Computational and eof a forced, time-dependent, methaneair coow

an indication of the overall ame shape. Computationally, we solve the transient equations for the conser-vation of total mass, momentum, energy, and species mass with detailed transport and nite rate chemistry

study hydrocarbon ame structure, soot forma-tion and NOx production. As the level of chemis-try increases in complexity in these systems, theyare almost always studied under steady, laminar

1540-7489/$ - see front matter 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.doi:10.1016/j.proci.2006.08.109

* Corresponding author. Fax: +1 203 432 6775.E-mail address: mitchell.smooke@yale.edu (M.D.

Smooke).

Proceedings of the Combustion Instit

Proceedingsof the

CombustionInstitutesubmodels. The governing equations are written using a modied vorticityvelocity formulation and aresolved on an adaptively rened grid using implicit time stepping and Newtons method nested with aBi-CGSTAB iterative linear system solver. Results of the study include an investigation of the start-up fea-tures of the time-dependent ames and the time it takes for initial transients to dissipate. We include adetailed description of the uid dynamic-thermochemical structure of the ame at a 20 Hz forcing frequen-cy for both 30% and 50% sinusoidal velocity perturbations. Comparisons of experimentally determinedand calculated temperature, CO and H2O mole fraction proles provide verication of the accuracy ofthe model. 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Diusion ame; Time-varying; Computation; Diagnostics

1. Introduction

Multidimensional ames have been used todiusion ame

S.B. Dworkin a, B.C. Connelly a, A.M. Schaer a, B.A.V. Bennett a,M.B. Long a, M.D. Smooke a,*, M.P. Puccio b, B. McAndrews b,

J.H. Miller b

a Department of Mechanical Engineering, Yale University, New Haven, CT 06520-8284, USAb Department of Chemistry, George Washington University, Washington, D.C. 20052, USA

Abstract

Forced, time-varying ames are laminar systems that help bridge the gap between laminar and turbulentcombustion. In this study, we investigate computationally and experimentally the structure of a periodical-ly forced, axisymmetric laminar methaneair diusion ame in which a cylindrical fuel jet is surrounded bya coowing oxidizer jet. The ame is forced by imposing a sinusoidal modulation on the steady fuel owrate. Rayleigh and spontaneous Raman scattering are used to generate the temperature and major speciesproles. Particle image velocimetry is used to determine the magnitude of the velocity at the exit of theburner and the phase of the forcing modulation. CH* ame emission measurements are used to providexperimental study

ute 31 (2007) 971978

www.elsevier.com/locate/proci

cussed. Results and conclusions are presented inthe last two sections.

2. Experimental procedure

2.1. Burner conguration

Atmospheric pressure, axisymmetric, coow-ing, nonpremixed laminar ames are generatedwith a burner in which the fuel ows from aninner tube of radius RI = 0.2 cm (wall thickness0.038 cm) into a concentric, 3.7 cm radius oxidizercoow (see Fig. 1). A speaker in the plenum of thefuel jet allows a periodic perturbation to beimposed on the exit parabolic velocity prole.Measurements were made both at Yale andGeorge Washington University. To facilitate mea-surements at dierent laboratories on multiplecopies of the same burner, it has been designedusing computer-aided-design software that isassociated with an online machine shop. By sub-mitting the CAD les, which are being made free-ly available, copies of the burner can be obtainedeasily.

The fuel contains a mixture of 65% methaneand 35% nitrogen, by volume. The addition of

Fig. 1. CAD drawing of the forced-ow burner used inthese experiments. Perforated plates in the coow

972 S.B. Dworkin et al. / Proceedings of the Combustion Institute 31 (2007) 971978ow conditions (see, e.g., [1]). However, practicalcombustion devices frequently operate underunsteady conditions and the ow eld is often tur-bulent. To be able to model more realistic com-bustion congurations, time-varying ow eldsneed to be incorporated into detailed chemistrystudies. Depending upon the magnitude of thevelocity eld variation, time-varying laminar dif-fusion ames form a class of non-premixed com-bustion problems that bridge the gap betweensteady laminar combustion and turbulent com-bustion. They oer a much wider range of interac-tions between the chemistry and the ow eldthan can be examined under steady-state condi-tions. The complex coupling between chemistryand uid ow in time-varying laminar ameseectively samples dierent regimes of tempera-ture, mixture fraction, residence time, strain, andscalar dissipation rates than are observed understeady conditions.

In forced time-varying ames, a periodic uc-tuation in time is imposed on the fuel ow rateof a steady laminar ame. The study of theseames helps in understanding the interactionsbetween uid transport and heat and mass trans-fer in practical combustion systems. Fundamentalstudies of these interactions, including detailedcombustion chemistry, are critical to an under-standing of pollutant formation processes and tothe modeling of turbulent diusion amesthrough the concept of laminar amelets. A num-ber of investigators have studied forced, time-varying laminar diusion ames [218]. Theseinvestigations have been experimental [210],computational [1113,18] or have combined bothexperimental and numerical techniques in theirapproach [1417].

In this paper, we investigate computationallyand experimentally the structure of a forced,time-varying, axisymmetric, coow, laminar,methaneair diusion ame. Computationally,we employ a modied vorticityvelocity formula-tion to solve the transient equations for the con-servation of mass, momentum, energy, andchemical species. Experimentally, Rayleigh andRaman scattering are used to obtain two-dimen-sional elds of temperature, and of mole frac-tions of N2, CO2, CH4, H2, O2, CO, and H2O.Measurements of excited-state CH (CH*) emis-sion are used to determine overall ame shapeduring the initial cycles after the forcing is initi-ated. Particle image velocimetry (PIV) is usedto determine the fuel tube exit velocity and phaseover a cycle of the forcing modulation. We com-pare the dierent numerical and experimentalspatial proles of temperature and species con-centrations at dierent times in the forcing cycleand we investigate the impact of start-up tran-sients. In the next section, the experimental pro-cedure is described. The problem is thenformulated and the computational method is dis-plenum provide additional ow straightening, but areomitted for clarity.nitrogen produces a steady ame with negligiblesoot. With increasing levels of forcing, the amountof soot in the ame increases [38]. An averageexit velocity of 35 cm/s is used for both the fuel(parabolic velocity prole) and the oxidizer (plugow). The ame is lifted approximately 0.6 cmabove the burner surface, preventing heat transfer

All thermodynamic, chemical, and transport

S.B. Dworkin et al. / Proceedings of the Combustion Institute 31 (2007) 971978 973from the ame to the burner. As a result, roomtemperature can be used as the boundary condi-tion for the numerical calculations.

2.2. Optical diagnostic measurements

Two-dimensional proles of temperature andmole fractions of N2, CO2, CH4, H2, O2, CO,and H2O were determined at dierent phases ofthe forced ames from vibrational Raman scatter-ing and Rayleigh scattering. Details of theRaman/Rayleigh measurements are similar tothose presented by McEnally et al. [19], and willbe outlined briey below. A frequency doubledNd:YAG laser (532 nm) was focused into a line(300 lm beam waist) over the center of the burner.To prevent breakdown of the gases at the laserfocus, the Q-switch was double-pulsed duringeach ashlamp pulse (100 ls pulse separation,150 mJ/pulse). The scattered light was imagedonto the entrance of a 0.27 m spectrograph, andthe resulting spatial/spectral images were recordedwith an image-intensied CCD detector. Thespectral coverage of the images allowed the mea-surement of the Rayleigh scattering as well asthe Stokes-shifted vibrational Raman intensitiesfrom all major species. Images from 1200 laserpulses were phase-averaged with respect to theburner forcing to improve signal/noise. Toaccount for the eects of broadband uorescenceinterference on the Raman signals, data wererecorded with polarizations parallel to and per-pendicular to the laser polarization. Subtractingthe cross polarized images (which contained pri-marily uorescence interference) from those withparallel polarization eectively reduced the uo-rescence contribution to shot-noise levels. Theresulting dierence image provided species molefractions and temperature along a single line inthe ame after processing that utilized spectralmodeling software and suitable calibration data.Two-dimensional images were formed by tilingtogether a series of line images. In the imagesshown, pixel volumes are 0.2 0.3 0.5 mm3 nearthe burner and 0.2 0.3 1 mm3 farther down-stream, where changes in the axial direction aresmaller.

The modulation of the fuel ow for the time-varying ame was calibrated using PIV for eachof the burners. The fuel ow was seeded withsugar particles using a TSI six jet atomizer. Twofrequency-doubled Nd:YAG lasers (300 ls pulseseparation) were focused into a sheet across theburner centerline. PIV images were recorded usinga fast interline transfer CCD camera. A cross-cor-relation algorithm was used to determine the cen-terline exit velocity as a function of the speakersforcing level. Forcing levels corresponding to30% and 50% modulation of the fuel ow wereinvestigated experimentally and computationally.The speaker was driven at 20 Hz.properties are evaluated using vectorized andhighly ecient libraries [26]. The divergence ofthe net radiative ux is calculated using an opti-cally thin radiation submodel with three radiatingspecies (H2O, CO, and CO2), the details of whichare found in [27,28].

Implementation of a vorticityvelocity formu-lation for time-dependent problems was anticipat-ed in [25] to cause convergence diculties for thelinear system solver since the Jacobian does nottend toward diagonal dominance for small timesteps. Therefore, the traditional approach ofshrinking the time step to aid convergence doesnot work. To maintain desired levels of discretiza-tion accuracy without employing extremely small(

accurately.

974 S.B. Dworkin et al. / Proceedings of the Combustion Institute 31 (2007) 971978The time-variation in the ame is produced byimposing a sinusoidal velocity uctuation on asteady ame, which has a parabolic axial velocityprole with an average velocity of 35 cm/s. Specif-ically, across the fuel jet, axial velocityvz 70:01 r2=R2I 1 a sinxt cm/s, where ais the velocity amplitude factor and x is the fre-quency of oscillation. Experiments and computa-tions were performed for velocity perturbationsof 30% and 50% of the steady parabolic fuel veloc-ity. Numerical and experimental sinusoidal veloc-ity proles agree to within 10% of each other overa given cycle. The velocity across the oxidizer jet is35 cm/s except for a thin boundary layer at thewall. Boundary conditions along the centerline(r = 0) are such that radial velocity vr and radialgradients of all the other unknowns vanish. Atthe outer boundary r = Rmax, the radial gradientstemporal discretizations (and the fully implicitnature of Newtons method) allow the use of larg-er time steps (between 106 and 104 s), but thenumber of time steps required to cover a timeinterval of interest is signicantly smaller. Also,unlike a primitive variable approach, the purelyelliptic nature of the governing equations removesany need for pseudo-time-stepping within eachreal-time step, resulting in a further speedup.The set of coupled, nonlinear, partial dierentialequations is discretized using nite dierencesand solved using a damped, modied Newtonsmethod [29]. At each adaptively chosen timestep[30] the linear Newton equations are solved usingBi-CGSTAB [31] with a block Gauss-Seidel pre-conditioner. Calculations were performed on a2.0 GHz AMD Opteron processor with 5 GBRAM.

4. Results and discussion

In this section, we discuss the experimental andcomputational results for a forced, time-varying,axisymmetric, unconned, methaneair diusioname. While we have utilized a C2 reaction setin prior work [16], the quantities in which we areinterested in this paper can be predicted well withonly C1 chemistry (16 species and 46 reversiblereactions [32]). We point out, however, that asone moves towards comparisons of computation-al and experimental soot volume fractions, thelevel of chemical complexity (and the CPU time)will increase dramatically. The computationaldomain covers a region from r = 0 toRmax = 7.5 cm in the radial direction and z = 0to z = 40 cm in the axial direction. The dimen-sions of the domain are set to values much largerthan the radius of the coowing oxidizer jet, RO,and the steady ame length, Lf, respectively, sothat the asymptotic approach of the solution pro-le to its free stream value can be predictedof vr and vz vanish, the temperature is 298 K, andthe mass fractions are specied as YO2 = 0.232,YN2 = 0.768,Yk = 0, k O2, N2. At the outowboundary, the axial gradients of the unknownsvanish. At the inow boundary z = 0, the radialvelocity vanishes and the temperature is 298 K.The mole fractions at the inlet are YCH4 = 0.65,YN2 = 0.35, Yk = 0, k CH4, N2. Across the fueltube, and the region where r > RO, vz vanishes.For RI < r < Rmax at the inlet, the mass fractionsare specied as YO2 = 0.232, YN2 = 0.768,Yk = 0, k O2, N2.

The computations were carried out on a non-uniform computational grid consisting of 137 by258 adaptively chosen points in the r and z direc-tions, respectively. The points are kept xed dur-ing the computation and were chosen to ensureresolution of the various high activity regions dur-ing a velocity cycle. The smallest spacing was0.005 cm in each direction.

In previous work [16], we were concernedabout the length of time necessary for the initialtransient features of the problem to die out so thatcomparisons could be made between the experi-ments and computations. Specically, in Fig. 2(top) we illustrate computational contours of thedierence between the computed CH3 eld in themidpoint of a cycle and the computed CH3 eldat the same point in the previous cycle. The exper-imental contours (bottom) illustrate the samequantities but for CH*. In both cases, the largestinitial transients disappear within several cycles.While the experimental transients are almosttotally gone by cycle four, the computationalresults indicate that some transient eects (whilesmall) are still observable after 10 cycles. The dif-ference in the speed with which these eects die ois partially related to the spatial extent and magni-tude of the two species being compared and to thenumerical renement used in the computations.Nevertheless, to explore this issue further, we havedened a correlation function CF(i) as a functionof the ames cycle number i

CFi PNpoints

n1 Varpi; n Varpi 1; nPNpoints

n1 Varp2; n Varp1; n; 1

where Varp = CH3 mole fraction for the computa-tions and Varp = CH* mole fraction for the exper-iments. The function is normalized by the sum ofthe dierences in Varp for the second cycle so thateach data set decays from an initial value of 1.0.As illustrated in Fig. 3, the two experimental datasets decay smoothly to values representative ofnoise, whereas the two numerical data sets decayinitially and then uctuate until cycle 9 for boththe 30% and 50% modulations. We anticipate thatthese oscillations will decrease as the number ofcycles increases. However, based upon these re-sults, we will make comparisons using the compu-tational data in cycle 10.

In Fig. 4, we plot the computed temperatureisotherms over a large axial portion of the domainfor the steady methane ame along with both the30% and 50% modulations at the midpoint of avelocity cycle. While the structure of the twoames are similar in the lower two centimetres

Fig. 2. Computational (top) and experimental (bottom)Each computational panel illustrates the dierence beexperimental panels illustrate the dierence between tw

Fig. 3. Correlation function CF(i) versus cycle number

S.B. Dworkin et al. / Proceedings of the Combustion Institute 31 (2007) 971978 975compatweeno conse

.of the domain, the enhanced modulation producesa more pronounced pinching of the tempera-ture prole as one moves higher up in the ame.As we move downstream the eects of the velocityoscillation begin to dampen. Computed and mea-sured isotherms for the 30% modulated ame at10 ms intervals of the 50 ms cycle are illustratedin Fig. 5. Due to the transient eects observed inFigs. 2 and 3, we have shifted the computationalisotherm a few milliseconds compared to theexperimental results to line up the features moreeasily. Frames (b) and (c) have been truncateddue to the fact that some soot was formed in theregion beyond 3.5 cm downstream during thispart of the oscillation, causing interference withthe Raman and Rayleigh measurements.

The ame lift-o height, dened as the smallestz value for which the temperature is greater than1000 K, was approximately 0.685 cm. In all theframes, the lift-o height remains essentially thesame (varying by less than 0.4 mm). However,the ame heights dened by the location of themaximum temperature at the centerline are4.25 cm in Fig. 5a (7.5 ms), 2.75 cm in Fig. 5b

rison of the start-up transients in the forced ow burner.two consecutive cycles of the CH3 mole fraction. Thecutive cycles of CH*.

(17.5 ms), 2.875 cm in Fig. 5c (27.5 ms), 3.5 cm inFig. 5d (37.5 ms), and 4.0 cm in Fig. 5e (47.5 ms)compared to 3.5 cm for the steady-state case. The

aximum temperature during a ame cycle variedetween 1963 and 1968 K.The transient behavior is very dierent from

hat we would expect to see in the steady-statease with similar mass ow rates of the fuel. Inhe steady-state case, the low temperature regionbove the burner along the axis of symmetrycreases and the overall length of the ame getsnger as the fuel mass ow rate is increased.he low temperature core above the burner ismallest for the case of the maximum velocity ofhe fuel. This behavior can be explained by theact that, during the time required for the eectf the uid parcel at the inlet to convect to theame height, the fuel velocity goes to a minimum.his low temperature region keeps increasing inngth even though the velocity keeps decreasing.verall, the spatial features of the temperatureeld agree qualitatively between the computationsnd the experiments.Proles for the CO and CO2 mole fractions are

lustrated in Figs. 6 and 7. The panels are at theame time intervals as in Fig. 5. The CO concen-ration in time-varying laminar ames has beenvestigated previously [6,10]. In methane amesoped with butane or butene so as to increaseheir sooting characteristics, it has been reportedhat increased amounts of soot in a ickeringame result in larger concentrations of CO as well

Fig. 5. Computational (ae) and experimental (fj)isotherms shown at 10 ms intervals for the 30% modu-lation ame. Panels b, c, g, and h between 3.5 and 5.0 cmare not shown as these regions exhibit the highest level ofparticulate interference in Rayleigh imaging.

ig. 4. Computed temperature isotherms for the steadynd 30% and 50% modulations in the forced methaneir ame.

976 S.B. Dworkin et al. / Proceedings of the Combustion Institute 31 (2007) 971978Faaas depletion of OH radicals. Although the 30%ame has minimal soot, we note that there is a15% increase in the peak CO mole fraction on

Fig. 6. Computational (ae) and experimental (fj)isopleths for CO mole fraction shown at 10 ms intervalsfor the 30% modulation ame. Panels b, c, g, and hbetween 3.5 and 5.0 cm are not shown as these regionsexhibit the highest level of particulate interference inRayleigh imaging.mb

wctainloTstfoTleOa

ilstindtt

oxidation whose products include CO [33remains uncertain. Future measurements and cal-culations are planned to study in detail aromaticoxidation chemistry in this ame region.

The oxidation of CO to CO2 proceeds primar-ily via the reaction CO + OH CO2 + H. Therate of CO oxidation depends on the availabilityof OH radicals. However, the presence of mosthydrocarbon species inhibits the oxidation ofCO. This can be attributed to the fact that the rateof the reaction H + O2 OH + O, is consider-ably smaller than the reaction rates of H atomswith hydrocarbon species and the rate of the COoxidation reaction is also smaller than the reac-tion rates of hydrocarbon species with OH. As aresult, small quantities of hydrocarbons can eec-tively restrict the oxidation of CO to CO2Although carbon monoxide and hydrogen arefound during the oxidation of the hydrocarbonspecies, it is not until after the hydrocarbonsand the hydrocarbon fragments have been con-sumed that the OH level rises and CO2 is formedThis pattern is maintained throughout a amecycle, i.e., in the axial direction the OH radicapool increases after the disappearance of themethane and the formation of CO. The CO is thenoxidized to form CO2 downstream of the regionsof high CH3, CH2O, and CO concentrations.

dation (Dr. Linda Blevins, contract monitor) forsupport of this work under Grants CTS-0328296

Combust. Theor. Model. 8 (3) (2004) 593606.[2] K.C. Smyth, J.E. Harrington, E.L. Johnson, W.M.

S.B. Dworkin et al. / Proceedings of the Combustion Institute 31 (2007) 971978 977]

.

.

lthe centerline during the course of a cycle.Whether this increase is due to stretch/straineects in the chemistry/uid coupling or sootand polynuclear aromatic hydrocarbon (PAH)

Fig. 7. Computational (ae) and experimental (fj)isopleths for CO2 mole fraction shown at 10 ms intervalsfor the 30% modulation ame. Panels b, c, g, and hbetween 3.5 and 5.0 cm are not shown as these regionsexhibit the highest level of particulate interference inRayleigh imaging.Pitts, Combust. Flame 95 (1993) 229239.[3] C.R. Shaddix, K.C. Smyth, Combust. Flame 99

(1994) 723732.[4] C.R. Shaddix, K.C. Smyth, Combust. Flame 100

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Combust. Inst. 26 (1996) 11611169.[7] K.C. Smyth, C.R. Shaddix, D.A. Everest, Combust.

Flame 111 (1997) 185207.[8] C.R. Shaddix, T.C. Williams, L.G. Blevins, R.W.

Schefer, Proc. Combust. Inst. 30 (2005) 15011508.[9] O.A. Ezekoye, K.M. Martin, F. Bisetti, Proc.

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W.Y. Crutcheld, W.A. Fiveland, et al. Western(Yale) and CTS-0330230 (GWU). In addition,the authors (M.D.S. and M.B.L.) would like toacknowledge support from the DOE Oce of Ba-sic Energy Sciences (Dr. Frank Tully, contractmonitor) under contract DE-FG02-88ER13966.

References

[1] M.D. Smooke, C.S. McEnally, J. Fielding, et al.,5. Conclusions

We have presented a combined experimentaland numerical solution of a forced, time-varying,axisymmetric laminar diusion ame. Raman andRayleigh scattering were used to provide acomplete series of temperature and major speciesmeasurements at 30% and 50% forcing levels forve dierent phases relative to the forcing. Particleimage velocimetrywas done tomeasure the velocityat the exit of the burner and to determine themagnitude and phase of the forcing modulation.Computationally, a fully transient model ofmethaneair combustion was applied to a amewith a pulsation frequency of 20 Hz. The overallstructures of the temperature and major speciesproles predicted by the computationswere in goodqualitative agreement with the experimentalmeasurements. Further investigation is needed intothe eects of themagnitude and the frequencyof thevelocity perturbations on the ame structure.

Acknowledgments

The authors thank the National Science Foun-

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978 S.B. Dworkin et al. / Proceedings of the Combustion Institute 31 (2007) 971978

Computational and experimental study of a forced, time-dependent, methane-air coflow diffusion flameIntroductionExperimental procedureBurner configurationOptical diagnostic measurements

Problem formulation and numerical solutionResults and discussionConclusionsAcknowledgmentsReferences