Computational and experimental study of standing methane edge flames in the two-dimensional axisymmetric counterflow geometry

Combustion and Flame 147 (2006) 133–149 www.elsevier.com/locate/combustflame

Computational and experimental study of standing methane edge flames in the two-dimensional axisymmetric counterflow geometry Giuliano Amantini a , Jonathan H. Frank b , Mitchell D. Smooke a , Alessandro Gomez a,∗ a Department of Mechanical Engineering, Yale Center for Combustion Studies, Yale University, P.O. Box 208286,

New Haven, CT 06520-8286, USA b Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551, USA

Received 11 November 2005; received in revised form 19 April 2006; accepted 4 May 2006 Available online 28 August 2006

Abstract The structure of steady methane/enriched-air edge flames established in an axisymmetric, laminar counterflow configuration was investigated computationally and experimentally. Computationally, the steady-state equations were solved implicitly in a modified vorticity–velocity formulation on a nonstaggered, nonuniform grid, with detailed chemistry and transport. Experimental boundary conditions were chosen to establish flames with a hole centered at the axis of symmetry, the location where the largest strain rate occurs, in order to investigate the structure of the edge flame established at the outer periphery of the hole. Experimentally, CO PLIF, OH PLIF, and an observable proportional to the forward reaction rate (RR) of the reaction CO + OH → CO2 + H were measured. Particle image velocimetry (PIV) was used to characterize the velocity field in the proximity of the fuel and oxidizer nozzles and to provide detailed boundary conditions for the simulations. Qualitatively, the flow field can be partitioned into two zones: a nonreactive counterflow region bound by two recirculation zones attached at the exits of the inlet nozzles, which aid mixing of products and reactants upstream of the edge flame; and a reactive region, where a premixed edge flame provides the stabilization mechanism for a trailing diffusion flame. Comparisons between the experimental and the computational data yielded quantitative agreement for all measured quantities. Further, we investigated the structure of the computational edge flames. We identified the most significant heatrelease reactions for each of the flame branches. Finally, we examined correlations among the propagation speed of the edge flame and curvature and mixture fraction gradient by varying the global strain rate of the flame. © 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Edge; Vorticity–velocity formulation; Counterflow; Triple; Diffusion; Premixed; Flame; Computational combustion

1. Introduction * Corresponding author. Fax: +1 (203) 432 7654.

E-mail address: [email protected] (A. Gomez).

Edge flames have been widely studied in a variety of geometries and flow conditions because of their importance in stabilizing diffusion flames, in the vicinity

0010-2180/$ – see front matter © 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2006.05.006

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Nomenclature Global strain rate Tangential momentum accommodation coefficient Absorption coefficient for OH Q(12) αOH αT Dimensionless thermophoretic diffusion factor δm Mixing layer thickness div Divergence operator D Particle Brownian diffusivity DT Thermal diffusivity of the mixture G Gravitational acceleration λ Thermal conduction coefficient hk Total enthalpy for the kth species k(T ) Forward rate constant of the elementary reaction CO + OH → CO2 + H NSPEC Number of gas-phase species μ Dynamic viscosity of the mixture υ Momentum diffusivity of the gas mixture ρ Density of the mixture r Radial coordinate R Nozzle radius RR Reaction rate of CO + OH → CO2 + H A α

of surfaces, and in local extinction/ignition phenomena in highly strained turbulent flames. Their ability to anchor diffusion flames [1] by propagating at an effective speed greater than the laminar flame speed [2] is one of their key features. The counterflow configuration provides a set of well-characterized boundary conditions where edge flames can be analyzed with ease. In this geometry, the entire phenomenology, from a vigorously burning laminar diffusion flame to a locally extinguished flame, can be investigated [3–6]. To understand the genesis of standing edge flames, consider that under conditions of high activation energy chemistry, that is, if the overall chemical reaction is strongly sensitive to temperature, two reaction regimes are possible in the mixing layer between two counterflowing jets of fuel and oxidizer. In the nearly frozen regime, mixing occurs without significant chemical reactions, while in the fast burning regime the reaction is diffusion-controlled, and the temperature and concentration fields can be qualitatively described using the Burke–Schumann approximation of infinite chemical reaction rate. Extinction, i.e., the transition from the fast burning regime to the frozen one, is abrupt and can be understood in terms of the relative magnitude of two characteristic times: a chemical time, tc , and a mechanical time, tm , which can be expressed either as the inverse scalar dissipa-

t T v vr vz Vk,r Vk,z VT χ Yk ω ω˙ k Z

Tangent vector Temperature Velocity vector Radial velocity component Axial velocity component Diffusion velocity in the radial direction for the kth species Diffusion velocity in the axial direction for the kth species Local particle drift velocity Scalar dissipation rate Mass fraction of the kth species Vorticity Production rate for the kth species Mixture fraction

Subscripts CH4 O2 p FUEL OXID ST

Fuel stream Oxidizer stream Particle Fuel stream at the nozzle mouth Oxidizer stream at the nozzle mouth Stoichiometric surface

tion rate, 1/χs , or in terms of the thickness of the mixing layer, δm , and the thermal diffusivity, DT , as 2 /D . The ratio of these two times is the Damköhler δm T 2 /(t D ). In the number, Da = tm /tc = 1/(tc χs ) = δm c T counterflow geometry, the local value of the Damköhler number is approximately constant in the zone of uniform strain between the nozzles and progressively increases outside this region. If Da becomes smaller than a critical value, Daext , then extinction occurs. This condition can be achieved in various ways: (a) by decreasing the mechanical time, through an increase in the strain rate; and (b) by increasing the chemical time, through an increase in the dilution of the feed streams, or by means of a heat sink introduced in the flame. Upon reduction of the local Damköhler number, the flame quenches and propagates outward in the radial direction. This extinction front turns into an ignition front once it exits the nozzle region and stabilizes at a radial location where the local gas velocity equals the speed of the front propagating in the opposite direction in the form of a triple flame [7]. The resulting standing edge flame and the initial unperturbed steady burning diffusion flame can be obtained with the same boundary conditions [8]. Much of the relevant literature on edge flames was reviewed up to 2000 in [9]. Here, we review the relevant edge-flame literature that was published

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after 2000. Boulanger et al. [10] performed numerical simulations of the liftoff height of a jet flame and compared the results with the cold flow theory, to show how the heat release deflects the streamlines upstream of the triple flame, thus increasing the propagation speed. Flame holes and flame disks in a laminar axisymmetric counterflow configuration were numerically investigated by Lu and Ghosal [11]. The authors described the time-varying topological structure of the edge flame, and they identified a critical radius that is an unstable bifurcation point and separates the shrinking and expanding flame-hole regimes. Extinction fronts were analyzed computationally for different geometries in [12–14], and all the investigators confirmed the existence of negative propagation speeds. Takagi et al. [12] computationally investigated the structure and propagation properties of counterflow, strain-controlled, H2 /N2 /air diffusion flames, reporting negative propagation speeds for high stretch rates. Im and Chen [13] studied the effects of flow strain on a hydrogen–air triple flame via a canonical model problem in which the propagating triple flame was subjected to a pair of counterrotating vortices, thereby generating compressive strain at the leading edge of the flame. Negative propagation speed was reported for an edge flame that was subjected to an intense compressive strain field induced by the vortex pair. Yoo and Im [14] numerically studied the dynamics of edge flames by quenching nonpremixed, hydrogen–air flames. In the presence of large strain, negative edge flame propagation speeds were observed during the early phase of the interaction due to the enthalpy loss in the transverse direction. Frouzakis et al. [8] analyzed the temporal evolution from a diffusion flame to an edge flame by increasing the fuel and oxidizer flow rates. The effects of stretch and Lewis number on the propagation speed of edge flames were investigated by Qin et al. [15] and Nayagam and Williams [16], respectively. Pantano and Pullin [17] studied the dynamics of a diffusion flame hole in the presence of a counterflow and constructed unsteady solutions of the onedimensional edge-flame model of Buckmaster [9]. The purpose of the present contribution is to perform a two-dimensional computational study of methane counterflow edge flames and validate it quantitatively with experimental results—a task hitherto unfulfilled in the literature. The model is used to analyze the structure of these flames and the dependence of the laminar flame speed on strain rate, curvature, and mixture fraction gradient. This effort is an intermediate step in a broader modeling program aimed at a complete examination of the entire vortex–flame interaction process.

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Fig. 1. Burner schematic.

2. Experimental methods 2.1. Burner Axisymmetric, counterflow edge flames were established using the burner configuration shown in Fig. 1. Each side of the burner was composed of a contoured 1.3-cm-diameter nozzle. The nozzles were surrounded by 76.2-mm-diameter flanges to facilitate the stabilization of triple flames and to provide well-specified boundary conditions. The flanges were water-cooled to maintain a constant wall temperature. The bottom portion of the burner was surrounded

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in Fig. 2 and are separated by a dashed line, which is the T = 450 K isotherm. 2.2. CO/OH reaction rate imaging

Fig. 2. Schematic of a standing triple flame in an axisymmetric burner. A temperature map is displayed, with superimposed streamlines (red curves). The solid black line is an isocontour of heat-release rate. The vertical line on the left indicates the burner axis.

by a coflowing nitrogen shroud to isolate the flame from external disturbances. The nozzle separation distance was kept constant at 1.3 cm. A CH4 /N2 mixture flowed from the bottom nozzle, and a O2 /N2 mixture flowed from the top nozzle. Experiments were conducted at a global strain rate of 130 s−1 and the stoichiometric mixture fraction was Zs = 0.54, using the Burke–Schumann definition of the stoichiometric mixture fraction. The compositions of the input streams were as follows: on the fuel side, YCH4 = 0.092 diluted in nitrogen; on the oxidizer side, YO2 = 0.427, diluted in nitrogen. The edge flame was produced by locally extinguishing a counterflow diffusion flame with a pair of counterpropagating toroidal vortices that were simultaneously injected from the fuel and the oxidizer sides. The extinction front propagated radially outward from the burner centerline, thereby creating a hole in the flame. After the vortices dissipated, a steady flame with a hole was established, and the edge flame at the perimeter of this hole was investigated. The geometry of the resulting edge flame is illustrated in Fig. 2. The figure shows a computed temperature distribution of a standing edge flame with superimposed streamlines and a heat-release rate contour. The details of the computations will be presented in following sections. The heat-release isocontour (solid black line) shows the typical tribrachial structure of the flame, and the streamlines show the flow redirection due to the heat released by the flame. Since the propagation speed of the flame in the laboratory frame of reference (ULF ) is zero, the minimum gas velocity (u) upstream of the flame on the stoichiometric surface can be used to identify the propagation speed of the flame (UEF ). Furthermore, the flame can be partitioned into two zones: a hot region, where chemical reactions occur, and a cold region where only frozen mixing occurs. These two regions are shown

The forward reaction rate of the reaction CO + OH → CO2 + H was measured by simultaneous imaging of single-photon OH LIF and two-photon CO LIF. This reaction is the dominant pathway for CO2 production in CH4 /air flames. A schematic diagram of the experimental system, consisting of two lasers, two cameras, and an axisymmetric counterflow burner, is shown in Fig. 3. The reaction rate imaging technique is described in detail elsewhere [18,19], and only a brief overview is given here. The forward reaction rate, RR, is given by RR = k(T )[CO][OH]. The product of the LIF signals from CO and OH can be approximated by fCO (T )fOH (T )[CO][OH], where the temperature dependence of the LIF signals is represented by f (T ). The pump/detection scheme determines the temperature dependence of the LIF signals and can be selected such that fOH (T )fCO (T ) ∝ k(T ). When this relationship is achieved, the pixel-by-pixel product of the OH LIF and CO LIF signals is proportional to the reaction rate. For OH LIF, the frequency-doubled output from a 10 Hz Nd:YAG-pumped dye laser was tuned near 285 nm to pump the Q1 (12) transition of the A– X(1, 0) band. An intensified CCD camera (512 × 512 pixels) with an f/1.8 Cerco quartz camera lens was used to record the OH LIF signal with a projected pixel size of 93.6 × 93.6 µm. The image intensifier was gated for 400 ns bracketing the dye laser pulse. The OH LIF images were corrected for spatial variations in the laser sheet using acetone LIF to record the beam profile. Two-photon CO LIF was excited by pumping overlapped transitions in the B–X(0, 0) Hopfield– Birge system of CO using the frequency-doubled output from a 10 Hz Nd:YAG-pumped optical parametric oscillator (OPO) (14 mJ) near 230.1 nm. The laser was tuned to maximize the CO LIF signal in a laminar, nonpremixed methane counterflow flame. Sheet forming optics were used to form an 11.5-mm-high laser sheet. The average laser beam profile was measured using CO LIF obtained from a mixture of CO in N2 (0.1% CO by volume). The CO fluorescence was imaged onto an intensified CCD camera (512 × 512 pixels) with a f/1.2 camera lens and an interference filter (λ = 484 nm and λ = 10 nm), which transmitted fluorescence from the B–A(0, 1) transition at 483.5 nm and blocked out-of-band interference. The projected pixel size was 93.6 × 93.6 µm. The image intensifier was gated for 400 ns, bracketing the OPO laser pulse. Averaging over 10 shots was implemented to improve the signal-to-noise ratio of the two-photon

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Fig. 3. Schematic diagram of the experimental system, consisting of two lasers, two cameras, and the axisymmetric counterflow burner.

CO LIF, which is a relatively weak process compared to single-photon LIF. Timing of the two laser pulses was controlled with digital delay generators. The OPO laser fired 600 ns after the dye laser to eliminate the possibility of cross talk between the two diagnostic systems. The reaction rate imaging technique requires careful matching of the OH and CO LIF images. A precise image matching technique was used to obtain accurate registration between the two CCD cameras [18]. Images were matched with an eight parameter bilinear geometric warping algorithm, and the residual matching error was in the subpixel range.

In the following sections, the experimental flow field will be compared to the computational flow field. For an accurate comparison, two experimental biases in the PIV measurements are taken into account in the computed velocity fields: first, the vaporization of the oil droplets, and second, thermophoresis. The former effect has been included by masking all the vectors corresponding to a local temperature larger than 570 K, which is the boiling point of the oil. Thermophoretic effects were evaluated from the computational data in the particle-laden region according to the relations provided by [20]. The local particle drift velocity was obtained using

2.3. PIV measurements

VT = (αT D)p (−∇T /T )

Velocity field measurements were performed in the nonreacting regions of the steady flames using particle image velocimetry. The fuel and oxidizer flows were seeded with oil droplets, which were consumed in the reaction zone. The PIV system (TSI) consisted of two pulsed Nd:YAG lasers and a 2000 × 2000 pixel CCD camera. The laser beams were formed into overlapping sheets, which intersected the burner axis. The lasers were sequentially pulsed with a 150-µs time delay, and the particle scattering from each laser pulse was imaged onto a separate frame of the camera. Velocity vectors were determined using a cross-correlation analysis with 32 × 32 pixel (0.675 × 0.675 mm) interrogation regions separated by 16 pixels. PIV data were averaged over 10 consecutive sets of data, with uncertainties estimated at 3 cm/s.

∼ = 0.75[1 + π/8α]υ(−∇T /T ).

(1)

These effects are important in the immediate vicinity of the flame where the temperature gradients are steeper. In such regions, the local particle drift velocity becomes larger than the uncertainty in the PIV data, and the thermophoretic effects need to be included in the computational velocity field. 2.4. Inlet experimental velocity boundary conditions The behavior of the steady velocity profile at the inlet nozzles was investigated for self-similarity at different strain rates, using PIV data from four different steady flames. The feed compositions of these flames are reported in Table 1. The velocity profiles for the four flames are displayed as a function of the radial coordinate in Figs. 4a and 4b for the

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Table 1 Compositions (mole fractions) of the fuel and oxidizer streams for flames 1, 2, 3, and 4 Flame

Methane (diluted in N2 ) mole fraction

Oxygen (diluted in N2 ) mole fraction

1 2 3 4

0.225 (top nozzle) 0.213 (top nozzle) 0.209 (top nozzle) 0.170 (bottom nozzle)

0.367 (bottom nozzle) 0.368 (bottom nozzle) 0.368 (bottom nozzle) 0.367 (top nozzle)

(a)

(b)

(c) Fig. 4. Velocity profile at the top (a) and bottom (b) nozzles for each of the four flames described in Table 1. The nondimensional velocity profiles and interpolating polynomial are shown in (c).

top and bottom nozzles, respectively. The magnitude of the axial velocity varies from 0 to 80 cm/s with values on the axis of symmetry ranging from 38 to 71 cm/s. In Fig. 4c, the velocity profiles for each nozzle are nondimensionalized with respect to the average velocity and the nozzle radius. The resulting eight nondimensional velocity profiles (two velocity profiles per flame) exhibit excellent self-similarity. The curve in Fig. 4c is a least-squares fit to the dimensionless profiles using a twelfth degree polynomial. The

analytical form of this polynomial is  2  4 r r vz (r/R) = 1.068 + 1.458 − 7.809 vAVG R R  6  8 r r + 36.99 − 74.35 R R  10  12 r r + 55.88 − 13.20 . (2) R R The reported PIV measurements show that the axial component of the velocity vector at each nozzle exit is relatively uniform in the vicinity of the axis of symmetry and overshoots close to the nozzle wall. When velocity measurements are performed on a single nozzle in a free jet configuration, no overshoot is detected, suggesting that the finite separation between the burners is responsible for this change in the inlet velocity profile. This finding can be explained qualitatively from Bernoulli’s principle. On the axis of symmetry at the stagnation surface, the axial velocity is zero and the static pressure is at its maximum. As a result, the streamlines in the proximity of the axis are subject to a larger adverse pressure gradient as compared to those near the nozzle walls, and the overshoot ensues. Note that despite this inevitable effect, the plug flow assumption still meets the requirements needed for quantitative one-dimensional modeling since the flow is relatively uniform in the vicinity of the centerline. However, consistent with Eq. (2) computed at r = 0, the axial velocity value must be increased from vAVG to 1.068vAVG to account for the radial nonuniformity. In the two-dimensional case, if quantitative comparisons between computational and experimental results are to be obtained, velocity measurements of the inlet boundary conditions are clearly indispensable.

3. Computational methods 3.1. Problem formulation The computational component of the study examines steady laminar, counterflowing edge flames, using an axisymmetric model that employs the gasphase conservation equations cast in a vorticity– velocity formulation. The result is a strongly coupled, highly nonlinear set of NSPEC + 4 elliptic partial differential equations, where NSPEC is the number of gas-phase species. The present study uses a C1 mechanism with 16 species and 46 reactions [21]. The effect of gas-phase radiation in the optically thin limit is considered by including a radiation submodel in which H2 O, CO, and CO2 are the significant radiating species [22].

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3.2. Governing equations Listed below in Eqs. (3)–(7) are the governing equations for the radial velocity, the axial velocity, the vorticity, whose only nonzero component is in the azimuthal direction, energy, and species, respectively, vr ∂(ρvz ) ∂(ρvr ) +ρ + = 0, ∂r r ∂z

(3)

  ∂ v · ∇ρ ∂ 2 vz ∂ 2 vz ∂ω 1 ∂vr − − , (4) + = − ∂r r ∂z ∂z ρ ∂r 2 ∂z2   ∂ μω ∂ 2 μω ∂ 2 μω + + ∂r r ∂r 2 ∂z2 vr ∂ω ∂ω + ρvz − ρω = ρvr ∂r ∂z r  v 2

¯ ·g ¯ ·∇ − ∇ρ + ∇ρ 2    + 2 ∇¯ div(v) · ∇μ 

∂μ ∂μ − ∇vz · ∇¯ , (5) ∂r ∂z ∂T ∂T + ρcp vz ρcp vr ∂r ∂z     ∂T ∂ ∂T 1 ∂ rλ + λ = r ∂r ∂r ∂z ∂z    NSPEC  ∂T ∂T + Vk,z ρcp,k Yk Vk,r − ∂r ∂z − ∇vr · ∇¯

k=1

−

NSPEC 

hk Wk ω˙ k ,

(6)

k=1

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nozzles was measured by thermocouples. On the outflow boundary, all normal derivatives are set to zero. The full set of boundary conditions employed in the computational simulations is reported below. At the top burner mouth (r < 0.65 cm, z = 1.3 cm): vr = 0 cm/s,

vz = vz (r/R), ∂vz ∂vr − , vAVG = 45.5 cm/s, ω = ∂z ∂r T = 345 K, YO2 = 0.427, YN2 = 0.573. At the bottom burner mouth (r < 0.65 cm, z = 0.0 cm): vr = 0 cm/s,

vz = vz (r/R), ∂vz ∂vr − , vAVG = 35.3 cm/s, ω = ∂z ∂r T = 315 K, YCH4 = 0.092, YN2 = 0.908. At the outlet of the computational domain (r = 4.0 cm, 0.0 cm < z < 1.3 cm): vr ∂(ρvz ) ∂vz ∂(ρvr ) +ρ + = 0, = 0, ∂r r ∂z ∂r ∂vz ∂T ∂Yi ∂vr − , = 0, = 0. ω= ∂z ∂r ∂r ∂r At the water-cooled flanges (0.65 cm < r < 4.0 cm, z = 0.0, 1.3 cm): vr = 0,

vz = 0,

T = 350 K,

ω=

∂vz ∂vr − , ∂z ∂r

∂Yi = 0. ∂z

On the axis of symmetry (r = 0.0 cm, 0.0 cm < z < 1.3 cm):

∂Yk ∂Yk + ρvz ρvr ∂r ∂z 1 ∂ ∂ =− (rρYk Vk,r ) − (ρYk Vk,z ) + Wk ω˙ k , r ∂r ∂z

∂vz = 0, ω = 0, ∂r ∂Yi ∂T = 0, = 0. ∂r ∂r

vr = 0, (7)

where ∇¯ = (∂/∂z, −∂/∂r) in (5).

3.4. Numerical solution 3.3. Boundary conditions PIV measurements are used to specify the inlet velocity boundary conditions at the nozzles. Stray light effects at the solid boundary caused a lack of PIV data in the region 1.1 mm downstream of the nozzle mouths. Hence, the velocity vectors at the burner inlets are extrapolated from the PIV data in the vicinity of the nozzles, and an interpolating polynomial is used to describe the general shape of the radial dependence of the velocity profile at the nozzle mouth. No-slip boundary conditions are imposed at the walls, and the temperature is held constant at the value of the water-cooled flanges. The temperature at the inlet

The solution of the governing equations proceeds with an adaptive, nonlinear boundary value method on a two-dimensional computational mesh. The details of this method have been presented elsewhere [23], and only the essential features are outlined here. The governing equations and boundary conditions are discretized using a finite difference technique on a nine-point stencil, transforming the set of partial differential equations into a set of NSPEC + 4 strongly coupled, highly nonlinear difference equations at each grid point. The resulting system of equations is written in residual form and is solved with a modified Newton’s

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method in which the Jacobian matrix is periodically re-evaluated. A preconditioned (block Gauss–Seidel) Bi-CGSTAB method solves the linear system within each Newton iteration. Pseudo-transient continuation is employed to ease the convergence of an arbitrary starting estimate on an initial grid [24]. The final computational mesh is adaptively determined through the equidistribution of solution gradient and curvature between adjacent mesh cells. The minimum grid spacing is 0.004 cm, and the grid size is 229 × 192, in the radial and axial directions, respectively. Local properties are evaluated with vectorized and highly optimized transport and chemistry libraries [25–27]. Steady edge flames can be obtained computationally by local annular extinction of diffusion flames with three alternative techniques: (a) imposing an ambient temperature for the boundary condition on the axis of symmetry; (b) first, reducing the fuel mass fraction until the flame extinguishes and then bringing it back to the original boundary conditions; (c) introducing opposing vortices from each side of the counterflow flame. In this contribution we combine methods (a) and (b). Method (c) requires the use of unsteady governing equations, which employ the physical unsteady terms, rather than pseudo-unsteady terms [24].

4. Results and discussion 4.1. Comparison between two-dimensional computational and experimental results Fig. 5 shows the computational (left) and experimental (right) velocity vectors superimposed on the corresponding axial velocity contours. Both experimental and numerical results are reported with the same scale. The radial and the axial dimensions of the image are 1.7 and 1.05 cm, respectively. The velocity measurements are omitted in the upper recirculation

region, near the outlet of the top burner, because the particle seeding in that region was too sparse for PIV. The outermost radial locations where vectors are reported denote the 570 K isotherm that bounds the edge flame. Clearly, the two images look very similar. The quantitative nature of the agreement is further substantiated by the axial and radial velocity profiles in Fig. 6. Fig. 6a shows axial scans at a radial distance of r = 0.2 and r = 0.4 cm, respectively, whereas Fig. 6b shows scans in the radial direction at the axial locations z = 0.3, z = 0.5, and z = 0.8 cm, passing through to the lower recirculation zone, the leading edge of the triple flame, and the upper recirculation zone at the exit of the top burner, respectively. These comparisons confirm that the experimental velocity field is properly modeled. In order to compare the experimental CO LIF and OH LIF signals with the computational results, we simulated the CO LIF and OH LIF signals using the computed temperatures and species concentrations. Two-photon CO LIF excitation of the B–X(0, 0) band was simulated using laser fluences from the experiments and absorption cross sections from [28]. Variations in the Boltzmann fraction population were determined from the computed temperatures. Depopulation of excited-state CO via photoionization and collisional quenching was included in the simulations using the photoionization cross section from [29], and the species and temperature-dependent quenching cross sections from [30], respectively. The OH LIF signals for excitation of the Q1 (12) transition in the A–X(1, 0) band were simulated using Boltzmann fractions and quenching rate calculations that were based on computed temperatures and concentrations of the major quenching partners. The quenching cross sections were from Tamura et al. [32]. Laserbeam absorption was incorporated into the simulations by computing the absorbance of CO and OH at each location in the computational domain and de-

Fig. 5. Computational (left) and experimental (right) velocity vectors superimposed onto the axial velocity contours. The radial and the axial dimensions of the image are 1.9 and 1.05 cm, respectively.

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(a)

(b) Fig. 6. Comparison of computational and experimental velocity profiles. Axial profiles (a) at r = 0.2 cm and r = 0.4 cm, and radial profiles (b) at z = 0.3 cm, z = 0.5 cm, and z = 0.8 cm.

termining the cumulative attenuation from the edge of the domain. The CO absorbance was determined from calculations of the CO absorption spectrum using the model of Di Rosa and Farrow [28]. The results indicated that two-photon absorption by CO was negligible, and the maximum attenuation of the 230 nm beam was estimated at 2%. The OH absorption spectrum was calculated using spectroscopic data from Luque and Crosley [31]. For OH absorption, the maximum attenuation of the 285 nm beam was 13%. Fig. 7 presents composite images of the computational (left) and experimental (right) results for the CO LIF signal, the OH LIF signal, and RR. The axis of symmetry is in the middle and the size of the reported experimental and numerical domains is 4.0 × 1.16 cm. The computational and experimental CO LIF signals were normalized with respect to the local maximum in the proximity of the leading edge; the OH LIF and RR were normalized with respect to the global maximum over the entire domain. Figs. 7a and 7b show that CO is present not only in the edge flame region but also in regions where neither heat release nor reactions are expected to take place, i.e., near the flanges. This behavior is due to the presence of the two recirculation regions (one at the exit of each nozzle), which entrain products from the premixed branches of the edge flame and advect them

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to the cold nonreactive region of the domain. These upper and lower recirculation regions, henceforth referred to as bubbles, as typical in the aerodynamic description of separated and subsequently reattached flows, are an inherent two-dimensional effect associated with counterflow geometry bound by solid walls. The flow issuing from the nozzles is not able to follow the sharp contour of the wall and separates at the nozzle exit. It eventually reattaches to the flange once the gases undergo the expansion associated with the heat released by the flame. In fact, ancillary calculations under cold (unreacted) flow conditions show that in the absence of the flame, reattachment of the lower bubble never takes place inside the computational domain. The agreement between the computed and the measured CO LIF signals is quantitative throughout the entire domain. Similarly quantitative agreements are shown in the comparison of OH LIF signals (Figs. 7c and 7d) and the reaction rates (Figs. 7e and 7f). For a more detailed comparison, we consider axial profiles of normalized CO LIF signals, OH LIF signals, and reaction rates. Figs. 8 and 9 show axial profiles at two radial positions, r = 1.6 cm, and r = 2.0 cm, respectively. The locations of these profiles are indicated by the red lines in Fig. 7c. To quantify the discrepancy between the computational and the experimental data, a RMS error was computed for each of the three variables at each radial location according to the following formula:

N 1 2 i=1 (EXP(zi , r) − NUM(zi , r)) N , Error(r) = NUMMAX (r) (8) where EXP (NUM) refers to the experimental (numerical) value of any of the variables at a given location. The errors are reported in Table 2 for CO LIF, OH LIF, and RR. The average error between experiments and calculations is on the order of 10% for CO and OH, and reaches 19% for the reaction rate image. This parameter provides additional confirmation of the quantitative nature of the comparison between experiments and modeling. 4.2. Flame structure Fig. 10 shows the computed CO LIF signal, OH LIF signal, and RR (left side of the three images in Fig. 7) superimposed with two computed isocontours of the heat-release rate for values of 108 (innermost) and 2.51 × 107 (outermost) W/m3 . The outer heatrelease contour exhibits the typical tribrachial structure, with a diffusion flame trailing lean (top) and rich (bottom) premixed branches. Only by lowering the contour threshold by a factor of 4 could we resolve the

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Fig. 7. Computational (a) and experimental (b) normalized CO LIF signals, computational (c) and experimental (d) normalized OH LIF signals, and computational (e) and experimental (f) normalized reaction rate. Experimental and computational domains extend 4.0 cm in the radial direction and 1.16 cm in the axial direction.

Table 2 RMS error between the computational and the experimental results across the crosscuts at radial locations r = 1.6 cm and r = 2.0 cm r = 1.6 cm r = 2.0 cm

CO LIF

OH LIF

RR

11.5% 10.0%

9.9% 10.9%

15.2% 19.0%

Note. RMS error is calculated according to Eq. (8).

trailing diffusion flame, which has significantly lower heat release than the premixed branches. We observe that the computed CO LIF signal straddles the leading edge of the heat-release contours, extends to a small portion of the lean premixed branch, and covers most of the rich premixed branch. The computed OH LIF signal captures mostly the trailing diffusion flame, but is also present in the rich premixed branch. The RR distribution shows an upper “whisker” which hints to the existence of the lean upper branch. The bulk of the long lower tail falls between the rich premixed branch and the trailing diffusion flame. Therefore, the experimental detection of the tribrachial morphology requires additional diagnostic techniques.

Table 3 Rich branch: Most important reactions Reaction

Percentage of heat release

CH3 + O = CH2 O + H CH3 + OH = CH2 O + H2 CH3 + H = CH4 CH2 O + H = HCO + H2 OH + H2 = H2 O + H CH2 O + OH = HCO + H2 O HCO + M = H + CO + M H + O2 = OH + O

40% 31% 18% 10% 9% 8% −17% −15%

To probe deeper into the chemistry of the flame, we rank-ordered the key chemical reactions in Tables 3–5 on the basis of their contributions to the heat released by each branch. We used the local maximum of the heat-release rate to identify the three branches. We integrated the net heat release of each reaction along each branch and normalized it by the total heat release along that branch. Namely, we have  HRi dsbranch , %HRbranch = NREACT  HRi dsbranch i=1

(9)

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(a)

(a)

(b)

(b)

(c)

(c)

Fig. 8. Experimental (triangles) and computational (solid line) normalized CO LIF signals (a), OH LIF signals (b), and RR (c) along r = 1.6 cm. The fuel nozzle is at z = 0.0 cm, and the oxidizer nozzle is at z = 1.3 cm.

Fig. 9. Experimental (triangles) and computational (solid line) normalized CO LIF signals (a), OH LIF signals (b), and RR (c) along r = 2.0 cm. The fuel nozzle is at z = 0.0 cm, and the oxidizer nozzle is at z = 1.3 cm.

Table 4 Lean branch: Most important reactions

Table 5 Diffusion branch: Most important reactions

Reaction

Percentage of heat release

Reaction

Percentage of heat release

CH3 + O = CH2 O + H CH2 O + OH = HCO + H2 O OH + HO2 = H2 O + O2 CH3 + OH = CH2 O + H2 HCO + O2 = HO2 + CO H + O2 = OH + O

38% 12% 11% 10% 9% −14%

H + O2 + M = HO2 + M CO + OH = CO2 + H H + OH + M = HO2 + M OH + HO2 = H2 O + O2 OH + H2 = H2 O + H H + HO2 = 2OH H + O2 = OH + O

26% 20% 19% 16% 11% 10% −13%

where NREACT is the number of elementary reactions, and HRi is the heat release of the ith reaction. In both the rich and lean branches, methane oxidation chemistry dominates with radical attack of the methyl radical by O and OH, leading to CH2 O production and, eventually, to the formyl radical, HCO. In the rich branch, methyl radical attack by O and OH yields the largest contributions of 40 and 31%, respectively. In the lean branch, CH3 + O = CH2 O + H accounts for 38% of the heat release, while CH3 + OH = CH2 O + H2 accounts for 10% of the

heat release. The primary difference between the two branches is that 18% of the total heat release in the rich branch is contributed by the radical recombination of CH3 + H, whereas in the lean branch 11% is contributed by the reaction OH + HO2 = H2 + O2 , as the third largest contribution. Hydrogen chemistry plays the dominant role in the trailing diffusion flame, with the exception of a 20% contribution by CO + OH = CO2 + H, the forward rate of which was imaged in the present experiments. The largest contri-

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Fig. 10. Computed CO LIF signal, OH LIF signal, and RR maps. Superimposed on the maps are two contours of the heat-release rate for values of 2.51 × 107 W/m3 , and 1 × 108 . Radial and axial extents are r = 4.0 cm and z = 1.3 cm, respectively.

bution comes from H + O2 + M = HO2 + M at 26%. These results confirm early findings in [33], suggesting that the trailing diffusion flame is the result of CO and H2 oxidation. Fig. 11 shows the computed mass fractions of methane, oxygen, carbon dioxide, water vapor, and nitrogen, as well as the mixture fraction. The images have an axial extent of 1.3 cm and a radial extent of 3.2 cm. The mixture fraction is based on the linear combination of C, H, and O mass fractions as defined by Bilger [34]. Superimposed on all the figures are the two streamlines separating the flow exiting the nozzles from the upper and lower recirculation zones. The stagnation and the stoichiometric lines are also reported as the solid and the dashed lines, respectively. The upper bubble at the exit of the top nozzle recirculates both reactants from the upper nozzle (O2 , N2 ) and products from the flame (H2 O, CO2 ), whereas the lower bubble recirculates only reactants from the lower nozzle (CH4 , N2 ). The

Fig. 11. Computed mass fractions of major species and mixture fraction. Superimposed on the maps are a contour of the heat-release rate for a value of 2.51 × 107 W/m3 , the stoichiometric line (dashed), the stagnation line (solid), and streamlines bounding the top and bottom recirculating zones (bubbles). Radial and axial extents are r = 3.2 cm and z = 1.3 cm, respectively.

fuel and oxidizer come into contact near the stagnation surface and interdiffuse in a mixing layer, whose thickness remains approximately constant within the nozzle radius and expands beyond the nozzle region. As previously shown in Fig. 2, the flow field can be divided into two regions: the cold nonreactive region, where pure mixing occurs; and the hot reactive region, where combustion occurs. At the interface between the cold and hot region is the premixed edge flame. Upstream of the flame, both the methane and the oxygen distributions show a whisker leaning obliquely

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Fig. 12. Computed two-dimensional maps of the divergence of (a) the velocity field, (b) the scalar dissipation rate, and (c) the temperature field. Superimposed on the maps are a contour of the heat-release rate for a values of 2.51 × 107 W/m3 , the stoichiometric line (dashed), the stagnation line (solid), and streamlines bounding the top and bottom recirculating zones (bubbles). Radial and axial extents are the same as in Fig. 11.

toward the other reactant (Figs. 11a and 11b). The reactants diffuse into each other in the cold mixing layer between the burner outlets and are convected outward in the radial direction when the edge flame redirects the flow. The whiskers are a direct consequence of the streamline expansion upstream of the edge flame. Both oxygen and methane leak through the edge flame, on the lean and rich sides, respectively. The stoichiometric mixture fraction line is located on the rich premixed branch as a consequence of how Zs is computed from the input feed stream concentrations. Since the trailing diffusion flame is fed by CO and hydrogen intermediates, this nonpremixed flame would lie on the stoichiometric line calculated for these reactants. Figs. 12a–12c present images of the divergence of the velocity field, the scalar dissipation rate, and temperature, with the superposition of one heat-release rate contour (corresponding to 2.51 × 107 W/m3 ) and streamlines to help orient the reader. The radial and the axial dimensions of these images are 3.25 and 1.3 cm, respectively. As shown in Frouzakis et al. [35], the divergence of the velocity field reaches its maxi-

mum in regions outside the reaction zone, where the diffusion of heat and mass dominate. The divergence is related to the density and temperature gradients through the continuity equation and the ideal gas law. Hence, it can be used to identify the location of the convective–diffusive boundary layers in which fuel and oxidizer are preheated before entering the reaction zone. Fig. 12a shows the structure of this thermal layer, located upstream of the heat-release region, approximately perpendicular to the stagnation surface. Fig. 12b illustrates the behavior of the scalar dissipation field, with the largest values reached in the cold region upstream of the edge flame. The scalar dissipation rate exhibits a minimum in the region immediately upstream of the edge flame, due to flow expansion induced by the heat release of the flame. The flow accelerates as it moves through the flame, due to the redirection of the flow induced by the curved nature of the edge flame and the heat release, and the scalar dissipation rate increases accordingly. Fig. 12c reports the temperature field, and it shows that a maximum temperature of 1890 K is reached on the diffusion tail of the triple flame. This result can be reconciled with

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Fig. 13. Streamlines and heat-release rates for edge flames of increasing global strain rate (120 s−1 (top) to 195 s−1 (bottom)) in constant increments. Streamlines are not shown at equispaced values of stream function. Radial and axial extents are the same as in Fig. 11.

the relatively small heat release associated with this branch of the flame if one considers that both inert and reactants entering the diffusion flame have been dramatically preheated by the leading edge of the edge flame further upstream. As the gases flow out of the domain, they cool down as a result of the heat transfer from the flame to the cooled flanges. 4.3. Strain rate effect on flame stabilization Figs. 13a–13f present the streamlines superimposed onto heat-release maps for flames of identical composition and momentum ratio, but increasing strain rates. The global strain rate, A, defined as [36]   2vOXID vFUEL ρFUEL 1/2 A= (10) , 1+ L vOXID ρOXID

spans the 120–195 s−1 range, in steps of 15 s−1 . To show the relative magnitude of the contributions from the various branches in Figs. 13a–13f, we report a two-dimensional image of the base-10 logarithm of the heat-release rate. The heat released at the triple point surpasses by one order of magnitude the heat released by the trailing diffusion flame. In fact, only by spanning a fairly broad dynamic range, can one observe a trailing diffusion flame in addition to the rich and lean premixed branches. For this reason, the selection of the appropriate diagnostic tool to discern the three branches is generally nontrivial, and sometimes a combination of diagnostic techniques is required [37]. The streamlines upstream of the triple flame have a converging–diverging shape, forming a toroidal nozzle. The radial acceleration in the converging section is partly counterbalanced by the deceleration due to the axisymmetric geometry. In the diverging section, on the other hand, the flow invariably decelerates. In this region, the edge flame is stabilized. As noted earlier, the heat released by the curved edge flame induces streamline divergence immediately upstream of the flame, causing a sudden redirection of the flow, which in turn results in reattachment of the flow to the burner flanges and the confinement of the recirculation zones within the computational domain. As the strain rate increases, several qualitative changes take place. First, the bubbles grow in size in the radial direction. This growth also occurs in the case of a vigorously burning, simply connected counterflow diffusion flame. Second, the edge flame is located increasingly closer to the bubbles, and, at the largest strain rate, it marginally “seeps” into the upper bubble. Third, the flame is invariably positioned in the diverging section of the stream tube and, as a consequence of the increasing momentum of the flow, it is anchored increasingly closer to the domain outlet at the radial location where gaseous speed and propagation speed are equal and opposite to each other. Fourth, as the strain rate increases, the curvature decreases. Next, we present the computed correlations of three quantities: the flame propagation speed, SEF , the mixture fraction gradient, ∂Z/∂t, and the flame curvature, k. The flame curvature is computed by fitting a circle to a heat-release isopleth in the region of the triple point. The value of the isopleth is 2.51 × 107 W/m3 . Fig. 14 shows the location at which the mixture fraction gradient, ∂Z/∂t, is calculated. This location is determined by the point where the temperature along the stoichiometric line reaches a value of 360 K. The three quantities, shown in Figs. 15a–15c, reflect, respectively, the strength of the flame compared to a freely propagating laminar premixed flame, the degree of mixing ahead of the flame, and the over-

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Fig. 14. Schematic of the point at which the mixture fraction gradient is computed. The mixture fraction is indicated by the color scale, and the dashed line represents the stoichiometric line. The streamlines are shown in color and a heat-release rate contour is indicated in black.

all shape of the flame. SL is the propagation speed of a one-dimensional adiabatic premixed flame with the same composition as the stoichiometric surface ahead of the edge flame. The flame curvature, k, is the inverse of the radius of curvature of the leading edge of the heat-release layer. The edge flame propagation speed is the minimum velocity reached along the stoichiometric line upstream of the edge flame. These correlations were obtained by increasing the global strain rate from 120 to 195 s−1 , as in Fig. 13. Since the global strain rate is not the critical variable, we chose to correlate quantities that are more intrinsic to the edge flame. As the strain rate increases, the edge flame recedes away from the nozzle region, and stabilizes closer to the lower flange. Consequently, the mixing ahead of the edge flame improves, reducing the tangential mixture fraction gradient ahead of the flame. As shown in Fig. 15, the flame curvature decreases with increasing strain rate due to the increased uniformity of the mixture fraction field. Increasing the global strain rate results in: (1) an increased propagation speed of the flame that approaches the one-laminar flame speed as shown in Figs. 15a and 15c; (2) decreased curvature of the flame’s leading edge, as shown in Figs. 15b and 15c; and (3) an improved mixing in the upstream region of the flame, leading to a ∂Z/∂t, as shown in Figs. 15a and 15b. These results are in full agreement with the experimental results obtained in [38], for methane edge flames in a different geometrical configuration. They are also consistent with [39], which reports an opposite dependence with the propagation speed of hydrogen edge flames increasing with curvature. This behavior is a direct consequence of the much lower Lewis number for hydrogen flames and can be qualitatively explained by Fig. 3 in [40], where methane and hydrogen flames are represented by the branches lF = 0 and lF = −5, respectively, in the authors’ notation. In this figure, as we move from edge flames to the corresponding fully premixed one-

147

(a)

(b)

(c) Fig. 15. Correlations of the edge flame propagation speed, SEF , the mixture fraction gradient,∂Z/∂t , and the flame curvature, k, in computed flames at different global strain rates, ranging from 120 to 195 s−1 .

dimensional flame, the propagation speed increases for the branch lF = 0, and decreases for the branch lF = −5. As a final remark, it is interesting to note that the minimum thickness of the edge flame thermal layer (measured between the isotherms 500 and 1500 K) is 0.5 mm for the strain rate A = 120 s−1 , as compared to the 0.4 mm thickness of a freely propagating one-dimensional premixed flame with the same composition found at the stoichiometric line of the edge flame.

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5. Conclusions

References

A computational and experimental study was performed on steady, two-dimensional, axisymmetric methane/enriched-air laminar edge flames. The edge flames were established by bringing about local extinction in a counterflow diffusion flame, near its axis of symmetry. Probing the edge of the resulting hole yielded information on the structure and properties of the axisymmetric edge flame. The model used experimental boundary conditions and was quantitatively validated with respect to measurements of the velocity field, CO LIF, OH LIF, and the forward reaction rate of the reaction CO + OH → CO2 + H. The comparison between the experimental and the computational data yielded excellent agreement for all the measured quantities. The two-dimensional flow field can be approximately partitioned into two regions: the cold nonreactive region near the burner centerline, where only mixing occurs, and the hot reactive annular region, where combustion occurs. The two regions are separated by the edge flame. In the cold region, fuel and oxidizer come into contact near the stagnation surface and interdiffuse in a mixing layer, whose thickness remains approximately constant within the nozzle radius and expands beyond the nozzle region. At the interface between the cold and the hot regions is a premixed edge flame. The flame was shown to have a tribrachial structure, with the bulk of the heat release associated with the premixed branches and a much smaller contribution from the trailing diffusion flame. The investigation identified the elementary chemical reactions that contributed to the heat release. It revealed details of the structure of the edge flame, and of the flame dependence on curvature and mixture fraction gradient in the transverse direction.

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Acknowledgments This research was supported by NSF, Grant CTS9904296 (Dr. Farley Fisher, Contract Monitor), and the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. The technical assistance of N. Bernardo (Yale University) and R. Sigurdsson (Sandia National Laboratories), in the construction of the hardware and in setting up the optical diagnostic system, respectively, and technical discussions with Professor A. Linan and James A. Cooke are gratefully acknowledged. The authors thank Drs. T.C. Williams and R.W. Schefer for the use of the PIV facility.

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