Paper # 070LT-0256 Topic: Laminar Flames

8th US National Combustion MeetingOrganized by the Western States Section of the Combustion Institute

and hosted by the University of UtahMay 19-22, 2013.

Effects of Fuel Dilution and Gravityon Laminar Coflow Methane-Air Diffusion Flames:

A Computational and Experimental Investigation

S. Cao1 B.A.V. Bennett1 B. Ma1 D. Giassi1 D.P. Stocker2

F. Takahashi3 M.B. Long1 M.D. Smooke1

1Department of Mechanical Engineering & Materials Science,Yale University, P.O. Box 208284, New Haven, Connecticut 06520–8284 USA

2NASA Glenn Research Center,Cleveland, Ohio 44135 USA

3National Center for Space Exploration Research on Fluids and Combustion,NASA Glenn Research Center, Cleveland, Ohio 44135 USA

In this study, the influences of gravity and fuel dilution on the structure, stabilization, and sootingtendency of laminar coflow methane-air diffusion flames were investigated both computationally andexperimentally. A series of nitrogen-diluted flames measured in the Structure and Liftoff in CombustionExperiment (SLICE) was assessed numerically under normal gravity and microgravity conditions withthe fuel stream CH4 mole fraction ranging from 0.4 to 1.0. Computationally, the vorticity-velocityformulation of the governing equations was employed to describe the reactive gaseous mixture, wherethe soot evolution process was considered as a classical aerosol dynamics problem and was representedby the sectional aerosol equations. Since each flame is axisymmetric, a two-dimensional computationaldomain was employed, where the grid on the axisymmetric domain was a nonuniform tensor productmesh. The governing equations and boundary conditions were discretized on the mesh by a nine-point finite difference stencil, with the convective terms approximated by a monotonic upwind schemeand all other derivatives approximated by centered differences. The resulting set of fully coupled,strongly nonlinear equations was then solved simultaneously at all points using a damped, modifiedNewton’s method and a nested bi-conjugate gradient stabilized (Bi-CGSTAB) linear algebra solverwith a block-line Gauss-Seidel preconditioner. Experimentally, flame shape, size, lift-off height, andsoot temperature were determined by flame emission images recorded by a digital camera, and sootvolume fraction was quantified through an absolute light calibration using a thermocouple. For a broadspectrum of flames in normal gravity and microgravity, the computed and measured flame profiles (e.g.,temperature, flame shape, lift-off height, and soot volume fractions) were compared first to assess theaccuracy of the numerical model. After its validity was established, the influences of gravity and fueldilution on the structure, stabilization, and sooting tendency of laminar coflow methane-air diffusionflames were explored further by examining profiles of heat release rates, species consumption rates,mixture fractions, and other quantities based on computational results.

1 Introduction

Improvement in the reliability and accuracy of numerical models for combustion is of great sig-nificance in both academic research and industrial applications. Fundamentally, computational

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8th US Combustion Meeting – Paper # 070LT-0256 Topic: Laminar Flames

Figure 1: Schematic structure of the SLICE burner. Left: computational approximation. Right: experimental config-uration.

research can facilitate the understanding of combustion processes by providing information thatis impossible or difficult to measure. In practice, numerical simulations can reduce time and costin the design of commercial combustion devices, and, as a consequence, accelerate progress inincreasing fuel efficiency and reducing pollutant emissions [1].

Microgravity provides an ideal yet rigorous environment in which to study flame structure andexamine computational models, because the structure of a microgravity flame is completely dif-ferent from its normal gravity counterpart, and microgravity flames have larger scales and longerresidence times, which makes it possible to study a wider range of flame conditions than under nor-mal gravity. As a result, a significant amount of research has been conducted under microgravityconditions (e.g., [2–7]) to study the effects of various physical parameters on flames.

In this study, previous computational and experimental investigations of coflow laminar diffusionflames (e.g., [2, 3]) were extended to explore further the influences of fuel stream dilution andgravity on structure, stabilization, and sooting behavior of laminar coflow methane/air diffusionflames. The flame front shape, soot temperature, and soot volume fraction were simulated andmeasured, and the results are presented in this paper. Additional results appear in a companionpaper [8].

2 Burner configuration

The burner, which is shown in Fig. 1, consists of a vertical inner tube (inner radius rI = 0.16

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8th US Combustion Meeting – Paper # 070LT-0256 Topic: Laminar Flames

Table 1: Summary of basic flame information. The quantities XCH4 and XN2 are the mole fractions of CH4 andN2 in the fuel stream; YCH4 and YN2 are the mass fractions of CH4 and N2 in the fuel stream; vz,I and vz,O are theaverage velocities of the fuel and coflow streams; and G is the gravitational acceleration.

Flame name XCH4 XN2 YCH4 YN2 vz,I (cm/s) vz,O (cm/s) G (g)40% CH4/60% N2 0.40 0.60 0.27586 0.72414 50.20 18.74 1.070% CH4/30% N2 0.70 0.30 0.57197 0.42803 45.60 18.74 1.0100% CH4/0% N2 1.00 0.00 1.00000 0.00000 46.28 18.74 1.040% CH4/60% N2 0.40 0.60 0.27586 0.72414 50.20 18.74 0.070% CH4/30% N2 0.70 0.30 0.57197 0.42803 45.60 18.74 0.0100% CH4/0% N2 1.00 0.00 1.00000 0.00000 46.28 18.74 0.0

cm, wall thickness wJET = 0.032 cm) and a surrounding coaxial square duct (width = depth =7.621 cm). Since the ratio of the flame diameter to the width of the square duct is negligible (i.e.,always smaller than 17.2% in the current investigation), the square duct was approximated as anaxisymmetric coaxial tube with an identical cross-sectional area (inner radius rO = 4.288 cm). Thefuel mixture flows through the inner tube, and air issues from the annular region between the innerand outer tubes. The fuel is methane, which is diluted with nitrogen to control soot loading. In thisstudy, a variety of flow conditions (see Table 1) were investigated under both normal gravity andmicrogravity conditions with identical coflow velocities and similar fuel velocities, to characterizethe effects of fuel stream dilution and gravity. Since the length-to-diameter ratio of the fuel tubeis sufficiently large, the inner jet is assumed to be fully developed. The coflow air flows through aceramic honeycomb, so the coflow is approximated as a flat velocity profile. In order to improvethe smoothness of the vorticity profile (which involves the derivatives of the velocities), the inletfuel and coflow velocities have been fitted to a hyperbolic tangent profile, given by vz(r) = vz,f [1−tanh( r−rI/1.5

0.05 cm)] + 0.5vz,co[tanh( r−1.1(rI+wJET)

0.03 cm) + tanh(0.99rO−r

0.04 cm)]. In this equation, the coefficients

vz,f and vz,co are determined numerically by the trapezoidal rule to match the inlet fuel and coflowmass fluxes specified in the experiments. Since temperature measurements near the fuel tubesurface are unavailable, the inlet temperature is uniformly set to 298 K.

3 Computational approach

The numerical model used in this research is similar to those employed in the authors’ previousworks (see, for example, [9]). Specifically, the gaseous mixture is assumed to be Newtonian, andthe diffusion of each species is approximated as Fickian. The flow’s small Mach number impliesthat pressure P can be approximated as being independent of location in the flame, and mixturedensity ρ can be directly obtained from the ideal gas law. To evaluate the divergence of the netradiative flux, the model includes an optically thin radiation submodel [10–12] with three radiatingspecies (H2O, CO, and CO2). A sectional soot model [13–16] is included to simulate soot inthe 70% CH4 and 100% CH4 flames. The gas-phase chemistry employed in this research is theGRI 3.0 mechanism [17] with all nitrogen-containing species (except N2) removed. In order tosimulate sooting process, a series of reactions related to the formation and oxidation of benzeneand related species were included (see Table 1 of [13]), with the resulting mechanism having 42species and 250 reactions. All thermodynamic, chemical, and transport properties are evaluated

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8th US Combustion Meeting – Paper # 070LT-0256 Topic: Laminar Flames

by the CHEMKIN [18, 19] and TRANSPORT [20, 21] subroutine libraries, parts of which wereoptimized for greater speed [22].

A new version of the vorticity-velocity formulation of the governing equations [23] is adopted,which consists of the elliptic radial velocity equation, an updated elliptic axial velocity equation,given by

∂2vz∂r2

+∂2vz∂z2

= −∂ω∂r− ω

r− 1

r

∂vz∂r− ∂

∂z

(v · ∇ρρ

), (1)

the vorticity transport equation, the energy conservation equation, and Nspecies balance equationsfor the mass of each gaseous species. To ensure that the mass fractions sum to unity, the speciesequation for nitrogen is replaced by YN2 = 1−∑n6=N2

Yn.

Since each flame is axisymmetric, a two-dimensional computational domain is employed, extend-ing radially to r = 4.288 cm and axially to z = 12.2 cm. Except for the specific values ofvelocities, temperatures, and concentrations at the inlet, the boundary conditions are similar tothose in [24, 25] and are outlined here briefly. At the bottom boundary (inlet), vr, vz, T , and Yn(n = 1, ..., Nspecies) are specified to values mentioned previously in Section 2, and the definitionof ω is applied. At the top boundary (outlet), the definition of ω is applied, and axial gradientsof all other variables vanish. Along the axis of symmetry (z-axis), vr and ω vanish; ∂vz/∂r,∂T/∂r, and ∂Yn/∂r (n = 1, ..., Nspecies) are set to zero. The boundary conditions on vz, T , andYn are discretized as discussed in [26], in order to avoid convergence difficulties and/or discretiza-tion inaccuracies. At the outer radial boundary, vr, vz, and ∂Yn/∂r (n = 1, ..., Nspecies) vanish,T = 298 K, and the definition of ω is applied.

The grid on the axisymmetric domain is a nonuniform tensor product mesh initially containing 67points in the r direction and 75 points in the z direction. After solving the flames on a series offiner grids, the grid used in all results presented here is a 186 × 206 mesh. The grid points areclustered towards the burner surface and the centerline in order to capture the sharp gradients inthese regions. Specifically, the mesh is uniformly spaced with ∆r = 0.01 cm for 0 ≤ r ≤ 1.5 cm,with increasingly larger spacing for 1.5 < r ≤ 4.288 cm; it is also uniformly spaced with ∆z =0.03 cm for 0 ≤ z ≤ 5.1 cm, with increasingly larger spacing for 5.1 < z ≤ 12.2 cm.

The governing equations and boundary conditions were then discretized on this tensor productgrid via standard nine-point finite difference stencils, which are second-order accurate in the re-gions of the grid that are equispaced and are between first- and second-order accurate elsewhere.The resulting set of fully coupled, highly nonlinear equations is then solved simultaneously at allgrid points using a damped modified Newton’s method [27, 28] with a nested Bi-CGSTAB linearalgebra solver [29]. To aid in convergence of Newton’s method, pseudo-transient continuation isperformed until the adaptively chosen pseudo-time step exceeds a cut-off value, after which thesteady-state equations are finally solved to a Newton tolerance of 10−5. The first flame to be mod-eled is a 65% CH4 flame under normal gravity, because it was studied in our previous investigations(e.g., [2, 3, 24]). The converged solution of this flame is then employed in a continuation techniquewhereby the inlet conditions and the gravitational acceleration are slowly changed. After eachincremental change in the flame parameters, the governing equations and boundary conditions arere-solved, ultimately producing converged solutions for the flames at microgravity and/or havingdifferent N2 dilution levels. All calculations were performed on workstations with 3.0-GHz IntelXeon E5472 processors, and the typical memory usage for a computation on the 186× 206 grid is

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8th US Combustion Meeting – Paper # 070LT-0256 Topic: Laminar Flames

Figure 2: Flame front shape comparison of the 40% CH4 flame (left: 1g; right: 0g). Computationally, flame frontshape is represented by the CH profile; experimentally, flame front shape is determined from Abel-inverted digitalflame images.

around 4.7 GB of RAM.

4 Experimental approach

The measurement of soot temperature used a ratio pyrometry approach, for which detailed in-formation can be found in [8, 30]. A digital single lens reflex camera (Nikon D300s)1 was fullycharacterized as a pyrometer for soot temperature measurement. The soot volume fraction wasobtained after determining temperature and performing an absolute light intensity calibration. Asmall S-type thermocouple with a cylindrical junction was placed above the flame. The incandes-cence of the flame-heated thermocouple with a known emissivity model and temperature was usedas the calibration source [31].

5 Preliminary results and discussion

Figure 2 shows the flame shape of the 40% CH4 flame under both normal gravity and micrograv-ity conditions. Because the spatial locations of CH and CH∗ have been shown to coexist [2] andare reasonable markers of the flame front region [32], the computed CH concentration profilesand the Abel-inverted digital flame images are given in Fig. 2. Since CH cannot be directly com-pared to the Abel-inverted digital flame image, the absolute magnitudes of the contours are not

1The product references are for clarification only and do not indicate an endorsement on the part of NASA or thefederal government.

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8th US Combustion Meeting – Paper # 070LT-0256 Topic: Laminar Flames

Figure 3: Temperature profiles of the 100% CH4 flame (left: 1g; right: 0g). Computationally, the maximum temper-atures are 2005 K (1g) and 2003 K (0g). Experimentally, the maximum temperatures are 1977 K (1g) and 1991 K (0g).

shown. For the 40% CH4 flame under normal gravity, the agreement is very good in terms oflift-off height, flame length, and flame width. On the other hand, while the computational modelcan faithfully represent the influence of gravitational acceleration on flame structure, the computedlift-off height under microgravity is significantly higher than the experimental measurement. Hereit is worth mentioning that the T = 298 K boundary condition at z = 0 cm, which is physicallyaccurate only for flames with large lift-off heights, acts to repel the flame from the burner surfaceat higher pressures. In other words, if it were possible to evaluate the temperature profile at theburner surface experimentally for the 40% CH4 flame, then that temperature profile could be em-ployed in the boundary condition to get even better computational/experimental agreement undermicrogravity conditions.

Figure 3 presents a comparison between the simulated temperature profile and the measured soottemperature of the 100% CH4 flame under both normal gravity and microgravity conditions. FromFig. 3, it can be seen that the agreement between the computed and measured temperature profilesis excellent in terms of maximum temperature and temperature distribution. Furthermore, theinfluences of buoyancy on temperature (i.e., the flame becomes wider as gravity is reduced) issuccessfully captured by the numerical model. Figure 4 compares the computed and measured sootvolume fractions of the 100% CH4 flame under both normal gravity and microgravity conditions.From Fig. 4, it can be observed that while the magnitudes of the predicted soot volume fractions areconsiderably lower than the corresponding experimental measurements, the shape and distributionof the soot volume fraction profile is successfully modeled. In addition, the numerical model iscapable of capturing the influence of reduced buoyancy (i.e., the maximum soot volume fraction

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8th US Combustion Meeting – Paper # 070LT-0256 Topic: Laminar Flames

Figure 4: Soot volume fraction profiles of the 100% CH4 flame (left: 1g; right: 0g). Computationally, the maximumsoot volume fractions are 1.35×10−7 (1g) and 1.77×10−7 (0g). Experimentally, the maximum soot volume fractionsare 5.14× 10−7 (1g) and 3.28× 10−6 (0g).

increases and moves from centerline to flame wing).

Table 2 summarizes the effects of fuel stream dilution and gravity on the structure (i.e., flameradius and flame length), stabilization (i.e., lift-off height, if applicable), temperature, and sootvolume fraction of coflow laminar methane-air diffusion flames. From Table 2, it is observed thatfor flames under both normal gravity and microgravity conditions, an increase in fuel stream CH4

concentration can expand the flame by increasing its width and length, improve its stability throughshifting the flame front towards the fuel tube, increase its maximum temperature, and intensify itssoot loading. On the other hand, it can be seen from Table 2 that changing gravity also has asignificant impact on laminar diffusion flames. Specifically, reducing gravitational accelerationwill eliminate buoyancy-induced entrainment, which, as a consequence, will broaden the flameand move the flame front towards the burner. In addition, it is worth mentioning that gravity hasremarkable influences on the sooting behavior of laminar methane-air diffusion flames: eliminatinggravity will increase the soot volume fraction considerably and move the peak soot volume fractionarea from the inception-dominated centerline region to the surface-growth-dominated flame wings.

6 Conclusion

A combined computational/experimental investigation was conducted to characterize the influ-ences of gravity and fuel stream dilution on the structure, stabilization, and sooting behavior of

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8th US Combustion Meeting – Paper # 070LT-0256 Topic: Laminar Flames

Table 2: Influence of fuel stream dilution and gravitational acceleration on the structure, stabilization, and sootingtendency of laminar coflow CH4-air diffusion flames. The quantity G is the gravitational acceleration; rf is the flameradius, defined as the maximum r value along the CH contour; Lf is the flame length, defined as the z-coordinateof the point on the centerline with the highest temperature; HL is the lift-off height, defined as the vertical distancebetween the burner tube wall and the point with maximum CH concentration; Tmax is the maximum temperature; andfv,max is the maximum soot volume fraction.

Flame name G (g) rf (cm) Lf (cm) HL (cm) Tmax (K) fv,max

40% CH4/60% N2 1.0 0.3752 2.5019 0.5700 1844 n/a70% CH4/30% N2 1.0 0.4295 3.1951 0.2400 1956 4.50× 10−8

100% CH4/0% N2 1.0 0.4876 4.5244 0.1800 2005 1.35× 10−7

40% CH4/60% N2 0.0 0.4636 2.4894 0.3900 1845 n/a70% CH4/30% N2 0.0 0.5471 3.2949 0.2100 1954 7.44× 10−8

100% CH4/0% N2 0.0 0.6540 4.6836 0.1500 2003 1.77× 10−7

laminar diffusion flames. Specifically, CH4-air coflow laminar diffusion flames with three levelsof N2 dilution in the fuel stream (40%, 70%, and 100% CH4) were assessed under both normalgravity and microgravity conditions. While very good agreement between simulations and mea-surements was achieved for most flame quantities under investigation, further effort is required toimprove the accuracy of the computed flame front structure (for the 40% CH4 flame under micro-gravity) and the soot volume fractions (of the 100% CH4 flame).

7 Acknowledgments

This research was supported by NASA, the US Department of Energy Office of Basic Energy Sci-ences (Dr. Wade Sisk, contract monitor), the National Science Foundation (Dr. Phil Westmoreland,contract monitor), and the US Air Force Office of Scientific Research (Dr. Fariba Fahroo and Dr.Misoon Mah, contract monitors), under contracts NNX11AP43A, DE-FG02-88ER13966, CTS-0328296, AFOSR FA9550-06-1-0164, and AFOSR FA9550-09-1-0571, respectively. We are alsograteful to Dr. Donald R. Pettit for conducting the SLICE experiments on the International SpaceStation.

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