Effect of CO2 diluent on the formation of pollutant NOx in the laminar non-premixed methane-air flame

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Effect of CO2 diluent on the formation of pollutant NOx in the laminar non-premixed methane-air flame Mohsen Nasiri Soloklou, Ali Akbar Golneshan∗ Department of Mechanical Engineering, Shiraz University, Shiraz, Fars 71348-51154, Iran

a r t i c l e

i n f o

Article history: Received 16 July 2019 Revised 23 October 2019 Accepted 16 November 2019 Available online xxx Keywords: Combustion Laminar SIMPLE non-premixed Diluent NOx

a b s t r a c t In this paper, the effects of changes in the concentration of diluent CO2 in methane and air fuels are investigated. A finite volume method (FVM) with staggered grids is used for numerical solution. Equations of continuity, momentum, energy, ideal gas state and kinetic equations with thermodynamic and thermo-chemical information of chemical species are solved using the numerical method of SIMPLE. The convective terms are discretized using Power Law scheme (PLS). The under-relaxation factor dependent on temperature has been utilized to solve the chemical kinetic equations. In this research, by increasing the diluent mass fraction, the mass fraction of the fuel is diminished to the same extent. Therefore, the sum of the diluent and fuel mass fraction values remains constant. The results depicted that as the amount of CO2 diluent in the fuel increases, the total lift-off height and flame length decreases linearly, and the maximum temperature in the combustion chamber becomes smaller than that at the inlet of the chamber. When the concentration of CO2 increases in the fuel, the temperature changes become negligible at the inlet of the combustion chamber. By using the CO2 diluent, shorter combustion chambers can be used. While the diluent is used, the increase in the length of the combustion chamber will not have any effect on the NOx emissions reduction. Therefore, the more concentration of the diluent is used, the smaller the combustion chamber can be selected. Moreover, by increasing the diluent, NOx pollutant decreases in the combustion chamber. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction In recent decades, there has been much effort to develop new combustion technologies for the purpose of pollutant emissions reduction and combustion systems improvement. Optimization of combustion systems is an important issue in order to diminish combustion instabilities [1,2] and achieve the flame stabilization and reduce pollutant emissions [3–5]. Comprehensive studies have been conducted in order to investigate the NOx formation in various combustion regimes [6–10]. In some applications, such as aircraft engines, domestic stoves, and power plants, a proper understanding of their structure is essential to enhance the efficiency of the system. Cho and Chung [11] investigated combustion dilution with CO2 and N2 . Their results illustrated that increasing the amount of diluent, leads to the reduction of the combustion chamber temperature and also the amount of NOx production. Numerical simulations of NOx prediction in flames was performed by Lopez-Parra and Turan [12–14]. In their work, various numerical methods were applied for simu∗

Corresponding author. E-mail address: [email protected] (A.A. Golneshan).

lating the formation of NOx, in different flames. The effect of CO2 diluent in methane gas flame was studied by Park et al. [15]. They claimed that the chemical and thermal effects of CO2 diminish the flame temperature and as a result reduce NOx emissions. In another study, the effect of CO2 diluent on NOx emissions was examined by Lee et al. [16]. It was shown that increasing the amount of CO2 diluent results in the reduction of the flame temperature and the amount of NOx production. Subsequently reduce. Their results depicted that for more than 40% of carbon dioxide diluent usages, a slight difference between temperature values and the amount of produced chemical species in the flame can be observed. Moreover, investigating laminar diffusion flames helps to model of turbulent diffusion flames [17], besides its fundamental concept. Smooke et al. [18] numerically studied two-dimensional axisymmetric and laminar co-flowing jet diffusion flame of methane and air both in the confined enclosure and the unconfined environment. A study of an axisymmetric laminar diffusion flame was performed by Walsh et al. [19] to investigate the effect of buoyancy and dilution on flame properties such as temperature, fuel and oxygen concentration. Their results were presented both in normal gravity and on the reduced-gravity.

https://doi.org/10.1016/j.ijheatmasstransfer.2019.119071 0017-9310/© 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: M.N. Soloklou and A.A. Golneshan, Effect of CO2 diluent on the formation of pollutant NOx in the laminar nonpremixed methane-air flame, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.119071

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The effect of the level of premixing on the properties of a partially premixed co-flow methane–air laminar flame was studied by Claramunt et al. [20]. Their study was carried out for five levels of premixing from  = =∞ (non-premixed flame) to  = 2.464. They examined pollutant formation (CO and NOx) in their investigations. Investigation of lift-off heights related to co-flow laminar diffusion flames was carried out by Walsh et al. [21]. It was observed that the lift-off heights and flame shapes obtained by the computations illustrate good agreement with measurement for both normal gravity and reduced gravity flames at low dilution levels but, as the fuel mixture is increasingly diluted, the lift-off heights become under predicted. In another research by Tarhan et al. [22], a novel CFD code was developed for the solution of continuity, momentum, energy and species equations for multi-component reacting systems. Parallel code was utilized for predicting a confined axisymmetric laminar co-flowing methane-air diffusion flame employing 1-, 5-, 10-step reaction mechanisms for the combustion sub-model. A combined experimental and numerical investigation of a forced, time-varying, axisymmetric CH4 -air laminar diffusion flame is performed by Dworkin et al. [23]. Measurements of temperature and species for five different phases relative to the forcing were presented. Bennett et al. examined oxygen-enhanced axisymmetric laminar methane flames experimentally and numerically. In their paper, it was claimed that the oxygen-enhanced flames are shorter, hotter, and attached to the burner in comparison to the base case flame, which is lifted [24]. Effects of fuel dilution, inlet velocity, and gravity on the shape and structure of laminar co-flow methane–air diffusion flames were studied by Cao et al. [25]. It was observed that flame lengths are proportional to the mass flow rate of the fuel mixture. In a similar study, a combined computational and experimental study was performed by Cao et al. [26] to characterize the effects of pressure and fuel stream dilution on the structure, shape, and sooting behavior of co-flow methane–air laminar diffusion flames. The results indicated that the maximum temperature increases with increasing CH4 concentration or pressure, the lift-off height diminishes remarkably with increasing pressure and the modified flame length is roughly independent of pressure. In the literature, there are numerous mechanisms of methane combustion. For example, Glarborg et al. [27], Miller and Bowman [28], and recently, Konnov [29], Huges et al. [30], and the standard Gri-mech [31], for reduced mechanisms: Westbrook and Dryer [32], and Jones and Lindstedt [33] (more than 2 global reaction). This research aims to investigate the quantification of the polluting emissions of a laminar diffusion flame by utilizing Dryer and Glassman’s three-stage chemical kinetics [34]. In a reacting flow such as the present study, there are significant time scale differences between the general flow characteristics and the chemical reactions. in order to solve and handle the numerical difficulties (chemical kinetic equations), a relaxation factor dependent on temperature has been used which has not been seen in the previous studies. Our code reveals that it has capability to model laminar CH4 flame with reasonable runtimes and our results show good agreement with previously reported experimental results. In this research, by increasing the diluent mass fraction, the mass fraction of the fuel is reduced to the same extent, so that the sum of the diluent and fuel mass fraction values remains constant. This type of diluent has not been reported by previous researchers. Also, the accurate details of the temperature distribution, flame length and NOx pollutant changes due to injections of different amounts of CO2 diluent in the dilution range of 0–1.25 have been reported in this work. Furthermore, the geometrical relationship between the combustion chamber and the distribution of NOx pollutant has been shown. Furthermore, the effect of CO2 dilution on the tem-

perature distribution, axial velocity, NOx concentration through the combustion chamber is examined. 2. Problem statement and governing equations In this section, the combustion of non-premixed laminar flow in a symmetrical two-dimensional chamber with insulating walls is investigated (Fig. 1). By changing the concentration of CO2 diluent in methane, the distribution of temperature and concentration of CO and NOx pollutants to determine the maximum amount and location of the highest pollutant emissions is investigated. In this step, before performing the basic calculations, the performance of the code in the two-dimensional symmetrical axial flow is investigated by comparing it with the results of others, and then the appropriate grid is chosen. This flame consists of two concentric tubes, where the inner tube and outer tubes have diameters of Din = 12.7 mm and Dout = 50.8 mm, respectively. The fuel is introduced into the combustion chamber through the central part at a velocity of U f = 4.55 cm/s, with a constant flow rate of m˙ f = 3.71 × 10−6 kg /s, temperature of T f = 298K and atmospheric pressure into the combustion chamber. Air containing a mixture of oxygen with mass fraction of YO2 = 22.8% and nitrogen with the mass fraction of YN2 = 75.09% along with water with mass fraction of YH2 O = 0.0211%Din = 12.7 YH2 O = 0.0211%YH2 O = 0.0211%YH2O = 2.11% are introduced into the combustion chamber at a velocity of 98.8 cm/s, the constant flow rate of m˙ air = 2.21 × 10−4 kg/s, temperature of Tair = 298 K and atmospheric pressure. If as a result of the combustion, the return flow occurs at the end of the combustion chamber, it will be assumed that the air encompassing the above-mentioned mass fractions enters into the combustion chamber from the outlet of the chamber. In this work, for simplifying the mathematical treatment of the problem the following assumptions are considered: 1 The flow is considered to be steady-state and two-dimensional. 2 Thermodynamic properties of species, density and viscosity of fluid are functions of temperature. 3 The pressure inside the combustion chamber is considered to be constant. 4 Every species of reactants and products obey the ideal gas state equation. 5 The effect of gravity (i.e. buoyancy) is neglected. 6 Radiation heat transfer is neglected.

Fig. 1. The geometry of the confined axisymmetric laminar diffusion flame.

Please cite this article as: M.N. Soloklou and A.A. Golneshan, Effect of CO2 diluent on the formation of pollutant NOx in the laminar nonpremixed methane-air flame, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.119071

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M.N. Soloklou and A.A. Golneshan / International Journal of Heat and Mass Transfer xxx (xxxx) xxx Table 1 Dryer and Glassman [34] global multi-step chemical kinetics mechanism and reaction rate coefficients∗ Reaction rate

C H4 + 32 O2 → CO + 2H2 O + 12 O2 → C O2 O2 → CO + 12 O2

r1 = 1011.70 × e T × [C H4 ]0.7 [O2 ]0.8 −20131 r2 = 1012.35 × e T × [CO]1.0 [H2 O]0.5 [O2 ]0.25 −21641 r3 = 1012.50 × e T × [CO]1.0 [H2 O]0.5 [O2 ]0.25

0.5

 −27123 

exp

After the above-mentioned simplifications, the governing equations including continuity, radial momentum, axial momentum, species mass fraction transport, energy conservation and equation of state are used (appendix). In the present study, reaction rate is calculated based on Dryer and Glassman global 3-step chemical kinetics mechanism, defined in Table 1 [35].

(4)

T

−24358

7 These walls are maintained at a constant temperature of 298 K.

0.5

[OH] = 2.129 × 103 T−0.57 [O]

[H2 O]

0.5

 −4595 

exp

(5)

T

4. Chemical kinetic equations Chemical kinetic governs the behavior of reacting chemical species. In general, a chemical reaction including ichemical species and k reaction can be written in the following form: I I   vik Xi ⇔ vik Xi ; (k = 1, 2, . . . , K )(6) i=1

In which:

i=1

I = number of chemical species in the system vik = Stoichiometric coefficient for reactant iin reaction k

3. NOx prediction model



To include NO formation for this type of flame, the Zeldovich mechanisms are employed [36]. The transport equation for NO can be written as follows:

∇ .(ρ VYNO ) = ∇ .(ρ De ∇ YNO ) + SNO

(1)

in which, YNO , De , and SNO are mass fraction, effective diffusion, and the source term, respectively. SNO can be calculated by the relation:

SNO

In this equation, values of O and OH radical concentrations are calculated as follows [38,39]

[O] = 36.34T0.5 [O2 ]

Reaction

3

vik = Stoichiometric coefficient for product iin reaction k Xi = chemical symbol denoting species i

Extended Zeldovich mechanisms are valid for both reversible and non-reversible reactions. Also, subscripts i and k denote chemical species and reactions, respectively. The production rate of the ith speciescan be calculated from:

ωi∗ =

I 

( k = 1, 2, . . . , K )

vik qk ;

(7)

i=1

d[NO] = MNO jl v dt

(2) d[NO] dt

Where MNO is the molecular weight of NO and is calculated by Zeldovich mechanism. The Zeldovich mechanism and rate constants for these reaction [37] illustrate in Table 2. The NO formation rate with the pseudo-equilibrium assumption in dilute fuels can be calculated as follows.



d[NO] = 2k1 [O][N2 ]  dt

2

k−1 k−2 [NO] k1 [N2 ]k2 [O2 ]

1−

1+



k−1 [NO] k2 [O2 ]+k3 [OH]

The right-hand terms of Extended Zeldovich mechanisms are obtained based on the following relations: 

vik = vik − vik qk = k f k

I 

(8)

[Xi ]

vik

− krk

i=1



(3)

I 

[Xi ]



vik

Wherein[Xi ], kf and kr are molar concentration of the ith species, forward reaction rate constant and backward reaction rate constant, respectively. Forward reaction rate constant may be written according to Arrhenius relation [40].

 −E 

k f k = Ak T βk exp

Table 2 Extended Zeldovich mechanism and constant reaction rate

(9)

i=1

k

RT

(10)

extended Zeldovich mechanism [36]

The constant reaction rate for extended Zeldovich mechanism for NO formation[37], kn ( m3 /gmol.s)

In which Ak , β k and Ek are pre-exponential factor, temperature exponent and activation energy for the reaction, respectively.

k1 N2 + O ⇔ NO + N k−1

k1 = 1.8 × 108 exp(−38370/T )

5. Boundary conditions

k2 N + O2 ⇔ NO + O k−2

k2 = 1.8 × 104 Texp(−4680/T)

k3 N + OH ⇔ NO + H k−3

k3 = 7.1 × 107 exp(−450/T )

k−1 = 3.7 × 107 exp(−425/T )

The domain in the combustion chamber (Fig. 1) is surrounded by the inlet and exit in the axial direction, the symmetric centerline and the solid wall in the radial direction. Therefore, the boundary conditions are classified as follows: Inlet (z = 0)

k−2 = 3.8 × 103 Texp(−20820/T )

k−3 = 1.7 × 108 exp(−24560/T )

Table 3 Lennard-Jones parameters for chemical species ε [=]K

Chemical species

σ [=]Å

kB

CH4 CO CO2 H2 O

3.758 3.690 3.941 2.641

148.6 91.7 195.2 809.1

ε [=]K

Chemical species

σ [=]Å

kB

NO N2 O2

3.492 3.798 3.467

116.7 71.4 106.7

0 ≤ r ≤ (Din /2 ) Tf = 298. K Uf = 4.55 m/s ur = 0. cm/s ˙ f = 3.71 × 10−6 kg/s m Yin−CH4 = 1./(S + 1. ) Yin−H2 O = 0.0 Yin−CO2 = S/(S + 1. ) S = {0.0, 0.25, 0.5, 0.75, 1.0, 1.25}

(Din /2 ) ≤ r ≤ (Dout /2 ) Tair = 298. K Uair = 98.8 cm/s ur = 0. cm/s ˙ air = 2.21 × 10−4 kg/s m Yin−O2 = 22.8% Yin−N2 = 75.09% Yin−H2 O = 2.11% (11)

Please cite this article as: M.N. Soloklou and A.A. Golneshan, Effect of CO2 diluent on the formation of pollutant NOx in the laminar nonpremixed methane-air flame, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.119071

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In this research, S is defined as the ratio of the diluted mass fraction to the fuel mass fraction (S = Exit (z = L = 30)

ur = 0,

Yin−CO

2 Yin−CH4

).

∂ uz ∂T ∂ Yi = 0, = 0, = 0; i = 1, 2, . . . , I ∂z ∂z ∂z

Viscosity, specific heats coefficient and thermal conductivity are evaluated as:

(12)

∂ uz ∂T ∂ Yi = 0, = 0, = 0, ; i = 1, 2, . . . , I ∂r ∂r ∂r

(13)

I 

Yi ki ; C p =

(14)

For investigation of the dilution effect on NOx distribution the non-dimensional values of S for dilution with CO2 are used.

I 

YiC pi ;

μ=

i=1

I 

Yi μi

(15)

i=1

Also, the viscosity of species, thermal conductivity and effective diffusion coefficient of species vary in terms of temperatures which are approximated as [28]:

μi = μi 0

Outer zone (r = Dout /2)

∂ Yi ur = 0, uz = 0, T = 298 K, = 0, ; i = 1, 2, . . . , I ∂r

k=

i=1

Axis of symmetry (r = 0)

ur = 0,

6. Thermodynamic relations

 T 0 . 7 T0

; ki = ki0

 T 0 . 7 T0

(16)

wherein T0 = 298 K and μi0 , ki0 and Di0 are the viscosity, thermal conductivity and effective diffusion coefficient of species, calculated at T0 = 298 K and atmospheric pressure. Moreover, the specific heat coefficient of species are written as [40]:

C pi = a1i + a2i T + a3i T 2 + a4i T 3 + a5i T 4 RT

(17)

Fig. 2. Comparison among our results and those of refs.[43–46], (A):The temperature distribution at the location of z = 1.2cm, (B): The chemical species at the location of z = =1.2 cm, (C): The nitrogen monoxide on the centerline, (E): The axial velocity at locations of z = =1.2 cm and z = =50 cm.

Please cite this article as: M.N. Soloklou and A.A. Golneshan, Effect of CO2 diluent on the formation of pollutant NOx in the laminar nonpremixed methane-air flame, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.119071

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Also effective binary diffusion coefficients Dim are written as [40]:

Dim = I

1 − Xi



j =i

X j /Di j



(18)

In which Xi , Dij are mole fraction and ordinary multicomponent diffusion coefficients. To use the above equation, the mass transfer coefficient of each chemical species must be calculated relative to each other. The dual mass transfer coefficient for the pair of chemical species A and B is obtained from the simplified relation below [41].

DAB =

0.0266T1.5 2 × P × MWAB × σAB D

(19)

With the following associated units: DAB = [ ]m2 /s,

T =

◦

[ ]K, P = [ ]Pa and σAB = [] A, the remaining terms are defined below:

MWAB = 2







1/ 1 MWA + /MWB

 −1. (20)

MWA and MWB are molecular weights of the chemical species A and B, respectively. Also

σAB = (σA + σB )/2.

(21)

where σ A and σ B are the hard-sphere collision diameter of species A and B, respectively. And collision integral D is defined from the following equation:

D =

1.06036 T∗ 0.15610

( ) +

+

0.19300 1.03587 + exp(0.47635 × T∗ ) exp(1.52996 × T∗ )

1.76474 exp(3.89411 × T∗ )

(22)

And where the dimensionless temperature T∗ is defined by

T∗ =

kB T

εAB

=

kB T

(εA εB )0.5

(23)

kB is the Boltzmann constant. And value of the characteristic Lennard-Jones, ɛn , are also tabulated in Table 2 [42].

5

7. Validation In order to evaluate the performance of the computer code, a comparison was made with the works done in [43–46]. In these papers, consideration is given to the characteristics of nonpremixed combustion in symmetric axial mode with insulating walls. Fig. 2 compares the results of the aforementioned references and the present study. In these temperature distribution diagrams, concentrations of chemical species, especially nitrogen monoxide and fluid velocity, are presented. As can be seen, the results of this study have very small disparency in comparison to those of other researchers. In order to validate our code, the results of mass fraction, temperature and velocity of the present study were compared with the predicted values by the experiments performed by experimental [43] and numerical [45,46] works. Fig. 2 (A) depicts comparisons between the current work results and those reported in [43,45,46] for the distribution of temperature at the location of z = 1.2cm. In this figure, as can be seen, the numerical results of the present study are in good agreement with the experimental and numerical results reported by aforementioned works. Furthermore, we can see that the numerical results are in good agreement with the experimental results in the zone of near the wall (oxidizer side) compared to the central zone of the combustion chamber (fuel side). It can be due to more oxygen penetration into the fuel side compared to the fuel penetration into the oxidizer side. Fig. 2 (B) illustrates a comparison between the mass fraction results of the combustion species obtained by simulation in this research and the work done by references [43,45] at the location of z = 1.2cm. In these graphs, there is also a slight difference between the results of the present research and the experimental results. Numerical and experimental results show that the mass fraction of CH4 is larger in the central zone and gradually the value of CH4 decreases toward the combustion chamber wall. In the central part, the amount of O2 is at its lowest level and gradually the value of O2 increases toward the chamber wall. The highest amounts of CO2 and H2 O are on the fuel side and these chemicals decrease in the oxidizer side. In the case of N2 , the present research also presents better numerical results than the results of Tarhan [45]. Fig. 2 (C) illustrates the concentration of nitrogen monoxide produced in the centerline in the present study and reference of [44]. Fig. 2 (D) shows the axial velocity value of the current work and those reported in [43,45] for different spatial values. It is clearly observed

Fig. 3. Total lift-off height and flame length variation.

Please cite this article as: M.N. Soloklou and A.A. Golneshan, Effect of CO2 diluent on the formation of pollutant NOx in the laminar nonpremixed methane-air flame, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.119071

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Fig. 4. Effect of the CO2 dilution on the injection of methane into the diffusion flame (A) The temperature distribution on the centerline (B) The temperature distribution at the location of z = =1.2 cm (C) The nitrogen monoxide on the centerline (D) The chemical species at the location of z = =1.2 cm (E) The nitrogen monoxide at the location of z = =1.2 cm (F) The axial velocity at locations of z = =1.2 cm and z = =50 cm.

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that the numerical results of the present research are more accurate than the results of Tarhan [45]. 8. Numerical scheme In this section, the governing equations are solved by using FORTRAN programming [47–49], A finite volume method (FVM) with staggered grids is used and SIPMLE algorithm is chosen for the coupling between the velocity and the pressure. For all simulations presented in this paper, a Power Law Scheme (PLS) was used for the conservation equation of momentum, and chemical species. The system of governing equations is solved simultaneously using numerical or TDMA (Tri-Diagonal Matrix Algorithm) finite difference methods. In order to solve the chemical kinetic equations, the under relaxation factor is used such that for the temperature range between 298–60 0, 60 0–120 0, 120 0–180 0, 180 0–240 0 and higher temperatures, the values of under relaxation factor are uses as 0.1, 0.05, 0.01, 0.0 05 and 0.0 01, respectively. This factor is assumed for the momentum and energy equations equal to the constant value of 0.6 and 0.7 and for the rest of the equations, under relaxation factor equals 0.5. The non-uniform grid of 50 × 30 is selected for half of the geometries (axial symmetric) and has been utilized for our code runs. 9. Results In this section, the changes in temperature, lift-off height, flame length, nitrogen monoxide concentration and fluid velocity are investigated at different locations in the combustion chamber by the injection of CO2 as a diluent in methane. Fig. 3 depicts the total lift-off height and flame length variation diagrams of laminar diffusion along with the diagram of maximum temperature variations due to the injection of CO2 diluent into the methane fuel. As

7

shown in the diagram, by increasing the mass ratio of S, the total lift-off height and flame length will be reduced linearly due to the increase of air permeation into the CO2 -diluted fuel, which alters the location of the maximum temperature of the combustion chamber to the inlet. This phenomenon reduces the total lift-off height and flame length. Furthermore, by increasing the CO2 diluent, we can observe a decrease in the maximum amount of temperature in the combustion chamber. It can be explained by absorbing the combustion energy by the CO2 diluent. The diagrams of Fig. 4 illustrate the effect of the CO2 dilution on the injection of methane into the diffusion flame. In this figure, the distribution of temperature, nitrogen monoxide concentration and fluid velocity are depicted along the centerline and at the outlet of the chamber (location of z = 30 cm) are investigated. As can be observed in the diagrams, as the CO2 diluent increases in the fuel, the maximum temperature in the centerline decreases and also the location of this maximum temperature moves toward the combustion chamber inlet, also we can see that there is no change in the fluid temperature with the diluent value change before maximum temperature in the centerline. According to the speed and direction of flow in this zone, there is no time required for the heat transfer and energy absorption by the diluent. However, after the maximum temperature in the combustion chamber toward the outlet opening, we can see a decrease in temperature due to the absorption of energy from the combustion to raise the CO2 dilution temperature in the combustion chamber (Fig. 4 (A)). Moreover, in this situation, the temperature at the outlet of the combustion chamber begins to decrease (Fig. 4 (B)). Utilizing the Zeldovich mechanism, the same procedure for the production of NO pollutant can be observed. With the increase of CO2 as diluent, the nitrogen monoxide production in the centerline and outlet of the combustion chamber are reduced (Fig. 4 (C,D)).

Fig. 5. Temperature distribution in different ratios of CO2 dilution, (A)[S = 0.00], (B)[S = 0.25], (C)[S = 0.50], (D)[S = 0.75], (E)[S = 1.01], (F)[S = 1.25].

Please cite this article as: M.N. Soloklou and A.A. Golneshan, Effect of CO2 diluent on the formation of pollutant NOx in the laminar nonpremixed methane-air flame, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.119071

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Fig. 6. Velocity profiles in different ratios of CO2 dilution, (A)[S = 0.00], (B)[S = 0.25], (C)[S = 0.50], (D)[S = 0.75], (E)[S = 1.01], (F)[S = 1.25].

According to Fig. 4 (F), with the increase of the concentration of CO2 diluent, the reduction of the axial velocity at the outlet of the combustion chamber can be observed. Furthermore, with the increase of CO2 , the axial velocity decreases along the centerline, gradually. The main reason for this, is considering the ideal gas assumption through the simulations. Because, as the temperature decreases, the average density increases, consequently, according to the mass conservation law, the velocity of the fluid diminishes. Therefore, it is reasonable to expect a decreasing velocity in accordance with the temperature diagram. In the profiles of Figs. 5 and 6, the values of the temperature distribution based on Kelvin, the distribution of the NO concentration based on PPM is illustrated for changes in the amount of CO2 in the methane injection in the combustion chamber. As indicated by the temperature distribution, the increase in the mass fraction of CO2 as a diluent in methane fuel reduces the temperature in the combustion chamber. In this state, the rate of air penetration into the fuel is increased by increasing the amount of CO2 , and the mixing of fuel and air takes place in a shorter length of the combustion chamber, thereby reducing the flame zone and volume of the high-temperature zone where NO is produced. Hence, this will diminish the total lift-off height and flame length in the combustion chamber, and reduces NO concentration in the combustion chamber, according to The Zeldovich mechanism.

The purpose of this study is to predict the effect of changes in the concentration of diluent CO2 in methane and air fuels. The main results of this work can be summarized as follows: 1 With the increase of the amount of CO2 diluent in the fuel, the total lift-off height and flame length decrease linearly, and the maximum temperature in the combustion chamber gets closer to the enclosure due to the absorption of the combustion energy by the CO2 as diluent. 2 In the case of an increase in the concentration of CO2 in the fuel, the temperature changes are negligible at the inlet of the combustion chamber due to the lack of time and opportunity for heat transfer and energy absorption by the CO2 diluent. However, it’s possible that the CO2 diluent absorbs more energy. Therefore, temperature decrease becomes significant as we move toward the end of the combustion chamber 3 Using the CO2 diluent permits shorter combustion chambers to be used. While the diluent is used, the increase in the length of the combustion chamber will not have any effect on the NOx emissions reduction. Therefore, the more concentration of the diluent is used, the smaller the combustion chamber can be selected. Also, by increasing the diluent, NOx pollutant reduces in the combustion chamber, especially at the maximum temperature of the combustion chamber, which is due to the increase in the rate of air penetration into the fuel, the Shrinking of the flame zone and the decrease in temperature in the flame range.

10. Conclusion In this paper, the finite volume method is used for numerical solution. Equations of continuity, momentum, energy, ideal gas state and kinetic equations with thermodynamic and thermochemical information of chemical species are solved using the numerical method of SIMPLE.

Appendix Governing equation in cylindrical laminar combustion flame, coordinates r and z; velocity components in these direction are ur and uz [46].

Please cite this article as: M.N. Soloklou and A.A. Golneshan, Effect of CO2 diluent on the formation of pollutant NOx in the laminar nonpremixed methane-air flame, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.119071

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1 Continuity:

1 ∂ ( ρ r ur ) + r ∂r

∂ ( ρ uz ) = 0 ∂z

2 Radial momentum:

















r ρ ur ∂∂urr + r ρ uz ∂∂uzr − 2 ∂∂r r μ ∂∂urr − ∂∂z r μ ∂∂uzr + 23 ∂∂r μ ∂ (∂rur r )    + 23 ∂∂r rμ ∂∂uzz − ∂∂z rμ ∂∂urr + 2μ urr − 23 μr ∂∂r (r ur ) − 23 μ ∂∂uzz − r ∂∂ pr =0 3 Axial momentum:



r ρ ur ∂∂urz + r ρ uz ∂∂uzz − ∂∂r r μ ∂∂urz − 2 ∂∂z r μ ∂∂uzz + 23 ∂∂z



μ ∂ (∂rur r ) +

2 ∂ 3 ∂z











rμ ∂∂uzz − ∂∂r rμ ∂∂uzr + r ∂∂ pz − rρ gz = 0

4 Species mass fraction transport equation:



 ∂ (ρ uzYi ) 1 ∂ ∂ Yi ∂ ∂Y = rρ Dim + ρ Dim i ∂z r ∂r ∂r ∂z ∂z

1 ∂ (ρ r urYi ) + r ∂r + ωi∗

5 Energy conservation:

1 ∂ ( ρ r ur T ) + r ∂r −



 ∂ ( ρ uz T ) 1 ∂ k ∂T ∂ k ∂T = r + ∂z r ∂ r Cp ∂ r ∂ z Cp ∂ z

N 1  ∗ ωi × h0f,i Cp i=1

6 Equation of state:

p = ρ RT

 Yi Mi

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Please cite this article as: M.N. Soloklou and A.A. Golneshan, Effect of CO2 diluent on the formation of pollutant NOx in the laminar nonpremixed methane-air flame, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019.119071