ISSN 19907931, Russian Journal of Physical Chemistry B, 2010, Vol. 4, No. 4, pp. 602–612. © Pleiades Publishing, Ltd., 2010. Original Russian Text © V.E. Kozlov, A.B. Lebedev, A.N. Sekundov, K.Ya. Yakubovskii, 2010, published in Khimicheskaya Fizika, 2010, Vol. 29, No. 7, pp. 37–47.

COMBUSTION, EXPLOSION, AND SHOCK WAVES

Emission of Carbon Oxides during the Combustion of Lean Methane–Air Premixed Mixtures V. E. Kozlov, A. B. Lebedev, A. N. Sekundov, and K. Ya. Yakubovskii Baranov Central Institute of Aviation Motors Development, Moscow, Russia email: [email protected] Received June 5, 2009

Abstract—A onedimensional problem of propagation of a laminar flame front through a uniform methane– air mixture was solved using the GRIMech 3.0 reaction mechanism. An analysis of the composition of the combustion products behind the flame front at a pressure of 10 atm, an initial mixture temperature of 600 K, and two values of the airtofuel equivalence ratio (α = 1.8 and 2.5) was performed. It was demonstrated that, at short residence times, the carbon oxide emission increases as the mixture is made leaner, with the opposite tendency being observed at long residence times. Numerical calculations of the characteristics of turbulent flow and combustion in two axisymmetric homogeneouscombustion model chambers with relatively long residence times were performed within the framework of a bulk (quasilaminar) combustion model. In cal culations, the methane–air mixture composition and the wall temperature of one of the chambers were var ied. The case of cooling air inflow through the chamber wall was considered. It was demonstrated that, over a wide range of parameters in the combustion chamber and on its wall, the CO emission monotonically decreases as the degree of mixture leaning grows, but it increases when the chamber wall is cooled and when cooling air is blown through the wall. DOI: 10.1134/S1990793110040111

In recent times, the combustion of lean hydro carbon–air premixed mixtures has received much attention, since this regime is widely used in the modern lowemission combustion chambers of sta tionary installations to substantially diminish NOx emission. In earlier designs of combustion chambers [1], stable combustion was ensured by using relatively rich mixtures, with an airtofuel equivalence ratio of α = 1.6–1.8. After such a combustion chamber, it was necessary to mix hot combustion products with cold air in a special chamber to increase α to 2.5– 3.0, since the temperature of the gas entering the engine turbine should not exceed a certain value. Such a sophistication of the chamber construction can be avoided by using leaner mixtures, with α = 2.5–3.0. This can be accomplished by creating large recirculation zone for combustion stabilization, thereby providing long residence times of the com bustion products in the chamber (τ ≈ 20–30 ms). The authors of [2–4] managed to change some of the seemingly traditional notions, notably those concerning the NOx formation mechanism. In light of the Zel’dovich thermal mechanism of NOx for mation, a longer residence time should enhance the emission of nitrogen oxides. It turned out, however, that, in lean mixtures, with α = 2.5–3.0, and, hence, low temperatures, the contribution from the thermal mechanism to NOx emission is negligibly small. Start

ing from α > 2, a larger contribution comes from the N2Orelated mechanism. An important feature of this mechanism is a weak dependence of the NO yield on the residence time of the combustion prod ucts in the chamber. It was demonstrated [5] that the existence of large recirculation zones only slightly affects NOx emission. These peculiarities make the homogeneous combustion chambers with ultralean mixtures and long residence times a promising choice. Most studies on the combustion of lean fuel–air premixed mixtures analyze in detail the mechanisms of the formation of nitrogen oxides (NO, NO2), but, at the same time, much less attention is paid to car bon monoxide formation. In a number of works (see, e.g., [6, 7]), the dubious statements are encountered that the CO concentration at the combustion cham ber outlet increases as the mixture becomes leaner (as α increases). In addition, the authors of [6] put forward a contentious explanation that an increase in CO emission is associated with the retardation of the oxidation of CO to СО2 within the cold near wall layer in the combustion chamber. The main purpose of the present work was to refine some of the existent concepts of CO emission from modern homogeneous combustion chambers. This work became possible due to an impressive progress in numerical simulations of combustion processes. Computational codes for modeling reac

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EMISSION OF CARBON OXIDES

tive gas flows (CHEMKIN, Fluent, etc.) have appeared. Some of them are adapted to detailed combustion mechanisms, for example, GRIMech 3.0 (53 components and 325 reactions [8]). The pre dictive possibilities of reduced kinetic mechanisms of combustion also have been substantially improved. For example, good results were obtained using the DRM19 mechanism (21 components and 84 reactions), which was tailored by reducing the GRIMech 1.2 kinetic mechanism [9]. These advances made it possible to numerically simulate the processes occurring in the combustion chamber at a higher level, using, for example, a vol ume model of homogeneous combustion of meth ane–air mixtures. In contrast to the known frontal models, which are approximately valid only near the flame front, this model makes use of the exact equa tions of transfer for all the components involved, with the equations being valid over the entire volume of the combustion chamber. Its main drawback is a forced simplification of the procedure of averaging of the rates of the chemical reactions for turbulent combustion:

W(T, Ci) = W ( T , Ci ) .

(1)

Therefore, this model is also referred to as the quasi laminar model, since relationship (1) is valid only in the absence of pulsations of the scalar parameters. Note, however, that, in this model, the turbulent char acter of the flow is taken into account through the tur bulent diffusion coefficients. In the present work, we numerically simulated the specifics of the formation of CO in the one dimensional flow behind the flame front and in two model combustion chambers at various degrees of mixture leaning and various conditions at the wall of one of the chambers. METHODOLOGY OF NUMERICAL SIMULATIONS OF COMBUSTION Simulations were performed for the onedimen sional and twodimensional cases (axisymmetric). Onedimensional case. The basic details of the formulation of the onedimensional problem of the steady propagation of a laminar flame were outlined in [10]. It was shown that a steady isobaric one dimensional flow of a combustible mixture is described by the following system of equations: (2) ρUdC / dx + dJ / dx − W = 0 , where x is the coordinate normal to the flame front; ρ is the density; U is the velocity; (ρU = const); C = {h, Y1, …, YK}, K is the number of components; h is the enthalpy of the mixture; Yk is the mass fraction of the kth component (k = 1, …, K); W = {0, ω1, …, ωK}; ωk is the rate of formation/consumption of the kth compo nent; J = {q, J1, …, JK}; q is the heat flux; and Jk is the RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B

603

diffusion flux of the kth component. In Eq. (2), radia tive heat transfer is disregarded. The thermal and caloric equations of state read as

pμ , h= ρ= RT

K

∑Y h (T ), k k

k =1

where p is the pressure (preset), μ is the molecular mass of the mixture, T is the temperature, R is the uni versal gas constant, T

hk (T ) =

hk0

∫

+ c p,k (T ) dT T0

is the specific enthalpy of the kth component with the enthalpy of formation hk0 included, c p,k is the specific heat at constant pressure of the kth component. The specific heats of the components were approximated by fourthorder polynomials in the temperature, the coefficients of which were taken from the database [8]. The transport characteristics of the chemical components, such as thermal diffu sivity and diffusion temperaturedependent coeffi cients were taken from the same database. We employed a model of multicomponent concentra tion and thermal diffusion using methods based on the work [11]. The oxidation of methane with the formation carbon oxides was simulated using the GRIMech 3.0 mechanism (53 components and 325 reactions [8]). Since the problem was solved numerically, the boundary conditions were specified at a finite dis tance from the reaction zone, at certain points far enough from the flame front. The inlet boundary conditions (cold boundary) corresponded to zero fluxes of all species and a constant temperature of the fresh mixture. The outlet boundary conditions (hot boundary) were formulated by setting the gradi ents of all the parameters involved at zero. The numerical simulations were performed using the PREMIX code from the CHEMKIN 4.0 soft ware package [12]. Calculations were performed on nonuniform grids. The convective terms were approximated using firstorder counterflow differ ence scheme. Such a scheme ensures a weaker dependence of the convergence of the Newton method (adaptive mesh refinement) on the initial approximation than a scheme with central differ ences does. Adaptive mesh refinement in areas with large gradients makes the uncertainty associated with the artificial viscosity of the firstorder scheme unessential. The above onedimensional formulation was applied to the problem of the propagation of a lami nar flame front through a uniform combustible mix ture at an initial temperature of 600 K and a pressure Vol. 4

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of 10 atm. Two values of the airtomethane equiva lence ratio were used, α = 1.8 and 2.5. Twodimensional case. We considered an axisym metric turbulent reactive flow. The Favreaveraged Navier–Stokes equations for density, momentum, species concentrations, and total enthalpy can be presented as [13, 14] ∇ ( ρ V ) = 0,

(3)

∇(ρVV) = −∇p + ∇Λ − ∇ (ρ v '' v '' ) ,

(4)

)

(

∇ ( ρ V Y i) = ∇ ( ρ Di∇ Y i) − ∇ ρ v ''Y i '' + ωi ,

(

∇ ( ρ V h0) = ∇ {( μ /Pr ) ∇ h0} − ∇ ρ v '' h0''

)+S . h

(5) (6)

Here, ρ is the averaged density, p is the averaged pres sure, V is the averaged velocity vector, v'' is the velocity pulsation component, Λ = μ{∇V + (∇V)T} – (2/3)μ∇VI is the viscous stress tensor (I is the unit tensor and μ is the dynamic viscosity), Yi is the averaged mass fraction of the ith species, h0 is the average total enthalpy, ρ v '' v '' is the Reynolds stresses, v ''Yi '' and v '' h0'' are the turbulent fluxes of the scalar parameters, D is laminar diffusion coefficient, Pr is the laminar Prandtl number, and 〈…〉 are the averaging brackets. The turbulence characteristics were described within the framework of the k – ε model [15], where k is the turbulence kinetic energy and ε is the rate of its dissipation. This model was used to calculate the cor relations v '' v '' in Eq. (4). The turbulent Schmidt and Prandtl numbers for calculating the turbulent fluxes v ''Yi '' and v '' h0'' in Eqs. (5) and (6) were Sct = 0.7 and Prt = 0.85. The source term ωi in the equations for the chem ical species was calculated as in the above one dimensional problem of laminar flame propagation. Radiative transfer was ignored. The source term Sh in the total enthalpy conservation equation (Eq. (6)) allows for viscous dissipation heating. The oxidation of methane with the formation of carbon oxides was described using the DRM19 mechanism (21 species, 84 reactions), which is a reduced version of the GRIMech 1.2 reaction mechanism [9]. The DRM19 reaction mechanism involves the following species: H2, H, O, O2, OH, H2O, HO2, CH2, CH2(S), CH3, CH4, CO, CO2, HCO, CH2O, CH3O, C2H4, C2H5, C2H6, Ar, and N2. The DRM19 reaction mechanism is presented in Table 1 in the CHEMKIN format. Boundary conditions. At the combustion chamber inlet, the following parameters were specified: the mixture consumption rate, turbulence parameters, mixture composition, and temperature. Near wall,

standard nearwall laws were normally used, except for the coldwall regime (Tw = 500 K), for which the laminar sublayer of the boundary layer was consid ered. In modeling the boundary cooling, the wall was replaced by an additional inlet boundary at which a constant velocity of gas inflow was specified. At the outlet of the combustion chamber, a constant value of the static pressure was set. Model combustion chamber no. 1, described in [16], operated without cooling at atmospheric pres sure (P = 1 atm) and an inlet mixture temperature of Tinit = 300 K. The combustion chamber consisted of two cylindrical segments 65 and 40 mm in diameter. The segment with larger diameter was 300 mm in length; the diameter of the inlet orifice through which the fresh mixture was admitted was 20 mm. The time of residence of the mixture in the combus tion chamber was τ ~ 32 ms. The experimental data reported in [16] were obtained at an airtofuel ratio of α = 1.05–1.54, whereas the combustion charac teristics were calculated using the volume combus tion model at α = 1.11, 1.24, and 1.37. The construction of model combustion chamber no. 2, which was designed at the Baranov Central Institute of Aviation Motors Development, is described in [17, 18]. The combustible mixture was admitted into this chamber (810 mm in length and 240 mm in maximum diameter) through an annular slit around the stabilizer, behind which the zone of reverse cur rents, ~300 mm in length, was located. At the calcu lation domain inlet, the flow direction vectors were specified so as to ensure a swirling according to the solidbody law. The swirling angle at the inlet cross section was 30°, whereas the static temperature was set constant over the entire inlet cross section: Tinit = 740 K. The inlet pressure was P = 10 atm, the wall temperature 1000 K, and the residence time 25 ms. The numerical simulations of the turbulent flow with combustion were performed at airtofuel equivalence ratios of α = 1.8, 1.9, 2.0, and 2.5. The calculations for both combustion chambers were performed within the framework of the bulk combustion model implemented in the Fluent soft ware package [14]. Previously, the authors of this work demonstrated that this model correctly pre dicts the turbulent burning velocity Ut, which is given by

U t / U n ≈ 0. 4(U nLt / a )0.5(u ' / U n)0.5 .

(7)

Here, Un is the laminar flame speed, Lt is the turbu lence scale, a is the thermal diffusivity, and u' is the rootmeansquare velocity fluctuation. Note that, according to this expression, Ut is proportional to Un, which is known to decrease with increasing airtofuel equivalence ratio α and to increase with the tempera ture as ~T0.8.

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Table 1. DRM19 kinetic mechanism Reac tion no. 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

A

Reaction O + H + M ⇔ OH + M H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ AR/0.70/ O + H2 ⇔ H + OH O + HO2 ⇔ OH + O2 O + CH2 ⇔ H + HCO O + CH2(S) ⇔ H + HCO O + CH3 ⇔ H + CH2O O + CH4 ⇔ OH + CH3 O + CO + M ⇔ CO2 + M H2/2.00/ O2/6.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/3.50/ C2H6/3.00/ AR/0.50/ O + HCO ⇔ OH + CO O + HCO ⇔ H + CO2 O + CH2O ⇔ OH + HCO O + C2H4 ⇔ CH3 + HCO O + C2H5 ⇔ CH3 + CH2O O + C2H6 ⇔ OH + C2H5 O2 + CO ⇔ O + CO2 O2 + CH2O ⇔ HO2 + HCO H + O2 + M ⇔ HO2 + M O2/0.0/ H2O/0.0/ CO/0.75/ CO2/1.50/ C2H6/1.50/ N2/0.0/ AR/0.0/ H + 2O2 ⇔ HO2 + O2 H + O2 + H2O ⇔ HO2 + H2O H + O2 + N2 ⇔ HO2 + N2 H + O2 + AR ⇔ HO2 + AR H + O2 ⇔ O + OH 2H + M ⇔ H2 + M H2/0.0/ H2O/0.0/ CH4/2.0/ CO2/0.0/ C2H6/3.0/ AR/0.63/ 2H + H2 ⇔ 2H2 2H + H2O ⇔ H2 + H2O 2H + CO2 ⇔ H2 + CO2 H + OH + M ⇔ H2O + M H2/0.73/ H2O/3.65/ CH4/2.0/ C2H6/3.0/ AR/0.38/ H + HO2 ⇔ O2 + H2 H + HO2 ⇔ 2OH H + CH2(+M) ⇔ CH3(+M) LOW/3.200E+27 –3.14 1230.0/ TROE/0.68 78.0 1995.0 5590.0/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ H + CH3(+M) ⇔ CH4(+M) LOW/2.477E+33 –4.76 2440.0/ TROE/0.783 74.0 2941.0 6964.0/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/ H + CH4 ⇔ CH3 + H2 H + HCO(+M) ⇔ CH2O(+M) LOW/1.35E+24 –2.57 1425.0/ TROE/0.7824 271.0 2755.0 6570.0/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/

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5.0E+17

n –1

E 0

5.0E+4 2.0E+13 8.0E+13 1.5E+13 8.43E+13 1.02E+09 6.02E+14

2.67 0 0 0 0 1.5 0

6290 0 0 0 0 8600 3000

3.0E+13 3.0E+13 3.9E+13 1.92E+7 1.32E+14 8.98E+7 2.5E+12 1.0E+14 2.8E+18

0 0 0 1.83 0 1.92 0 0 –0.86

0 0 3540 220 0 5690 47800 40000 0

3.0E+20 9.38E+18 3.75E+20 7.0E+17 8.3E+13 1.0E+18

–1.72 –0.76 –1.72 –0.8 0 –1.0

0 0 0 0 14413 0

9.0E+16 6.0E+19 5.5E+20 2.2E+22

–0.6 –1.25 –2.0 –2.0

0 0 0 0

2.8E+13 1.34E+14 2.5E+16

0 0 –0.8

1068 635 0

1.27E+16

–0.63

383

6.6E+8 1.09E+12

1.62 0.48

10840 –260

606

KOZLOV et al.

Table 1. (Contd.) Reac tion no. 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 61 62 63 64 65 66 67 68 69

A

Reaction H + HCO ⇔ H2 + CO H + CH2O(+M) ⇔ CH3O(+M) LOW/2.2E+30 –4.8 5560.0/ TROE/0.758 94.0 1555.0 4200.0/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ H + CH2O ⇔ HCO + H2 H + CH3O ⇔ OH + CH3 H + C2H4(+M) ⇔ C2H5(+M) LOW/1.2E+42 –7.62 6970.0/ TROE/0.9753 210.0 984.0 4374.0/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5 /CO2/2.0/ H + C2H5(+M) ⇔ C2H6(+M) LOW/1.99E+41 –7.08 6685.0/ TROE/0.8422 125.0 2219.0 6882.0/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ H + C2H6 ⇔ C2H5 + H2 H2 + CO(+M) ⇔ CH2O(+M) LOW/5.07E+27 –3.42 84350.0/ TROE/0.932 197.0 1540.0 10300.0/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ OH + H2 ⇔ H + H2O 2OH ⇔ O + H2O OH + HO2 ⇔ O2 + H2O OH + CH2 ⇔ H + CH2O OH + CH2(S) ⇔ H + CH2O OH + CH3 ⇔ CH2 + H2O OH + CH3 ⇔ CH2(S) + H2O OH + CH4 ⇔ CH3 + H2O OH + CO ⇔ H + CO2 OH + HCO ⇔ H2O + CO OH + CH2O ⇔ HCO + H2O OH + C2H6 ⇔ C2H5 + H2O HO2 + CH2 ⇔ OH + CH2O HO2 + CH3 ⇔ O2 + CH4 HO2 + CH3 ⇔ OH + CH3O HO2 + CO ⇔ OH + CO2 CH2 + O2 ⇔ OH + HCO CH2 + H2 ⇔ H + CH3 CH2 + CH3 ⇔ H + C2H4 CH2 + CH4 ⇔ 2CH3 CH2(S) + N2 ⇔ CH2 + N2 CH2(S) + AR ⇔ CH2 + AR CH2(S) + O2 ⇔ H + OH + CO CH2(S) + O2 ⇔ CO + H2O CH2(S) + H2 ⇔ CH3 + H CH2(S) + H2O ⇔ CH2 + H2O CH2(S) + CH3 ⇔ H + C2H4 CH2(S) + CH4 ⇔ 2CH3

n

E

7.34E+13 5.4E+11

0 0.454

0 2600

2.3E+10 3.2E+13 1.08E+12

1.05 0 0.454

3275 0 1820

C2H6/3.0/

C2H6/3.0/ AR/0.7/ 5.21E+17

–0.99

1580

1.15E+08 4.3E+7

1.9 1.5

7530 79600

2.16E+8 3.57E+4 2.9E+13 2.0E+13 3.0E+13 5.6E+7 2.501E+13 1.0E+8 4.76E+7 5.0E+13 3.43E+9 3.54E+6 2.0E+13 1.0E+12 2.0E+13 1.5E+14 1.32E+13 5.0E+5 4.0E+13 2.46E+6 1.5E+13 9.0E+12 2.8E+13 1.2E+13 7.0E+13 3.0E+13 1.2E+13 1.6E+13

1.51 3430 2.4 –2110 0 –500 0 0 0 0 1.6 5420 0 0 1.6 3120 1.228 70 0 0 1.18 –447 2.12 870 0 0 0 0 0 0 0 23600 0 1500 2.0 7230 0 0 2.0 8270 0 600 0 600 0 0 0 0 0 0 0 0 0 –570 0 –570

C2H6/3.0/ AR/0.7/

C2H6/3.0/ AR/0.7/

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Table 1. (Contd.) Reac tion no.

A

Reaction

n

E

70

CH2(S) + CO ⇔ CH2 + CO

9.0E+12

0

0

71

CH2(S) + CO2 ⇔ CH2 + CO2

7.0E+12

0

0

72

CH2(S) + CO2 ⇔ CO + CH2O

1.4E+13

0

0

73

CH3 + O2 ⇔ O + CH3O

2.675E+13

0

28800

74

CH3 + O2 ⇔ OH + CH2O

3.6E+10

0

8940

75

2CH3(+M) ⇔ C2H6(+M) LOW/1.77E+50 –9.67 6220.0/ TROE/0.5325 151.0 1038.0 4970.0/ H2/2.0/ H2O/6.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/ AR/0.7/

2.12E+16

–0.97

620

76

2CH3 ⇔ H + C2H5

4.99E+12

0.1

77

CH3 + HCO ⇔ CH4 + CO

2.648E+13

0

78

CH3 + CH2O ⇔ HCO + CH4

3.32E+3

2.81

5860

79

CH3 + C2H6 ⇔ C2H5 + CH4

6.14E+6

1.74

10450

80

HCO + H2O ⇔ H + CO + H2O

2.244E+18 –1.0

17000

81

HCO + M ⇔ H + CO + M H2/2.0/ H2O/0.0/ CH4/2.0/ CO/1.5/ CO2/2.0/ C2H6/3.0/

1.87E+17

–1.0

17000

82

HCO + O2 ⇔ HO2 + CO

7.6E+12

0

83

CH3O + O2 ⇔ HO2 + CH2O

4.28E–13

7.6

84

C2H5 + O2 ⇔ HO2 + C2H4

8.4E+11

0

Note:

10600 0

400 –3530 3875

k = A Tn exp(–E/RT); the dimensionalities: cm, mol, s, and cal.

We used the timemarching method in conjunc tion with the second and thirdorder finitediffer ence schemes. The computational grid was refined in highgradient areas, with the total number of meshes reaching 24 000–37 000. Iterations were continued until the carbon oxide emission at the burner outlet reached a constant value. The CO emission index was defined as the CO mole fraction averaged over the consumption rate and then reduced to the standard conditions corresponding to a 15% oxygen content.

ONE DIMENSIONAL COMBUSTION The calculation results show that, at α = 1.8, the laminar flame speed is Un = 14.5 cm/s, whereas at α = 2.5, it becomes as low as 4.3 cm/s. [CO], ppm 10000 1000

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1

100

Note that the nitrogen oxide emission cannot be calculated within the framework of the DRM19 kinetic model, but it can be simulated using the postprocessor code of the Fluent software package, which makes it possible to solve the equations for the NOx concentrations on the basis of the temper ature and velocity fields calculated with the help of the DRM19 model. The underlying kinetic scheme includes several NOx formation pathways: the Zel’dovich thermal mechanism, Fennimore promptNOx mechanism, and N2O + O mecha nism.

10 2 1 0.1

0

5

10

15

20

25 30 t, ms

Fig. 1. Dependence of the CO concentration on the resi dence time of the flow behind the flame front at Tinit = 600 K, P = 10 atm, and α = (1) 2.5 and (2) 1.8. Vol. 4

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Table 2. Equilibrium CO concentrations (in mole fractions) at various the airtofuel equivalence ratios and combustion prod ucts temperatures Tf, K

α 1400

1200

1000

800

1.8

17.5 × 10–4

7.13 × 10–4

23.9 × 10–5

6.56 × 10–5

2.0

9.50 × 10–4

3.42 × 10–4

9.98 × 10–5

2.32 × 10–5

2.2

5.40 × 10–4

1.74 × 10–4

4.49 × 10–5

0.89 × 10–5

2.5

2.52 × 10–4

0.71 × 10–4

1.52 × 10–5

0.24 × 10–5

3.0

0.86 × 10–4

0.19 × 10–4

0.32 × 10–5

0.04 × 10–5

Figure 1 shows the dependence of the CO con centration on the residence time of the flow behind the flame front. As can be seen, the CO concentra tion increases as the mixture becomes leaner (in passing from α = 1.8 to 2.5) only if the residence time of the flow behind the flame front in the high temperature zone (T > 1000 K) is shorter than 13 ms. A similar situation takes place when the parame ters of the problem are varied over wide ranges. For example, we considered cases of increasing the ini tial mixture temperature (up to Tinit = 740 K) of decreasing the pressure (down to P = 5 atm), and of changing from the GRIMech 3.0 kinetic model to a more updated kinetic model from [19, 20]. Irre spective of all these variations, the form of the dependences of the CO concentration on α and τ (Fig. 1) remained unchanged—only the character istic residence time τp of the flow behind the flame front changed.

Y, m [OH]: 0.04

0.0001

0.0008

Note that, at present, homogeneous combustion chambers are largely used in stationary gas turbine installations. Such chambers have large sizes and long residence times (τ > 15 ms). Therefore, for such chamber, one should expect a monotonic decrease in the CO emission as the mixture becomes leaner. At long residence times of the flow in the com bustion chamber, the CO concentration approaches its equilibrium value. Therefore, it is useful to ana lyze how the equilibrium CO concentration (in mole fractions) depends on the temperature of the com bustion products and on the mixture composition (i.e., α). The equilibrium concentrations of the combustion products were calculated at a constant pressure (P = 10 atm) and a constant enthalpy using the CHEMKIN software package in conjunction with the GRIMech 3.0 database. The calculation results are listed in Table 2, where the temperature of the combustion products Tf is specified irrespective of the airtofuel equiva lence ratio α, a situation that can be realized near a cooled wall or during air inflow from the wall into

0.0016

0.0023

0.0030

0.0038

0.02 0 −0.02 −0.04 0

0.05

0.10

0.15

0.20

0.25

0.30

0.35 X, m

Fig. 2. Hydroxyl concentration field and streamlines in model combustion chamber no. 1 at α = 1.24, Tinit = 300 K, and P = 1 atm. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B

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Figure 2 shows the calculated hydroxyl concen tration (in mass fractions) field and streamlines at α = 1.24. It is known that the OH concentration reaches its maximum value at the flame front; there fore, this parameter is a reliable indicator of the position of the front. As can be seen, the front begins at the boundary of the zone of reverse currents and ends at the axis of the combustion chamber.

[CO], ppm 100009 8 7 6 5 4 3 2

10009

8 7 6 5 4

2

3 2

1

1009

8 7 6 5

1.1

609

1.2

1.3

1.4

α

1.5

Fig. 3. Dependence of the CO emission from combustion chamber no. 1 on α at Tinit = 300 K and P = 1 atm: (1) experiment [7] and (2) calculations.

the bulk of the combustion chamber. In these cases, approaching the wall is accompanied by a tempera ture decrease and an α increase. The data presented in Table 2 suggest that at least the equilibrium CO concentration will monotonically decrease with the distance to the wall. MODEL COMBUSTION CHAMBERS First, we performed calculations for model com bustion chamber no. 1 [16]. Recall that this chamber operated without cooling at atmospheric pressure (P = 1 atm), a mixture inlet temperature of Tinit = 300 K, and a residence time of τ = 32 ms.

Y, m

A comparison of the calculated and measured CO emission values [16] as functions of the airtofuel equivalence ratio α is displayed in Fig. 3. In this case, the CO emission was calculated without using the pro cedure of reducing the mixture concentration to the 15% oxygen fraction. As can be seen, the CO emission decreases monotonically with increasing α, both in experiments and calculations. As can be seen, the calculation and experimental results are in satisfac tory agreement. This suggests that the problems under consideration can be successfully tackled using the DRM19 reduced reaction mechanism and the selected model of bulk combustion. Let us now consider model combustion chamber no. 2, the construction of which is closer to that of practical combustion chambers. This chamber was designed at the Baranov Central Institute of Aviation Motors Development; some of the results of experi mental and theoretical studies of this chamber were reported in [17, 18]. As was demonstrated by onedimensional calcu lations of the combustion characteristics for lean mixture (at large α), the laminar flame speed Un is very low. Since the turbulent burning velocity is directly proportional to Un (formula (2)), it also decreases with increasing α. Therefore, as the mix ture becomes leaner, the angle of inclination of the flame front is expected to decrease. The calculation results support this conclusion.

[OH]: 4.2E05 2.2E04 4.0E04 5.7E04 7.5E04 9.2E04 1.1E03

0.10

α = 1.8

0.05 0 −0.05 α = 2.5

−0.10 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 X, m

Fig. 4. Hydroxyl concentration field and streamlines in model combustion chamber no. 2 at Tinit = 740 K, P = 1 atm, and α = 1.8 (upper panel) and 2.5 (lower panel). RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B

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The calculated CO emission (with allowance for the reduction to the 15% oxygen fraction) at the out let of chamber no. 2 monotonically decreases with increasing α (at to α = 2.5). Figure 5 compares these results to the experimental data from [17, 18]. Gen erally, the agreement is satisfactory. The sharp rise in the CO concentration observed in [17, 18] at α > 3.0 is probably associated with the fact that, in this case, the flame front spreads to the outside of the combus tion chamber, and, therefore, unburnt fuel, together with carbon monoxide, leaves the chamber.

[CO], ppm 16

12

8

1 2

4

0 1.6

1.8

2.0

2.2

2.4

α

2.6

Fig. 5. Dependence of the CO emission from combustion chamber no. 2 on α at Tinit = 740 K and P = 10 atm: (1) experiment [17, 18] and (2) calculations.

Figure 4 shows the OH concentration (mass frac tion) field, the maximum of which, as noted above, is located at the flame front. As can be seen from the results for α = 1.8 and a wall temperature of Tw = 1000 K (upper part of Fig. 4), the flame front is rather steep, approaching the chamber wall not far from the stabilizer. At α = 2.5, the situation is differ ent (lower part of Fig. 4): the flame front has a very small angle of inclination with respect to the stream lines and is located near the wall virtually up to the chamber outlet.

At the wall of model combustion chamber no. 2, two types of boundary conditions were specified: an impermeable wall with constant temperature Tw and a permeable wall with a fixed inflow velocity Vb. The latter case imitated a different type of combus tion chamber cooling, when cooling air is intro duced into the bulk of the chamber. For an impermeable wall and α = 2.5, two tem peratures were considered Tw = 500 K (cold wall) and Tw = 1000 K (hot wall). The calculations were performed using a finemesh grid, which made it possible to resolve the laminar sublayer of the boundary layer. The CO concentration at the cham ber outlet was 2.7 ppm (when reduced to the 15% oxygen fraction) for the hot wall and 89.9 ppm for the cold wall. On the face of it, this result contra dicts the above onedimensional analysis and the data on the equilibrium CO concentration. As the wall is cooled, the boundary layer temperature and velocity Ut decrease, as does the flame front inclina tion angle, whereas its extent increases. For a cool wall and α = 2.5, the flame front spreads nearly to the combustion chamber outlet. All these facts act so as increase the CO concentration at the chamber

Y, m [CO]: 0.0004 0.0006 0.0008 0.0012 0.0018 0.0026 0.0038 0.0056 0.10

Tw = 500 K

0.05 0 −0.05 Inflow, Tw = 1000 K

−0.10 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 X, m

Fig. 6. Carbon monoxide concentration field in model combustion chamber no. 2 at low wall temperature (upper panel) and for air blowing from the wall (lower) at α = 2.5 in both cases. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B

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not only near the wall. Note that the authors of [6] also observed a significant increase in the CO emis sion in passing from convective wall cooling to boundary cooling (during air inflow from the com bustion chamber walls).

[CO] 10−2 Вдув, Tw = 1000 K

10−3

CONCLUSIONS

10−4

A numerical simulation of CO emission during the onedimensional combustion of a methane–air mixture behind the flame fronts in two different model combustion chambers was performed. A one dimensional analysis demonstrated that leaner mix tures produce more CO at short residence times, with the opposite situation being realized at long res idence times.

Tw = 500 K

10−5 10−6 10−7

611

Tw = 1000 K

0

0.02

0.04

0.06 Y, m

Fig. 7. Transverse CO concentration profile (mole frac tions) at the outlet of model combustion chamber no. 2 at α= 2.5 and various conditions at the chamber wall.

outlet. Note that, at the expense of turbulent diffu sion, increased CO concentrations at the flame front appear even near the axis of the chamber. It is necessary to emphasize that such an influ ence of a cold wall is typical only of combustion chamber no. 2, in which the zone of reverse currents is located near the chamber axis (Fig. 6). A different picture is observed for combustion chamber no. 1 (Fig. 2), in which the zone of reverse currents is located near the wall, with the flame front being closed at the chamber axis. In this case, no apprecia ble influence of the chamber wall temperature on the CO emission is noticeable. A permeable wall was thought of (in calculations by the Fluent code) as an inlet boundary at which a normaltoboundary velocity of Vb = 1 m/s, a static inlet air temperature of Tinit = 740 K, and a pressure of 10 atm were specified. Such an intense blowing resulted in an additional air consumption of 40%. In this case, the CO concentration at the chamber outlet was 4320 ppm. Such a sharp increase in the CO emission (Tw = 500 K) can be explained by that the flame does not end at the wall, but rather leaves the combustion chamber (Fig. 6); therefore, com bustion continues outside the chamber, thereby leading to an increase in the concentrations of CO and unburnt hydrocarbons. The CO concentration profiles (mole fraction) at the combustion chamber outlet for a hot and cold permeable wall are displayed in Fig. 7 (the solid and dashed and dotted lines, respectively). As can be seen, the abovementioned increase in the CO con centration for the cold wall and for air blowing is observed over the entire cross section of the chamber, RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B

Using the bulk combustion model, we numeri cally simulated the combustion of a methane–air mixture and the effects of mixture leaning and con ditions at the wall on the CO emission from combus tion chambers nos. 1 and 2. According to our calcu lations, as the mixture becomes leaner, the CO emis sion monotonically decreases as long as burning occurs inside the combustion chamber. The calcula tion results were found to be in close agreement with the available experimental data. For model combustion chamber no. 2, we ana lyzed two types of boundary conditions: an imper meable wall at low temperature and a permeable wall with incoming flow perpendicular to it. For a cold wall, the CO concentration at the outlet of combus tion chamber no.2 turned out to be higher (by more than a factor of 30) than that in the case of a hot wall. The change in the CO emission was especially signif icant in passing from an impermeable wall to a per meable one. In this case, the increase in the CO emission was more 4000 ppm. The calculation results show that this increase is associated with an incomplete burning in the combustion chamber, with the flame front spreading to the outside of it. Note that, even in this case, no CO freezing near a cold wall occurs. All the above examples of enhanced CO emission are associated with the kinematic peculiarities in the behavior of the flame front, more specifically, when it is located near the wall or extends to the outside of the combustion chamber. ACKNOWLEDGMENTS This work was supported by the Russian Founda tion for Basic Research, project no. 090100348a and the Council for Grants of the President of the Russian Federation for Support of Young Russian Scientists and Leading Scientific Schools (grant no. NSh596.2008.8). Vol. 4

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