Imaging a conserved scalar in gas mixing by means of alinear spark
Robert W. Schmieder and Alan Kerstein
A straight filamentary spark produced by a laser has been used to image the spatial distribution of gases ina jet of methane in air. The technique provides a direct map of a conserved scalar quantity useful in mod-eling turbulent reacting flows and may have other experimental advantages.
1. Introduction
The statistical properties and detailed structure ofturbulent gas mixing are of increasing interest to com-bustion, principally due to the development of newtheoretical methods and computer codes for includingchemical reactions in fluid-dynamic models. Onefruitful approach' has been to parametrize the reactingflow by two scalars, one (Q) representing the mass frac-tion of the chemical elements (H,C,N, . . .) comprisingthe fuel gas, the other (0) describing the progress of thereactions that convert the mixture to stable products.The scalar t can assume any value between 0 (pure ox-idizer) and 1 (pure fuel), and will vary with position inthe flow. However, for a given packet of fluid, t is in-dependent of time, hence its reference as a conservedscalar. This is true because the relative atomic abun-dances in the packet are not altered by the chemicaltransformations (neglecting selective diffusion). Onthe other hand, the parameter 0 varies with both posi-tion in the flow and time, since the mixture progressesfrom fully unreacted ( = 0) to fully reacted ( = 1).Thus, 0 is not a conserved scalar. Xi (sometimes calledthe mixture fraction) obeys the diffusion equation fora chemically inert species. Theta is closely related tothe gas temperature and obeys the same diffusionequation as I, but with an additional source term thatrepresents the heat released by the reactions.
Clearly, critical tests of model calculations requireexperimental measurements of the scalars t and 0 overa suitable spatial region. Pseudopoint measurements
The authors are with Sandia National Laboratories, Livermore,California 94550; R. W. Schmieder is in Combustion Physics Divisionand Alan Kerstein is in Energy Systems Studies Division.
of the reduced temperature 0 normally are obtainedwith a thermocouple and, less easily, by laser-opticaltechniques such as Rayleigh and Raman scattering.2Flowfield images usually are obtained by shadowgraphor schlieren photography3, but these do not representthe conserved scalar t. One method of measuring isto seed the fuel with relatively inert particulates suchas TiO2 and measure their probability density functionby laser light scattering.4
In this paper we report a demonstration that a laserspark can be used to image mixing patterns of differentgases. This technique is potentially advantageous be-cause the images are direct spatial maps of the con-served scalar t.
II. Experimental
Figure 1 shows a diagram of the experimental appa-ratus. A jet of methane (CH4) issuing from a flat-endedpipe of 0.05-cm (inside) diam was oriented vertically inlaboratory air. Pulses from a CO2 laser (wavelength10.6 gum, energy 0.08 J, duration 1 ysec, beam diam 0.5cm) were focused with a ZnSe lens of 15-cm focal lengthon the tip of a stainless steel needle point projecting intothe jet from the side. Breakdown was initiated at thepoint and propagated backward toward the laser at aroughly constant velocity in the range (0.5-2) X 106cm/sec. In appropriate conditions, a linear filamentaryspark 1 cm long and 150 pum in diam was produced. Thejet could be positioned so that the spark probed anydesired line in the flow.
The spark was photographed on 35-mm color film(Ektachrome, ASA 64) at 1oX magnification. Figures2-5 are prints of some of these transparencies at anadditional magnification.
Color film provides a rough spectral analysis of thespark emission, which is the basis of this technique.However, for some purposes, panchromatic film(Pan-X, ASA 25 or Plus-X, ASA 80) was useful for ob-taining higher contrast images of spark structures (Fig.
5). These photographs are time-integrated, since theduration of the luminous spark (-1 /usec) is much lessthan the shutter speed (-1 sec). The striated appear-ance of these sparks 5 is due to the pulse-train output ofthe laser and is not significant to this work. Actuallythe striations are produced successively, 7.8 nsec apart:and hence provide a convenient time reference, al-though a more uniform spark would have given a betterimage of the mixing.
Ill. Sparks in Jets
Figure 2(a) shows a spark in pure (laboratory) air. Itsblue color is characteristic of air for these sparks.Figure 2(b) shows a similar spark, 1 cm above the endof the pipe, this time with CH4 flowing slowly (1.6cm3 /sec, corresponding to a nozzle velocity of 8 m/secor a Reynolds number of 135). The red color is dueprincipally to hydrogen and therefore is characteristicof the fuel. Note the gradual transition from CH4 onthe left to air on the right over distance of about tenstriations, -0.05 cm (the striations are 50 um apart inair).
The width W of the transition region can be esti-mated assuming molecular diffusion to be the dominanttransport mechanism. The diffusion time t from for-mation of the methane-air interface at the nozzle toobservation of the interface at the spark is approxi-mately 10-3 sec. Assuming a diffusion constant D =0.2 cm2 /sec gives an e-folding distance for methaneconcentration W = J t = 0.4 cm consistent with thespatial variation of methane concentration indicatedin Fig. 2(b).
Figure 2(c) shows a spark in the same conditions asFig. 1(b) except that flow rate was increased to -20cm3/sec, giving a nozzle velocity of 102 m/sec orReynolds number -103. Note the abrupt transitionfrom CH4 to air along a diagonal at -45°. This couldonly occur if, at the moment the spark occurred, therewas a relatively sharp interface between two fluid ele-ments, possibly caused by a turbulent cell or vortex.The photograph indicates that the interface is <50 ,Imwide.
A lower bound on the relative velocity of fluid ele-ments on either side of the interface can be inferredfrom the image. Estimating the e-folding distance Wfor methane concentration to be <50 Aim and again as-suming a molecular diffusion constant D = 0.2 cm2/sec,the elapsed time from the formation of the methane-airinterface is bounded by t < W2 /(2D) = 6 X 10-5 sec.The relatively sharp transition is observed along aninterface at least 0.2 cm in extent. Therefore, the rel-ative velocity of the fluid elements that formed the in-terface is at least (0.2 cm)/(6 X 10-5 sec) = 3 m/sec, aplausible result since the mean flow velocity for thisconfiguration was mucii greater than this value.
These simple calculations indicate that the inter-pretation of these images as representations of mixingphenomena is consistent with basic fluid-dynamicprinciples.
Figure 3 shows three more sparks taken successivelyunder conditions similar to Fig. 2(c), except that the
laser pulse was slightly shorter. This makes the sparkshorter but otherwise has little effect. These photo-graphs show complex structures that indicate chaoticmixing. Again, features on the 50-jum scale are readilyvisible. The fact that the structures are almost totallyincoherent between different plates is evidence that realspatial distributions are being imaged.
IV. Sparks in Flames
Figure 4 shows the use of these sparks to probe aflame. The jet used in Fig. 2(b) was ignited and a flame3 cm high, measured from the end of the pipe to the tipof the yellow sooting tip, was stabilized. Fig. 4(a) showsa spark just above the yellow tip, which is visible belowthe spark slightly off-center. Figure 4(b) shows a sparkpenetrating the visible flame front. In both photo-graphs the film was exposed to the flame for -30 sec atfill while the spark lasted about 1 Asec.
There is no evidence of turbulent structure in Figs.4(a) or (b), consistent with the fact that the jet is lami-nar. The spark shows no significant abrupt changeacross the flame front giving additional evidence thatthe image is not dependent on molecular reactions.The pink halo around the core of the spark appearslarger in CH4 than in air, undoubtedly due to the fluo-rescence of CH4 excited by UV photons from the spark.Detailed study of the spectra obtained with a 1-mspectrograph has shown that emission from the sparkcore is exclusively that of atoms and ions with negligiblemolecular components.
There is a certain dependence of the spark structureon the composition. Figure 5 shows panchromaticphotographs of sparks very near the end of the pipe.Figure 5(a) shows a spark in air similar to Fig. 2(a), andFig. 5(b) shows the effect of the high velocity CH4 jet[conditions as in Fig. 2(c)]. Figure 5(c) shows additionalmodifications present when the low velocity jet is ig-nited, comparable to Fig. 4(b). The widely spacedhigh-contrast striations seem to be characteristic ofsparks in hydrogen-containing gases near 1 atm. Atpressures near 100 torr, air sparks have a similar ap-pearance. These photographs serve as a warning thatthe sparks may appear to depend on chemical reactions.However, the lack of any significant change in the sparkon the scale of the flame front shows that the differencebetween Figs. 5(b) and (c) is related to atomic compo-sition and density, not temperature. In other words,properly interpreted, even complex images such as Fig.5(c) give information primarily about the conservedscalar t.
It was not possible to stabilize a turbulent diffusionflame with the present apparatus, and no image ofturbulent structure in a reacting flow was obtained thatwould be comparable to Figs. 2-5. However, the evi-dence given in these images indicates that the sparkemission technique will be applicable to that case aswell: the images represent the true distributions [Figs.2(a), (b), and 3]; turbulent structures can be observedwith good spatial resolution [Fig. 2(c)]; and the imagesare not significantly altered by chemical decomposition[Figs. 4(b) and 5].
01 HFig. 1. Diagram of the experiments. The numbers refer to the
numbers of subsequent figures.
(a)
- (b)~~F7
= == (~~~~~~~~c)
Fig. 2. Three sparks produced by a laser (incident from the right).(a) air; (b) low velocity CH4 jet issuing from a pipe below and to theleft of the photograph showing diffusive mixing of CH4 (red) and air(blue); (c) high velocity CH4 jet, showing the edge of a turbulent
mixing interface as the interface between CH 4 and air. (20X)
(a)
(a)
(b)
1 ~~~~~~~~~C
Fig. 3. Three more sparks in a CH 4 jet in air. Conditions weresimilar to Fig. 2(c) (see text). (20X)
(a)
(b)
(b)
Fig. 4. Sparks in a CH 4 /air flame. The flame was stabilized on thejet of Fig. 2(b). (a) just above the sooting tip of the flame; (b) across
the luminous flame front. (14X)
(c)
Fig. 5. Panchromatic images of the three sparks. (a) air; (b) highvelocity CH4 jet; (c) CH 4 flame. These photographs show thatstructural as well as spectral features of the spark are determined
The principal potential advantages of this sparktechnique over conventional techniques are:
(1) The image gives directly the atomic abundances,and thus the conserved scalar, without the need forseeding and independent of refractive-index gradi-ents.
(2) The extremely high brightness of the spark maymake it useful in difficult environments such as chemi-luminescent, sooting, or corrosive gases in which tracersor seed particles may be altered, degraded, or unob-servable.
(3) The filamentary spark is a quasiline, nonprojec-tive, essentially instantaneous probe.
There are some obvious disadvantages of the sparktechnique:
(1) Although photography of the spark is simple, itsproduction requires a pulsed laser and optics for pro-ducing the linear sparks.
(2) The spark is a destructive probe with relativelylow repetition rate. The gasdynamic effects of a sparkin and near a jet or flame have been investigated.6
(3) There are some gas movements while the sparkis still luminous, complicating the interpretation of themicrostructure of the image. For example, in Figs. 2-5,the feathery regions outside the core of the spark are duepartially to flow of the plasma at first laterally, thendiagonally.
(4) The spark probes only a small volume and cannotgive large scale images. However, it may be possible touse multiple simultaneous sparks or even produce asheet spark to image a larger volume of the gas.
Improvements in this technique would include: (1)more uniform sparks, and (2) better spectral contrast.For the former, preionization in the laser cavity, reduced
laser gain, increased pulse length, and long focal lengthlenses will be useful. For the latter, multiple cameraswith narrowband filters, a lensless spectrometer witha predispersing element, and false-color imaging den-sitometer processing of photographs would enhancecontrast. For least ambiguity it may be desirable toimage selected spectral lines of individual elements.The fully resolved spark emission spectral analysistechnique has been used to determine fuel/air ratios ina double concentric diffusion flame and to perform anelemental abundance analysis on a sample of shale oilvapor. In reasonably good conditions, the achievableprecision is probably near 10-4 for major species.
The able assistance of Jon Meeks in the laboratoryis gratefully acknowledged. Fruitful discussions ofthese data were held with B. R. Sanders, R. W. Dibble,and R. W. Bilger.
This work was supported by the U.S. Department ofEnergy, Basic Energy Sciences, Division of ChemicalPhysics.
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3. J. Laufer, Ann. Rev. Fluid Mech. 7, 307 (1975).4. I. M. Kennedy and J. H. Kent, Seventeenth Symposium on
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