

+

+

+

-8

+

0.06

OH

O

+

+

10 0.05

+ + +

0.07

0.08

0.09

10 0.02

0.1

0.04

Distance(Sec)

0.06

0.08

0.1

Distance(cm)

(c)

(d)

Fig 12. Spatial variation of (a) mass density and axial velocity, (b)major fuel species, (c) minor radicals and (d) other selected species using PREMIXED model predicted by the M1 skeletal mechanism and compared with the GRI-3.0 detailed mechanism, T0=300 K, P=1.0, 10.0, 20.0, 30.0 atm, ɸ=0.5, 1.0, 1.5, 2.0.

3.3.

Speed Up of The M1 Mechanism

To investigate the speed up of the M1 skeletal mechanism in comparison with the detailed GRI-3.0 mechanism, PSR, IGNITION and PREMIXED reactor models of CHEMKIN software are used here. Table 5 shows the run time of the M1 mechanism in comparison with the GRI-3.0. Run times obtained by IGNITION model show that the run time of the M1skeletal mechanism is 72% less than the GRI-3.0 mechanism, while the usage of the M1 skeletal mechanism in the PREMIXED model reduces the run time by 80%. One may use the M1 skeletal mechanism in an optimization procedure as well. Assume one wants to optimize the rate coefficients of a five-step global mechanism to fit a detailed GRI-3.0 mechanism, using a PSR-PFR reactor model, Using M1 mechanism in this optimization problem may reduce the run time by more than 75%.

Model Ignition PSR Premixed PSR-PFR with Optimization

Table 5. Comparing run times of the present mechanism with GRI-3.0 mechanism Run time(Sec) objective or target GRI-3.0 Skeletal Species concentration, Sensitivity coefficients 110 30 Species concentration, Sensitivity coefficients 2.0 0.5 Species concentration, Sensitivity coefficients 36 7 Optimum rate coefficients of a five-step global mechanism 10000 2500 (for 5000 iteration)


Energy & Fuels

4. Applicability of K1 Skeletal Mechanism 4.1.

Performance of K1 at The Reference Combustion Condition

To analyze the performance of the K1 skeletal mechanism produced by the proposed procedure, its performance at a reference operating condition is compared with the base (skeletal) mechanism of Wang[7] for kerosene oxidation (74% ndecane-15% n-propyl benzene, 11% n-propyl cyclohexane). Performance of this mechanism is examined. The reference combustion condition is: stoichiometric equivalence ratio, atmospheric pressure, and inlet temperature of 1500 K. The base mechanism include 382 reactions, 106 species, and the proposed procedure has produced a K1 skeletal mechanism including 180 reactions, 79 species. Here we will use three reactor models including IGNITION [51], PSR [52], and PREMIXED [53] of CHEMKIN software. In Figure 13, the temporal variations of the flame temperature, concentration of major fuel species, minor radicals and other selected species predicted by the proposed skeletal mechanism are compared with results of [7] for the same operating conditions. Therefore the temporal performance of K1 and the skeletal mechanism of Wang are very similar. 100

2800 Wang -382 reaction & 106 species Present- 180 reaction & 72 species

(a)

2600

Lines: Wang (382 reaction,106 species) Sybols: Present (180 reaction, 72 species)

(b)

10-1 Species mole fraction

Temperature(K)

2400 2200 2000 1800 1600

C2H4 n-decane

10-2

CO

n-propylbenzen

10-3

10-4

1400 1200 -7 10

10-6

10-5

10-4

Time(Sec)

10-510-7

10-3

10-6

10

-1

10

-2

10-2

+

+


+ + + + +

CH2O

+ +

-3

+

-4

+ + + + +

10

+

OH

HO2

H +

10-4

(d)

(c)

+

10-5

Time(Sec)

10-1


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 31

+

+

10

+

+

+

+

+ +

+

+

O

+

+ +

+

+

+

+

+

+

10

C3H6 H2

-3

C2H6

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+ +

+ +

10

-4

+

+

CH4

+ + +

CO2

+ +

10

-5 + + +

-5

10

HCO

+ +

+

+

10

-6

10

-7

+ + + +

-6

10

10-6

10-5

Time(Sec)

10-4

-6

10

-5

10

Time(Sec)

10

-4

Fig 13. Comparison of temporal variations of (a)temperature, (b) major fuel species, (c) minor radicals, and (d) other selected species using IGNITION model, T0=1500 K, P=1.0 atm, ɸ=1.0, fuel composition is 74%n-decane, 15%n-propylbenze, 11% propyl cyclohexane.

Next the PSR model of CHEMKIN software [52] which is a homogenous zero-D model is used. In Figure 14, variations of the flame temperature, concentration of the major fuel species, the minor radicals, and other selected species are shown in terms of equivalence ratio, and are compared with the basis skeletal mechanism of Wang.


Page 21 of 31

0

2900

10

CO

10-2

2800



(b)

Wang- 382 reaction & 106 species Present- 180 reaction & 72 species

(a)

2700

2600

10

-4

10-6 10

C2H4

-8

10-10

2500 10

n-decane

-12 +

+

+

+

+

+

n-propylbenzen +

+

+

+

+

+

+

+

+

+

propylcyclohexane

2400 0.5

1

1.5

2

10-14 0.5

1

-1

10

10

(c)

-2

10

10


OH O

10

-4

10

HO2

-5

10

-6

10

CH2O -7

10

(d)

-2

CO2 H2

10

-4

10

-6

10

-8

CH4

C3H6

10

-10

HCO

C2H6

10-12

10-8 10-9 0.5

1

1.5

2

0

H

-3

1.5

Equivalence ratio

Equivalence ratio

Species ole fraction

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

10

2

Equivalence ratio

-14

0.5

1

1.5

2

Equivalence ratio

Fig 14. Comparison of variations of (a)temperature, (b) major fuel species, (c) minor radicals, and (d) other selected species versus equivalence ratio in PSR model, T0=1500 K, P=1.0 atm, ɸ=1.0, fuel composition of 74%n-decane, 15%n-propylbenze, 11% propyl cyclohexane.

To analyze the spatial performance of the proposed mechanism we have used the one-D PREMIXED reactor model of CHEMKIN software [53] which includes transport effects. Figure 15 shows the spatial distribution of the flame temperature, concentration of major fuel species, minor radicals, and other selected species in comparison with the basis skeletal mechanism of Wang. Studying results of these simulations and comparisons with results of the skeletal mechanism of Wang (figures 13, 14 and 15), shows that reduction of reactions from 382 to 180 reactions, and species from 106 to 79 has almost no effect in accuracy of prediction of the main combustion characteristics, while the computational expense is much less.


Energy & Fuels

2400

0

10 (a)

(b) -1

10



2100 Wang- 382 reaction & 103 species Present- 180 reaction & 72 species

1800 1500 1200 900

CO n-decane

-2

10

n-propylbenzen -3

+

+

+

+

+

+

10

+

+ +

C2H4

+ +

propylcyclohexane +

-4

10

+ + +

10-5

+ + +

10-6

600

+ +

300

0

0.1

0.2

0.3

0.4

0.5

0.6

10-7 0.02

0.7

0.04

0.06

10

0.08

0.1

0

-1

10

(d)

(c)

CO2

10-1 -2

OH +

+

+

+

+

+

+ +

O

+

10

-3

+

CH2O + + +

10

+ +

-4

+ + +

H

10

-5

+

HO2


10

+ +

-2

10

H2

-3

10

C3H6

-4

+

10

+

+

+

+

+

+

+ + + +

+

+

+ +

-5

10

+

+ +

C2H6

-6

10

CH4 + +

-7

10

+

+

+

+

-6

10 0.02

0.12

Distance(cm)

Distance(cm)


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 31

0.04

0.06

-8

0.08

0.1

10 0.02

0.12

0.04

Distance(cm)

0.06

0.08

0.1

0.12

Distance(cm)

Fig 15. Comparison of the spatial variations of (a)temperature, (b) major fuel species, (c) minor radicals, and (d) other selected species using PREMIXED model, T0=300 K, P=1.0 atm, ɸ=1.0, fuel composition is 74%n-decane, 15%n-propylbenze, 11% propyl cyclohexane.

4.2.

Performance of K1 for a Range of Combustion Conditions

To analyze performance of the K1 skeletal mechanism, the combustion characteristics of the K1 kerosene fuel under a range of operating conditions, i.e., T0 = 1500-1800 K, P = 1.0, 10.0, 30.0 atm, ɸ = 0.5-2.0 are studied here, and are compared with the skeletal mechanism of Wang [7]. This investigation is performed using reactor models of IGNITION [51], PSR [52], and PREMIXED [53] of CHEMKIN software. In this section, the effects of the inlet temperature, equivalence ratio and pressure on the combustion parameters i.e., ignition delay time, flame temperature, gas velocity, concentration of major species, and minor radicals are examined for the given composition of fuel (74%n decane 15% n-propyl benzene 11% n-propyl cyclohexane). This study is based on the simulation of the proposed K1 mechanism and results are compared with results obtained from the skeletal mechanism of Wang [7]. Figure 16 shows the ignition delay time based on the inlet temperature in the range of 1500-1800 K and the equivalence ratios in the range of 0.5-2.0, and pressures of 1.0, 20.0, 30.0 atm.


Page 23 of 31

10

-2

10-3 (b): T0=1600 K



(a): T0=1500 K

10-3 1.0 atm

10

-4

10.0 atm

10

-5

10

-6

1.0 atm

10-4

10.0 atm

10-5

30.0 atm

Lines: Wang skeletal mechanism Symbols: Present skeletal mechanism

0.5

1


1.5

10-6

2

0.5

1

Equivalence ratio 10

-4

(d): T0=1800 K

10-5



2

10-4

1.0 atm

10.0 atm

30.0 atm

10

1.5

Equivalence ratio

(c): T0=1700 K

-6

0.5

1

1.5

1.0 atm

10

10.0 atm

10

2

-5

-6

0.5

1

Equivalence ratio

1.5

2

Equivalence ratio

Fig 16. Comparison of ignition delay time versus equivalence ratio based on IGNITION model (generated by our K1 skeletal mechanism) with the skeletal mechanism of Wang,T0=1500-1800 K, P=1.0 atm, ɸ=1.0, the fuel composition of 74%n-decane, 15%n-propylbenze, 11% propyl cyclohexane.

Figure 17 shows the flame temperature versus residence time under the inlet temperature of 1500, 1800 K, equivalence ratio of 0.5, 2.0, and pressures of 10.0, 30.0 atm for the same fuel composition. In Figure 18, the concentration of the selected species has been provided in terms of equivalence ratio in the range of 0.5-2.0, inlet temperature of 1600, 1800 K, and pressure of 10.0, 30.0 atm with the same fuel composition. 2790

2550

(b): φ=0.5, Τ0=1800 Κ

(a): φ=0.5, Τ0=1500 Κ

2780

30.0 atm

2540

30.0 atm



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

2530

10.0 atm

2520

2770 2760 2750 2740

10.0 atm

2510 2730 Lines: Wang skeletal mechanism Symbols: Present skeletal mechanism

2500

2

4

6

2720

8

10

2

4

6

Residence time(ms)

Residence time(ms)


8

10

Energy & Fuels

2960

2700

(d): φ=2.0, Τ0=1800 Κ

(c): φ=2.0, Τ0=1500 Κ



2690 30.0 atm

2680 2670

10.0 atm

2660 2650

30.0 atm

2940

2920

10.0 atm

2900

2640 2630

4

6

8

2880

10

4

6

8

10

Residence time(ms)

Residence time(ms)

Fig 17. Comparison of flame temperature versus residence time predicted by the K1 skeletal mechanism with skeletal mechanism of Wang using PSR model, T0=1500,1800 K, P=10.0, 30.0 atm, ɸ=0.5, 2.0, fuel composition of 74%n-decane, 15%n-propylbenze, 11% propyl cyclohexane. 0

10

10

-1

(b): P=30.0 atm, T0=1600 K

10-2

OH

10-2



(a): P=10.0 atm, T0=1600 K

H -4

10

O

HO2

-6

10

HCO

+

+

+

+

+

+

+

+

+

+

+ + + +

-8

+

10

10

-3

10

-4

10

-5

OH H

+

10-6

HCO

-7

1

1.5

10

2

+

+

+

+

-8

CH2O

+

-9 +

0.5

1

2

100 (d): P=30.0 atm, T0=1800 K

-2

10

-2

10

CO2


H2 -4

10

-6

10

CH4 -8

10

C3H6

CO2 H2

-4

10

10-6 CH4

10-8 -10

10

C3H6

-12

10 C2H6

C2H6

10-14 0.5

-14

0.5

1.5

Equivalence ratio

(c): P=10.0 atm, T0=1800 K

10

+

+

0

-12

+

+

Equivalence ratio

10

+

+

0.5

-10

+

+

10 10

-10

10

+

+


10

+ +

+

+

10

O

HO2

CH2O

+


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 24 of 31

1

1.5

2

1

1.5

2

Equivalence ratio

Equivalence ratio

Fig 18. Comparison of concentration of selected species versus equivalence ratio in PSR model of the k1 skeletal mechanism with the skeletal mechanism of Wang, T0=1600,1800 K, P=10.0, 30.0 atm, ɸ=0.5-2.0, fuel composition of 74%n-decane, 15%n-propylbenze, 11% propyl cyclohexane.

4.3.

Application of K1 to Different Compositions of Kerosene

In this section, we examine the combustion parameters for different mixtures of kerosene using the present K1 skeletal mechanism compared to the skeletal mechanism of Wang under various operating conditions. Kerosene, a heavy hydrocarbon fuel, is a mixture of alkanes, cycloalkanes, and aromatics. Its kinetics has been studied at different range of operating conditions with experimental tools, such as jet stirred reactors, shock tubes, and flat flame burners. In these experimental studies, many different mixtures of kerosene are used. Some of these studies are listed here: a mixture including


Page 25 of 31

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

79% n-undecane, 11% 1,2,4-trimethylbenzene, 10% n-propyl cyclohexane at the atmospheric pressure and temperature range of 873-1033 K [54], mixture of 100%-n-decane at pressure range of 1.0-40.0 atm and temperature range of 750-1150 K [55], mixture of 100%-n-decane at temperature range of 550-1600 K at the atmospheric pressure [56], four mixtures including 100% n-decane, 74% n-decane, 26% n-propylbenzene, 74% n-decane, 26% n-propylcyclohexane, and 74%n-decane, 15%n-propylbenzene, 11% n-propylcyclohexane under atmospheric pressure and temperature range of 900-1300 K [50], again these four mixtures under pressure of 1-40 atm [57] and many other studies such as [58-62]. Here we select three other mixtures of kerosene (different from mixture of 74%n-decane, 15%n-propylbenze, 11% propyl cyclohexane used above to generate K1) to study how the K1 skeletal mechanism may predict combustion characteristics of other mixtures. For this purpose, three different mixtures of kerosene fuel (Table 6) were examined using models of PREMIXED [53], IGNITION [51] and PSR [52] of CHEMKIN software. Table 6. Different fuel compositions for qualifying proposed K1 skeletal mechanism

K2 K3 K4

Fuel composition C10H22 C9.2H18.8 C9.2H19.3

Alkane name % n-decane 100 n-decane 80 n-decane 78

Cycloalkane name ----cyclohexane

% ----9.8

Aromatic Name --benzene toluene

% --20 12.2

Ref. [60] [61] [62]

First we use the PREMIXED model to reconsider spatial variation of selected species, axial velocity, and mass density of the gases predicted by the K1 mechanism for combustion of the K2 kerosene fuel i.e., 100% n-decane. Results are shown in figure 19 and are compared with the skeletal mechanism of Wang under stoichiometric equivalence ratio, atmospheric pressure, and initial temperature of 300 K. Figure 19 shows that the skeletal mechanism is well capable to model combustion of the K2 Fuel as well as Wang skeletal mechanism. Since laminar flame speed is one of the most important and useful global combustion properties for many industrial applications, the performance of both the M1 model for methane and the K1 model for kerosene to predict it using the PREMIXED model of CHEMKIN are compared with values predicted by their parent mechanisms in figures 8-a and 19-b. Based on studies by Gottgens et al. [63] for methane, the laminar flame speed is mostly a function of combustion conditions and the adiabatic flame temperature, and since we have shown in figures 3, 6, 7, 10, 11 for methane (and figures 5, 13-15, 17 for kerosene) that our skeletal mechanisms predict the flame temperature with a high accuracy, one expects that the proposed mechanisms would predict the flame speed with an acceptable degree of accuracy.


Energy & Fuels

1.2

(a): 100% C10H22

-1

-2

10

-3

10

-4

10

-5

H OH

&

& & & &

&

&

& & & &

+

HO2

H2O2

& + & + & + &

+ +

& +

+

+ &

+

10

+ +

-6

&

&

&

2 0.8 1.5 0.6 1

0.4

&

O +

CH2O

+

0.06

0.08

0.1

0.5

0.2

+

+

-7

&

1

+

+

10 0.04

2.5

CO

C10H22

10

(b): 100%C10H22 P=1.0 atm, φ=1.0,Τ0=300 Κ

P=1.0 atm, φ=1.0,Τ0=300 Κ

Mass density(kg/m3)


10

0

Axial velocity(m/s)

10

0.12

0.02

0.14

Distance(cm)

0.04

0.06

0.08

0.1

0.12

0.14

Distance(cm)

Fig 19. Spatial variation of concentration of (a)selected species, (b)axial velocity and mass density, using PREMIXED model predicted by the present K1 skeletal mechanism comparing with skeletal mechanism of Wang, T0=300 K, P=1.0 atm, ɸ=1.0, fuel composition of 100%n-decane.

Next we consider application of K1 mechanism using IGNITION model to the K3 mixture, i.e., 80% n-decane, 20% benzene. Figure 20 shows the temporal variations of the concentration of the selected species and the temperature of gases obtained by the K1 skeletal mechanism, and compared with the skeletal mechanism of Wang. The simulation conditions are equivalence ratio of 0.5, pressure of 10.0 atm, and the inlet temperature of 1800 K. This figure shows that both models have similar temporal accuracy. 10

0

2800 (a): 80%C10H22 , 20%C6H6

(b): 80%C10H22,20%C6H6

P=10.0 atm, φ=0.5, Τ0=1800 Κ

-1

10

2600

-2

+

CO

10

+

+

+

+ +

+

+ +

OH

10

+

+

+

+

+

+

+

+

+

+ +

+

+

O

+

-3

+

Temperature(K)


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 26 of 31

H

+

-4

10

-5

10

2400

2200

2000

HCO

1800

-6

10

-7

10

P=10.0 atm, φ=0.5, Τ0=1800 Κ

10-7

10-6

10-5

1600 -7 10

10-4

10

Time(Sec)

-6

10

-5

10

-4

Time(Sec)

Fig 20. Temporal variation of (a) concentration of selected species, and (b) temperature using IGNITION model predicted by the K1 skeletal mechanism, compared with the skeletal mechanism of Wang, T0=1800 K, P=10.0 atm, ɸ=0.5, fuel composition of 80%n-decane, 20% benzene.

For the K4 kerosene mixture, i.e., 80% n-decane, 20% benzene, we use the PSR model. Figure 21 shows the concentration distribution of the selected species and temperature of the gases obtained from the combustion of the third kerosene fuel using the K1 skeletal mechanism compared to the skeletal mechanisms of Wang. The combustion conditions are equivalence ratio of 0.5, pressure of 20.0 atm, and the inlet temperature of 500 K. Figures 19 to 21 show that the proposed K1 skeletal mechanism is able to accurately predict all of the combustion characteristics in a wide range of operating conditions (ɸ = 0.5-2.0, P = 1.0-30.0 atm, T0 = 500-1800 K), and for various mixtures of kerosene fuel.


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10

2800

0

(a): 78%C10H22,9.8%C6H6,12.2%Toluen

(b): 78%C10H22 ,9.8%C6H6,12.2%Toluen

H2

2600

10

-2

10

-4

Temperature(K)

P=20.0 atm, T0=500 K, τ=0.07 Sec


H O OH

10

-6

10

-8

HO2

-10

10

0.5

P=20.0 atm, T0=500 K, τ=0.07 Sec

2400

2200

2000

1800

HCO

1

1.5

1600 0.5

2

1

Equivalence ratio

1.5

2

Equivalence ratio

Fig 21. Concentration of (a) selected species, and (b) temperature versus equivalence ratio in PSR model predicted by the k1 skeletal mechanism, and compared with the skeletal mechanism of Wang, T0=500 K, P=20.0 atm, ɸ=0.5-2.0, fuel mixture of 78%n-decane, 9.8%cyclohexane, 12.2% toluen.

To assess performance of the M1 mechanism for methane and the K1 mechanism for kerosene in the range of 1000K to 1400K, we have computed the ignition delay time using the IGNITION model of CHEMKIN and have compared results with corresponding parent mechanisms, i.e., GRI-3 for methane, and Wang’s mechanism [7] for kerosene. The reference data are shown by lines, and results of our simulation are shown by symbols. Results are shown in figure 22. For these simulations, the equivalence ratio is 1.0 and the pressure is 1.0 bar. One observes that the skeletal mechanism for methane behaves well for the whole range, but the mechanism for heavier molecules of kerosene over-predicts the ignition delay time. It is obvious that one may regenerate the skeletal mechanism by selecting a lower base temperature, to make this difference in lower temperatures as low as he desires. 101 GRI-3 [48] Present skeletal for methane Wang [7] Present skeletal for kerosene

0

10 Ignition delay time (sec)

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

-1

10

-2

10

10-3 Lines: Base mechanisms Symbols: Generated mechanisms -4

10

0.7

0.75

0.8

0.85

0.9

0.95

1

1000 (K)/T0(K)

Figure 22. Comparison of ignition delay time predicted by the IGNITION model of CHEMKIN for skeletal mechanism of M1 for methane (compared with GRI-3) and K1 for Kerosene (compared with [7]) for lower inlet temperatures of 1000K-1400K. (P=1atm and ɸ=1).


Energy & Fuels

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4.4.

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Speed up of the K1 Mechanism

The main advantage of the K1 skeletal mechanism is its speed up with respect to the skeletal mechanism of Wang. To quantify this advantage, we use the PREMIXED model of CHEMKIN software. This combustion model is the best bench mark since it includes most components of a real 3D computation. For this comparison we have used the reference combustion conditions of section 2. Table 7 shows that the use of the K1 skeletal mechanism in the PREMIXED model reduces the run time by 92%. Table 7. Comparing run times of the K1 mechanism with the skeletal mechanism of Wang Model PREMIXED

Run time(Sec) Wang Present mechanism mechanism 357 25

5. Conclusion Here we proposed an algorithm useful for reduction of detailed mechanisms generally used in simulations of gas turbine combustors, and have applied the procedure on two fuels widely used in gas turbines, i.e., methane and kerosene, and two detailed or skeletal mechanisms, i.e., GRI-3.0 and Wang’s mechanism [7], which are widely used in this industry. In a detailed mechanism, most reactions have little contribution or effect on the flame temperature, final concentrations of species and the delay time. A procedure is introduced to reduce a detailed full or skeletal mechanism of oxidation of hydrocarbon fuels to a lower cost simpler skeletal mechanism. The procedure is based on sensitivity analysis and a so called GEIE procedure, for simultaneous accurate prediction of flame temperature, combustion delay and NO concentration of hydrocarbon fuels oxidation in high temperature conditions. A cut of limit is used in this procedure, which may be reduced to increase the accuracy, which will result in mechanisms with more details and reactions. In this study a 3% limit for each parameter is considered. The procedure is applied to oxidation of methane and kerosene, and the resulting skeletal mechanisms are applied to many benchmark problems to show its validity, efficacy and generality. First, the detailed mechanism of GRI-3.0 including 325 reactions and 53 species is reduced to M1 mechanism with 118 reactions and 39 species. For validation of this new procedure, performance of the M1 mechanism in a reference condition is studied, and also its performance in a wide range of combustion conditions is analyzed and is compared with the GRI-3.0 detailed mechanism. Three homogenous models, i.e., IGNITION, PSR, and PREMIXED of CHEMKIN software are used to study validity and applicability of the M1 model in prediction of flame temperature, ignition delay, burnt gas velocity, concentration of selected species and radicals, under a wide range of operating conditions, i.e., equivalence ratio of 0.5-2.0, pressure of 1.030.0 atm and inlet temperature of 300-1800 K. All comparisons verify that the M1 skeletal mechanism well follows the GRI-3.0 mechanism, and most often has a relative error in combustion characteristics named above much less than 1%. The new M1 mechanism provide speed-ups higher than 4 for most simulations considered here. Next, a similar study is performed using the skeletal mechanism of Wang for kerosene oxidation with 382 reaction and 106 species, which resulted in a skeletal mechanism with 180-reaction and 79-species, called here K1. The K1 mechanism


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Energy & Fuels

is applied to three different mixtures of kerosene fuel (100%n-decane, 80%n-decane-20%benzene, and 78%n-decane, 9.8%cyclohexane, 12.2%toluene) and results are compared with results of Wang, and well agreement for all three fuels are shown. Again three homogenous models, i.e., IGNITION, PSR, and PREMIXED are used to study validity and applicability of the K1 skeletal mechanism for the same combustions characteristics and the same ranges of combustion conditions. The local errors are most often less than 2%. It is shown that the resulting skeletal mechanisms reliably capture main properties of the oxidation with an acceptable accuracy level, while provide speed up to 14 for kerosene simulations. Applicability of the procedure for heavier hydrocarbon molecules and very large detailed mechanisms shall be assessed in the near future.

Acknowledgment The authors are grateful to professor Quan-De Wang for providing the data of the base skeletal mechanism in CHEMKIN format.

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