air flames

Computational and Experimental Study of Axisymmetric Coflow Partially Premixed Methane/Air Flames BETH ANNE V. BENNETT,* CHARLES S. MCENALLY, LISA D. PFEFFERLE, and MITCHELL D. SMOOKE Center for Combustion Studies, Yale University, New Haven, CT 06520-8284

Six coflowing laminar, partially premixed methane/air flames, varying in primary equivalence ratio from ⬁ (nonpremixed) to 2.464, have been studied both computationally and experimentally to determine the fundamental effects of partial premixing. Computationally, the local rectangular refinement solution–adaptive gridding method incorporates a damped modified Newton’s method to solve the system of coupled nonlinear elliptic partial differential equations for each flame. The model includes a C2 chemical mechanism, multicomponent transport, and an optically thin radiation submodel. Experimentally, both probe and optical diagnostic methods are used to measure the temperature and species concentrations along each flame’s centerline. Most experimentally measured trends are well predicted by the computational model. Because partial premixing decreases the flame height when the fuel flowrate is held constant, computational and experimental centerline profiles have been plotted against nondimensional axial position to reveal additional effects of partial premixing. Heat release profiles, as well as those of several species, indicate that the majority of the partially premixed flames contain two flame fronts: an inner premixed front whose strength grows with decreasing primary equivalence ratio; and an outer nonpremixed front. As the amount of partial premixing increases, computational results predict a continual reduction in the amount of flow radially inward; the resulting decrease in radial transport is responsible for various effects observed both computationally and experimentally, including a cooling of the gases near the burner surface. At the same time, radiative losses decrease with increasing amounts of premixing, resulting in higher flame temperatures. © 2000 by The Combustion Institute

INTRODUCTION When a fuel stream mixes with a substoichiometric amount of (primary) air before encountering a separate oxidizer (secondary air), the resulting flame is referred to as being partially premixed. Because of their stability, partially premixed flames are used in Bunsen burners, staged combustors, and several other common combustion devices. In addition, even when the fuel and oxidizer are nonpremixed, turbulent flow conditions may produce partial premixing locally [1]. While today’s computers are still not powerful enough to solve exact numerical models of three-dimensional, unsteady, turbulent combustion in realistic devices, the fundamental effects of partial premixing can be determined via sophisticated adaptive numerical methods to model chemically complex, axisymmetric laminar flames. Many previous computational and/or experimental studies have examined laminar partially premixed flames [2–11] in various physical con*Corresponding author. E-mail: [email protected] 0010-2180/00/$–see front matter PII S0010-2180(00)00158-9

figurations. Validation of detailed numerical models against experiments is necessary, so that the former may be reliably utilized in situations in which the latter cannot provide data. Such computational/experimental comparisons are lacking for laminar partially premixed flames in coflow configurations, mainly because of the difficulty in computing multidimensional flames with detailed chemistry and multicomponent transport. The present work bridges this gap, focusing on six axisymmetric flames in coflow, each of which is modeled computationally using detailed C2 chemistry, multicomponent transport, and an optically thin radiation submodel; each flame has also been measured experimentally, with many of the latter results appearing as part of a previous study [9]. The primary equivalence ratios of these flames range from ⌽ 3 ⬁ to ⌽ ⫽ 2.464, which are obtained by holding the CH4 flowrate constant in the inner jet and incrementing the primary air flowrate, starting from zero. The first flame is nonpremixed, whereas the last flame contains a visible inner premixed flame front and an outer nonpremixed flame. This COMBUSTION AND FLAME 123:522–546 (2000) © 2000 by The Combustion Institute Published by Elsevier Science Inc.

COFLOW PARTIALLY PREMIXED METHANE/AIR FLAMES

523

TABLE 1 Flame Parameters for Computations ⌽ Inner jet ⬁ 12.320 6.160 4.107 3.080 2.464 Outer jet All

Q CH 4 (cm3/min)

Q air (cm3/min)

vz (cm/s)

Y CH 4,B

Y O 2,B

Y N 2,B

330 330 330 330 330 330

0 210 420 630 840 1050

5.67 9.28 12.89 16.50 20.11 23.71

1.00000 0.46420 0.30226 0.22408 0.17803 0.14769

0.00000 0.15071 0.19627 0.21826 0.23121 0.23975

0.00000 0.38509 0.50147 0.55766 0.59076 0.61256

0

44000

10.48

0.00000

0.23200

0.76800

so-called double flame structure has been observed by other researchers in both the axisymmetric coflow [3, 4, 6 –9, 11] and counterflow configurations [5, 10], as well as for the porous cylindrical (Tsuji) burner [2]. The main objective of the present work is to learn about the effects of partial premixing by identifying trends which are both numerically predicted and experimentally observed. More specifically, computational confirmation of previously noted experimental trends is sought, and model predictions of difficult-to-measure quantities (i.e., streamlines, chemical production rates, etc.) are used to explain experimental observations. To these ends, the computational results are first examined throughout each flame, and these results are then compared with experimental data obtained along each flame’s centerline.

last entries in those same columns, are held fixed for all six cases. The primary air is oxygenenriched (25% O2 by volume), whereas the secondary air is “regular” air (20.9% O2). The remainder of Table 1 is discussed below. The burner is the same as that studied in [12–14], a schematic of which is shown in Fig. 1. The inner jet’s inner radius is r I ⫽ 0.555 cm,

NUMERICAL MODEL AND SOLUTION TECHNIQUES Problem Formulation The six flames modeled computationally and characterized experimentally in the present work are generated using an axisymmetric coflow burner configuration. The primary equivalence ratio ⌽ (primary air flowrate required for complete combustion, divided by the actual primary air flowrate) for each flame appears in Table 1. The methane and primary air flowrates in the inner jet are given by the first six entries in the Q CH 4 and Q air columns, respectively. Flowrates in the outer jet, represented by the

Fig. 1. Schematic of the burner used for the six flames.

524 and the tube through which it flows has a wall thickness of w JET ⫽ 0.080 cm. The outer jet’s inner radius is r O ⫽ 4.76 cm, and the inner radius of the cylindrical shield is r max ⫽ 5.10 cm. Computations are performed in a two-dimensional domain with radial boundaries at r ⫽ 0 and r ⫽ 5.10 cm and axial boundaries at z ⫽ 0 and z ⫽ 20.0 cm; for formulation of boundary conditions, the latter can be considered “infinitely” far from the flame. The gas is assumed Newtonian and diffusion is Fickian: the nth species diffusion velocity is given by Vn ⫽ ⫺D n ⵜ ln Y n , where D n and Y n are the diffusion coefficient and mass fraction, respectively, of the nth species. The Soret and Dufour effects are neglected; viscous dissipation, however, is not neglected. The flow’s small Mach number implies that pressure can be taken as constant in the ideal gas law, from which the mixture density ␳ is then calculated. The present model includes an optically thin radiation submodel [15–17] with three radiating species (H2O, CO, and CO2), used to calculate ⵜ 䡠 q R , the divergence of the net radiative flux. No soot model is included, because the peak soot volume fraction in the nonpremixed ⌽ 3 ⬁ case (the sootiest flame considered) is only 0.4 ppm [14]; absence of a soot model is not anticipated to affect agreement with the experimental data to any significant degree. In each case, the velocity profile across the inner jet exit consists of zero radial velocity and a constant axial velocity of v z,I , and that across the coflow jet exit also has v r ⫽ 0 but a constant axial velocity of v z,O ; velocities v z,I and v z,O for the six flames are given in the v z column of Table 1. Across the thickness of the inner and coflow jets’ walls (located at 0.555 cm ⬍ r ⬍ 0.635 cm, z ⫽ 0 cm), all velocities vanish. Based on v z,I , the inner jet diameter, the inlet temperature of 298 K, and the inlet chemical compositions stated in the last three columns of Table 1, the Reynolds numbers for the six flames range from 31 (for ⌽ 3 ⬁) to 167 (for ⌽ ⫽ 2.464), all of which are in the laminar regime. Governing Equations and Boundary Conditions The governing equations are expressed using the vorticity–velocity formulation [18 –20],

B. A. V. BENNETT ET AL. where vorticity is defined as ␻ ⫽ ⭸v r /⭸ z ⫺ ⭸v z /⭸r. Combining the vorticity definition and the steady-state continuity equation produces the elliptic velocity equations; the curl of the momentum equation produces the vorticity transport equation. The N2 species conservation equation is replaced by the constraint that all mass fractions must sum to unity. The dependent variables are velocity components v r and v z , vorticity ␻, temperature T, and the species mass fractions Y n , n ⫽ 1, . . . , N spec, where N spec is the number of chemical species. Because the governing equations are nearly identical to those appearing in [21] for the diffusion flame, they are not repeated here. The only difference is that the right-hand side of the energy equation now includes the following viscous dissipation term, in which ␮ represents the dynamic viscosity: viscous dissipation ⫽

冋冉 冊 冉冊 冉 冊 冉 冊 册

␮ 2 ⫹

⭸v r ⭸r

2

⫹2

⭸v r ⭸v z ⫹ ⭸z ⭸r

vr ␶

2

⫺

2

⫹2

⭸v z ⭸z

2 共div(v兲) 2 3

2

(1)

Inclusion or exclusion of this term, which would normally be neglected as part of the low Mach number assumption, affects the results only negligibly; it is included here for slightly greater accuracy. The chemical mechanism employed is GRI-Mech version 2.11 with all nitrogen-containing species removed, except for N2, resulting in 31 species and 173 reversible reactions [22]. All thermodynamic, chemical, and transport properties are evaluated using the CHEMKIN [23, 24] and TPLIB [25, 26] subroutine libraries, parts of which have been rewritten and restructured for greater speed [27]. The boundary conditions are as follows. Along the z-axis (axis of symmetry), v r and ␻ vanish, as do radial gradients of all other dependent variables, and the v z boundary condition is discretized as discussed in [21], in order to avoid solution inaccuracies and/or convergence difficulties. At the outer radial boundary, v r and v z vanish, the ␻ definition is applied (using a centered discretization of ⭸v r /⭸ z and a backward discretization of ⭸v z /⭸r), and radial gradients of T and Y n vanish. At the inflow (bottom)

COFLOW PARTIALLY PREMIXED METHANE/AIR FLAMES boundary, the inlet velocity profile described earlier is applied, as well as the ␻ definition (using a forward discretization of ⭸v r /⭸ z and a centered discretization of ⭸v z /⭸r), and the inflow T is set to 298 K; the effects of this latter boundary condition will be discussed in the “Flame Heights” and “Temperatures” sections. Individual species mass Y n (at z ⫽ 0) is conserved as follows, where B represents the burner surface, ␭ the thermal conductivity, c p the heat capacity at constant pressure, and Len ⫽ ␭ / ␳ c p D n the Lewis number for the nth species:

␳ v z共Y n ⫺ Y n,B兲 ⫽

冉冊

1 ␭ ⭸Y n . Len c p ⭸ z

(2)

Species mass fractions Y n,B at the burner surface (at z 3 0 ⫺ ) appear in Table 1. The partial derivative in Eq. 2 is discretized via a forward difference. At the outflow (top) boundary, v r vanishes, as do axial gradients of the remaining dependent variables. Numerical Methods The initial grid, identical for each of the six flames, is a nonequispaced tensor product mesh of size 66 ⫻ 84, with finer spacing in the region immediately above the burner surface than in, for example, parts of the domain very far removed from the inlet. Specifically, this initial mesh is uniformly spaced with ⌬r ⫽ 0.02 cm for 0 ⱕ r ⱕ 0.90 cm, with increasingly larger spacing for 0.90 ⱕ r ⱕ 5.1 cm, and it is also uniformly spaced with ⌬z ⫽ 0.03 cm from z ⫽ 0 to z ⫽ 0.90 cm, with increasingly larger spacing for 0.90 cm ⱕ z ⱕ 20.0 cm. Developing an acceptable starting estimate for the steadystate Newton’s method on this grid is difficult because the governing equations are strongly coupled and extremely nonlinear. Therefore, the solution of the flame sheet problem, discussed in more detail in [28, 29], serves as a starting estimate for the full-chemistry nonpremixed flame (⌽ 3 ⬁). The solution to the latter problem, obtained via a time-relaxation process leading to steady-state Newton’s method, is then used in a continuation method whereby the oxygen-enriched air is slowly added in the inner

525

jet, ultimately producing converged solutions on the initial grid for the other five desired primary equivalence ratios. Once the solution on the starting (structured) grid for each of the six flames is known, more accurate results are computed using the local rectangular refinement (LRR) solution–adaptive gridding method, described extensively in [21, 30]. This technique automatically refines the grid cell by cell as needed, based on weight functions involving gradients of the dependent variables. In the current research, the chosen adaption variables are Y CH 4 and Y C 2H 6; the majority (roughly 95%) of the adaption occurs because of gradients in the former. The governing equations and boundary conditions are discretized on the resulting unstructured grids via multiple-scale discretizations, shown to have smaller errors than standard single-scale discretizations in most cases [21, 30]. The resulting coupled system is solved using a damped modified Newton’s method and a nested Bi-CGSTAB linear algebra solver with a block Gauss-Seidel preconditioner; further information can be found in the references within [21]. Pseudo-transient terms are appended to the spatially elliptic governing equations [31] to make the Newton’s method Jacobian more diagonally dominant and thus improve the linear system solver’s convergence. This timerelaxation procedure is employed for a specified number of adaptively chosen time steps [28]. The steady-state equations then undergo a series of four Newton solves with steadily decreasing tolerances, to a final Newton tolerance of 10⫺4. This cycle of adapting the grid, then discretizing, and finally solving the governing equations continues until the weight functions are subequidistributed to within 5%. All calculations have been performed on a 2GB-RAM IBM RS/6000-590 workstation. On each adaptive grid, using an interpolation of the previous adaptive grid’s converged solution as an initial guess, the LRR method typically takes several hours of computer time to advance this estimate (via iterative solution of the pseudotransient problem) to the point where the steady-state problem will quickly converge. The LRR method then requires an additional hour of computer time to solve the steady-state prob-

526 lem. Obviously, the larger the number of grid points, the longer the total solution time. Efficiency of the LRR method is explored in a later section. EXPERIMENTAL TECHNIQUES The burner is described in previous work [12– 14]; the measurement techniques are detailed elsewhere [9, 13, 32] and are only briefly summarized here. Gas temperatures are measured using uncoated thermocouples [32]; these measurements have an absolute uncertainty of 50 K, a relative uncertainty of 10 K, and a spatial resolution of 0.3 mm. Species concentrations are determined by extracting gas samples with a narrow-tipped quartz sample probe and analyzing them via on-line mass spectrometry [13]. An electron-impact/quadrupole mass spectrometer (EQMS) is used to measure methane, formaldehyde, acetylene, oxygen, water, and carbon dioxide mole fractions, while mole fractions of C2H2O and other higher hydrocarbons are measured using a photoionization/time-of-flight mass spectrometer (PTMS) [13]. The concentration measurements of methane, acetylene, oxygen, water, and carbon dioxide have absolute uncertainties of 30%; measurements of formaldehyde, C2H2O, and other higher hydrocarbons have relative uncertainties of 30% and absolute uncertainties of up to a factor of 3. OH concentrations, measured using laser-induced fluorescence (LIF), have relative uncertainties of 30%. All concentrations, regardless of the diagnostic technique, are spatially resolved to 1 mm. Multiple trials have been run, and the results are seen to be repeatable to within experimental uncertainties. Data are acquired along the centerline of each flame, as functions of z, the axial distance from the burner surface. The absolute uncertainties in z and in the radial location of the centerline are 1 mm, and the relative uncertainties are considerably smaller than the spatial resolution of the temperature and species measurements. All experimental flowrates are estimated to be accurate to ⫾5%. Several quantities are derived from these flowrates: primary equivalence ratios; jet velocities; and chemical compositions

B. A. V. BENNETT ET AL. within each jet—in short, many of the quantities which are listed in Table 1 and are employed in the burner boundary conditions in the numerical model. These experimental uncertainties (⫾10% for the derived quantities) can be expected to produce some differences between the computed and measured results. For purposes of experimental calibration of the species measurements, the fuel and primary air mixtures are diluted with argon; the argon’s volumetric flowrate is always 1% of that of the total fuel mixture, as documented in [9]. This dilution is not modeled numerically because it does not significantly alter flame structure. RESULTS AND DISCUSSION This section opens by examining the LRR adaptive grids and the efficiency and accuracy of the LRR computational method. Next, arguments are made for the subsequent spatial nondimensionalization of the data in the axial direction. Then, the computational results are studied throughout the domain, and finally, computational and experimental data are compared along the flame centerlines. The reader should note that all species results are plotted as mole fractions (Xn), not mass fractions. LRR Adaptive Grids The left half of each of Figs. 2a–f displays 51 isopleths of X CH 4, ranging from the computed minimum to the computed maximum in each case; only a portion of the computational domain is shown. The right half shows the corresponding portion of the LRR Adaption 2 grid for each flame. Refinement always occurs near the fuel consumption zone because the grids adapt automatically based primarily on gradients of Y CH 4 and secondarily on gradients of Y C 2H 6. Immediately apparent is the fact that, as partial premixing occurs and the flames get shorter, the refinement regions also shrink, while continuing to “hug” the fuel consumption zones. It should also be noted that the isopleths of X CH 4 range from being very widely spaced in

COFLOW PARTIALLY PREMIXED METHANE/AIR FLAMES

527

Fig. 2. For each of the six flames, computations have been performed on a series of LRR adaptive grids. The left half of each figure shows 51 isopleths of X CH 4, ranging from computed minimum to computed maximum; the right half illustrates the corresponding final LRR adaptive grid. A portion of the computational domain (that portion in which most of the adaption occurs) is displayed for (a) ⌽ 3 ⬁; (b) ⌽ ⫽ 12.320; (c) ⌽ ⫽ 6.160; (d) ⌽ ⫽ 4.107; (e) ⌽ ⫽ 3.080; and (f) ⌽ ⫽ 2.464.

the nonpremixed ⌽ 3 ⬁ flame of Fig. 2a to closely packed in the ⌽ ⫽ 2.464 flame of Fig. 2f; in other words, X CH 4 (and Y CH 4) gradients greatly increase as partial premixing occurs, and the overall region containing CH4 dramatically decreases in extent. Three levels of refinement comprise each Adaption 2 grid displayed: Level 0 (the nonuniform base grid); Level 1 (finer spacing); and Level 2 (finest spacing). These three levels are much more visible in Figs. 3a–f, which focus on the portion of each flame’s grid near the burner surface. As expected, the refined region is more spread out in the earlier figures and narrows as partial premixing occurs. Furthermore, the Level 2 refinement region extends to increasingly higher z values as ⌽ decreases, triggered

by the very high Y CH 4 gradients near the inner premixed flame front. The envelope of the Level 2 region actually closes at the centerline (near the premixed flame front) for the four most premixed cases. The fact that these six flames, very different in structure and size, are adaptively solved using the same automated method, starting from identical base grids, demonstrates the flexibility of the LRR method. The efficiency and accuracy of the LRR method are demonstrated via comparisons with solutions computed on equivalent tensor product (ETP) grids. The latter grids are formed by extending all grid lines of a given LRR grid out to the edges of the computational domain; such grids represent those available to researchers using adaptive globally refined (structured)

528

B. A. V. BENNETT ET AL.

Fig. 3. The LRR adaptive grids are shown in greater detail near the burner surface, illustrating the presence of a base grid plus two additional refinement levels, for (a) ⌽ 3 ⬁; (b) ⌽ ⫽ 12.320; (c) ⌽ ⫽ 6.160; (d) ⌽ ⫽ 4.107; (e) ⌽ ⫽ 3.080; and (f) ⌽ ⫽ 2.464.

rectangular grids. Once each ETP grid has been determined, the solution process is exactly the same as that on the LRR grids. For brevity, comparisons are made only for the ⌽ ⫽ 2.464 flame computation. The first few columns of Table 2, related to efficiency, show the gridding method (LRR or ETP), the adaption number, the number of grid points N pts , and the normalized total CPU time per point t/N pts , where CPU time has been normalized by the time of one base-grid Jacobian formation. The final LRR adaptive grid has 44% as many points as the final ETP grid. Unfortunately, the memory required to solve on the final ETP grid exceeds that available (memory requirements are discussed in [21, 30]). The per-point solution time is smaller for LRR Adaption 1, as compared to the corresponding ETP solution. The remaining three columns of Table 2, monitoring calculation accuracy, display the z value HT at which maximum centerline tem-

perature Tmax,C occurs, Tmax,C, and HS/HT, where HS is the z value at which a sharp minimum occurs in ⭸2T/⭸z2 along the centerline (all will be discussed in much greater detail below). The values obtained by the LRR method begin to asymptote as the grids undergo adaption; moreover, these values are identical to those calculated on the corresponding ETP grids, demonstrating no loss of accuracy between the conventional ETP grids and the adaptive LRR grids. Similar data characteristics (asymptotic approach to final values; exact or very close LRR/ETP agreement) have also been observed for the other five flames of the current study. Flame Heights The comparison of numerically computed and experimentally measured results begins with the flame heights. The more partial premixing that occurs, the smaller the amount of secondary

TABLE 2 Comparison of LRR and ETP Solutions for ⌽ ⫽ 2.464 Method LRR

ETP

a

Ad.

N pts

t/N pts (norm.)

HT (cm)

T max,C (K)

H S /H T

0 1 2 0 1 2

5544 8835 17124 5544 13802 38988

0.0002 0.0067 0.0092 0.0002 0.0072 —a

3.200 3.400 3.400 3.200 3.400 —a

1991 1997 1999 1991 1997 —a

0.469 0.484 0.492 0.469 0.484 —a

Size of problem exceeded 2GB RAM limit.

COFLOW PARTIALLY PREMIXED METHANE/AIR FLAMES

529

TABLE 3 Flame Characteristics: Comparison of Computational and Experimental Results T max,C (K)

H T (cm) ⌽

Comp.

⬁ 12.320 6.160 4.107 3.080 2.464 a

8.00 6.25 5.00 4.50 3.80 3.40

Exp.

Comp.

5.70 5.20 4.90 4.50 4.20 3.80

1868 1900 1925 1950 1974 1999

H S /H T Exp. 1960 2000 2020 2040 2060 2090

Comp. a

— —a 0.55 0.51 0.51 0.46

Exp. —a —a 0.49 0.51 0.50 0.47

No single sharp minimum present in ⭸ 2 T/⭸ z 2 .

oxygen that must diffuse inward to create a stoichiometric mixture, and thus the smaller the axial distance required for this necessary diffusion to occur. This argument implies that the flame height will shrink with increased premixing, when the CH4 flowrate is held constant. For each of the six flames studied, Table 3 contains the computed and experimental values of H T ; indeed, the computed and experimental H T decrease by 58% and 33%, respectively, over the total ⌽ range investigated. Although the computed and experimental H T values agree to within roughly 10% for the four most premixed flames, agreement is not very good for the ⌽ 3 ⬁ and ⌽ ⫽ 12.320 flames. Disagreements are not unexpected, given that heat is transferred (in the experiment) from each of the flames to the oncoming reactants via the fuel tube wall, but the thermal boundary condition in the numerical model sets the initial reactant temperature to 298 K. This value is chosen primarily because the experimental technique does not allow temperature measurement within a certain distance of the burner, so the true value is not known. The effect of such TABLE 4 Flame Characteristics: Additional Computational Results

⌽ ⬁ 12.320 6.160 4.107 3.080 2.464

H f /H T

Radiative Heat Loss

T max (K)

(r, z/H T ) for T max (cm)

1.08 1.05 1.09 1.06 1.11 1.11

17.6% 15.8% 14.4% 13.8% 13.2% 12.8%

1969 1967 1973 1986 2008 2032

(0.66, 0.19) (0.62, 0.25) (0.60, 0.31) (0.56, 0.44) (0.54, 0.53) (0.52, 0.56)

a choice, in the case of a nonpremixed flame, is the overprediction of the flame height by 15%, as reported in [14]; similar behavior in flame height (for the ⌽ 3 ⬁ flame) is observed in the current study. Because the main goal of the present work is to employ computational and experimental comparisons to examine trends in the data as partial premixing occurs, no attempt has been made to select a different inlet temperature through trial and error, for the sole purpose of forcing a match between computational and experimental data. Whereas the computational choice of T at the burner surface certainly affects absolute values of fluid-dynamic and chemical quantities, relative trends in the data should remain largely unaffected, as seen in previous work [14]. In most coflowing nonpremixed burners, including the axisymmetric configuration of the Santoro burner [12] and the Wolfhard-Parker slot configuration of the NIST burner [33], heat is transferred between the flame and the burner, resulting in flames that are steady and are resistant to probe disturbances. Therefore, the ability to compare results from such burners with numerical model predictions is desirable. However, the computed flame height is very sensitive to the choice of chemical mechanism, the assumed transport properties, and the inlet boundary conditions, so it is unlikely that any given model will accurately predict the flame heights. Moreover, in the present study, the decrease of flame height with ⌽ is additional motivation to employ a comparison technique that factors out flame height differences. A tool which has worked here is the nondimensionalization of the axial coordinate z through division by HT.

530

B. A. V. BENNETT ET AL.

Fig. 4. Isopleths of heat release (in W/cm3) are displayed as functions of radial position (r) and nondimensional axial position ( z/H T ) in a portion of the computational domain, for (a) ⌽ 3 ⬁; (b) ⌽ ⫽ 12.320; (c) ⌽ ⫽ 6.160; (d) ⌽ ⫽ 4.107; (e) ⌽ ⫽ 3.080; and (f) ⌽ ⫽ 2.464. In each case, the plotted isopleths range from the computed minimum to one-fifth of the computed maximum.

As observed previously for CH4/air [9] partially premixed flame experimental data, H T is an appropriate surrogate to the mixturestrength flame height H f , defined as the z value at which the centerline local equivalence ratio is unity [34, 35]. The validity of this experimental assumption is demonstrated here computationally: H T is within 11% of H f for every flame, as

shown by the H f /H T column of Table 4. Therefore, H T is also a reasonable computational surrogate for H f , since they are proportional to each other, within grid point spacing accuracy. Furthermore, since H T is consistently 10% smaller than H f , then assuming H T ⬇ H f will incur the same relative error in every flame. The remainders of Tables 3 and 4 are discussed later.

COFLOW PARTIALLY PREMIXED METHANE/AIR FLAMES

531

Fig. 5. Isopleths of heat release are shown in greater detail near the burner surface, illustrating the existence of a double flame structure, for (a) ⌽ 3 ⬁; (b) ⌽ ⫽ 12.320; (c) ⌽ ⫽ 6.160; (d) ⌽ ⫽ 4.107; (e) ⌽ ⫽ 3.080; and (f) ⌽ ⫽ 2.464.

Heat Release Figures 4a through 4f illustrate isopleths of heat release in a portion of the computational domain, for each of the six flames. The vertical spatial coordinate is the nondimensional axial position z/H T . For every flame, the maximum heat release occurs in a small annular region just above the burner surface. In this region, the heat release rate is an order of magnitude larger than anywhere else in the domain. Therefore, in each case, the chosen color scale runs from the minimum value to one-fifth of the maximum, in order to make the structure of the other regions more visible. For the ⌽ 3 ⬁ case, as well as for the outer nonpremixed flame in the other cases, heat is released in two bands which approach the centerline near z/H T ⫽ 1.0, with negligible heat release on the centerline. (In each of these two bands, partially burnt fuel products are undergoing further burning; the first band mainly results from the conversion of HCO to CO, and the second band results from the conversion of CO to CO2.) As partial premixing occurs, heat release diminishes at the outer flame front and increases at the inner flame front. Figures 4d through 4f show that the latter flame front intersects the centerline near z/H T ⫽ 0.5—a location remarkably insensitive to the value of ⌽. Although not at all visible in Figs. 4b and 4c, the inner flame front is in fact present in all five partially premixed cases and grows in strength with decreasing ⌽; it will be seen below to be

responsible for a “shoulder” in the centerline temperature profiles. Unlike the outer nonpremixed flame, the inner flame front’s highest heat release rate occurs near the centerline. Figure 5 focuses on the portion of the computational domain near the burner surface. From these heat release isopleths, shown in greater detail than those of the previous figure, a double flame structure (inner rich premixed flame, outer nonpremixed flame) is now apparent for all six flames, including the ⌽ 3 ⬁ flame. However, the inner premixed flame is extremely weak in the latter case, to the point of being barely present. In general, flame fronts are defined as being locations of heat release, but because experimental measurement of heat release as a function of position throughout the domain is not possible, it is desirable to correlate heat release with species concentrations which can be measured. Previously published data [36, 37] indicate that HCO correlates closely with heat release in unsteady (near-)stoichiometric premixed flames, a result which is extended in the present work to partially premixed flames over a wide range of ⌽ values. Figures 6k, l and 6m,n contain isopleths of HCO and CH2O (formaldehyde) mole fractions, respectively; other parts of Fig. 6 will be examined in the next section. These two species might be thought to be reasonable flame front markers (HCO for the reasons specified in [37]; CH2O for its role in forming HCO). Results for

532

B. A. V. BENNETT ET AL.

Fig. 6. Isopleths of some interesting quantities are displayed as functions of radial position (r) and nondimensional axial position ( z/H T ) in a portion of the computational domain. Shown are (a, b) isotherms (in K); (c, d) isopleths of CH4 mole fraction (X CH 4); (e, f) isopleths of O2 mole fraction (X O 2); (g, h) isopleths of CO2 mole fraction (X CO 2); (i, j) isopleths of OH mole fraction (X OH ); (k, l) isopleths of HCO mole fraction (X HCO ); (m, n) isopleths of CH2O mole fraction (X CH 2O ); and (o, p) isopleths of HCCO mole fraction (X HCCO ). The left half of each figure pair displays the pertinent isopleths for ⌽ 3 ⬁, and the right half for ⌽ ⫽ 2.464. In each case except (k, l), the plotted isopleths range from the computed minimum to the computed maximum. Note that for each of (k, l), the plotted isopleths range from the computed minimum to one-fifth of the computed maximum.

the ⌽ 3 ⬁ case occupy the left half of each picture and ⌽ ⫽ 2.464 the right half. The reader should note that the color scale in each half of the HCO figure ranges from the minimum (zero) to one-fifth of the computed maximum, just as in the heat release figures; a similar color scale adjustment did not illuminate any addi-

tional features of the CH2O plot and was thus deemed unnecessary. These two potential flame front markers are now visually compared with the plots of heat release for the ⌽ 3 ⬁ and ⌽ ⫽ 2.464 cases, appearing in Figs. 4a and 4f, respectively. It is clear that HCO best mimics the four main

COFLOW PARTIALLY PREMIXED METHANE/AIR FLAMES features present in the heat release plots. First, the bulk of the HCO is present in a small annulus near the burner surface (for both the ⌽ 3 ⬁ and ⌽ ⫽ 2.464 cases). Second, in the ⌽ 3 ⬁ flame, HCO appears only at the nonpremixed flame front and disappears near the centerline. Third, in the ⌽ ⫽ 2.464 case, a large secondary concentration of HCO appears adjacent to the centerline, along the inner flame front. Fourth and last, small amounts of HCO are present in the outer flame region for ⌽ ⫽ 2.464, but these fade to negligible amounts well away from the centerline. The other heat-release-correlation contender, CH2O, is deficient in predicting one or more of these features. However, on the practical side, CH2O is far easier to measure than HCO and turns out to be a good qualitative indicator of the inner flame front location.

533

premixing, and Figs. 6e and 6f contain isopleths of O2 mole fraction. In the ⌽ 3 ⬁ flame, CH4 and O2 coexist in only a very small region, as is expected in a nonpremixed flame. In the ⌽ ⫽ 2.464 flame, however, these species coexist in a conical region between the burner surface and the inner (premixed) flame front. The gradual consumption of CH4 in the ⌽ 3 ⬁ (nonpremixed) flame contrasts with its rapid disappearance over a narrow region near the inner flame front of the ⌽ ⫽ 2.464 flame. OH mole fractions are displayed in Figs. 6i and 6j. For both the ⌽ 3 ⬁ and ⌽ ⫽ 2.464 flames, OH appears in approximately the same spatial regions. Because CH4, H2, C2H2, and other hydrocarbons react quickly with OH, O, and H radicals [38], negligible OH is present in the fuel-rich region due to the high OH destruction rate. It is only in the vicinity of the nonpremixed flame front that the OH production finally exceeds its destruction.

General Appearance of Computational Results

Temperatures

Figure 6 displays isopleths of temperature, as well as those of some major and minor species concentrations, in a portion of the computational domain, for two of the six flames studied: the ⌽ 3 ⬁ flame (left half of each picture) and the ⌽ ⫽ 2.464 flame (right half of each picture). Note that the color scales in the left and right halves of some pictures differ when the computed minima and/or maxima are not the same for the ⌽ 3 ⬁ and ⌽ ⫽ 2.464 cases. From the isotherms of Figs. 6a and 6b, it is apparent that in both the ⌽ 3 ⬁ flame and the ⌽ ⫽ 2.464 flame, the high-temperature region has a “wishbone” structure. The temperature rise at the base of the flame occurs more gradually in the nonpremixed case; the T gradient is quite steep at the conical inner flame front for the ⌽ ⫽ 2.464 flame. The difference between these two T rises would be even more apparent were z to be placed on the vertical axis, instead of z/HT. The peak temperature is approximately 100 K higher in the latter flame. Figures 6c and 6d show isopleths of CH4 mole fraction, in which the difference in the domain maxima is an obvious consequence of partial

Gas temperatures along the centerline of each of the six flames are shown in Fig. 7, with the computational data displayed in the upper half (a) and the experimental results in the lower half (b). In Fig. 7 and in most of the remaining figures, nondimensional axial position z/H T is plotted on the abscissa. Catalytic ignition on the thermocouple surface produced interferences in the temperature measurements near the burner surface in the partially premixed flames; removal of this data has caused the experimental profiles to start at increasing z/H T as ⌽ decreases. Soot deposition on the thermocouple causes a dip in the nonpremixed flame profile around z/H T ⫽ 0.7; this interference is much smaller in the partially premixed (less sooty) flames. In general, the computational temperatures are consistently lower than the corresponding experimental values by 85 to 100 K (roughly 5% of the flame temperatures); this behavior is consistent with that observed in a previous computational and experimental study of a nonpremixed methane/air flame [14]. This behavior partly results from the thermal boundary condition at the burner surface: the numerical model includes neither heating of the burner lip, nor,

534

B. A. V. BENNETT ET AL.

Fig. 8. Streamlines originating in the coflowing jet are displayed as functions of radial position (r) and nondimensional axial position ( z/H T ) in a portion of the computational domain, along with the flame front, for (a) ⌽ 3 ⬁ and (b) ⌽ ⫽ 2.464. Fig. 7. Profiles of temperature (T) along the flame centerline, as functions of nondimensional axial position ( z/H T ), are displayed for the six flames. Both (a) computational and (b) experimental results are shown. The symbols do not correspond to specific data points; rather, they help to distinguish among the various plotted curves.

consequently, preheating of the reactants. Experimental uncertainties may also play a role, as well as approximations in the numerical model (such as uncertainties in the chemical mechanism, for example). Therefore, the computed steady-state temperatures are lower overall than those measured experimentally. Three effects of partial premixing are present in both the computational and experimental results. First, the peak centerline temperature T max,C , listed in Table 3 for each flame, increases by 7% from the nonpremixed flame to the ⌽ ⫽ 2.464 flame for both the computational and the experimental data—a trend obviously very well predicted by the model. Other researchers have observed a similar trend [7, 39], likely caused in part by the increasing strength of the inner flame front, leading to increased heat release near the centerline (Fig. 4). An-

other reason for the T max,C increase may be that less of the (cooler) coflowing air is entrained as partial premixing occurs. This hypothesis is supported by the streamlines depicted in Fig. 8, which are computed in the same way as in [40]. The second effect of partial premixing present in the temperature profiles is the “shoulder” that forms near z/H T ⫽ 0.5 due to heat release at the inner flame front [2, 7]—a feature present in both the computational and experimental results. The initial absence of a shoulder (⌽ 3 ⬁ and ⌽ ⫽ 12.320), followed by an increase in the shoulder’s sharpness (⌽ ⫽ 6.160 to ⌽ ⫽ 2.464), is entirely expected, given the corresponding increase in strength of the inner flame front as seen in the heat release profiles, above. The location of this shoulder, denoted by H S , is defined by a local minimum in ⭸ 2 T/⭸ z 2 . Values of H S /H T are given in Table 3. Although a slight decreasing trend is apparent in the computational H S /H T values, both the computational and experimental H S /H T data hover around 0.5, indicating that the inner flame height is approximately half that of the outer (nonpremixed) flame height. Similar results have been found previously [7].

COFLOW PARTIALLY PREMIXED METHANE/AIR FLAMES The third effect of partial premixing is the reduction in centerline temperatures near the burner surface ( z/H T ⱕ 0.4)—an experimentally observed trend very well predicted by the computational results, and apparent both in Fig. 6a, b and in Fig. 7. This effect is best explained by the decrease in the amount of flow radially inward, in the region z/H T ⱕ 0.4. This latter behavior, reflected in the streamlines of Fig. 8, subsequently reduces the heat transfer from the outer flame front toward the centerline. The same phenomenon also decreases the inward radial transport of chemical species formed off-axis (H2O, CO2, CO, etc.), thus delaying the rise of their centerline profiles. In turn, the decrease in the CH4 and O2 centerline concentrations is also delayed, as will be seen below. Not evident in the centerline temperature profiles is the trend in overall maximum temperature T max , since T max occurs off-axis in all flames studied. Computed values of T max and their locations in each flame are listed in Table 4. Immediately apparent is the change in location: as the flames undergo partial premixing, T max occurs closer to the centerline and further from the burner surface. This effect is also apparent in Figs. 6a and 6b. Both the drift toward the centerline and the continuing movement away from the burner surface can be attributed primarily to the increasing heat release (Fig. 4) from the ever-strengthening inner flame front. Table 4 also lists the nonsoot radiative heat loss in each flame (up to z/H T ⫽ 2.0) as a percentage of the total heat released; the radiative loss calculation is largely insensitive to the chosen axial cutoff value of z/H T ⫽ 2.0. Because the flames get shorter during partial premixing, these integrated radiative losses decrease with decreasing ⌽, and the percentages are in line with others reported in the literature [6, 39]. However, examination of the spatial distribution of the radiative losses (not shown here for the sake of brevity) indicates that the peak nonintegrated radiative loss increases with decreasing ⌽ and is approximately 15% higher in the ⌽ ⫽ 2.464 case, as compared with the ⌽ 3 ⬁ case. In addition, as ⌽ decreases, radiative losses occur nearer to the centerline and over a broader nondimensional axial region, in agreement with the axial broadening of the high temperature region.

535

Fig. 9. Profiles of CH4 mole fraction (X CH 4) along the flame centerline, as functions of nondimensional axial position ( z/H T ), are displayed for the six flames. Both (a) computational and (b) experimental results are shown. The symbols do not indicate specific data points.

CH4 Mole Fractions Examination of the mole fractions of major species begins with those of CH4, depicted along the centerline in Fig. 9. It should be noted that although each computed flame is generated using the same flow conditions (flowrates, mole fractions, etc.) as its experimental counterpart, some computational/experimental discrepancies appear near the burner surface in Fig. 9. Specifically, the experimental CH4 mole fractions for the ⌽ 3 ⬁ and ⌽ 3 12.320 flames do not appear to match the computed values when extrapolated to the burner surface. This behavior is believed to be caused by argon concentrations that are slightly lower than those assumed (species calibrations depend upon an assumed argon concentration of 1% throughout the measurement domain [13]).

536 However, these experimental data still fall within the stated absolute uncertainty of 30%, particularly considering the sharp gradients present near the burner surface. In general, the computational and experimental results are in good agreement, and the values of z/H T at which the CH4 disappears are well predicted by the numerical model. Three trends are observed as partial premixing occurs. First, the initial concentrations of CH4 decrease, because the CH4 is being diluted by primary air. Second, the initial concentrations of CH4 persist to larger heights above the burner surface, as evidenced by the longer flat region at the start of each profile. This behavior is consistent with the decrease in coflow entrainment seen above, responsible for decreased dilution of the centerline reactants, and it also indicates a decrease in radial transport. Moreover, the axial component of velocity increases as partial premixing occurs (due to the increased flowrate in the inner jet), further decreasing the relative impact of radial transport. The third trend apparent in both the computational and experimental CH4 centerline data is the increase in the rapidity with which the concentrations vanish. This feature is particularly noticeable when comparing the gradual decrease of CH4 for 0 ⱕ z/H T ⱗ 0.9 in the nonpremixed flame with the quick decrease for 0.3 ⱗ z/H T ⱗ 0.6 in the most premixed flame. The sharpening of the flame front (especially the inner flame front) is also visible in the computational results of Figs. 6c and 6d; the change from red to dark blue occurs over a much shorter distance in Fig. 6d. O2 Mole Fractions Mole fractions of O2 along the centerline are illustrated in Fig. 10. As described in the first paragraph of the preceding section, the argon calibration procedure for the species measurements relies on the assumption of a constant (known) argon concentration. The fact that the absolute experimental O2 mole fractions near the burner surface are lower than those found numerically indicates that this assumption is probably a poor one near the burner surface in the less premixed flames. Elsewhere, the computational and experi-

B. A. V. BENNETT ET AL.

Fig. 10. Profiles of O2 mole fraction (X O 2) along the flame centerline, as functions of nondimensional axial position ( z/H T ), are displayed for the six flames. Both (a) computational and (b) experimental results are shown. The symbols do not indicate specific data points.

mental results are in fairly good agreement, and the values of z/H T at which the O2 first disappears (near z/H T ⬇ 0.55) and later reappears (near z/H T ⬇ 0.9) are well predicted by the numerical model. In the nonpremixed flame, some O2 is entrained through the weak flame front near the burner lip, as evidenced by the nonzero centerline concentrations for z/H T ⱗ 0.6 in both the computational and experimental datasets; similar entrainment has been observed previously [41– 44]. The computational and experimental O2 profiles both show three effects of partial premixing. First, the initial concentrations of O2 increase, because the air concentration in the inner jet increases. Second, the initial concentrations persist further into the flame (i.e., the profiles remain flatter further above the burner), which is a consequence of the decreased coflow entrainment and decreased inward radial

COFLOW PARTIALLY PREMIXED METHANE/AIR FLAMES

537

transport discussed previously. Third, near z/H T ⬇ 0.55, the O2 disappears much more sharply as partial premixing occurs, indicating the increasing strength of the inner flame front. Over the entire range of ⌽ investigated (including ⌽ 3 ⬁), the wide separation of the locations of O2 disappearance and subsequent reappearance implies that the double flame structure (i.e., inner premixed flame, outer nonpremixed flame) exists in all of the flames, although the inner flame may not produce significant heat release or visible light for larger ⌽. This ever-present double flame structure in the axisymmetric configuration contrasts with the behavior observed in the counterflow configuration, where the two flame fronts merge as ⌽ increases beyond 1.5 to 3 (depending upon strain rate) [2, 5, 10, 11]. H2O Mole Fractions Centerline mole fractions of H2O are displayed in Fig. 11. Because the low vapor pressure of H2O (at nonflame temperatures) makes experimental calibration difficult, the experimental values are multiplied through by a scale factor chosen such that the nonpremixed flame’s H2O concentration at z/H T ⫽ 1 agrees with the computed value. Thus, no statements can be made regarding the agreement of absolute concentrations, but the good agreement observed in profile shape is meaningful. The computational and experimental data both show two features resulting from partial premixing. First, the absence of H2O at z/H T ⫽ 0 persists further above the burner surface as partial premixing increases; in other words, the increase in H2O concentration occurs later downstream. This behavior results from decreased radial transport (of H2O toward the centerline, in this case), as mentioned above in conjunction with related trends in the centerline T profiles. Second, the increase in concentrations gets sharper as ⌽ decreases from ⬁ to 2.464, in accordance with the strengthening of the inner flame front. After peaking near the inner flame front, both the computational and experimental profiles are roughly flat for z/H T ⲏ 0.8. At z/H T ⫽ 1.0, H2O concentrations are very close to those at equilibrium, calculated using STANJAN [45], and the observed flatness

Fig. 11. Profiles of H2O mole fraction (X H 2O ) along the flame centerline, as functions of nondimensional axial position ( z/H T ), are displayed for the six flames. Both (a) computational and (b) experimental results are shown. The symbols do not indicate specific data points.

just upstream is consistent with the behavior at equilibrium. Most of the H2O formation occurs at the inner flame front, demonstrated by the fact that the concentrations at the inner flame front are within a few percent of their maximum values—a statement which holds true even for the ⌽ 3 ⬁ flame. For z/H T ⬇ 0.5, no small-scale structure can be extracted from the experimental dataset, but the computational results for the more premixed flames depict an overshoot in the H2O mole fractions. The magnitude of this phenomenon is within experimental error. The location of the overshoot coincides with a local minimum in the C:H ratio, as seen below; thus, diffusion of H2 and H toward the centerline is also partly responsible for the higher H2O concentrations at z/H T ⬇ 0.5. The abrupt decrease on the high-z/H T side of the overshoot may be caused by diffusion of H2O away from the

538

B. A. V. BENNETT ET AL.

Fig. 13. Computed profiles of CO mole fraction (X CO ) along the flame centerline, as functions of nondimensional axial position ( z/H T ), are displayed for the six flames. The symbols do not indicate specific data points.

Fig. 12. Profiles of CO2 mole fraction (X CO 2) along the flame centerline, as functions of nondimensional axial position ( z/H T ), are displayed for the six flames. Both (a) computational and (b) experimental results are shown. The symbols do not indicate specific data points.

centerline in the immediate post-inner-flame region (0.5 ⱗ z/H T ⱗ 0.8), particularly because the temperature in that region is approximately 250 K higher in the most premixed flame as compared to the ⌽ 3 ⬁ flame. CO2 Mole Fractions Mole fractions of CO2 along the centerline are plotted in Fig. 12. The computational and experimental results show good agreement, displaying similar features. The primary effect of partial premixing is that the increase in CO2 (from its initial value of zero) occurs further downstream, which may also be seen by examining Figs. 6g and 6h. The phenomenon responsible for this effect is the reduced radial transport (of CO2 toward the centerline, in this case), which similarly affects the other species and T. The subsequent rate of

increase is gradual in most cases except for the most premixed flame. The computational and experimental CO2 datasets peak at nearly identical concentrations (X CO 2 ⬇ 0.105), largely independent of the amount of partial premixing. This value is very close to the equilibrium values calculated with STANJAN [45] (X CO 2 ⫽ 0.101 for ⌽ 3 ⬁; X CO 2 ⫽ 0.104 for ⌽ ⫽ 2.464). In contrast to H2O, which peaks near the inner flame front, CO2 maxima occur near z/H T ⫽ 1.0. These differing behaviors are partly explained by fundamental oxidation kinetics [38], in which H2O is formed by many abstraction reactions of the fuel (CH4) and its immediate products. It is only once all hydrocarbons have been consumed that the OH radical reaches high enough concentrations to oxidize CO, forming CO2. Another reason for CO2 to peak near z/H T ⫽ 1.0 is that this behavior is consistent with that at equilibrium. (The CO2 peaks slightly further downstream in the computational data than in the experimental data; this discrepancy is expected, given that for the nonfuel hydrocarbons discussed below, the computational concentrations disappear further downstream than those found experimentally.) CO and H2 Mole Fractions Figures 13 and 14 illustrate computed centerline mole fractions of CO and H2, respectively;

COFLOW PARTIALLY PREMIXED METHANE/AIR FLAMES

539

Fig. 14. Computed profiles of H2 mole fraction (X H 2) along the flame centerline, as functions of nondimensional axial position ( z/H T ), are displayed for the six flames. The symbols do not indicate specific data points.

experimental results are not available for either species. Each profile starts at zero, rises gradually (with the sharpest rise occurring in the ⌽ ⫽ 2.464 flame, similar to the trends seen above in the centerline T, XH2O, and XCO2 profiles), and then returns to zero slightly above the outer flame front, near z/HT ⫽ 1.1. As partial premixing occurs, the increase in the maximum values of both CO and H2 is consistent with published counterflow flame measurements [2]. For z/HT ⱗ 1.0, the ⌽ ⫽ 2.464 flame is closer to equilibrium than the ⌽ 3 ⬁ flame, which is consistent with the higher T of the former. The CO and H2 values at z/HT ⫽ 1.0 are both fairly close to the STANJAN [45] equilibrium values. CO and H2 concentrations in the ⌽ 3 ⬁ flame do not exhibit very distinct peaks, since concentrations remain within a few percent of the maxima for 0.4 ⱗ z/H T ⱗ 0.8 (for CO) and 0.2 ⱗ z/H T ⱗ 0.6 (for H2). In each of the partially premixed flames, however, definite peaks are readily discernible— even in the ⌽ ⫽ 12.320 flame, for which there is no clear shoulder in the T profile. From the ⌽ ⫽ 12.320 flame down to the ⌽ ⫽ 2.464 flame, the CO (H2) peaks occur at z/H T ⫽ 0.63 (0.53), 0.61 (0.55), 0.56 (0.52), 0.54 (0.51), and 0.49 (0.47), respectively. Thus, the CO maxima always appear slightly downstream of the inner flame front, and the H2 maxima at or just upstream of the same front. These observations,

Fig. 15. Profiles of OH mole fraction (X OH ) along the flame centerline, as functions of nondimensional axial position ( z/H T ), are displayed for the six flames. Both (a) computational and (b) experimental results are shown. The symbols do not indicate specific data points.

coupled with the previous species profiles, demonstrate that CH4 and O2 are converted to H2O, CO, and H2 at the inner premixed flame, and that the outer (nonpremixed) flame transforms CO and H2 to CO2 and additional H2O. OH Mole Fractions Centerline OH mole fractions are shown in Fig. 15, plotted on a vertical log scale for both the computational and experimental results. Because the instability of OH at reference conditions makes experimental calibration difficult, the experimental values are multiplied through by a scale factor chosen such that the ⌽ ⫽ 2.464 flame’s maximum OH concentration agrees with the computed value. Thus, no statements can be made regarding the agreement of absolute concentrations, but the agreement evident in profile shapes is significant. The small non-

540 monotonicity near z/H T ⫽ 0.45 in the experimental ⌽ 3 ⬁ flame data is spurious, likely due to interference from soot and polycyclic aromatic hydrocarbons (PAH). Computed OH mole fractions in a portion of the domain also appear in Figs. 6i and 6j. In all computational and experimental profiles of Fig. 15, the OH is undetectable from 0 ⱕ z/H T ⱕ 0.4, due to the fact that any existing OH will quickly react with CH4, H2, and other hydrocarbons. In fact, the computational profile of OH production rate (excluded for brevity) shows that the majority of each case’s OH production occurs in the region 0.6 cm ⱕ r ⱕ 0.8 cm, for 0 ⱕ z/H T ⱕ 0.25. Consumption mainly occurs in the region located just radially inside the production region. Downstream of the fuel-rich area, OH then rises in concentration near z/H T ⫽ 0.4 because of inward transport from off-axis peaks. In each profile, the OH concentration reaches its maximum near z/H T ⫽ 1.0, because of the high OH formation rate at the outer (nonpremixed) flame front. The reader should note that the peak OH values increase with decreasing ⌽, for both the computational and experimental results. In the two most premixed cases (⌽ ⫽ 3.080 and ⌽ ⫽ 2.464), the inner flame front is strong enough that a secondary OH peak is evident, both in the computational and experimental results. This secondary peak is largest in the ⌽ ⫽ 2.464 data. The computed and measured ratios between the primary and secondary OH peaks are in reasonable agreement, for both flames. Throughout all six flames, OH is in superequilibrium. Of particular note are the large magnitudes by which OH values exceed equilibrium values at z/H T ⫽ 1.0. For the ⌽ 3 ⬁ flame, the computed X OH ⫽ 9.56 ⫻ 10 ⫺4 (corresponding STANJAN [45] equilibrium value is only 8.73 ⫻ 10⫺5)—a factor of 11 above equilibrium. For the ⌽ ⫽ 2.464 flame, the computed X OH ⫽ 1.92 ⫻ 10 ⫺3 (corresponding equilibrium value is only 3.39 ⫻ 10⫺4)—a factor of 6 above equilibrium. This behavior indicates that equilibrium calculations cannot be used to predict accurately the OH concentrations in these flames.

B. A. V. BENNETT ET AL.

Fig. 16. Profiles of C2H2 mole fraction (X C 2H 2) along the flame centerline, as functions of nondimensional axial position ( z/H T ), are displayed for the six flames. Both (a) computational and (b) experimental results are shown. The symbols do not indicate specific data points.

C2H2 Mole Fractions Mole fractions of acetylene (C2H2) are illustrated in Fig. 16. For both the computational and experimental datasets, the primary effect of partial premixing is to delay the initial increase in C2H2 until further downstream, similar to the trends observed above in centerline T, X H 2O , X CO 2, X CO , and X H 2. A secondary effect present in both datasets is the earlier disappearance (i.e., at smaller values of z/H T ) of C2H2, in the vicinity of 0.8 ⱗ z/H T ⱗ 1.0, as partial premixing occurs. While the computational and experimental absolute concentrations agree well for the ⌽ 3 ⬁ flame, the less satisfactory results for the remaining cases illustrate the importance of studying partially premixed flames. Two major differences between the computational and experimental datasets are apparent.

COFLOW PARTIALLY PREMIXED METHANE/AIR FLAMES

541

First, with the exception of the ⌽ ⫽ 3.080 and ⌽ ⫽ 2.464 maxima, which are roughly the same, the peak computational C2H2 concentrations increase as ⌽ decreases. In the experimental results, however, the overall trend in the concentration peaks is a decreasing one, as also observed in [6]. This behavior is expected, given that the CH4 mole fractions decrease with partial premixing, thus reducing CH3 recombination, and oxidation rates rise, as shown by the increased OH concentrations. Second, C2H2 disappears, on average, near z/H T ⬇ 0.95 in the computational data, but it vanishes near z/H T ⬇ 0.8 in the experimental measurements. These two differences may be due to underprediction of the C2H2 oxidation rates in the GRI-Mech version 2.11 chemical mechanism, particularly for the conditions present in the partially premixed flames. C2H2O Mole Fractions The oxygenated hydrocarbon C2H2O has two possible isomers: ketene (CH2CO) and an alcohol (HCCOH). Although the isomers of C2H2O are not classified as hazardous air pollutants, ketene has a toxicity similar to phosgene, a World War I– era chemical warfare agent, with potential to cause pulmonary disease [46]. In general, oxygenated hydrocarbons tend to be much more toxic than regular hydrocarbons of similar size. Because these hydrocarbons may have a detrimental effect on the environment, and because their concentrations are expected to increase as partial premixing occurs, their accurate prediction and measurement are of great interest. In addition, C2H2O is closely related to HCCO, which is important in NOx prediction. Figure 17 compares the numerically predicted and experimentally measured C2H2O concentrations. The computational results are a sum of the concentrations of both isomers, each of which is included in the chemical mechanism. The experimental PTMS data contain both isomers, as well as interference from C3H6 (propene); specifically, the secondary peak near z/HT ⫽ 0.35 in the ⌽ 3 ⬁ flame has been attributed [9], at least in part, to C3H6. Because the experimental data have been calibrated by assuming the same sensi-

Fig. 17. Profiles of (a) computational C2H2O mole fraction (X C 2H 2O ) and (b) sum of experimental C2H2O and C3H6 mole fractions (X C 2H 2O and X C 3H 6, respectively) along the flame centerline, as functions of nondimensional axial position ( z/H T ), are displayed for the six flames. The symbols do not indicate specific data points.

tivity as for benzene, they are accurate only to within a factor of 3. To within experimental error, the computational and experimental results display good agreement in absolute concentrations. In the five partially premixed flames, both datasets depict concentration maxima that are located near the inner flame front; in addition, they each contain a “knee” to the downstream side of the peak. Clearly, partial premixing greatly increases the C2H2O concentrations: the computational peaks are two to four times higher for the partially premixed flames, as compared to the nonpremixed flame, and the experimental partially premixed peaks are two to three times higher than the nonpremixed peak. Although not shown here, computational and experimental formaldehyde (CH2O) concentrations also increase with partial premixing, supporting the

542

B. A. V. BENNETT ET AL.

Fig. 18. Computed profiles of CH2CO and HCCOH production rates along the flame centerline, as functions of nondimensional axial position ( z/H T ), are displayed, for (a) ⌽ 3 ⬁ and (b) ⌽ ⫽ 2.464.

idea of a general increasing trend in oxygenate concentrations. Partial premixing also causes C2H2O to decrease earlier in the flame—an effect particularly noticeable in the computational profiles. The decreases occur near z/H T ⫽ 1.0 in the computational data but near z/H T ⫽ 0.8 in the experimental measurements. The persistence of C2H2O in the numerical results may be partly explained by the fact that not all possible destruction reactions are included in the chemical mechanism. Figures 18a and 18b present the centerline molar production rates of CH2CO and of HCCOH, for the ⌽ 3 ⬁ and the ⌽ ⫽ 2.464 flames, respectively. Immediately apparent is the fact that both isomers are destroyed nearly as rapidly as they are produced—an observation which holds true for all six flames studied, although only two of the six are shown here for brevity. By examining the (simpler) bottom half of each plot first, it is apparent that HCCOH is formed through the reaction of OH with C2H2, and it (HCCOH) is then destroyed via conversion to CH2CO. As partial premixing occurs, the OH concentrations increase near the inner flame front ( z/H T ⬇ 0.5) as observed above, resulting in a new formation peak for HCCOH.

A similar process occurs for CH2CO, displayed in the top half of each plot. The increase in OH due to partial premixing leads sequentially to more HCCO, as seen in Figs. 6o and 6p, which subsequently results in higher concentrations of CH2CO. Axial Velocities and Residence Times Computed axial velocities (v z ) along the centerline, as functions of dimensional axial position, are plotted in Fig. 19. Also appearing in the same figure is the theoretical axial velocity profile hypothesized by Roper [47, 48], who postulated that the initial v z could be neglected and also assumed a constant buoyant acceleration of 25 m/s2. Roper’s theoretical v z profile has been seen to be reasonably accurate for various nonpremixed flames [48 –50]. The present study shows that the theory gives, in fact, a reasonable prediction for a large range of ⌽. The wide variation in centerline v z values at the burner surface is rapidly overwhelmed by buoyant acceleration, resulting in computed velocities which do not differ greatly with partial premixing, particularly within the flames (recall that the largest H T is 8.0 cm, for the ⌽ 3 ⬁ flame).

COFLOW PARTIALLY PREMIXED METHANE/AIR FLAMES

543

Fig. 19. Profiles of axial velocity (v z ) along the flame centerline, as functions of axial position ( z), are displayed for the six flames. Computational results are accompanied by Roper’s theory. The symbols do not indicate specific data points.

Axial velocities are necessary for determining residence times, which play an important factor in rate-limited processes; for example, increased residence times in certain parts of flames have been found to lead to increased soot formation [49, 50]. Therefore, residence times (␶) along the centerline have been calculated from vz and are shown in Fig. 20 as functions of nondimensional axial position z/HT. Because HT decreases with partial premixing, the residence time for a fluid parcel at a given z/HT decreases significantly with ⌽; at any given z/HT, ␶ for the nonpremixed flame is

Fig. 21. Computed profiles of (a) C:O ratio, (b) C:H ratio, and (c) local equivalence ratio along the flame centerline, as functions of nondimensional axial position ( z/H T ), are displayed for the six flames. The symbols do not indicate specific data points.

more than twice that for the most premixed flame. These large differences in ␶ are partly responsible for the experimentally observed decrease in soot concentrations that occurs with premixing. Atomic Ratios and Local Equivalence Ratios

Fig. 20. Computed profiles of residence time (␶) along the flame centerline, as functions of nondimensional axial position ( z/H T ), are displayed for the six flames. The symbols do not indicate specific data points.

Figure 21 illustrates the computed atomic C:O ratio, C:H ratio, and the resulting local equivalence ratio (LER). Near the burner surface, the C:O ratio differs dramatically across the six flames due to differing amounts of oxygen in the inner jet. However, these differences rapidly disappear, so that the six profiles are almost indistinguishable for z/H T ⱖ 0.6. The C:O profile for the ⌽ ⫽ 2.464 flame contains a small nonmonotonicity near z/H T ⫽ 0.45 (just upstream of the inner flame front), which most likely results from H2O preferentially diffusing

544

Fig. 22. Computed profiles of (a) H2 mole fraction and (b) H mole fraction, at seven values of nondimensional axial position ( z/H T ), are displayed for ⌽ ⫽ 2.464.

toward the flame centerline in that high T region. In the remaining flames, this effect is not apparent, dominated by the greater radial convection. Because the fuel is CH4, the C:H ratio begins at 1/4 in every flame. It eventually undergoes a substantial increase to roughly 0.36 near z/H T ⫽ 1.0 (the outer flame front) as a result of preferential diffusion of H2 and H away from the centerline. Between these extremes, however, the C:H ratio dips (to as low as 0.20 for the ⌽ ⫽ 2.464 flame) for each of the partially premixed flames, just upstream of the inner flame front. This decrease is due to H2 preferentially diffusing from the off-axis annular maxima toward the centerline. The H radical behaves similarly, but its concentrations are much smaller than those of H2, so H2 diffusion is primarily responsible for the C:H ratio dip. These hypotheses are supported by Fig. 22, which contains radial plots of H2 and H mole fractions at various values of z/H T up to the

B. A. V. BENNETT ET AL. inner flame front, in the most premixed flame (⌽ ⫽ 2.464). Although inward preferential diffusion is not readily apparent in the H profiles, the H2 profiles clearly demonstrate the effect. Profiles A through F are concave up on the centerline, indicating inward diffusion, although the H2 peaks are not close enough to the centerline for this diffusion to influence greatly the centerline concentrations until profiles C through F ( z/H T ⫽ 0.397 through 0.441). Profile G ( z/H T ⫽ 0.500) is concave down, indicating diffusion away from the centerline, corresponding to the postdip increase observed in the C:H ratio of Fig. 21b. The nonmonotonicities appearing in Figs. 21a and 21b should be taken into account when forming correlations based on atomic ratios. Figure 21c depicts the computed LER, which begins at the value of the primary equivalence ratio for each flame. All LER profiles monotonically decrease, taking on similar values by z/H T ⬇ 0.6. By z/H T ⬇ 0.8, the LER is nearly independent of primary equivalence ratio. Because of the LER’s extremely slow variation for z/H T ⲏ 0.8, it would be difficult to make an accurate experimental determination of H f (the centerline z value for which LER ⫽ 1) through species measurements. This potential problem further validates the use of H T instead of H f for nondimensionalization purposes. CONCLUSIONS In this paper, six coflowing laminar partially premixed methane/air flames have been studied computationally (via the LRR solution– adaptive gridding method applied to a model including complex chemistry, multicomponent transport, and radiation submodeling) and experimentally (via several probe and optical diagnostic techniques) over a wide range of primary equivalence ratios. It has been shown that HT, formerly seen to be an appropriate surrogate for Hf in experimental results, can successfully play the same role in computational predictions. Therefore, centerline data have been plotted against the nondimensional axial coordinate z/HT to remove the flameheight-reduction effect of partial premixing, occurring when the fuel flowrate is held

COFLOW PARTIALLY PREMIXED METHANE/AIR FLAMES fixed—an effect which can obscure other important phenomena. Every flame studied here contains at least one flame front: a nonpremixed one. In addition, in the partially premixed flames (i.e., excluding the nonpremixed case), evidence supporting the existence of an inner premixed flame front near z/HT ⫽ 0.5 abounds. In each of these five flames: the heat release profile exhibits a double flame structure; both computational and experimental temperature profiles contain a shoulder near z/HT ⫽ 0.5; both computational and experimental O2 profiles display a wide separation between the disappearance and reappearance of O2 on the centerline; near z/HT ⫽ 0.5, centerline H2O concentrations are within a few percent of their maxima; and centerline OH concentrations rise to non-negligible amounts near z/HT ⫽ 0.5. All of these observations indicate an inner flame front, strengthening with decreasing primary equivalence ratio. As the amount of partial premixing increases, the increasing strength of the inner flame front is accompanied by other fundamental effects of partial premixing. According to computational predictions, a reduction in the flow radially inward decreases radial mass and heat transport, causing overall flame temperatures to increase. This latter effect, observed experimentally as well, also results from decreased radiative losses. Increases take place in the production of the toxic hydrocarbon C2H2O due to reactions at the inner flame front—a rise observed both computationally and experimentally. Finally, just upstream of the inner flame front, the preferential diffusion of H2 from its off-axis maxima inward causes a dip in the C:H ratio. This nonmonotonic behavior should be considered when forming atomic-ratio-based correlations. Two of the authors (B.A.V.B. and M.D.S.) would like to acknowledge support from the Office of Naval Research (Grant N00014-95-1-0412) and the Department of Energy Office of Basic Energy Sciences (Grant DE-FG02-88ER13836). The other two authors (C.S.M. and L.D.P.) appreciate the assistance of Elanor Williams in conducting the experiments, and they would like to acknowledge partial financial support from the

545

United States Air Force (Grant F49620-94-10085), the United States Environmental Protection Agency (Grant R821206-01-0), and the National Science Foundation (Grant CST-9714222).

REFERENCES 1.

2.

3.

4. 5.

6. 7.

8. 9. 10. 11.

12. 13. 14.

15. 16. 17. 18. 19. 20.

Rogg, B., Behrendt, F., and Warnatz, J., Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, pp. 1533–1541. Yamaoka, I., and Tsuji, H., Fifteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1974, pp. 637– 644. Ramakrishna, C., Zhan, N. J., Kelkar, A. S., and Gore, J. P., Proceedings of the 1995 Central States/Western States/Mexican Sections of the Combustion Institute Joint Technical Meeting, The Combustion Institute, Pittsburgh, 1995, pp. 442– 447. Kim, T. K., Alder, B. J., Laurendeau, N. M., and Gore, J. P., Combust. Sci. Technol. 110 –111:361–378 (1995). Tanoff, M. A., Smooke, M. D., Osborne, R. J., Brown, T. M., and Pitz, R. W., Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996, pp. 1121–1128. Gore, J. P., and Zhan, N. J., Combust. Flame 105:414 – 427 (1996). Nguyen, Q. V., Dibble, R. W., Carter, C. D., Fiechtner, G. J., and Barlow, R. S., Combust. Flame 105:499 –510 (1996). Mitrovic, A., and Lee, T.-W., Combust. Flame 115: 437– 442 (1998). McEnally, C. S., and Pfefferle, L. D., Combust. Flame 118:619 – 632 (1999). Blevins, L. G., and Gore, J. P., Combust. Flame 116:546 –566 (1999). Blevins, L. G., Renfro, M. W., Lyle, K. H., Laurendeau, N. M., and Gore, J. P., Combust. Flame 118:684 – 696 (1999). Santoro, R. J., Semerjian, H. G., and Dobbins, R. A., Combust. Flame 51:203–218 (1983). McEnally, C. S., and Pfefferle, L. D., Combust. Sci. Technol. 116 –117:183–209 (1996). Smooke, M. D., McEnally, C. S., Pfefferle, L. D., Hall, R. J., and Colket, M. B., Combust. Flame 117:117–139 (1999). Edwards, D. K., Advances Heat Transfer 12:115–193 (1976). Hall, R. J., J. Quant. Spec. Rad. Tran. 49:517–523 (1993). Hall, R. J., J. Quant. Spec. Rad. Tran. 51:635– 644 (1994). Ern, A. (1994). Ph.D. thesis, Yale University, New Haven, CT. Ern, A., Douglas, C. C., and Smooke, M. D., Int. J. Supercomput. Appl. 9:167–186 (1995). Smooke, M. D., Ern, A., Tanoff, M. A., Valdati, B. A., Mohammed, R. K., Marran, D. F., and Long, M. B., Twenty-Sixth Symposium (International) on Combus-

546

21. 22.

23.

24.

25.

26.

27.

28. 29. 30. 31.

32. 33.

34.

B. A. V. BENNETT ET AL. tion, The Combustion Institute, Pittsburgh, 1996, pp. 2161–2170. Bennett, B. A. V., and Smooke, M. D., Combust. Theory Model. 2:221–258 (1998). Bowman, C. T., Hanson, R. K., Davidson, D. F., Gardiner, Jr., W. C., Lissianski, V., Smith, G. P., Golden, D. M., Frenklach, M., Wang, H., and Goldenberg, M. (1995). http://www.gri.org Kee, R. J., Miller, J. A., and Jefferson, T. H. (1980). Chemkin: A General-Purpose, Problem-Independent, Transportable, Fortran Chemical Kinetics Code Package, Sandia National Laboratory Rept. SAND80-8003. Kee, R. J., Rupley, F. M., and Miller, J. A. (1987). The Chemkin Thermodynamic Database, Sandia National Laboratory Rept. SAND87-8215. Kee, R. J., Warnatz, J., and Miller, J. A. (1983). A Fortran Computer Code Package for the Evaluation of Gas-Phase Viscosities, Conductivities, and Diffusion Coefficients, Sandia National Laboratory Rept. SAND838209. Kee, R. J., Dixon-Lewis, G., Warnatz, J., Coltrin, M. E., and Miller, J. A. (1986). A Fortran Computer Package for the Evaluation of Gas-Phase, Multicomponent Transport Properties, Sandia National Laboratory Rept. SAND86-8246. Giovangigli, V., and Darabiha, N., in Mathematical Modeling in Combustion and Related Topics (C.-M. Brauner and C. Schmidt-Laine´, Eds.), Nijhoff, Dordrecht, 1988, pp. 491–503. Smooke, M. D., Mitchell, R. E., and Keyes, D. E., Combust. Sci. Technol. 67:85–122 (1989). Keyes, D. E., and Smooke, M. D., J. Comput. Phys. 73:267–288 (1987). Bennett, B. A. V., and Smooke, M. D., J. Comput. Phys. 151:684 –727 (1999). Smooke, M. D., Mitchell, R. E., and Kee, R. J., in Numerical Boundary Value ODEs (U. M. Ascher and R. D. Russell, Eds.), Birkha¨user, Boston, 1985, pp. 303–317. ¨. O ¨ ., Pfefferle, L. D., and McEnally, C. S., Ko ¨ylu ¨, U Rosner, D. E., Combust. Flame 109:701–720 (1997). Smyth, K. C., Miller, J. H., Dorfman, R. C., Mallard, W. G., and Santoro, R. J., Combust. Flame 62:157–181 (1985). Roper, F. G., Combust. Flame 29:219 –226 (1977).

35.

36.

37. 38. 39. 40.

41. 42. 43.

44. 45.

46. 47. 48. 49.

50.

McEnally, C. S., and Pfefferle, L. D., Twenty-Seventh Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1998, pp. 1539 –1547. Paul, P. H., and Najm, H. N., Twenty-Seventh Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1998, pp. 43–50. Najm, H. N., Paul, P. H., Mueller, C. J., and Wyckoff, P. S., Combust. Flame 113:312–332 (1998). Westbrook, C. K., and Dryer, F. L., Prog. Energy Combust. Sci. 10:1–57 (1984). Chou, C.-P., Chen, J.-Y., Yam, C. G., and Marx, K. D., Combust. Flame 114:420 – 435 (1998). Bennett, B. A. V., Fielding, J., Mauro, R. J., Long, M. B., and Smooke, M. D., Combust. Theory Model. 3:657– 687 (1999). Mitchell, R. E., Sarofim, A. F., and Clomburg, L. A., Combust. Flame 37:227–244 (1980). Saito, K., Williams, F. A., and Gordon, A. S., ASME/ J. Heat Transfer 108:640 – 648 (1986). Smooke, M. D., Lin, P., Lam, J. K., and Long, M. B., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 575–582. Xu, Y., Smooke, M. D., Lin, P., and Long, M. B., Combust. Sci. Technol. 90:289 –313 (1993). Reynolds, W. C. (1986). The Element Potential Method for Chemical Equilibrium Analysis: Implementation in the Interactive Program STANJAN, Department of Mechanical Engineering, Stanford University, Palo Alto, CA. Budavari, S., Ed. The Merck Index, 12th ed., Merck & Co., Inc., Whitehouse Station, NJ, 1996, p. 904. Roper, F. G., Smith, C., and Cunningham, A. C., Combust. Flame 29:227–234 (1977). Roper, F. G., Combust. Sci. Technol. 40:323–329 (1984). Gomez, A., and Glassman, I., Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1986, pp. 1087–1095. Santoro, R. J., Yeh, T. T., Horvath, J. J., and Semerjian, H. G., Combust. Sci. Technol. 53:89 –115 (1987).

Received 5 October 1999; revised 27 April 2000; accepted 4 May 2000