Mixing enhancement in a lobed injector

Mixing enhancement in a lobed injectorL. L. Smith, A. J. Majamaki, I. T. Lam, O. Delabroy, A. R. Karagozian,a) F. E. Marble,and O. I. SmithMechanical and Aerospace Engineering Department, University of California,Los Angeles, California 90095-1597

~Received 1 July 1996; accepted 11 November 1996!

An experimental investigation of the non-reactive mixing processes associated with a lobed fuelinjector in a coflowing air stream is presented. The lobed fuel injector is a device which generatesstreamwise vorticity, producing high strain rates which can enhance the mixing of reactants whiledelaying ignition in a controlled manner. The lobed injectors examined in the present study consistof two corrugated plates between which a fuel surrogate, CO2, is injected into coflowing air.Acetone is seeded in the CO2 supply as a fuel marker. Comparison of two alternative lobed injectorgeometries is made with a straight fuel injector to determine net differences in mixing and strainfields due to streamwise vorticity generation. Planar laser-induced fluorescence~PLIF! of the seededacetone yields two-dimensional images of the scalar concentration field at various downstreamlocations, from which local mixing and scalar dissipation rates are computed. It is found that thelobed injector geometry can enhance molecular mixing and create a highly strained flowfield, andthat the strain rates generated by scalar energy dissipation can potentially delay ignition in a reactingflowfield. © 1997 American Institute of Physics.@S1070-6631~97!01003-9#

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INTRODUCTION

The enhancement of fuel-air mixing processes in cobustion systems can have substantial benefits with respecombustion or incineration completeness1 as well as NOx orother toxic emission reduction2–7 due to the reduced likeli-hood of the formation of stoichiometric diffusion flameRapid mixing associated with high fluid mechanical strarates can suppress the ignition of diffusion flames,8–10 in-stead forming premixed or partially premixed regions thcan be made locally lean. When strain rates relax, ignitthen occurs in a premixed mode, allowing a more compconsumption of the fuel species while reducing NO formtion via the well known Zeldovich or thermal mechanism2

NO formation can then be limited to the~normally less im-portant! ‘‘prompt’’ mechanism, suggesting the potential fosignificant NO emissions reduction.

The present study examines the flow and mixing pcesses associated with a fuel injector configuration whichthe potential for such enhanced fuel-air mixing. This cofiguration, the ‘‘lobed’’ injector, is designed to generate verapid initial mixing of reactants through streamwise vorticgeneration11 and associated high strain rates. A schemadiagram of the generic lobed injector is shown in Fig. 1. Tinjector consists of two initially flat, parallel plates whic‘‘grow’’ downstream into corrugated lobes as shown. Fueinjected from between the plates into an axially coflowiairstream. The oppositely oriented secondary flows whdevelop along the sides of each of the lobes roll up icounter-rotating vortical structures oriented in the streawise direction. The array of counter-rotating vortices strafluid interfaces, in this case, those separating fuel and a

The general principle of the lobed or louvered geomehas been applied to two-stream mixing in turbofan engi

a!Author to whom correspondence should be addressed: Phone:~310! 825-5653; Fax:~310! 206-4830; Electronic mail: [email protected]

Phys. Fluids 9 (3), March 1997 1070-6631/97/9(3)/667/12

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using a single corrugated plate or interface to mix initiaseparated fluids.12–21Skebeet al.18 report that the secondar~cross-stream! flow induced by the lobed mixer is generateinviscidly by the mixer shape. As a consequence the strewise circulation generated at each half of a lobe wavelenat the exit plane of the mixer may be predicted by inviscanalysis. This streamwise circulationG is shown to take theform18

G'C1Uh~ tana!, ~1!

whereC1 is a constant which is sensitive to the specific locorrugation geometry,U is the mass-averaged streamwivelocity,h is the peak-to-peak lobe height, anda is the lobehalf-angle~see Fig. 1!. Vortex strength predicted by equatio~1! is consistent with the experimental results in Ref. 18well as with those of McCormick and Bennett.17 Recent nu-merical simulations by O’Sullivanet al.21 in fact confirmthat the estimate in~1! for vortex strength can even be extended to cases where the flow has separated, for lobeanglesa as high as 25°.

Further experiments by Eckerleet al.16 demonstratestrong secondary velocities near the exit plane of a lomixer which evolve into a sheet of streamwise vorticity aeventually coalesce into distinct streamwise counter-rotavortices, with scales on the order of the mixer lobe widFurther downstream, turbulent breakdown of the streamwvortices occurs, the location of which is dependent onratio of axial velocities on either side of the mixer. Vortebreakdown is seen by Eckerleet al.16 to be the critical phe-nomenon that significantly enhances turbulent mixing duethe generation of smaller scale turbulence at breakdown.Yu et al.19 find that enhanced mixing can actually occur ustream of the region in which vortex breakdown occurs, dto the localized, rapid production of turbulent kinetic energSkebeet al.18 and Yu et al.19 further note that sinusoidallyshaped lobes tend to produce lower secondary flow veloc

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and to mix less efficiently than a geometry with parallel losidewalls due to the merger of sidewall boundary layersthe troughs of the former geometry. Flow instabilitiesplane wakes and shear layers have been studied for a lmixer type geometry with small lobe ramp angles (a,1°)and moderate Reynolds numbers;22,23an uncoupled development of streamwise and spanwise vorticity by the lobed tring edge is seen here. Axisymmetric lobed or corrugamixer geometries have also been investigated;24,25 these alsodemonstrate the propensity for streamwise vorticity genetion.

Combustion in a lobed mixer geometry, with roughequal regions of fuel and oxidizer initially separated bysingle lobed splitter plate, has also been studied.26–28Whenusing a lobed splitter plate, the flame spread angle is dothe flame spread angle of a flat splitter plate, indicatinghanced mixing and an increased rate of flame propagatio26

Mixing rate augmentation due to the addition of streamwvorticity was found to be less sensitive to the detrimeneffects of heat release than the mixing rate for a planar slayer configuration.28

FIG. 1. Schematic of the general lobed injector geometry.

668 Phys. Fluids, Vol. 9, No. 3, March 1997


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For combustor applications, the lobed injector~Fig. 1!reported in the present paper has several potential advanover the lobed mixer. In the lobed injector, fuel is injectdirectly into the region of highest strain rates and highstreamwise vorticity. As a consequence, all of the fuel begto be mixed with oxidizer within a rapidly strained flowfieldso that mixing may occur under conditions which delignition.8–10 Further, when a thin ‘‘strip’’ of fuel is sand-wiched between the oxidizer streams, ignition delay cancur at smaller strain rates than when fuel and oxidizer mat only one independent interface,29 hence ignition delay canbe easier to achieve in a lobed injector rather than a lomixer geometry. The lobed injector also has an advantover other types of fuel injection schemes in that enelosses and pressure drop are small, while mixing takes pover a comparatively short distance.15

The present study investigates mixing in a chemicanonreacting, isothermal flow downstream of two alternatlobed injector geometries, and compares mixing charactetics for each of these injectors with those for a straight~non-lobed! injector. The measured parameters of greatest intefor combustion applications are the scalar dissipation r~from which the local strain rate may be estimated! and mix-edness or unmixedness. These preliminary measuremwere made in nonreacting flow in order to remove the effeof chemical reaction and heat release when comparingnet effect of streamwise vorticity generation on mixing astrain rate. It has also been suggested30 that the local strainfield in a cold, non-reacting turbulent flow may be usedpredict local reactive flow quantities in an equivalent cobusting flow, irrespective of the extent of chemical equilirium in the reacting flowfield. Thus the present results habroader implications for the processes of mixing and ignitdelay in a reacting flowfield associated with the lobed fuinjector.

EXPERIMENTAL FACILITY AND METHODS

In the present experiments, three different fuel injecgeometries were each studied in a low speed wind tunwith a square test section having 9.5 cm sides, as shschematically in Fig. 2. A blower at the wind tunnel exdrew air through the wind tunnel at speeds between 1 and

FIG. 2. Schematic of the wind tunnel and experimental apparatus.

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m/s. The wind tunnel entrance contained a honeycombtion to straighten the flow, followed by a contraction sectiof 4:1 area ratio. Hot-wire measurements in the empty wtunnel~injector removed! confirmed that the velocity profilewas uniform in the test section and that turbulence levwere less than one percent of the free stream velocity, exwithin 1.2 cm of the wind tunnel walls. Quartz windowwere fitted in the two vertical side walls of the test sectiand at the downstream end of the wind tunnel~in a planeperpendicular to the bulk flow! for optical access. The windtunnel was attached to a traversing table to allow movemof the tunnel relative to a laser sheet passing through thewall windows ~see optics description below!.

Three different fuel injectors were studied in this wintunnel; exit plane geometries are shown schematically in3. The lobed injectors were constructed of aluminum usan electron discharge machining or EDM device. Lobedjector A was constructed of two plates which were planand parallel at the upstream edge and sinusoidally corrug~lobed! at the downstream edge. The plates were separby a small gap~on average, 0.071 cm at the downstream eplane! through which fuel surrogate flowed; the wall thicness at the exit was approximately 0.038 cm. It shouldnoted that, due to machining inaccuracies, the gap widthwall thickness of this injector did vary along the exit plalobes. Both thicknesses became more than twice the nomvalue at the peaks and troughs of the sine wave. The wlength l of the lobes was 1.905 cm, and the peak-to-peamplitude at the exit was 3.721 cm. The injector had filobes and spanned the width of the wind tunnel; it was 1cm in length~in the direction of flow!, so that the lobes grew

FIG. 3. Comparison of exit plane geometries for the three injectors exined in the present experiments.

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at a constant ramp half-anglea of approximately 7°.Lobed injector B had a wavelength of 3.175 cm, a pe

to-peak amplitude of 3.518 cm, a ramp half-angle of 6.6°slot width of 0.056 cm, and a wall thickness of approxmately 0.076 cm at the exit plane. Wall thickness and swidth were much more uniform along the lobes in injectorthan in injector A. In injector B, the three lobes were dsigned as rounded square waves with parallel side walls.different geometry and larger wavelength-to-amplitude rawere chosen in an attempt to reduce the boundary lathickness in the injector troughs and to examine this effon vortex roll-up and mixing effectiveness. Streamwise vtex strengthG for injectors A and B was estimated usinequation~1!, with coefficientsC152.4 for injector A andC154.0 for injector B, per the conclusions of Skebeet al.18

for alternative lobe geometries.Finally, injector C was a straight slot injector with th

same slot width as in injector B, but with a wall thickness0.127 cm at the exit plane. There was no aerodynamic loing for injector C, and hence the principal mechanismstreamwise vorticity generation was removed. We examithis configuration in an attempt to isolate the effects oflobes’ streamwise vorticity generation on mixing from theffects of spanwise vorticity generation when the upper alower air flow velocities were unequal and from the wakcaused by the finite thickness of the injector walls. Althouthe injector wall thicknesses differed on average betweenlobed geometries and the straight geometry, for the flow cditions studied, this difference had little effect on mixincharacteristics31 as compared with the effect of slot widthwhich was on average about the same among the three intors.

Carbon dioxide (CO2) was used in the present experments as a fuel surrogate because of its similarities to ppane fuel in terms of molecular weight and diffusivity. Awas passed above and below the injector. CO2 was suppliedto the injector by a rectangular pipe of the same dimensias the upstream edge of each injector. The pipe pasthrough the entrance and contraction sections of the wtunnel, and was fastened flush with the upstream surfacethe injector. This pipe separated the wind tunnel into thalves in the section between the contraction and the injeexit.

Each of the three injectors was tested for different setsoperating conditions. In flow set I, the axial velocities of athe streams (v f for fuel, vaa for the air flow above the injec-tor, andvab for the air flow below the injector! were matchedas closely as possible, although due to nonuniformities inlobed injector geometry, the fuel velocities were not pcisely matched with airflow, especially at the peaks atroughs in injector A. Flow set II involved matched air velocities but with a quantifiably higher fuel exit velocity. Thlast set of flow conditions, set III, consisted of mismatchupper and lower air velocities, with the fuel velocity setthe mean of the upper and lower air stream velocities. Thflow conditions, appropriate for each of the three injectoare summarized in Table I.

For the flow conditions outlined above, the momentuthicknesses above and below the lobe peaks~at the injection

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plane! were measured using a pitot probe. A summarymomentum thicknessesu for the range of bulk airflow con-ditions examined is shown in Table II. Velocity measurments were made from the top of the wind tunnel tobottom, vertically passing through the central peak of elobed injector. The lobed shape clearly thins the boundlayer above the upper plate at the lobe peak and thickensboundary layer below the lower plate at the lobe peak wcompared with values for the flat injector C. While the dferences inu for the lobed injectors A and B were not alarge as were expected, the differences may have beenficient to have had an effect on downstream mixing charteristics. The momentum thicknesses for the lobe side walso shown in Table II, indicated a consistently thinner siwall boundary layer thickness for injector B than for injectA, as would be expected from the design.

Scalar mixing was studied in the present experimeusing planar laser-induced fluorescence~PLIF! imaging ofacetone seeded in the CO2 supply as a tracer. Acetone waexcited with 308 nm laser light from a XeCl excimer lasepumping several lines in the acetoneA←X system, resultingin fluorescence proportional to the acetone concentratio32

The 300 mJ, 25 ns laser beam was formed into a 5 cmtallsheet, passing through the wind tunnel test section perdicular to the direction of bulk flow, with a sheet thickness600mm or less. By moving the laser sheet along the streawise axis of the tunnel, the evolution of the CO2 or ‘‘fuel’’concentration field driven by the developing vortices wvisualized. Nonresonant fluorescence of acetone occuover a broad spectrum from 350 to 650 nm, peaking at ab435 nm.

Acetone fluorescence was detected and imaged byintensified CCD camera located outside the wind tunndownstream end window. Long-pass optical filters weplaced in front of the imaging lens to prevent elasticascattered laser light from reaching the intensified CCD arrAcetone phosphorescence~200ms lifetime! was rejected by

TABLE I. Flow conditions used to study each injector.

Velocity range, m/s Velocity ratio range

Flow condition set v f vaa vab vab /vaa 2v f /(vaa1vab)

I 1–11.5 1–11.5 1–11.5 1 1II 9–13.5 4.5 4.5 1 2–3III vaa1vab

23–5 15–18 3–6 1



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gating the image intensifier on for a period of 500 ns. TCCD array contained 6103492 pixels, and the imaging lenand CCD array combination gave a pixel resolution of bethan 200mm.

To obtain quantitative measurements of acetone conctration, it was desirable to operate in the regime of linefluorescence. Lozanoet al.32 give the fluorescence lifetimefor acetone as 2.7 ns, and the absorption cross-sections for308 nm light as 1.6310220 cm2. This gives a saturation photon flux density ofNsat52.331019 photons/(cm22ns). Inthe present experiment the photon flux density was less1.231017 photons/(cm22ns), or more than 2 orders of magnitude smaller than the saturation photon flux density. Tfluorescence signal was therefore linear in acetone contration and linear in laser energy in the present experimeWhile the acetone concentrations introduced into the injtors were about 90 000 ppm, the average concentrationacetone downstream in the test section was well be90 000 ppm, and beam absorption was negligible.

All PLIF images of acetone~including calibration im-ages! were normalized by laser pulse energy to correctshot-to-shot variations in laser energy. The normalized Pimages of mixing were corrected for intensity nonuniformin the laser sheet and imaging optics and simultaneously cbrated for acetone concentration by dividing by the normized calibration image on a pixel-by-pixel basis. Pixel valuin the scalar concentration images varied between 0 anrepresenting the mass fractionY of CO2 at each pixel loca-tion.

These PLIF images were converted from CO2 mass frac-tion (Y) images to mixture fraction (j) images using therelation j5Y/Yf , whereYf represents the maximum CO2~‘‘fuel’’ ! mass fraction in the flowfield, at injection. Mixturfraction gradients“j were calculated from the pixel valueusing central differencing with a low-pass spatial filter. Tscalar dissipation rate9 x was then calculated ax52D“j•“j, whereD is the average mass diffusivity; inthe present experiments, gradients were calculated indimensions only, since instantaneous images were obtain relatively widely spaced two-dimensional planes at diffeent points in time. While this evaluation clearly does nproduce the complete value of scalar dissipation ratex, it isreasoned that the component ofx arising from the stream-wise or axial gradient inj should be roughly the samamong the three different injectors for the same flow contions. Hencecomparisonsof x among the three injector

TABLE II. Momentum thicknesses at exit plane for each injector.

Air speed~m/s! Momentum thicknessu ~cm!

Injector vaa5vab u above peak u below peak u left lobe u right lobe

A 4.7 0.0061 0.203 0.035 0.024A 11.5 0.0092 0.179 0.033 0.024B 4.9 0.011 0.198 0.024 0.018B 12.1 0.013 0.148 0.018 0.019C 4.4 0.081 0.095 – –C 11.4 0.072 0.132 – –

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Following descriptions in Refs. 9, 30, and 33, it is posible to relate the scalar dissipation ratex to strain ratee atstoichiometric contours in a reactive flow, assuming theterfaces between fuel and air to behave as locally steopposed flow diffusion flames. In a flowfield in which onmolecular mixing occurs at strained fluid interfaces, thelationship between strain rate and the dissipation rate ofconserved scalar takes the same form when applied atmaxima inx or ‘‘strained dissipation layer’’ contours. Thirelationship between strain ratee and scalar dissipation ratx at a dissipation layer contourjst is given by30

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As pointed out by Bish and Dahm,30 the values of the conserved scalar well above and below the mixing interfaj1 andj2 , can have a critical effect on the magnitude of tlocal strain rate experienced by the interface. This is escially important, yet is difficult to quantify, as dissipatiolayers are brought close together in a strain field as occuthe present situation. In the present study, an automatednique was used34 in which the dissipation layer contoursjstwere determined by searching for local maxima in the scgradient field; it was at these locations thatx was computed.j1 andj2 were then estimated locally by a curve fit to therror function solution.

The degree of molecular mixing within a flowfield mabe quantified using the concept of mixedness35,36 as well asthe concept of unmixedness.37,38 Both concepts quantifymixing in terms of the second moment of the scalar conctration field, enabling comparisons of the local scalar fieldbe made with the scalar field that would be present iffluids were completely mixed or completely unmixed. In tpresent analysis the concept of unmixedness is used to qtify molecular mixing processes; this is defined as followafter Dimotakis and Miller:38

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whereY0 andY1 are the minimum and maximum CO2 massfractions present within a given interrogation area, resptively, p(Y) is the probability density function of the masfraction, and the mean value of the mass fraction withinlocal interrogation area,Y, is given by

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It is noted that the unmixednessU approaches unity for thecase of completely non-molecularly mixed fluids, i.e., tsecond moment in the numerator of Eq.~3! approaches thedenominator, andU approaches zero for complete molecumixing of two fluids, i.e., a local mass fraction ofY every-where within the integration region.



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The degree of mixedness or unmixedness in a flowfiis sensitive to the integration area over which the secmoment is evaluated, as pointed out by Marble.35 For appli-cation of the present flowfield to combustion systems,globalmixing of all fuel and air present at each cross-sectof the wind tunnel is not the most useful information, sinignition is not dependent on complete mixing of fuel with afar above and below the injector. It is thelocal degree offuel-air mixing at strained stoichiometric interfaces that dtermines the local ‘‘equivalence ratio’’~fuel-air ratio com-pared with stoichiometric! that would be present when igntion occurs in a reacting case, from which reactant csumption rates and local NO concentrations, for exammay be estimated. As a consequence, in quantitatively cparing mixing characteristics among the three injectors,chose an integration area which included~at the injectionplane! only a single side of each of the lobes for injectorsand B, with equivalent areas of surrounding air; a stripinjector C of equal length and surrounding area was chofor comparison. Initial fluid interface lengths, areas of pu‘‘fuel,’’ areas of pure air, and total integration areas wealso kept constant among the three injectors. Hence compsons of unmixedness among the three injectors yieldedferences which arose mostly from secondary flows alonglobes and subsequent streamwise vorticity generationwhich were not due to increased interfacial length at injtion.

The integration area and location for the evaluationunmixedness were maintained as constants with downstrlocation. This is another difficulty with the concept of mixedness or unmixedness: As the integration area~laser sheetlocation! is moved downstream, new, entrained fluidcounted within the integration area, while some fluid orignally present at injection may have been lost from the ingration area. Yet as noted above, using the entire crsectional area of the wind tunnel~in which no fluid is gainedor lost! as the integration area would yield nonuseful mixiinformation from a combustion perspective.

RESULTS

Flow visualization by smoke from TiCl4 as well as ac-etone PLIF was performed in laminar flow with airstreavelocities of 1 m/s in order to examine flow path and vortrollup. Acetone PLIF images for the three-lobed injectorare shown in Fig. 4 for different downstream locatiowithin the mixing tunnel. For these and all test conditioshown, effective streamwise circulationG was estimated using equation~1!, with C152.4 for injector A andC154.0 forinjector B, as suggested in Ref. 18. Figure 4 shows thclose to the injector exit, CO2 remained concentrated withithe region of injection, while further downstream, KelvinHelmholtz vortical structures formed along the injector lobwhich eventually rolled up further downstream into larscale vortical structures, becoming concentrated near thejector inflection points. The vortical structures near theflection points appeared to draw injector fluid from the peaand troughs of the injector toward the center of the flowfieThe secondary, cross-stream velocities induced by the lo

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Instantaneous acetone PLIF images in Figs. 5, 6, anshow flow evolution at higher speed air streams for injectA, B, and C, respectively, again for flow condition I. As witthe low speed flow, CO2 remained concentrated within thregion of injection close to the exit plane, later experiencdistortion by small scale vortical structures along the injeclobes~Figs. 5 and 6!. Pairing and merger of these structurinto larger vortical structures were observed to occur dowstream, although evolution of the vortices into single larscale streamwise structures was not as obvious in thesstantaneous images of the turbulent flow as in the lamflow. Neither was any significant breakdown in the streawise vortical structures noted within 100 mm of injection fflow condition I. Lobed injector B did demonstrate the abity of the streamwise vortical structures to draw injector flufrom the peaks and troughs toward inflection points; this wnot observed in injector A, possibly due to the somewsmaller effective circulation for injectors of this type as was the injector’s larger gap width at the peaks and troug

Figures 8~a!–~c! and Figs. 9~a!–~c! show acetone PLIFimages at a specific downstream location~60 mm! for each

FIG. 4. PLIF images of the mixture fraction of CO2 for the 3-lobed injectorB under flow condition I with low speed air flow at 1 m/s and estimastreamwise circulationG'0.016 m2 / s. Images are shown at locations 240, 60, 80, and 100 mm downstream of injection.



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injector at flow conditions corresponding to case III~at highspeed! and case II~at moderate speed!, respectively. Theimages in Fig. 8 for mismatched upper and lower air speare similar to those for matched air speeds in Figs. 5–7for other air velocity ratios examined.39 Lobed injector B didappear to draw fluid from peaks and troughs toward injecinflection points more efficiently for this flow condition@Fig.

FIG. 5. PLIF images of the mixture fraction of CO2 for the 5-lobed injectorA under flow condition I with high speed air flow at 11.5 m/s and estimastreamwise circulationG'0.132 m2/s. Images are shown at locations 2040, 60, and 80 mm downstream of injection.

FIG. 6. PLIF images of the mixture fraction of CO2 for the 3-lobed injectorB under flow condition I with high speed air flow at 11.5 m/s and estimastreamwise circulationG'0.195 m2/s. Images are shown at locations 2040, 60, and 80 mm downstream of injection.

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8~b!# than for flow condition I with equal air flow rates~Fig.6!, despite a somewhat higher estimated streamwise cirction in case I. Since the effective air speed mismatch whigher at the injector troughs than at the peaks for caseone might expect a non-symmetric mixing of CO2 and airbetween peaks and troughs, but this did not appear to htaken place for either lobed injector to any significant degrThe images in Fig. 9 for a moderate air spe(vaa5vab54.5 m/s! and higher injectant velocity(v f /vaa52) in general are similar to PLIF images for othflow conditions, but there are a few important differencBecause the flow rate of CO2 injectant is higher than that oair, injectant in the peaks and troughs of the lobed injectpersisted much further downstream in case II flows thancases I or III. This is especially evident in Fig. 9~b! for lobedinjector B. The higher injectant flow rate also acts to increthe generation of vorticity oriented normal to the streamwdirection; this can also assist with fuel-air mixing.

Quantitative mixing and strain field data may be etracted from mixture fraction images such as those showFigs. 5–9. Figures 10~a!–~d! show the downstream evolutioof unmixednessU for several different cases of matched aunmatched air and fuel flow rates. As noted above, the inrogation areas for the computation of unmixedness were csen to include one sidewall of each lobed injector, for coparison with unmixedness in an equal length of the strainjector C. Results for interrogation areas which includedwhole injector flowfield~with differing interrogation widthsto match interfacial lengths and fluid areas! gave similar re-sults for unmixedness. Each data point in Figs. 10~a!–~d! isan average of four to six instantaneous PLIF images forsame flow conditions.

In all high flow rate cases@Figs. 10~a!–~c!#, the lobedinjectors appeared generally to produce a lower overall

FIG. 7. PLIF images of the mixture fraction of CO2 for the straight injectorC under flow condition I with high speed air flow at 11.5 m/s. Imagesshown at locations 20, 40, 60, and 80 mm downstream of injection.



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mixedness~i.e., greater mixing! at each downstream locatiocompared with the straight injector. Interestingly, for thehigh flow rate cases, the unmixedness for both lobed intors was roughly the same near the exit@in Fig. 10~b! injectorA had a somewhat higher unmixedness# and the unmixed-ness for the lobed injectors was generally lower than forstraight injector in the farfield. This suggests that initstreamwise vorticity generation by the lobed injectors dassist in increased initial mixing of injectant with surrouning air. Near a downstream location ofx 5 35–45 mm, how-ever, the five-lobed injector A consistently produced a mrapid drop inU than did the three-lobed injector B. AcetonPLIF images~e.g., in Figs. 5 and 6! indicated that, upstreamof roughly 40 mm, ‘‘fuel’’ injectant in each side lobe mixewith air fairly independently of the fuel in adjacent sidlobes, whereas downstream of 40 mm, fuel from adjacside lobes in injector A appeared to interact. The fuel inmore widely separated side lobes in injector B did not ehibit such interaction until much further downstream, ifall. Thus the sudden increase in mixing exhibited by injecA could have arisen from the transport of fuel from an adcent lobe into the interrogation area of a given lobe. Airflovelocity mismatch@Figs. 10~b! and 10~c!# appeared to yieldsomewhat greater mixing than for equal upper and lowerspeeds in both lobed injector geometries. This finding mbe consistent with the observations of Yuet al.19 that highturbulence generation occurs much sooner for mismatcair flows in lobed mixers~especially for sawtooth geometriesimilar to injector A! than for matched air flows.

Lower airspeeds and higher injectant [email protected]~d!# were found to actually produce lower downstreafluid mixing ~increased unmixedness! for the lobed injectorgeometries than for the straight injector. The lower axialspeeds for the flow condition here reduced the magnitudsecondary velocities in the lobes, apparently reducinginitial degree of mixing by streamwise circulation for thlobed injectors. Beyond this, the fuel-air velocity mismatacted to increase spanwise vorticity generation, particulafor the straight injector, increasing its overall degree of flumixing. It is possible that the increase in spanwise vorticfor the lobed injectors was inhibited by the lobed shape, ahence was not sufficient to increase their overall mixingcompared with that for injector C.

It should be noted that for all three injectors the unmednessU was less than 0.4 at the first measurement locat20 mm downstream of the injector exit, for all flow condtions. This indicated very rapid initial mixing. In this respethe lobed injector geometry is different from the lobed mixgeometry studied by previous researchers.12–21 In the lobedmixer geometry the stirring action generated by the loshape must penetrate well into both fluid streams beforenificant mixing occurs. In the lobed injector geometry, hoever, fuel is injected directly into the region of streamwivorticity generation, and is rapidly mixed with and diluted bcoflowing air. For this reason, the scalar boundary conditifor the dissipation layers must be carefully evaluated whestimating fluid mechanical strain rates, as noted previou

The local scalar dissipation ratex along strained dissi-pation contoursjst was determined as described previous

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673Smith et al.


y71

FIG. 8. PLIF images of the mixture fraction of CO2 at the downstream locationx560 mm for flow condition III with high speed flow at an airflow velocitratio vab /vaa56 with vab518 m/s. Comparisons are made among injectors A~a!, B ~b!, and C~c!. Estimated streamwise circulations are 0.115 and 0.1m2/s for injectors A and B, respectively.

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from acetone PLIF images. The average diffusivityD in thepresent experiments was taken to be 1.531025 m2/s. Plots ofthemeanvalue ofx along this contour of maximum scalagradient at a given downstream location are shown in F11~a!–~d!, for flow conditions corresponding to thoseFigs. 10~a!–~d!, respectively. It should be noted that in thnearfield~x 5 20–40 mm downstream!, each strained dissipation layer was resolved by 5–7 pixels, so that the grad“j, and hencex, were probably underestimated. In thfarfield ~x560–100 mm!, layers were resolved by at least 2pixels and hencex values were probably more accuratAgain it should be noted that the scalar dissipation rates wcalculated only from mixture fraction gradients in the planof the PLIF images. As expected, for all flow conditionscalar dissipation rates for the lobed injectors tended to sout relatively high, then to decay due to viscous dissipatwith downstream distance. For straight injector C,x did notvary substantially with downstream distance, suggesting



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significant rollup of spanwise vorticity into streamwise votical structures by this injector.

In contrast to the results for unmixedness, at high as was low speeds the three-lobed injector B appeared to cremuch higher mean scalar dissipation rate than did eitlobed injector A or straight injector C in nearly all cases@anotable exception being the equal flowrate case in F11~a!#. This observation is consistent with the generahigher effective streamwise circulation associated wrounded square wave lobes as in injector B as comparedthe sinusoidal injector of type A for the same floconditions.18 The fact that injector B tended to draw fluifrom the peaks and troughs toward the inflection points meffectively~in the PLIF images! provided further evidence othe higher degree of streamwise vorticity that was generaand thus the higher local strain rate. That the average scdissipation ratex for injector A decayed to even lower levein the farfield than for straight injector C for the airspe

Smith et al.


ynd

FIG. 9. PLIF images of the mixture fraction of CO2 at the downstream locationx560 mm for flow condition II with low speed flow at a fuel-to-air velocitratio v f /vaa52 with vaa5vab54.5 m/s. Comparisons are made among injectors A~a!, B ~b!, and C~c!. Estimated streamwise circulations are 0.049 a0.073 m2/s for injectors A and B, respectively.

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mismatch cases@Figs. 11~b! and 11~c!# was unexpectedWhile airspeed mismatch appeared to assist lobed injectwith streamwise vorticity generation and vortex rollup@espe-cially as seen in Fig. 11~b!#, promoting the transport of injectant from peaks and troughs to inflection regions, airspmismatch appeared to inhibit initial streamwise vorticgeneration and vortex rollup for injector A. A significandrop in x is also generally seen for lobed injector B in thfarfield. The very high initial scalar dissipation rates seenboth lobed injectors in Fig. 11~d! may be associated with thmore coherent, laminar-like rollup of vortices seen in tPLIF images for this moderate flow condition~see Fig. 9!.

The only case in which injector B did not create a highmean scalar dissipation rate at high speeds is shown in11~a! for flow condition I. As seen in the PLIF images, vlocity mismatch in this flow regime~especially for conditionIII ! seemed to augment the~initial! process of streamwis



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vortex rollup for injector B and hence to augment fluid mchanical strain. This could explain the initial and overdrop inx for injector B in Fig. 11~a! for matched airspeedsThe equal airspeed condition in Fig. 11~a! did cause the av-erage scalar dissipation rate field generated by A to becreased above that for the other flow conditions shown, hever. These findings for injector A may be consistent wthe observations of Yuet al.19 concerning the delay in vortexbreakdown for matched air flows, yet the observationsinjector B appeared to contradict Yuet al.’s results. The factthat Yuet al.’s results are for the lobed mixer rather than tlobed injector, however, may point to fundamental flowfiedifferences between the two configurations.

DISCUSSION

The results above provide information with respectmixing and scalar energy dissipation characteristics fo

675Smith et al.


B,

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FIG. 10. Local unmixednessU as a function of downstream distancex ~in mm! for different flow conditions, with comparisons made among injectors A,and C:~a! Flow condition I with high speed air flow at 11.5 m/s. Estimated streamwise circulations are 0.132 m2/s and 0.195 m2/s for injectors A and B,respectively.~b! Flow condition III with high speed flow at an airflow velocity ratiovab /vaa54 with vab516 m/s. Estimated streamwise circulations a0.110 m2/s and 0.163 m2/s for injectors A and B, respectively.~c! Flow condition III with high speed flow at an airflow velocity ratiovab /vaa56 withvab518 m/s. Estimated streamwise circulations are 0.115 m2/s and 0.171 m2/s for injectors A and B, respectively.~d! Flow condition II with low speed flowat a fuel-to-air velocity ratiov f /vaa52 with vaa5vab54.5 m/s. Estimated streamwise circulations are 0.049 m2/s and 0.073 m2/s for injectors A and B,respectively.

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lobed injector configuration. It is seen that, for local fuel-mixing along injector lobes, the five-lobed injector A constently mixed fuel and air more rapidly than did the threlobed injector B or straight injector C at high speeds,though transport of injectant from adjacent lobes cleaplayed a role in this quantification. Yet at high speedsscalar dissipation rate, which is proportional to local strrate, was in general substantially higher for injector B thfor the other two injectors. If both rapid premixingandhighstrain rates are required for ignition delay and NOx reductionin a combustion environment, the question arises as to winjector might be optimal.

In examining Eq.~2! relating strain rate and scalar disipation rate, one finds that high strain rates can occurlarge scalar dissipation ratesx but where values of (j1 ,j2) may be close to~1,0! or are roughly symmetric aboujst50.5. High strain rates are also possible with smaller slar dissipation rates if values of (j1 , j2) differ more sig-nificantly from ~1,0! or are more greatly skewed about thvalue of jst . In the present study,both of these situationswere observed for lobed injector geometries. The five-lob



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injector A mixed fluid more rapidly, diluting values ofj1

and j2 downstream, but did not necessarily generate hvalues ofx, while the three-lobed injector B mixed less raidly but could generate higher scalar dissipation rates. Emates of strain rate at 80 mm~where there was sufficiendissipation layer resolution to computej1 andj2 with someconfidence! confirmed the effects of these trends. For thigh flow speed cases considered, the strain rates infarfield were of the order 250–700 s21 for both lobed injec-tors A and B, and were of the order 300–400 s21 for thestraight injector C. At 80 mm one would expect the averastrain field to have relaxed due to viscous dissipation; tsuggests that strain rates in the nearfield may have bhigher, perhaps substantially so, than in the farfield.

The critical strain rate required for ignition delay of a 0cm-thick propane fuel strip in air29,40 for the present configu-ration is roughly of the order 400 s21. Recall that the strainrates estimated above for the present experiments were cputed from only two components of the gradient in mixtufraction and as such should be regarded to be aminimalprediction of farfield strain rate. Hence it is reasonable

Smith et al.


ions

.

FIG. 11. Mean value of the scalar dissipation ratex along the contours of maximumx as a function of downstream distancex ~in mm! for different flowconditions, with comparisons made among injectors A, B, and C:~a! Flow condition I with high speed air flow at 11.5 m/s. Estimated streamwise circulatare 0.132 m2/s and 0.195 m2/s for injectors A and B, respectively.~b! Flow condition III with high speed flow at an airflow velocity ratiovab /vaa54 withvab516 m/s. Estimated streamwise circulations are 0.110 m2/s and 0.163 m2/s for injectors A and B, respectively.~c! Flow condition III with high speed flowat an airflow velocity ratiovab /vaa56 with vab518 m/s. Estimated streamwise circulations are 0.115 m2/s and 0.171 m2/s for injectors A and B, respectively~d! Flow condition II with low speed flow at a fuel-to-air velocity ratiov f /vaa52 with vaa5vab54.5 m/s. Estimated streamwise circulations are 0.049 m2/sand 0.073 m2/s for injectors A and B, respectively.

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estimate that there should be a delay of ignition innearfield region of a lobed fuel injector flowfield due to higfluid mechanical straining, and quite possibly further dowstream as well, based on the present results. As seen in10~a!–~c!, this region just downstream of the injector is oduring which fuel and air can strongly mix on a moleculevel. Thus the present results suggest that a lobed fuejector is likely to produce substantially premixed flame strutures, more so than in a non-lobed injector, which is mlikely to ignite stoichiometric diffusion flames.

CONCLUDING REMARKS

The present experimental study has demonstrated thetential of the lobed injector flowfield for applications tolow-NOx combustor. Both lobed injector designs under cosideration demonstrated the possibility of an improvemenmixing over a straight~non-lobed! injector, in some cases b30% or more. Fluid mechanical straining of the fuel-air iterface, as evidenced by scalar dissipation rates, can be msignificantly greater for the lobed injector geometries th



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for non-lobed injection. Although accurate values of strarate near the injection plane were not possible in the preexperiments, farfield strain rates were sufficiently highsuggest that the nearfield strain rates~typically higher! willdelay ignition of the fuel. It thus seems reasonable to expthat flame structures that form in the lobed fuel injector flofield would be detached, locally premixed or partially prmixed flames, with the potential for lowered NO productio

ACKNOWLEDGMENTS

Thanks are expressed to Mark Mitchell of UCLA fomeasuring the momentum thicknesses reported. The autwish to acknowledge helpful discussions with Professorbastien Candel of Ecole Centrale de Paris, with ProfesWerner Dahm of the University of Michigan, and with Professor Ian Waitz of MIT. The research reported here wsupported by the Office of Naval Research under GrantN00014-93-1-1383 and by NASA Dryden Flight ResearCenter under Grant No. NCC-2-374.

677Smith et al.


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Mixing enhancement in a lobed injector