Research Article A Comparison of the ... - Hindawi

Hindawi Publishing CorporationJournal of CombustionVolume 2013 Article ID 860508 15 pageshttpdxdoiorg1011552013860508

Research ArticleA Comparison of the Characteristics of Planar andAxisymmetric Bluff-Body Combustors Operated underStratified Inlet Mixture Conditions

G Paterakis K Souflas E Dogkas and P Koutmos

Laboratory of Applied Thermodynamics Department of Mechanical Engineering and Aeronautics University of Patras26504 Patras Greece

Correspondence should be addressed to P Koutmos koutmosmechupatrasgr

Received 29 April 2013 Revised 13 July 2013 Accepted 16 July 2013

Academic Editor Constantine D Rakopoulos

Copyright copy 2013 G Paterakis et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The work presents comparisons of the flame stabilization characteristics of axisymmetric disk and 2D slender bluff-body burnerconfigurations operating with inletmixture stratification under ultralean conditions A double cavity propane air premixer formedalong three concentric disks supplied with a radial equivalence ratio gradient the afterbody disk recirculation where the first flameconfiguration is stabilized Planar fuel injection along the center plane of the leading face of a slender square cylinder against theapproach cross-flow results in a stratified flame configuration stabilized alongside the wake formation region in the second setupMeasurements of velocities temperatures OHlowast andCHlowast chemiluminescence local extinction criteria and large-eddy simulationsare employed to examine a range of ultralean and close to extinctionflame conditionsThevariations of the reacting front dispositionwithin these diverse reacting wake topologies the effect of the successive suppression of heat release on the near flame regioncharacteristics and the reemergence of large-scale vortical activity on approach to lean blowoff (LBO) are investigated The cross-correlation of the performance of these two popular flame holders that are at the opposite ends of current applications mightoffer helpful insights into more effective control measures for expanding the operational margin of a wider range of stabilizationconfigurations

1 Introduction

The requirements in the design of fuel flexible low emissionsand versatile transportation and power generation systemsare placing heavy demands on the development and perfor-mance of current combustion devices [1 2] As a result thepursuit of new combustion concepts or modes is ongoingand a significant part of the overall design effort is devotedto maintain satisfactory flame stability and efficient emissiontargets [2 3]

Over the years lean premixed combustion has gainedpopularity and has become widely exploited as it addressessome of the above issues over a range of applications [2ndash4] However the anticipated operation of future combustorsunder increased loads and mixing and burning rates mayresult in complications such as sensitivity to mixing lowreaction and heat release rates extinctions and instabilities[3ndash5]

Partially premixing and stratifying the reactive mixtureis becoming an increasingly widespread strategy for burnerdesign in the effort to expand the stability margin of thelean fully premixed concept and at the same time meet thesecombined requirements [2 4ndash6] The effective control ofspatially varying local fuel-air ratio distributions within thecombustor offers significant operational flexibility Leanerregions increase efficiency and reduce pollutant formationand richer mixtures improve ignition performance and allowfor better control of instabilities However nonuniformitiesin the local fuel-air ratio can also lead to spatially varyingcombustion performance with implications that have to beaddressed in relation to the local turbulent chemistry thestabilization method and its interaction with the stabilitymargin (lean blow-out (LBO)) of the particular flame con-figuration [4ndash7]

Evidently due to the complexity of the above describedphenomena better knowledge of the details of the turbulent

2 Journal of Combustion

transport and reaction processes over a range of operatingconditions from lean to ultra-lean and approaching blowoff(LBO) is important if a full exploitation or even extensionof the operational margin is to be realised (eg [4 6ndash8])A range of systematic experiments have been performed tostudy the structure of such flame configurations (eg [4ndash8])along with a number of supporting simulations that employvarious levels of complexity for the turbulence-chemistrytreatment and usually involve adaptive local gridding withina time-dependent procedure (eg [9]) Phenomenologicalanalyses (eg [2 6 8]) and global correlations (eg [3 10])are also utilized to complement the overall developmenteffort and relieve the burden and cost involved in themultiscalar approaches

These experimental and computational works have so farproduced detailed descriptions of the ultra-lean behaviour intraditional stabilizers such as fully premixed axisymmetric(eg [3 4 7 8]) and slender two-dimensional (eg [611]) bluff-body arrangements However stratified bluff-bodyflames operated at ultra-lean and near blow off conditionshave not been investigated as extensivelyMoreover the grow-ing combination of burner and mixture placement setups inlean combustors has increased current interest for a morecomplete description of such flame types Therefore compar-ative examinations of the performance of the axisymmetricversus the slender two-dimensional bluff-body stabilizationconfiguration under stratified conditions arewarranted thesecould provide useful information regarding themore effectivecontrol exploitation or even extension for example throughappropriate placement of pilot injection of the operationalmargin under both setups (eg [2 4 6 11 12])

This work then compares the ultra-lean performance andtopology characteristics of propane flames stabilized in anaxisymmetric double cavity fuel-air premixerdisk arrange-ment [13] and a counterinjected 2D slender square cylinder[11] under stratified conditions The above geometries werechosen because these comprise two of themost popular stabi-lizers at the opposite end of the field of practical applicationsand comparisons of their limiting performance could provideuseful directions in the design process for a wide range ofconfigurations Identification of the individual characteris-tics such as for example flame and recirculation lengthsflame front topologies turbulence levels vortical activityand under successively weakening stabilization within thesame geometry arrangement may help determine suitablemethodologies to extend stability in a fashion tailored notonly for the particular flame geometries but also for arange of intermediate variants upgrades or retrofits [2 412] Furthermore both of these setups have been systemati-cally investigated under fully premixed conditions and theiroperation under stratified conditions could then be directlycontrasted against such a range of well documented data

Measurements of turbulent velocities temperatureschemiluminescence imaging of OHlowast and CHlowast flame frontvisualization and gas analysis provided information for leanultra-lean and close to blowoff flames Supporting large-eddysimulations were also undertaken employing the thickenedflame model [14 15] and a nine-step mechanism for propanecombustion [11 13] to complement the experimental effort

and assist in the more complete interpretation of the opticalmeasurements

The combined methodology helped to elucidate some ofthe parametric characteristics of these diverse flame topolo-gies and improve understanding regarding the differencesand similarities between these two stabilizers when operatedwith a stratified inlet mixture as opposed to a fully premixedoperation In addition the local extinction behavior wasexamined by using the combination of three measured orcomputed parameters namely a local Karlovitz numbera local temperature threshold and the ratio of the OHlowastCHlowast chemiluminescence signature The credibility of thisparameterization is appraised where possible by using bothmeasurements and simulations

2 Flame Stabilization Configurations

The two burner setups are shown in Figures 1(a) 1(b) 1(c)1(d) 1(e) and 1(f) In the first configuration stratified flamesestablished by staged fuel-air premixing in a double-cavityarrangement (Figure 1(c)) formed along three concentricdisks and stabilized in the vortex region of the afterbody A(119863

119887= 0025) under the additional action of a coflowing

swirl stream (Figure 1(b)) are investigated The combustiontunnel and the studied burner are similar to those reported in[13] and have been optimized through a series of systematictests [16] Fuel is supplied through the central shaft (119863

119901=

0010) that is running along the central air supply tube (119863119888=

0052) into the internal hollow of the active bluff-body disk B(Figure 1(c))Then it is injected through an annular 1mm slotinto the primary fuel air-mixing cavity and is mixed with thecentral air supply This maintains an afterbody equivalenceratio gradient between a Φmin asymp 035 to 020 and a Φmax asymp098 to 05 depending on flame condition as measured withflame ionization detection from local gas samples at theafterbody exit (Figure 1(d)) Limiting conditions approachingblowoff were obtained by reducing the fuel level which thendecreased the peak Φ at the primary zone inlet In all cases aregulated stratified reactive mixture profile is attained acrossthe most favourable position for leading edge flame front sta-bilization at the disk burner rim (Figure 1(d)) The simulatedcavity flows for a lean flame at 119878 = 10 are shown in Figure 1(d)to illustrate the overall flow patterns obtained within and atthe exit of the premixer system these remain largely unalteredbetween lean and ultra-lean operation The global Φ basedon the totalmass flows of fuel and central air togetherwith therange of investigated conditions and parameters is shown inTable 1 The blockage ratio (BR) in the afterbody annular jetsupplying the primary zone is BR = (119863

119887119863

119888)2

= 023 [13]The second setup involves the study of partially premixed

and stratified flames established by planar injection (discretejets of small aspect ratio) of propane along the center planeof the leading face of a slender square cylinder Propane issupplied through the cylinder ends issued through 135 holesof 1mm diameter spaced at 05mm apart on the symmetryplane over a width of 200mm along the upstream face ofthe square and reaction is stabilized within and adjacentto the downstream wake formation region (Figures 1(e) and

Journal of Combustion 3

Ue UeUs UsUc

(a)

1418552

Tangential air

Ws

(b)

25

75

75

51

13

53

10

A

B

C

Fuel

(c)

Fuel supply

Afte

rbod

y

Peripherally injected fuelPrimary recirculation

mf

Air or mixture supply at UoΦo r Φ(r)

Φmax

Φmin

(d)

Countercurrent injection

Airflow

Planar fuel jet

H

A

A998400

Square cylinderburner

Injector holes(1mm)

A-A998400 view

W

(e)

Air flow

Fuel injection

Square flame stabilizer

h = 8mm

Uo

y Φ(y)Φmax

Φmin

(f)Figure 1 Axisymmetric disk ((a) (b) (c) and (d)) and slender square ((e) (f)) burner arrangements including respective flow patternsfuel-air placements and mixture stratifications at inlet to the stabilization regions

1(f)) The level of stratification across the square flanks iscontrolled by the velocity ratio between the fuel injection andthe approach cross-flow with peak levels ranging from 16to 06 The blockage ratio of the square burner in the two-dimensional tunnel was BR = ℎ119867 = 010 [11] The Reynoldsnumbers of the cold flow were maintained at 7980 and 5800for the disk and the square respectively

A high swirl case was chosen for study in the diskconfiguration The geometric swirl number 119878 (119878 = 100 forthis investigation) used for the quantitative representation ofswirl intensity was expressed here as the ratio of integrated(bulk) tangential to primary axial air velocities (119882

119904119880

119904)

measured through LDV in the coflow swirl stream Squareburner flames formed by counterinjection with a low fuel-to-approach-air velocity ratio operated toward the lean LBOlimit were chosen for the second case Under both casesstrong recirculation regions assist in flame stabilization underhigh stretch rates leading to a spread in the disposition of

the flame front alongside the wake flanks The wake devel-opment in the square is affected by periodically asymmetricvortex shedding with strength that drastically varies betweenisothermal and low or high fuel injection reacting conditions[6 11 12 17] On the other hand the axisymmetric diskexhibits low frequency vortex rollup from the rim peripherywhich is again stronger under isothermal conditions [1318] The interaction of the locally evolving extinction processwith the underlying turbulent wake dynamics presents severaldifferences between the above two flameholders (eg [4 6ndash8 12 13 17]) This facilitates a useful evaluation of theirdifferent behaviors under ultra-lean operation and allows foran appraisal of the adopted modelling methodology

All fuel flows were regulated by Bronkhorst MV-304306High-Techmass flow controllers Necessary supply valves theignite and a flame-out detection device were used and wereall controlled electronically by a central unit


Table 1 Operating conditions and parameters

Case 120575 () 119880Fuel 119879max (K) 119871119891119863

119887119871119877119863

119887ΦGlobal Ka

DiskLean 50 143 1860 56 143 0147 6Ultralean 18 112 1732 52 136 0115 185Near LBO 6 1 1508 44 128 0102 47

SquareLean 94 124 2050 85 55 0031 15Ultralean 65 105 1850 35 35 0025 35Near LBO 14 073 1600 14 145 0018 72

(1) 120575 is percent deviation from LBO 120575 = (119898Fuel minus119898FuelLBO)119898fuelLBO ()(119898fuelLBO fuel flow at lean blowoff)119880FBO = 095ms for disk and 064msfor square(2) 119879max maximum measured wake temperature(3) 119871

119891 visible flame length 119871

119877 measured recirculation length

(4) Central air supply velocity for disk 119880119888= 487ms and ReDb = 7980 for

all cases coflow velocities in annular swirl stream at 119878 = 10 119880119904= 119882

119904=

105ms surrounding shielding stream velocity 119880119890= 10ms Approach

airflow for square119880infin= 67ms and Re

119867= 5800 for all cases

(5)ΦGlobal global equivalence ratio based onmass flows of injected fuel and(a) air supply in the central pipe for the disk or (b) approach airflow over thetunnel height for the square(6) 119879max location for the disk was at (119909119863

119887 119903119863

119887) = (04 045) while for the

square this was at (119909ℎ 119910ℎ) = (07 to 10 09)

Flame nomenclature in both cases is denoted on thebasis of the proximity to LBO defined by 120575 = (119898Fuel minus119898FuelLBO)119898FuelLBO () where 119898FuelLBO is the fuel flow atlean blow-out The global Φ based on the total mass flows offuel and approach air together with the range of investigatedconditions and parameters is included in Table 1

3 Experimental Methods

The burners have been previously investigated under isother-mal operation to establish the mixing topologies that sustainthe reacting fields presented below [11 13 16 19] Meanand turbulent velocities temperatures and OHlowast and CHlowast

chemiluminescence (CL) images were obtained using atwo-component LDV system thin digitally compensatedthermocouples and a chemiluminescence imaging system(LaVision Flame Master consisting of a CCD camera animage intensifier IROunit camera optical filter at 307plusmn10nmand achromat lens for OH imaging)

Transverse profiles of the time-averaged mean and tur-bulent streamwise and cross-stream velocities and statisticswere obtainedwith a two-component 2Watt Argon-Ion laserfiber optics linked to TSI transmitting and receiving opticsand described in detail in [19] The fuel and air flows wereseeded with dried magnesium oxide powder (approximately5 120583m nominal diameter before agglomeration) dispersed bytwo purpose-built cyclone separators In order to minimizebias errors due to unequal particle densities in the fuel andair streams the two flowswere seeded separately with rates ofparticles in proportion to the flow rates in each one Extremedeviations were determined by seeding only one of the twostreamsThe filtered Doppler signals were processed by a TSIfrequency counter (1980B) Mean and statistical values were

postprocessed from 20480 data weighed by the time betweenparticles to correct for velocity bias Velocity spectra wereobtained by sampling at 4 kHz and performing a fast fouriertransform (FFT) on 20 sets of 1024 values [11 19]

Temperatures were measured with Pt-Pt10Rhuncoated beaded S-type 25 to 75 120583m thermocouples Atwin bore ceramic cladding of 130 times 09mm with 02mmcapillary holes oriented along the flow supported the stemTheTC outputwas interfaced to aDaqTemp 7AOmega cardThe thermocouple acts as a low-pass filter with a responseof the order of 50 Hertz for for example 100120583m wiresthat depend on local parameters (position temperaturejunction geometry and material gas velocity conductivityheat capacity and density and flame structure) Here usingan FFT algorithm the signalrsquos frequency spectrum wasestimated the amplitude and the phase were correctedand the signal was transformed back to the time domainaccording to the methodology described in [20] so thatabout 60 of the temperature fluctuations spectrum could becalculated [11 19 20] No correctionwas applied for radiationbut for propane flames and uncoated wires the systematicerror in the mean can be up to 10 at 1900K [19] Meanand rms temperatures were derived at a sampling frequencyof 400Hz Maximum uncertainties in the velocities wereless than 85 in the mean and less than 15 in the rmsUncertainties in the estimation of the thermocouple timeconstant are rather unimportant for the mean temperaturebut according to the present compensation procedure mayaffect the variance by between 25 and 35

Chemiluminescence measurements of the electronicallyexcited OHlowast and CHlowast radicals are frequently employed toidentify the topology of the flame front since for examplethe electronically excitedOHlowast existsmainly in the flame frontregion (eg [4ndash7 12]) Image acquisition and data reductionwere performed using the Davis 80 software from LaVisionThe background images taken under the same integrationtime and gain were subtracted from the originals Averageswere produced from 300 instantaneous images recorded at16 to 60 frames per second depending on the binning andthe interrogation window The signal-to-noise ratio of theinstantaneous images was better than 8 1 and the exposuretime was 21ms under a single frame mode operation Themaximum CCD chip resolution was 1626 times 1236 pixelsIntensifier gate times of the order of 100 120583s were used forthe measurements with a gain up to about 85 Since theCCD is combined with an intensifier the effective exposureis determined by the image intensifier gate which typically isof the order of several nsecs whilst the image collection alsodepends on the attainable CCD recording rate The cameraexposure is a temporal envelope that integrates the phosphoremission of the intensifier whilst maintaining an exposuretime greater than the sum of the delay and the gate times

A direct qualitative comparison between the time-meansimulated OH mole fraction fields with the experimentallymeasuredmean OHlowast chemiluminescence fields is not imme-diately possible This is because the experimental measure-ments are effectively a 2D image of projected line of sightmeasurements from a cylindrically symmetric process (in themean) whilst the numerical results are a 2D axisymmetric


slice through the axis of symmetry of the cylindrically sym-metric process To compare the two different datasets a trans-formation process is required to be applied to one or both ofthe datasets As the time-average flame is axisymmetric thelocation of the reaction zone can therefore be observed fromconverting the ensemble average chemiluminescence image(obtained from a set of 300 images) with an Abel transformThree-pointAbel deconvolution formulations given byDasch[21] were used to extract two-dimensional information fromthe ensemble average chemiluminescence images as thethree-point Abel inversion algorithm was previously foundto be more accurate and efficient when compared to onionpeeling filtered backprojection and two-point Abel decon-volution methods as demonstrated in [7 21]

A quartz microprobe was used to obtain samples atthe afterbody annular exit and flame ionization detection(employing a Signal 3010 MINIFID device) was employedto measure the concentration of the hydrocarbon at thisposition and allow the evaluation of the equivalence ratiolevels with an uncertainty of the order of 4 Global exhaustemissions could also be measured by extracting flue gasesand measuring bulk species (NO

119909 CO CO

2 O

2 and C

119909H119910)

concentrations with a Kane-May KM9106 Quintox flue gasanalyzer further downstream of the burner [11 13]

4 Simulation Model Formulation

41 Aerodynamic Model The flames were simulated with theANSYS Fluent 140 (ANSYS Inc) software [22] It offeredmesh adaption flexibility near the fuel injectors and facilitatedthe exploitation of reduced chemistry within the context ofan adequate modeling scheme for the turbulent reactionsWithin the Large Eddy Simulation procedure employed herethe flow variables 119865 can be decomposed into resolvable 119865and subgrid 1198651015840 scale quantities using a Favre-weighed filter119865 = 120588119865120588 The equations describing the resolvable flowquantities are for example [9 13 14 22]

Continuity Momentum is

120597120588

120597119905+120597 (120588

119894)

120597119909119894

= 0 (1)

120597120588119894

120597119905+

120597 (120588119894119895)

120597119909119895

= minus120597119901

120597119909119894

+120597

120597119909119895

[120583(120597

119894

120597119909119895

+

120597119895

120597119909119894

)]

minus

120597120591119886

119894119895

120597119909119895

+ (Δ120588infin) 119892

119894

(2)

and Scalars are

120597120588119896

120597119905+

120597 (120588 119895119896)

120597119909119895

=120597

120597119909119897

(120588119863119896

120597119896

120597119909119897

)

minus120597119869

119897

120597119909119897

+ 120588120596119884119896 119896 = 1119873

(3)

The solution of an energy equation completes the abovesystem (120588 120583 119879 119906

119894 and 119884

119896are the density viscosity temper-

ature velocity and species composition of the gas and 119894 =

1 2 3 in a Cartesian system (119909 119910 119911)) 120591120572119894119895= 120591

119894119895minus 13120591

119894119895120575119894119895

is the anisotropic part of the subgrid stress tensor 120591119894119895 with

the isotropic part of the viscous and subgrid stress beingadsorbed into the pressure The subgrid stresses are modeledas 120591120572

119894119895= minus2120583sgs119878119894119895 where 120583sgs = 120588(119862119904Δ)

2

(2119878119894119895119878119894119895)12 119878

119894119895is the

resolvable strain tensor and Δ is the filter width related to thelocal mesh spacingΔ = 3radicΔ119909

119894Δ119910

119894Δ119911

119894 A gradient assumption

is used for the subgrid scalar flux 119869119896= 120588(119906

119897119884119896minus 119906

119897119884119896) =

minus(120583sgsScsgs)(120597119884119896120597119909119897) where Scsgs is the subgrid Schmidtnumber Turbulent transport is modelled with the dynamicSmagorinsky model (eg [9 11 22]) with bounded 119862

119904(0 lt

119862119904lt 023) Pressure-velocity coupling was handled via a

time-dependent SIMPLE algorithm (eg [9 22]) A second-order accurate time discretization was used and the timestep was chosen to maintain a maximum Courant numberbetween 04 and 06 Rms values were computed from theresolved scale quantities including the contributions fromthe subgrid scale stresses The simple P-1 radiation modelavailable in the software (ANSYS Inc) was adopted in thesimulations (although no correction for radiationwas appliedto the temperature measurements its use in the simulationsallows some flexibility in future processing of the presentdata)

The employed commercial software has frequently beenused to investigate with success premixed flame stabilizationin complex bluff-body configurations under stable (eg [23])and approaching blowoff [24] conditions in a fashion similarto the present study One should nevertheless exercise greatcaution in interpreting the results obtained regarding thebehaviour and development of the flame front at the finalstages toward LBO centers of excellence in combustion stud-iesworldwide are currently trying to develop such a capabilityand capture this complex phenomenon with sufficient accu-racy [23] Notwithstanding the above comments here everyeffort wasmade to improve the basic capability of the softwarethrough use (a) of the higher order differencing schemesavailable within the software for LES (b) of a well-establishedturbulence-chemistry closure such as the thickened flamemodel (c) of the extended nine-step chemical scheme forpropane chemistry and (d) through careful mesh refinementin the main reaction zone With these improvements theperformance of the software was deemed satisfactory inproviding useful information at ultralean and near LBOconditions and this was tested where possible against thepresent measurements

42 Combustion Model To represent the mixed regimecombustion that may result from the various fuel settingsthe thickened flame model (TFM) (eg [14 15 22 23])was employed This formulation was coupled to a nine-stepreduced scheme for propane (ie Rxn 1 C

3H8+ O

2+ OH +

H rarr 3CO + 5H2 Rxn 2 CO + OHharr CO

2+ H Rxn 3 3H

2

+ O2harr 2H

2O + 2H Rxn 4 2H + M rarr H

2 Rxn 5 H

2+ O

2

harr 2OH Rxn 6 C3H8+ O + OH + H rarr C

2H2+ CO + H

2O

+ 3H2 Rxn 7 C

2H2+O

2harr 2CO +H

2 Rxn 8 2O +MharrO

2

Rxn 9O2+HharrO+OH)This represents an extension of the

mechanism described in [11 13 16] now including the radicalOH to facilitate more direct comparisons with the measured


chemiluminescent OHlowast and has been tuned to reproduce theflame speed over a section of the leanΦ range as described in[11] All the species are explicitly solved on the computationalgrid and it is likely that intermediate radicals with shortertime scales might not be properly resolved within the contextof the employed refinement In the present low Reynoldsnumber laboratory flames the exploitation of the abovecombination of turbulencemodels and chemistry scheme canbe considered attractive in providing a more detailed andextensive description of the developing flame front propertieswhile also allowing for amore direct comparison with opticalexperimental results

The averaged reaction rate source terms were computedwith the ISAT algorithm (eg [7 19 22]) Previous mea-surements [11 13] have suggested that the lean flames lie inthe thin reaction regime The present ultra-lean flames arecloser to the broken reaction zone boundary with Karlovitznumbers [1] (Ka = 120591ch120591k where 120591ch and 120591k are the chemicaland Kolmogorov timescales) of about 80 and local grid-basedKarlovitz numbers (eg [9]) of higher values

43 Local Extinction Monitoring Parameters An effort wasalso made to examine the local extinction behaviour at nearLBO conditions by considering the combination of threemeasured or computed parameters First the parameterΛ = KaKaex computed from the transient simulations waschosenwhereKa is the local Karlovitz number andKaex is theKarlovitz stretch factor for symmetric counterflow laminarflame extinction being a function of the local equivalenceratio with Λ gt 1 signifying local extinction (eg [2 10])

Second the computed statistical distribution of the tem-perature difference Δ119879

119888between the local instantaneous

temperature119879inst and a chosen threshold temperature119879limitΔ119879c = 119879inst minus 119879limit was evaluated and local extinction isconsidered when Δ119879

119888lt 0 the usefulness of a threshold

temperature value has been demonstrated from the extensiveexperimental investigations on C

3H8flame extinction of

reference [3] For conditions close to the present experimentvalues of 119879limit of around 1400K have been reported forswirl grid and porous plate burners [3] while a similarrange of limiting extinction temperatures was measured andcomputed in laminar counterflow setups [2] Present tests inthe simulations suggested a value between 1325 and 1350K

Third the trends in the variations of the ratio of themeasured time-mean OHlowastCHlowast chemiluminescence signa-ture evaluated at selected locations close to the reactingflame front stabilization region within the recirculation zoneat 119909119863

119887= 044 for the disk and at 119909ℎ = 16 for the

square were examined for possible correlation with theproximity to blowoff Although local extinction events areundoubtedly instantaneous phenomena the proximity toLBO has routinely been assessed for preliminary as well aspractical studies through time-averaged criteria for exampleDamkholer numbers and so forthTherefore the exploitationof the average OHlowast to CHlowast ratio cannot be excluded as auseful criterion Furthermore due to the complexity of thephenomena involvedwithin time scales of a fewmillisecondsapart from fast recording instrumentation customarily more

than one parameter has been examined to determine theflame condition something that in most cases is and shouldbe technical practice Here the possibility of using theabove parameters in combination as likely local markers fordelineating reactive from nonreactive regions in the presentstratified flameswith inletmixture nonuniformities that placethem neither in the nonpremixed nor in the fully premixedregime and the likelihood of extrapolating this behaviour todetermine the proximity to LBO are tentatively explored

44 Computational Details Particular emphasis was given tothemesh distributions near the low aspect ratio injectors withrespective dimensions (1 25 52mm) rarr (annular injectionslot afterbody central pipe) for the disk and (1 8 80mm)rarr (injection hole square cylinder height tunnel height)for the square (see Figure 1) The mesh for the disk extendedover a 360∘ sector while for the square the resolved spanwas chosen to include seven injection holes plus one halfspacing on each side over a width of 175 h with symmetryboundary conditions at the lateral boundaries The completepremixer cavities section was included in the mesh for thedisk and the computations started well upstream of thecomplex premixerburner system to incorporate the effectsof the mean and turbulent inflow conditions measured atthis position Similarly the computations for the squarestarted 7119863

119887upstream of the burner face where measured

inlet velocity and turbulence profiles were available Hybridmeshes were utilised unstructured near the compoundregions of the disk or the square injectors and the burnerboundaries and structured in other locations with expansionto the outlet which was placed 15119863

119887downstream of the

bluff bodies Typical meshes of 145 and 175 Mcells wereemployed for the disk and the square respectively in thebasic runs No-slip boundary conditions were used nearthe walls with the node close to the burner surface placedat Δ119910119863

119887= 000175 while the law of the wall was applied

elsewhere Inlet conditions were taken from measurementswhile a static pressure boundary condition was applied atthe outlet and all outflowing quantities were extrapolatedfrom the interior node The LES quality was checked bycalculating the resolved fraction of the turbulence energy119877119896= 119896res(119896res + 119896sgs) with values up to 95 within the

main reaction zones Run times on 48 30GHz processors (4XEON 5660) and 24 38GHz processors (4 i7) run in parallelwere about 17 CPU hrs for the simulation of one throughflow time (120591 = 119863

119887119880

119888= 5 times 10

minus3 s) for the disk while morecomputational time was necessary for the square due to thedenser meshes utilized to resolve the discrete small aspectratio series of injector holes Time series of various quantitieswere collected for for example the disk over about 225120591 andrelevant statistics were postprocessed from this sample

5 Results and Discussion

A description of the isothermal flow and the stable flamecharacteristics under operation away from the blow off limitregion has been presented in references [11 13 16 19] forthe two burner configurations respectivelyThe present work


(a) (b)

Figure 2 Simulated time-mean disk burner wake characteristics (a) temperature (b) OHmole fraction radical andOHlowast chemiluminescencedistributions for various ultra-lean flame settings

(a) (b)

Figure 3 Simulated time-mean square burner wake characteristics (a) temperature (b) OH mole fraction radical and OHlowast chemilumines-cence distributions for various ultra-lean flame settings

focuses on the comparative examination of the topologiesobtained in the disk flame operated under a high swirl level(119878 = 1) and the square burner counterinjected with a lowfuel-to-approach-air velocity ratio at ultra-lean conditionslocated near the LBO margin The data presented for thetwo configurations are obtained for flame settings withsuccessively reduced fuel flows that is at reduced 120575 levels (asindicated in Table 1)

An overall picture of the two reacting wake flows emergesin the simulated time-averaged patterns displayed in Figures2 and 3 respectively in the form of mean temperatureand OH radical mole fraction contours together with thecorresponding distributions of measured OHlowast chemilumi-nescence A peak temperature region is initially situatedwithin and adjacent to the afterbody disk recirculation andextends up to 225119863

119887with a conical growth of the hot wake

at the fuel lean condition (120575 = 50 Figure 2(a)) At theleaner setting the flame retains its conical shape but thepeak temperature envelope suffers a noticeable reductionwith a moderate narrowing of the downstream wake spreadCloser to blowoff (at 120575 = 6) the peak temperature regionnow recedes considerably closing in on the axis with thepeak temperatures withdrawn toward the rim shear layersThe computed time-averaged OHmole fraction contour plotin Figure 2(b) also suggests that the leading edge of thetoroidal flame front gradually weakens and detaches fromthe disk rim while its trailing edge moderately retractsThe accompanying time-averaged OHlowast chemiluminescenceimages in Figure 2(b) (Abel transformed images) corroborateto some extent the flame detachment but suggest a thinnerreacting front with a much weaker activity particularlyclose to the disk axis These plots imply that the present


0

05

1

15

2

25

0 1 2 3 4 5 6 7 8 9 10 11

minus1

minus05

UU

c

xDb

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(a)

0

02

04

06

08

0 2 4 6 8 10 12xDb

Urm

sUc

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(b)

Figure 4 Comparisons between simulated andmeasured time-mean streamwise velocity (a) and turbulence intensity (b) distributions alongthe near wake of the disk burner

0

04

08

12

0 2 4 6 8 10 12 14minus04

minus08

Comp 120575 = 94Exp 120575 = 94

UU

0

xh

(a)

0

01

02

03

04

0 2 4 6 8 10 12 14

Comp 120575 = 94Exp 120575 = 94

xh

Urm

sU0

(b)

Figure 5 Comparisons between simulated and measured time-mean streamwise velocity (a) and turbulence intensity (b) distributions forthe near wake of the square burner

partially premixed disk flames behave somewhat differentlythan the fully premixed axisymmetric configurations burningmethane that were visualized in [7] to drastically close inon the axis at the limiting lean operation the disk flamedisposition with the present leaner outward gradient inletstratification follows closely the behaviour reported in [5] forsimilar stratification conditions

Time-mean temperature contours for the square cylinderreacting wakes are presented in Figure 3(a) for medium lowand limiting fuel injection velocities The counterinjectedconfiguration allows for partial premixing prior to ignitionand stabilization around the cylinder flanks thus resulting intemperature shear layers that enclose the recirculation zoneGradual fuel reduction here seems to lead to an attendant

shortening of these flanking flame fronts as illustrated bythe computed time-mean OH radical contours and theincluded OHlowast images in Figure 3(b) It should be notedthat fuel injection directly into the vortex region wouldresult in an altogether different reacting configuration of thenonpremixed type [11 19]

Thedevelopment of the nearwake recirculation regions interms of the measured and computed time-mean streamwisevelocity and turbulence intensity distributions is shownin Figures 4 and 5 for the disk and the square burnersrespectively operating at lean conditions (Table 1) Goodagreement is maintained in the axial velocity profile com-parisons (Figure 4(a)) at a range of conditions spanning theplane wake (119878 = 0) with lower turbulence levels and the


200

500

800

1100

1400

1700

2000

0 2 4 6 8 10 12xDb

T(K

)

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(a)

0

02

04

06

08

1

12

200 600 1000 1400 1800T (K)

rD

b

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(b)

400

800

1200

1600

2000

0 5 10 15 20

T(K

)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

xh

(c)

0

02

04

06

08

1

12

14

16

18

200 600 1000 1400 1800 2200T (K)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

yh

(d)Figure 6 Comparisons between simulated and measured time-mean streamwise and cross-stream temperature distributions for disk ((a)(b)) and square ((c) (d)) burners respectively Cross-stream temperature distributions were taken at 119909119863

119887= 04 for the disk and at 119909ℎ = 06

for the square

higher swirl case (119878 = 1) with elevated turbulence levels(Figure 4(b)) In the disk wake the recirculation lengthswere found to vary from 143119863

119887for the lean (120575 = 50)

to 128119863119887for the weaker (120575 = 6) flame respectively

gradually approaching the cold vortex zone length and thistrendwas followedwell by the simulationsOn the other handin the square burner the recirculation regionwas significantlyelongated in both measurements and simulations by up to55 times with respect to the cold wake due to heat releaseand this effect is depicted by the extensive backflow regionin the time-mean streamwise velocity profile comparisonsshown in Figure 5(a) Maximum axial turbulence intensitiesare obtained for the disk at the higher swirl level of 119878 = 1

(Figure 4(b)) and are of similar magnitude to the intensitiesattained in the square burner flame (Figure 5(b)) justifyingthe choice of the higher swirl disk case for direct comparisonswith the square burner configuration

Time-mean temperature distributions for the disk andthe square are shown in Figures 6(a) 6(b) 6(c) and 6(d) inthe form of center-line (-plane) profiles along the wakes andradial (cross-stream) traverses taken close to the stabilizersacross the recirculation zone respectively The measuredaxial temperature variations (Figure 6(a)) are reproducedsatisfactorily by the combined methodology in the nearaxisymmetric wake up to 119909119863

119887= 4 while discrepancies can

be identified very close to the diskwall and in the downstreamregion where a faster wake development is computed Thelack of a more complete heat transfer modelling near the wall(apart from the use of the simple radiation model) the defi-ciencies of the TFMmodel in the vicinity of the wall due to acombination of inadequate mesh resolution and likely short-comings in the performance of the chemistry scheme thereor the increased thermocouple measurement errors closer tothe wall may be in part responsible for this discrepancy


Instantaneous temperature distribution

120575 = 50

120575 = 30

120575 = 18

120575 = 12

120575 = 6

400 800 1200 1600 2000

Instantaneous extinctiontopology based on

0 05 10

(Λ ΔTc parameters)

(a)


120575 = 94

120575 = 65

120575 = 35

120575 = 14

120575 = 6

400 1200 1600


0 05 10


(b)Figure 7 Snapshots of temperature and extinction topologies for a range of simulated flame settings as LBO is approached (a) disk and (b)square burner

The cross-stream traverses in Figure 6(b) (obtained at119909119863

119887= 04) are consistent with the overall distributions

shown in Figure 2(a) and suggest that a wider flame spreadis obtained in the computed profiles The peak 119879 located inline with the disk rim vortex where flame stabilization occurssuffers a gradual drop from 1860K to 1700K and then to1500K with the leaner profile producing a more discernibleoff-axis temperature peak in accordance with the overalltopology of Figure 2(a) These distributions could offer someguidance as far as the possible methodologies for examplepilot injection placement that can be adopted to mitigate theevolution toward LBO in the stabilization region close to theburner rim

The influence of varying the local equivalence ratio strat-ification on the simulated and measured time-mean center-plane and cross-stream (taken at 119909ℎ = 06) temperature dis-tributions for the square burner and for the fuel levels alreadyseen in Figure 3(a) is depicted in the plots of Figures 6(c) and6(d) Significantly lower temperatures within a much longerrecirculation zone are now exhibited in this topology andthis trend is maintained for all successive fuel reductionsPeak values are found at the flanks of the developing wakeof the square center-body at 119910ℎ = 09 in line with amore spreadout flame front stabilization disposition due tothe displacing effect of the flanking recirculations on thesquare sides (Figures 3(a) and 3(b)) In fully premixed slenderbluff-body stabilization setups studied in for example [6 12]the flame was distinctly drawn within the recirculation andinteracted with the reappearing vortex shedding mechanismHere the adjacent flame fronts with no apparent mutualinteraction at the lean and ultra-lean level gradually retractalong the flanks of the wake engulfing the hot product vortexzone and it can be conjectured that this separation effectivelydelays the full reemergence of the Von Karman instability out

of the formation region [11 19] These characteristics will befurther verified from instantaneous images presented below

Figures 7(a) and 7(b) display a sequence of LES snapshotsof the temperature and the corresponding extinction topol-ogy as inferred from two of the criteria discussed previouslyfor a range of fuel settings as we get closer to LBO The darkareas demarcate reactive regionswhere both theKarlovitz (Λ)and the temperature threshold (Δ119879

119888) criteria are simultane-

ously valid Within the present formalism this is a necessarybut not a sufficient condition for sustaining reaction withinthe indicated areas From these plots it appears (Figure 7(a))that once the side rim vortex loses its stabilizing effectivenessthe flame destabilizes and is unable to recover despite theoccasional excursion of reacting fragments into the core ofthe main recirculation

The square extinction topology (Figure 7(b)) indicates anefficient and resistant stabilization of the two reacting frontswithin the flanking side vortices However it appears thatwhen the two reactive layers are sufficiently retracted theinherent intense large-scale instability [12 17] is reinstatedat the flame trailing edges This has a detrimental effect onthe overall stability and the attribute of the anchoring in thestrong flanking vortices is cancelled leading thereafter to amore rapid approach to LBO in the final stages with respectto the disk behavior Animation sequences from the simu-lations supplied as supplementary material and taken aftera sudden fuel reduction to the LBO levels provide a moredetailed illustration of the flow and flame events that occur atthe final stages of the blow-out process for the two burners

The local parameters used to monitor the local extinctionbehavior are discussed next The instantaneous scatterplotsof the simulated Karlovitz parameter monitored at a positionclose to the trailing edge (corner) of the two stabilizers nextto the temperature shear layer(s) (at 119909119863

119887 119903119863

119887= 032 04


4

3

2

1

019 20 21 22

Time (s)

KaK

a ex

Disk burner flame at120575 = 6

(a)

4

3

2

1

017 18 19

Time (s)

KaK

a ex


(b)

4

3

2

1

0

Time (s)

KaK

a ex

Square burner flame at120575 = 14

76 78 8 82 84 86

(c)

Figure 8 Scatterplots of the normalized Karlovitz number for the disk ((a) (b)) and the square (c) at different levels of local extinction (Λ =KaKaex values limited to 4 for clarity of extinction events signified by values greater than 1)

10

08

06

04

02

00minus1000 minus800 minus600 minus400 minus200 0 200 400 600 800 1000

Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 6 120575 = 50

Disk burnerflames

Tlimit = 1325KΔTc = Tinst minus Tlimit

ΔTc = Tinst minus Tlimit (K)

(a)

10

08

06

04

02

00minus200 0 200 400 600 800 1000

Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 94120575 = 14

Square burnerflames



(b)

Figure 9 Statistical distributions of the instantaneous temperature difference parameter for the disk (a) and the square (b) at different levelsof local extinction


15

125

1

075

05

025

00 02 04 06 08 1

Disk burner

OHlowastCHlowast intensity ratio

rD

b

120575 = 50

120575 = 18

120575 = 6

(a)

2

18

16

14

12

10

08

06

04

02

000 03 06 09 12 15

120575 = 94

120575 = 65

120575 = 14

yh


Square burner

(b)

Figure 10 Cross-stream profiles of the ratio of the mean OHlowast to CHlowast chemiluminescence across the flame front within the recirculationzone for three ultra-lean and limiting flame settings (a) disk and (b) square burner Chemiluminescence profiles were taken at 119909119863

119887= 044

for the disk and at 119909ℎ = 16 for the square

for the disk and at 119909ℎ 119910ℎ = 05 07 for the square) areshown in Figures 8(a) 8(b) and 8(c) for each burner andtwo levels of fuel reduction Depending on the level of localextinction these plots exhibit distinctly different dispersionsconsistent with the reduction of the local reactivity as deter-mined by the Karlovitz criterion Interestingly the scatterplotdistribution for the square depicted in Figure 8(c) displaysa recursive appearance of four major extinction events Thiscorroborates the onset of vortical development at the flametongues that seem to be reinstated as LBO is approached asalso implied by the low 120575 snapshots of Figure 7(b) Such abehavior has been reported previously for fully premixed forexample [6 12] and partially premixed configurations [11]

The computed statistical distributions (frequency counts)of the instantaneous temperature threshold parameter Δ119879

119888

are displayed for the same monitoring position in Figures9(a) and 9(b) for the two setups respectively A thresholdtemperature has been previously exploited as a practical andcomplementary diagnostic parameter for indicating extinc-tion [2 3 10] Based on the present experimental and compu-tational tests and various studies on laminar counterflow [210] and turbulent flames [3] a limit value of 1325K was heretentatively used for the present conditions The dispositionof the successive distributions of Δ119879

119888 shown in Figures 9(a)

and 9(b) consistently delineates the increased probability forlocal extinction since the selectedmonitoring point lays closeto the stabilizing shear layers these in combination withfurther monitoring parameters could also be considered asindicative of the proximity to global extinction

Figures 10(a) and 10(b) display the cross-stream profilesof the ratio of the time-mean OHlowastCHlowast chemiluminescencewithin the recirculation regions and across the flame frontsat 119909119863


square away from the burner face The OHlowast and CHlowast diskprofiles have been projected onto an axisymmetric planethrough an inverse Abel transform for a more consistentcomparison of their ratio The results imply that the flamescloser to extinction consistently attain a higher value of thisratio for both burners and this trend if further elaboratedcould likely be suitable for demarcating limiting conditions Itcould be postulated that apart from monitoring the transientbehavior of the above or additional parameters at judiciouslychosen locations the examination of time-mean data couldbe equally useful in producing useful overall criteria in afashion similar to the exploitation of a local Damkohlernumber an attribute that merits further verification over arange of flame topologies and conditions

Figure 11 displays instantaneous OHlowast chemilumines-cence images obtained at a fuel setting of 120575 = 6 forthe disk and of 120575 = 14 for the square respectively Theaxisymmetric reacting wake structures in the disk imagesindicate a flame topology with highly variable peripheralliftoff distance with time These flame front structures forma wide angle relative to the incoming flow due to the effectof the high swirl intensity and seem to occasionally penetratefrom the periphery toward the base of the flame within therecirculation regionThe overall disposition of the flame frontunder stratification seems to differ both in terms of lengthplacement and anchoring behaviour fromboth nonpremixed[16 19] and fully premixed axisymmetric [4 7 8] counterparttopologies The transient OHlowast chemiluminescent images forthe square verify the two-tongued flame front placementpreviously implied by the time-mean experimental andsimulation results (Figure 3) The two fronts independentlyreciprocate back and forth in time without any apparentinteraction The images do not provide any indication of


60

50

40

30

20

10

0minus20 0 20 minus20 0 20 minus20 0 20 minus20 0 20 minus20 0 20

Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)

minus20 0 20 minus20 0 20 minus20 0 20 minus20 0 20 minus20 0 20

Position (mm)

Counts175

125

75

25

(a)

60

50

40

30

20

10

0


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(b)

Figure 11 InstantaneousOHlowast images for disk (a) and square (b) burner operating with amixture level of 120575 = 6 (disk) and 120575 = 14 (square)

reaction within the formation region which is in starkcontrast to the reported behavior [6 12] of ultralean andlimiting slender body stabilization of fully premixed flames

6 Summary and Conclusions

Measurements and simulations of axisymmetric swirling diskand 2D slender square bluff-body reacting wakes working

with an inlet mixture gradient have been performed underultra-lean and near blowoff conditions Results have beenpresented and compared to highlight some differences andsimilarities in the flame characteristics of each stabilizerunder a variable stratified inlet mixture profile sustainedacross the leading edge flame front stabilization regionThesedata can also provide a useful assessment of the ultra-leanoperation of these two popular stabilizers under stratified


inlet mixture conditions as compared against the moretraditional fully premixed operation

The axisymmetric flames exhibited a more compactfrustum-like shaped near fame region with significant radialspread dependent on swirl intensity Recirculating hot prod-ucts occupied a toroidal region with an extent of about 20 to40 longer than the isothermal length This was maintainedacross the examined mixture strengths and was shorter thanthat found in counterpart fully premixed axisymmetric casesOver the ultra-lean range and at the limiting flame conditionsreacting front fragments were identified to penetrate withinthis recirculation region from the rim vortex stabilizationregion The formation of ring vortical structures that hasbeen identified in toroidal disk flames at fully premixedoperation was somewhat curtailed under stratified operationand this aspect requires further investigations since it affectsthe stability of these flames

The slender square body flames were stabilized at therim vortices formed on the square flanks establishing a two-tongued appearance The lengths of the two individual react-ing fronts were from two to eight square heights dependingon mixture strength Similarly with reaction the cold wakeformation region was expanded by about four to five timesin the lean cases this was drastically shortened at the weakerinlet mixtures Peak temperatures for the disk were locatedboth in the toroidal shear layer and extended well within therecirculation zone while for the square these were clearlypositioned along the square flanks The development of Von-Karman vortical instability was clearly identified to emerge inthe square flames as the flame fronts were significantly with-drawn back closer to the burner face this behaviour is alsodifferent from fully premixed configurations that have beenreported to maintain periodic symmetric or antisymmetricvortical structures across a wide range of equivalence ratios

The adopted LES procedure with an appropriate choiceof combustion and chemistry submodels reproduced satis-factorily the measured mean velocity and temperature distri-butions while providing useful qualitative descriptions of theexamined species fields which are compared quite favourablywith the chemiluminescence imaging measurements Themethod also provided some insight into the topology of theleading edge flame front anchoring adjacent to the flanks ofaxisymmetric or plane geometry stabilizers in the vicinityof equivalent ratio peaks within the context of a stratifiedinlet mixture gradient for ultra-lean and near to blowoffconditions

Conflict of Interests

There is no conflict of interests that arises from the method-ologies the instrumentations or the software used for theproduction and appraisal of the present research resultswithin the context of the present work performed by theauthors

Acknowledgment

This work was partly supported by the Research Council ofthe University of Patras

References

[1] B W Bilger S B Pope K N C Bray and J F DriscollldquoParadigms in turbulent combustion researchrdquo Proceedings ofthe Combustion Institute vol 30 no 1 pp 21ndash42 2005

[2] D Bradley ldquoCombustion and the design of future engine fuelsrdquoProceedings of the Institution ofMechanical Engineers C vol 223no 12 pp 2751ndash2765 2009

[3] G E Andrews N T Ahmed R Phylaktou and P King ldquoWeakextinction in low NOx gas turbine combustionrdquo in Proceedingsof the ASME Turbo Expo pp 623ndash638 June 2009

[4] M Stohr I Boxx C Carter et al ldquoDynamics of lean blowoutof a swirl-stabilized flame in a gas turbine model combustorrdquoProceedings of the Combustion Institute vol 33 no 2 pp 2953ndash2960 2011

[5] M S Sweeney S Hochgreb and R S Barlow ldquoThe structureof premixed and stratified low turbulence flamesrdquo Combustionand Flame vol 158 no 5 pp 935ndash948 2011

[6] S G Tuttle S Chaudhuri K M Kopp-Vaughan et al ldquoBlowoffdynamics of asymmetrically-fueled bluffbody flamesrdquo in Pro-ceedings of the 49th AIAA Aerospace Sciences Meeting AIAAOrlando Fla USA 2011

[7] J R Dawson R L Gordon J Kariuki et al ldquoVisualizationof blow-off events in bluff-body stabilized turbulent premixedflamesrdquo Proceedings of the Combustion Institute vol 33 no 1pp 1559ndash1566 2011

[8] Q Zhang S J Shanbhogue T Lieuwen and JOrsquoConnor ldquoStraincharacteristics near the flame attachment point in a swirlingflowrdquo Combustion Science and Technology vol 183 no 7 pp665ndash685 2011

[9] C Duwig K-J Nogenmyr C-K Chan andM J Dunn ldquoLargeeddy simulations of a piloted lean premix jet flame using finite-rate chemistryrdquo Combustion Theory and Modelling vol 15 no4 pp 537ndash568 2011

[10] E-S Cho S H Chung and T K Oh ldquoLocal karlovitz numbersat extinction for various fuels in counterflow premixed flamesrdquoCombustion Science and Technology vol 178 no 9 pp 1559ndash1584 2006

[11] P Koutmos and K Souflas ldquoA study of slender bluff bodyreacting wakes formed by con-current or counter-current fuelinjectionrdquo Combustion Science and Technology vol 184 no 9pp 1343ndash1365 2012

[12] K M Kopp-Vaughan T R Jensen B M Cetegen et al ldquoAnal-ysis of blowoff dynamics from flames with stratified fuelingrdquoProceedings of the Combustion Institute vol 34 no 1 pp 1491ndash1498 2013

[13] C Z Xiouris and P Koutmos ldquoFluid dynamics modelingof a stratified disk burner in swirl co-flowrdquo Applied ThermalEngineering vol 35 no 1 pp 60ndash70 2012

[14] O Colin F Ducros D Veynante and T Poinsot ldquoA thickenedflame model for large eddy simulations of turbulent premixedcombustionrdquoPhysics of Fluids vol 12 no 7 pp 1843ndash1863 2000

[15] G Wang M Boileau and D Veynante ldquoImplementation of adynamic thickened flame model for large eddy simulations ofturbulent premixed combustionrdquo Combustion and Flame vol158 no 11 pp 2199ndash2213 2011

[16] P Koutmos G Paterakis E Dogkas and C H Karagian-naki ldquoThe impact of variable inlet mixture stratification onflame topology and emissions performance of a premixerswirlburner configurationrdquo Journal of Combustion vol 2012 ArticleID 374089 12 pages 2012


[17] R R Erickson and M C Soteriou ldquoThe influence of reactanttemperature on the dynamics of bluff body stabilized premixedflamesrdquo Combustion and Flame vol 158 no 12 pp 2441ndash24572011

[18] J J Miau T S Leu T W Liu and J H Chou ldquoOn vortexshedding behind a circular diskrdquo Experiments in Fluids vol 23no 3 pp 225ndash233 1997

[19] A G Bakrozis D D Papailiou and P Koutmos ldquoA study ofthe turbulent structure of a two-dimensional diffusion flameformed behind a slender bluff-bodyrdquo Combustion and Flamevol 119 no 3 pp 291ndash306 1999

[20] D Trimis Verbrennungsvorgange in Porosen Inerten MedienBEV 955 ESYTEC Elangen Germany 1996

[21] C Dasch ldquoOne-dimensional tomography a comparison ofAbel onion-peeling and filtered back-projection methodsrdquoApplied Optics vol 31 no 8 pp 1146ndash1152 1992

[22] ANSYS Fluent Release 120 Theory Guide ANSYS 2009[23] L Gicquel G Staffelbach and T Poinsot ldquoLarge Eddy Simula-

tions of gaseous flames in gas turbine combustion chambersrdquoProgress in Energy and Combustion Science vol 38 no 6 pp782ndash817 2012

[24] A Briones and B Sekar Effect of Von Karman Vortex Sheddingon Regular and Open-Slit V-Gutter Stabilized Turbulent Pre-mixed Flames Spring Technical Meeting of the Central StatesSection of the Combustion Institute University of Dayton AirForce Research Laboratory Dayton 2012

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



transport and reaction processes over a range of operatingconditions from lean to ultra-lean and approaching blowoff(LBO) is important if a full exploitation or even extensionof the operational margin is to be realised (eg [4 6ndash8])A range of systematic experiments have been performed tostudy the structure of such flame configurations (eg [4ndash8])along with a number of supporting simulations that employvarious levels of complexity for the turbulence-chemistrytreatment and usually involve adaptive local gridding withina time-dependent procedure (eg [9]) Phenomenologicalanalyses (eg [2 6 8]) and global correlations (eg [3 10])are also utilized to complement the overall developmenteffort and relieve the burden and cost involved in themultiscalar approaches

These experimental and computational works have so farproduced detailed descriptions of the ultra-lean behaviour intraditional stabilizers such as fully premixed axisymmetric(eg [3 4 7 8]) and slender two-dimensional (eg [611]) bluff-body arrangements However stratified bluff-bodyflames operated at ultra-lean and near blow off conditionshave not been investigated as extensivelyMoreover the grow-ing combination of burner and mixture placement setups inlean combustors has increased current interest for a morecomplete description of such flame types Therefore compar-ative examinations of the performance of the axisymmetricversus the slender two-dimensional bluff-body stabilizationconfiguration under stratified conditions arewarranted thesecould provide useful information regarding themore effectivecontrol exploitation or even extension for example throughappropriate placement of pilot injection of the operationalmargin under both setups (eg [2 4 6 11 12])

This work then compares the ultra-lean performance andtopology characteristics of propane flames stabilized in anaxisymmetric double cavity fuel-air premixerdisk arrange-ment [13] and a counterinjected 2D slender square cylinder[11] under stratified conditions The above geometries werechosen because these comprise two of themost popular stabi-lizers at the opposite end of the field of practical applicationsand comparisons of their limiting performance could provideuseful directions in the design process for a wide range ofconfigurations Identification of the individual characteris-tics such as for example flame and recirculation lengthsflame front topologies turbulence levels vortical activityand under successively weakening stabilization within thesame geometry arrangement may help determine suitablemethodologies to extend stability in a fashion tailored notonly for the particular flame geometries but also for arange of intermediate variants upgrades or retrofits [2 412] Furthermore both of these setups have been systemati-cally investigated under fully premixed conditions and theiroperation under stratified conditions could then be directlycontrasted against such a range of well documented data

Measurements of turbulent velocities temperatureschemiluminescence imaging of OHlowast and CHlowast flame frontvisualization and gas analysis provided information for leanultra-lean and close to blowoff flames Supporting large-eddysimulations were also undertaken employing the thickenedflame model [14 15] and a nine-step mechanism for propanecombustion [11 13] to complement the experimental effort

and assist in the more complete interpretation of the opticalmeasurements

The combined methodology helped to elucidate some ofthe parametric characteristics of these diverse flame topolo-gies and improve understanding regarding the differencesand similarities between these two stabilizers when operatedwith a stratified inlet mixture as opposed to a fully premixedoperation In addition the local extinction behavior wasexamined by using the combination of three measured orcomputed parameters namely a local Karlovitz numbera local temperature threshold and the ratio of the OHlowastCHlowast chemiluminescence signature The credibility of thisparameterization is appraised where possible by using bothmeasurements and simulations

2 Flame Stabilization Configurations

The two burner setups are shown in Figures 1(a) 1(b) 1(c)1(d) 1(e) and 1(f) In the first configuration stratified flamesestablished by staged fuel-air premixing in a double-cavityarrangement (Figure 1(c)) formed along three concentricdisks and stabilized in the vortex region of the afterbody A(119863

119887= 0025) under the additional action of a coflowing

swirl stream (Figure 1(b)) are investigated The combustiontunnel and the studied burner are similar to those reported in[13] and have been optimized through a series of systematictests [16] Fuel is supplied through the central shaft (119863

119901=

0010) that is running along the central air supply tube (119863119888=

0052) into the internal hollow of the active bluff-body disk B(Figure 1(c))Then it is injected through an annular 1mm slotinto the primary fuel air-mixing cavity and is mixed with thecentral air supply This maintains an afterbody equivalenceratio gradient between a Φmin asymp 035 to 020 and a Φmax asymp098 to 05 depending on flame condition as measured withflame ionization detection from local gas samples at theafterbody exit (Figure 1(d)) Limiting conditions approachingblowoff were obtained by reducing the fuel level which thendecreased the peak Φ at the primary zone inlet In all cases aregulated stratified reactive mixture profile is attained acrossthe most favourable position for leading edge flame front sta-bilization at the disk burner rim (Figure 1(d)) The simulatedcavity flows for a lean flame at 119878 = 10 are shown in Figure 1(d)to illustrate the overall flow patterns obtained within and atthe exit of the premixer system these remain largely unalteredbetween lean and ultra-lean operation The global Φ basedon the totalmass flows of fuel and central air togetherwith therange of investigated conditions and parameters is shown inTable 1 The blockage ratio (BR) in the afterbody annular jetsupplying the primary zone is BR = (119863

119887119863

119888)2

= 023 [13]The second setup involves the study of partially premixed

and stratified flames established by planar injection (discretejets of small aspect ratio) of propane along the center planeof the leading face of a slender square cylinder Propane issupplied through the cylinder ends issued through 135 holesof 1mm diameter spaced at 05mm apart on the symmetryplane over a width of 200mm along the upstream face ofthe square and reaction is stabilized within and adjacentto the downstream wake formation region (Figures 1(e) and


Ue UeUs UsUc

(a)

1418552

Tangential air

Ws

(b)

25

75

75

51

13

53

10

A

B

C

Fuel

(c)

Fuel supply

Afte

rbod

y


mf


Φmax

Φmin

(d)


Airflow

Planar fuel jet

H

A

A998400


Injector holes(1mm)

A-A998400 view

W

(e)

Air flow

Fuel injection


h = 8mm

Uo

y Φ(y)Φmax

Φmin




119904119880

119904)






Case 120575 () 119880Fuel 119879max (K) 119871119891119863

119887119871119877119863

119887ΦGlobal Ka








119904=





119887 119903119863

119887) = (04 045) while for the














119909 CO CO

2 O

2 and C

119909H119910)





120597120588

120597119905+120597 (120588

119894)

120597119909119894

= 0 (1)

120597120588119894

120597119905+

120597 (120588119894119895)

120597119909119895

= minus120597119901

120597119909119894

+120597

120597119909119895

[120583(120597

119894

120597119909119895

+

120597119895

120597119909119894

)]

minus

120597120591119886

119894119895

120597119909119895

+ (Δ120588infin) 119892

119894

(2)

and Scalars are

120597120588119896

120597119905+

120597 (120588 119895119896)

120597119909119895

=120597

120597119909119897

(120588119863119896

120597119896

120597119909119897

)

minus120597119869

119897

120597119909119897

+ 120588120596119884119896 119896 = 1119873

(3)


119894 and 119884




119894119895minus 13120591

119894119895120575119894119895




2

(2119878119894119895119878119894119895)12 119878

119894119895is the


119894Δ119910

119894Δ119911



119897119884119896minus 119906

119897119884119896) =


119904(0 lt





3H8+ O

2+ OH +


2+ H Rxn 3 3H

2

+ O2harr 2H


2 Rxn 5 H

2+ O

2


2H2+ CO + H

2O

+ 3H2 Rxn 7 C

2H2+O

2harr 2CO +H

2 Rxn 8 2O +MharrO

2


























119887119880

119888= 5 times 10





(a) (b)


(a) (b)







0

05

1

15

2

25

0 1 2 3 4 5 6 7 8 9 10 11

minus1

minus05

UU

c

xDb

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(a)

0

02

04

06

08

0 2 4 6 8 10 12xDb

Urm

sUc

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(b)


0

04

08

12

0 2 4 6 8 10 12 14minus04

minus08

Comp 120575 = 94Exp 120575 = 94

UU

0

xh

(a)

0

01

02

03

04

0 2 4 6 8 10 12 14

Comp 120575 = 94Exp 120575 = 94

xh

Urm

sU0

(b)







200

500

800

1100

1400

1700

2000

0 2 4 6 8 10 12xDb

T(K

)

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(a)

0

02

04

06

08

1

12

200 600 1000 1400 1800T (K)

rD

b

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(b)

400

800

1200

1600

2000

0 5 10 15 20

T(K

)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

xh

(c)

0

02

04

06

08

1

12

14

16

18

200 600 1000 1400 1800 2200T (K)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

yh



for the square


119887for the lean (120575 = 50)









120575 = 50

120575 = 30

120575 = 18

120575 = 12

120575 = 6

400 800 1200 1600 2000


0 05 10


(a)


120575 = 94

120575 = 65

120575 = 35

120575 = 14

120575 = 6

400 1200 1600


0 05 10













119887 119903119863

119887= 032 04


4

3

2

1

019 20 21 22

Time (s)

KaK

a ex


(a)

4

3

2

1

017 18 19

Time (s)

KaK

a ex


(b)

4

3

2

1

0

Time (s)

KaK

a ex


76 78 8 82 84 86

(c)


10

08

06

04

02


Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 6 120575 = 50

Disk burnerflames



(a)

10

08

06

04

02

00minus200 0 200 400 600 800 1000

Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 94120575 = 14

Square burnerflames



(b)



15

125

1

075

05

025

00 02 04 06 08 1

Disk burner


rD

b

120575 = 50

120575 = 18

120575 = 6

(a)

2

18

16

14

12

10

08

06

04

02

000 03 06 09 12 15

120575 = 94

120575 = 65

120575 = 14

yh


Square burner

(b)


119887= 044




119888









60

50

40

30

20

10


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(a)

60

50

40

30

20

10

0


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(b)













Acknowledgment


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Ue UeUs UsUc

(a)

1418552

Tangential air

Ws

(b)

25

75

75

51

13

53

10

A

B

C

Fuel

(c)

Fuel supply

Afte

rbod

y


mf


Φmax

Φmin

(d)


Airflow

Planar fuel jet

H

A

A998400


Injector holes(1mm)

A-A998400 view

W

(e)

Air flow

Fuel injection


h = 8mm

Uo

y Φ(y)Φmax

Φmin




119904119880

119904)






Case 120575 () 119880Fuel 119879max (K) 119871119891119863

119887119871119877119863

119887ΦGlobal Ka








119904=





119887 119903119863

119887) = (04 045) while for the














119909 CO CO

2 O

2 and C

119909H119910)





120597120588

120597119905+120597 (120588

119894)

120597119909119894

= 0 (1)

120597120588119894

120597119905+

120597 (120588119894119895)

120597119909119895

= minus120597119901

120597119909119894

+120597

120597119909119895

[120583(120597

119894

120597119909119895

+

120597119895

120597119909119894

)]

minus

120597120591119886

119894119895

120597119909119895

+ (Δ120588infin) 119892

119894

(2)

and Scalars are

120597120588119896

120597119905+

120597 (120588 119895119896)

120597119909119895

=120597

120597119909119897

(120588119863119896

120597119896

120597119909119897

)

minus120597119869

119897

120597119909119897

+ 120588120596119884119896 119896 = 1119873

(3)


119894 and 119884




119894119895minus 13120591

119894119895120575119894119895




2

(2119878119894119895119878119894119895)12 119878

119894119895is the


119894Δ119910

119894Δ119911



119897119884119896minus 119906

119897119884119896) =


119904(0 lt





3H8+ O

2+ OH +


2+ H Rxn 3 3H

2

+ O2harr 2H


2 Rxn 5 H

2+ O

2


2H2+ CO + H

2O

+ 3H2 Rxn 7 C

2H2+O

2harr 2CO +H

2 Rxn 8 2O +MharrO

2


























119887119880

119888= 5 times 10





(a) (b)


(a) (b)







0

05

1

15

2

25

0 1 2 3 4 5 6 7 8 9 10 11

minus1

minus05

UU

c

xDb

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(a)

0

02

04

06

08

0 2 4 6 8 10 12xDb

Urm

sUc

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(b)


0

04

08

12

0 2 4 6 8 10 12 14minus04

minus08

Comp 120575 = 94Exp 120575 = 94

UU

0

xh

(a)

0

01

02

03

04

0 2 4 6 8 10 12 14

Comp 120575 = 94Exp 120575 = 94

xh

Urm

sU0

(b)







200

500

800

1100

1400

1700

2000

0 2 4 6 8 10 12xDb

T(K

)

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(a)

0

02

04

06

08

1

12

200 600 1000 1400 1800T (K)

rD

b

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(b)

400

800

1200

1600

2000

0 5 10 15 20

T(K

)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

xh

(c)

0

02

04

06

08

1

12

14

16

18

200 600 1000 1400 1800 2200T (K)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

yh



for the square


119887for the lean (120575 = 50)









120575 = 50

120575 = 30

120575 = 18

120575 = 12

120575 = 6

400 800 1200 1600 2000


0 05 10


(a)


120575 = 94

120575 = 65

120575 = 35

120575 = 14

120575 = 6

400 1200 1600


0 05 10













119887 119903119863

119887= 032 04


4

3

2

1

019 20 21 22

Time (s)

KaK

a ex


(a)

4

3

2

1

017 18 19

Time (s)

KaK

a ex


(b)

4

3

2

1

0

Time (s)

KaK

a ex


76 78 8 82 84 86

(c)


10

08

06

04

02


Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 6 120575 = 50

Disk burnerflames



(a)

10

08

06

04

02

00minus200 0 200 400 600 800 1000

Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 94120575 = 14

Square burnerflames



(b)



15

125

1

075

05

025

00 02 04 06 08 1

Disk burner


rD

b

120575 = 50

120575 = 18

120575 = 6

(a)

2

18

16

14

12

10

08

06

04

02

000 03 06 09 12 15

120575 = 94

120575 = 65

120575 = 14

yh


Square burner

(b)


119887= 044




119888









60

50

40

30

20

10


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(a)

60

50

40

30

20

10

0


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(b)













Acknowledgment


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Case 120575 () 119880Fuel 119879max (K) 119871119891119863

119887119871119877119863

119887ΦGlobal Ka








119904=





119887 119903119863

119887) = (04 045) while for the














119909 CO CO

2 O

2 and C

119909H119910)





120597120588

120597119905+120597 (120588

119894)

120597119909119894

= 0 (1)

120597120588119894

120597119905+

120597 (120588119894119895)

120597119909119895

= minus120597119901

120597119909119894

+120597

120597119909119895

[120583(120597

119894

120597119909119895

+

120597119895

120597119909119894

)]

minus

120597120591119886

119894119895

120597119909119895

+ (Δ120588infin) 119892

119894

(2)

and Scalars are

120597120588119896

120597119905+

120597 (120588 119895119896)

120597119909119895

=120597

120597119909119897

(120588119863119896

120597119896

120597119909119897

)

minus120597119869

119897

120597119909119897

+ 120588120596119884119896 119896 = 1119873

(3)


119894 and 119884




119894119895minus 13120591

119894119895120575119894119895




2

(2119878119894119895119878119894119895)12 119878

119894119895is the


119894Δ119910

119894Δ119911



119897119884119896minus 119906

119897119884119896) =


119904(0 lt





3H8+ O

2+ OH +


2+ H Rxn 3 3H

2

+ O2harr 2H


2 Rxn 5 H

2+ O

2


2H2+ CO + H

2O

+ 3H2 Rxn 7 C

2H2+O

2harr 2CO +H

2 Rxn 8 2O +MharrO

2


























119887119880

119888= 5 times 10





(a) (b)


(a) (b)







0

05

1

15

2

25

0 1 2 3 4 5 6 7 8 9 10 11

minus1

minus05

UU

c

xDb

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(a)

0

02

04

06

08

0 2 4 6 8 10 12xDb

Urm

sUc

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(b)


0

04

08

12

0 2 4 6 8 10 12 14minus04

minus08

Comp 120575 = 94Exp 120575 = 94

UU

0

xh

(a)

0

01

02

03

04

0 2 4 6 8 10 12 14

Comp 120575 = 94Exp 120575 = 94

xh

Urm

sU0

(b)







200

500

800

1100

1400

1700

2000

0 2 4 6 8 10 12xDb

T(K

)

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(a)

0

02

04

06

08

1

12

200 600 1000 1400 1800T (K)

rD

b

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(b)

400

800

1200

1600

2000

0 5 10 15 20

T(K

)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

xh

(c)

0

02

04

06

08

1

12

14

16

18

200 600 1000 1400 1800 2200T (K)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

yh



for the square


119887for the lean (120575 = 50)









120575 = 50

120575 = 30

120575 = 18

120575 = 12

120575 = 6

400 800 1200 1600 2000


0 05 10


(a)


120575 = 94

120575 = 65

120575 = 35

120575 = 14

120575 = 6

400 1200 1600


0 05 10













119887 119903119863

119887= 032 04


4

3

2

1

019 20 21 22

Time (s)

KaK

a ex


(a)

4

3

2

1

017 18 19

Time (s)

KaK

a ex


(b)

4

3

2

1

0

Time (s)

KaK

a ex


76 78 8 82 84 86

(c)


10

08

06

04

02


Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 6 120575 = 50

Disk burnerflames



(a)

10

08

06

04

02

00minus200 0 200 400 600 800 1000

Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 94120575 = 14

Square burnerflames



(b)



15

125

1

075

05

025

00 02 04 06 08 1

Disk burner


rD

b

120575 = 50

120575 = 18

120575 = 6

(a)

2

18

16

14

12

10

08

06

04

02

000 03 06 09 12 15

120575 = 94

120575 = 65

120575 = 14

yh


Square burner

(b)


119887= 044




119888









60

50

40

30

20

10


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(a)

60

50

40

30

20

10

0


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(b)













Acknowledgment


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119909 CO CO

2 O

2 and C

119909H119910)





120597120588

120597119905+120597 (120588

119894)

120597119909119894

= 0 (1)

120597120588119894

120597119905+

120597 (120588119894119895)

120597119909119895

= minus120597119901

120597119909119894

+120597

120597119909119895

[120583(120597

119894

120597119909119895

+

120597119895

120597119909119894

)]

minus

120597120591119886

119894119895

120597119909119895

+ (Δ120588infin) 119892

119894

(2)

and Scalars are

120597120588119896

120597119905+

120597 (120588 119895119896)

120597119909119895

=120597

120597119909119897

(120588119863119896

120597119896

120597119909119897

)

minus120597119869

119897

120597119909119897

+ 120588120596119884119896 119896 = 1119873

(3)


119894 and 119884




119894119895minus 13120591

119894119895120575119894119895




2

(2119878119894119895119878119894119895)12 119878

119894119895is the


119894Δ119910

119894Δ119911



119897119884119896minus 119906

119897119884119896) =


119904(0 lt





3H8+ O

2+ OH +


2+ H Rxn 3 3H

2

+ O2harr 2H


2 Rxn 5 H

2+ O

2


2H2+ CO + H

2O

+ 3H2 Rxn 7 C

2H2+O

2harr 2CO +H

2 Rxn 8 2O +MharrO

2


























119887119880

119888= 5 times 10





(a) (b)


(a) (b)







0

05

1

15

2

25

0 1 2 3 4 5 6 7 8 9 10 11

minus1

minus05

UU

c

xDb

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(a)

0

02

04

06

08

0 2 4 6 8 10 12xDb

Urm

sUc

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(b)


0

04

08

12

0 2 4 6 8 10 12 14minus04

minus08

Comp 120575 = 94Exp 120575 = 94

UU

0

xh

(a)

0

01

02

03

04

0 2 4 6 8 10 12 14

Comp 120575 = 94Exp 120575 = 94

xh

Urm

sU0

(b)







200

500

800

1100

1400

1700

2000

0 2 4 6 8 10 12xDb

T(K

)

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(a)

0

02

04

06

08

1

12

200 600 1000 1400 1800T (K)

rD

b

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(b)

400

800

1200

1600

2000

0 5 10 15 20

T(K

)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

xh

(c)

0

02

04

06

08

1

12

14

16

18

200 600 1000 1400 1800 2200T (K)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

yh



for the square


119887for the lean (120575 = 50)









120575 = 50

120575 = 30

120575 = 18

120575 = 12

120575 = 6

400 800 1200 1600 2000


0 05 10


(a)


120575 = 94

120575 = 65

120575 = 35

120575 = 14

120575 = 6

400 1200 1600


0 05 10













119887 119903119863

119887= 032 04


4

3

2

1

019 20 21 22

Time (s)

KaK

a ex


(a)

4

3

2

1

017 18 19

Time (s)

KaK

a ex


(b)

4

3

2

1

0

Time (s)

KaK

a ex


76 78 8 82 84 86

(c)


10

08

06

04

02


Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 6 120575 = 50

Disk burnerflames



(a)

10

08

06

04

02

00minus200 0 200 400 600 800 1000

Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 94120575 = 14

Square burnerflames



(b)



15

125

1

075

05

025

00 02 04 06 08 1

Disk burner


rD

b

120575 = 50

120575 = 18

120575 = 6

(a)

2

18

16

14

12

10

08

06

04

02

000 03 06 09 12 15

120575 = 94

120575 = 65

120575 = 14

yh


Square burner

(b)


119887= 044




119888









60

50

40

30

20

10


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(a)

60

50

40

30

20

10

0


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(b)













Acknowledgment


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
































119887119880

119888= 5 times 10





(a) (b)


(a) (b)







0

05

1

15

2

25

0 1 2 3 4 5 6 7 8 9 10 11

minus1

minus05

UU

c

xDb

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(a)

0

02

04

06

08

0 2 4 6 8 10 12xDb

Urm

sUc

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(b)


0

04

08

12

0 2 4 6 8 10 12 14minus04

minus08

Comp 120575 = 94Exp 120575 = 94

UU

0

xh

(a)

0

01

02

03

04

0 2 4 6 8 10 12 14

Comp 120575 = 94Exp 120575 = 94

xh

Urm

sU0

(b)







200

500

800

1100

1400

1700

2000

0 2 4 6 8 10 12xDb

T(K

)

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(a)

0

02

04

06

08

1

12

200 600 1000 1400 1800T (K)

rD

b

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(b)

400

800

1200

1600

2000

0 5 10 15 20

T(K

)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

xh

(c)

0

02

04

06

08

1

12

14

16

18

200 600 1000 1400 1800 2200T (K)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

yh



for the square


119887for the lean (120575 = 50)









120575 = 50

120575 = 30

120575 = 18

120575 = 12

120575 = 6

400 800 1200 1600 2000


0 05 10


(a)


120575 = 94

120575 = 65

120575 = 35

120575 = 14

120575 = 6

400 1200 1600


0 05 10













119887 119903119863

119887= 032 04


4

3

2

1

019 20 21 22

Time (s)

KaK

a ex


(a)

4

3

2

1

017 18 19

Time (s)

KaK

a ex


(b)

4

3

2

1

0

Time (s)

KaK

a ex


76 78 8 82 84 86

(c)


10

08

06

04

02


Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 6 120575 = 50

Disk burnerflames



(a)

10

08

06

04

02

00minus200 0 200 400 600 800 1000

Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 94120575 = 14

Square burnerflames



(b)



15

125

1

075

05

025

00 02 04 06 08 1

Disk burner


rD

b

120575 = 50

120575 = 18

120575 = 6

(a)

2

18

16

14

12

10

08

06

04

02

000 03 06 09 12 15

120575 = 94

120575 = 65

120575 = 14

yh


Square burner

(b)


119887= 044




119888









60

50

40

30

20

10


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(a)

60

50

40

30

20

10

0


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(b)













Acknowledgment


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)


(a) (b)







0

05

1

15

2

25

0 1 2 3 4 5 6 7 8 9 10 11

minus1

minus05

UU

c

xDb

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(a)

0

02

04

06

08

0 2 4 6 8 10 12xDb

Urm

sUc

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(b)


0

04

08

12

0 2 4 6 8 10 12 14minus04

minus08

Comp 120575 = 94Exp 120575 = 94

UU

0

xh

(a)

0

01

02

03

04

0 2 4 6 8 10 12 14

Comp 120575 = 94Exp 120575 = 94

xh

Urm

sU0

(b)







200

500

800

1100

1400

1700

2000

0 2 4 6 8 10 12xDb

T(K

)

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(a)

0

02

04

06

08

1

12

200 600 1000 1400 1800T (K)

rD

b

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(b)

400

800

1200

1600

2000

0 5 10 15 20

T(K

)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

xh

(c)

0

02

04

06

08

1

12

14

16

18

200 600 1000 1400 1800 2200T (K)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

yh



for the square


119887for the lean (120575 = 50)









120575 = 50

120575 = 30

120575 = 18

120575 = 12

120575 = 6

400 800 1200 1600 2000


0 05 10


(a)


120575 = 94

120575 = 65

120575 = 35

120575 = 14

120575 = 6

400 1200 1600


0 05 10













119887 119903119863

119887= 032 04


4

3

2

1

019 20 21 22

Time (s)

KaK

a ex


(a)

4

3

2

1

017 18 19

Time (s)

KaK

a ex


(b)

4

3

2

1

0

Time (s)

KaK

a ex


76 78 8 82 84 86

(c)


10

08

06

04

02


Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 6 120575 = 50

Disk burnerflames



(a)

10

08

06

04

02

00minus200 0 200 400 600 800 1000

Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 94120575 = 14

Square burnerflames



(b)



15

125

1

075

05

025

00 02 04 06 08 1

Disk burner


rD

b

120575 = 50

120575 = 18

120575 = 6

(a)

2

18

16

14

12

10

08

06

04

02

000 03 06 09 12 15

120575 = 94

120575 = 65

120575 = 14

yh


Square burner

(b)


119887= 044




119888









60

50

40

30

20

10


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(a)

60

50

40

30

20

10

0


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(b)













Acknowledgment


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

05

1

15

2

25

0 1 2 3 4 5 6 7 8 9 10 11

minus1

minus05

UU

c

xDb

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(a)

0

02

04

06

08

0 2 4 6 8 10 12xDb

Urm

sUc

Comp 120575 = 50 S = 0

Exp 120575 = 50 S = 0

Comp 120575 = 50 S = 1

Exp 120575 = 50 S = 1

(b)


0

04

08

12

0 2 4 6 8 10 12 14minus04

minus08

Comp 120575 = 94Exp 120575 = 94

UU

0

xh

(a)

0

01

02

03

04

0 2 4 6 8 10 12 14

Comp 120575 = 94Exp 120575 = 94

xh

Urm

sU0

(b)







200

500

800

1100

1400

1700

2000

0 2 4 6 8 10 12xDb

T(K

)

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(a)

0

02

04

06

08

1

12

200 600 1000 1400 1800T (K)

rD

b

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(b)

400

800

1200

1600

2000

0 5 10 15 20

T(K

)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

xh

(c)

0

02

04

06

08

1

12

14

16

18

200 600 1000 1400 1800 2200T (K)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

yh



for the square


119887for the lean (120575 = 50)









120575 = 50

120575 = 30

120575 = 18

120575 = 12

120575 = 6

400 800 1200 1600 2000


0 05 10


(a)


120575 = 94

120575 = 65

120575 = 35

120575 = 14

120575 = 6

400 1200 1600


0 05 10













119887 119903119863

119887= 032 04


4

3

2

1

019 20 21 22

Time (s)

KaK

a ex


(a)

4

3

2

1

017 18 19

Time (s)

KaK

a ex


(b)

4

3

2

1

0

Time (s)

KaK

a ex


76 78 8 82 84 86

(c)


10

08

06

04

02


Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 6 120575 = 50

Disk burnerflames



(a)

10

08

06

04

02

00minus200 0 200 400 600 800 1000

Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 94120575 = 14

Square burnerflames



(b)



15

125

1

075

05

025

00 02 04 06 08 1

Disk burner


rD

b

120575 = 50

120575 = 18

120575 = 6

(a)

2

18

16

14

12

10

08

06

04

02

000 03 06 09 12 15

120575 = 94

120575 = 65

120575 = 14

yh


Square burner

(b)


119887= 044




119888









60

50

40

30

20

10


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(a)

60

50

40

30

20

10

0


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(b)













Acknowledgment


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










200

500

800

1100

1400

1700

2000

0 2 4 6 8 10 12xDb

T(K

)

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(a)

0

02

04

06

08

1

12

200 600 1000 1400 1800T (K)

rD

b

Comp 120575 = 50Comp 120575 = 18Comp 120575 = 6

Exp 120575 = 50Exp 120575 = 18Exp 120575 = 6

(b)

400

800

1200

1600

2000

0 5 10 15 20

T(K

)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

xh

(c)

0

02

04

06

08

1

12

14

16

18

200 600 1000 1400 1800 2200T (K)

Comp 120575 = 94Comp 120575 = 65Comp 120575

Exp 120575 = 94

Exp 120575 = 14 = 14Exp 120575 = 65

yh



for the square


119887for the lean (120575 = 50)









120575 = 50

120575 = 30

120575 = 18

120575 = 12

120575 = 6

400 800 1200 1600 2000


0 05 10


(a)


120575 = 94

120575 = 65

120575 = 35

120575 = 14

120575 = 6

400 1200 1600


0 05 10













119887 119903119863

119887= 032 04


4

3

2

1

019 20 21 22

Time (s)

KaK

a ex


(a)

4

3

2

1

017 18 19

Time (s)

KaK

a ex


(b)

4

3

2

1

0

Time (s)

KaK

a ex


76 78 8 82 84 86

(c)


10

08

06

04

02


Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 6 120575 = 50

Disk burnerflames



(a)

10

08

06

04

02

00minus200 0 200 400 600 800 1000

Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 94120575 = 14

Square burnerflames



(b)



15

125

1

075

05

025

00 02 04 06 08 1

Disk burner


rD

b

120575 = 50

120575 = 18

120575 = 6

(a)

2

18

16

14

12

10

08

06

04

02

000 03 06 09 12 15

120575 = 94

120575 = 65

120575 = 14

yh


Square burner

(b)


119887= 044




119888









60

50

40

30

20

10


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(a)

60

50

40

30

20

10

0


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(b)













Acknowledgment


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120575 = 50

120575 = 30

120575 = 18

120575 = 12

120575 = 6

400 800 1200 1600 2000


0 05 10


(a)


120575 = 94

120575 = 65

120575 = 35

120575 = 14

120575 = 6

400 1200 1600


0 05 10













119887 119903119863

119887= 032 04


4

3

2

1

019 20 21 22

Time (s)

KaK

a ex


(a)

4

3

2

1

017 18 19

Time (s)

KaK

a ex


(b)

4

3

2

1

0

Time (s)

KaK

a ex


76 78 8 82 84 86

(c)


10

08

06

04

02


Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 6 120575 = 50

Disk burnerflames



(a)

10

08

06

04

02

00minus200 0 200 400 600 800 1000

Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 94120575 = 14

Square burnerflames



(b)



15

125

1

075

05

025

00 02 04 06 08 1

Disk burner


rD

b

120575 = 50

120575 = 18

120575 = 6

(a)

2

18

16

14

12

10

08

06

04

02

000 03 06 09 12 15

120575 = 94

120575 = 65

120575 = 14

yh


Square burner

(b)


119887= 044




119888









60

50

40

30

20

10


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(a)

60

50

40

30

20

10

0


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(b)













Acknowledgment


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










4

3

2

1

019 20 21 22

Time (s)

KaK

a ex


(a)

4

3

2

1

017 18 19

Time (s)

KaK

a ex


(b)

4

3

2

1

0

Time (s)

KaK

a ex


76 78 8 82 84 86

(c)


10

08

06

04

02


Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 6 120575 = 50

Disk burnerflames



(a)

10

08

06

04

02

00minus200 0 200 400 600 800 1000

Nor

mal

ized

freq

uenc

y co

unts

Distributions of

120575 = 94120575 = 14

Square burnerflames



(b)



15

125

1

075

05

025

00 02 04 06 08 1

Disk burner


rD

b

120575 = 50

120575 = 18

120575 = 6

(a)

2

18

16

14

12

10

08

06

04

02

000 03 06 09 12 15

120575 = 94

120575 = 65

120575 = 14

yh


Square burner

(b)


119887= 044




119888









60

50

40

30

20

10


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(a)

60

50

40

30

20

10

0


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(b)













Acknowledgment


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










15

125

1

075

05

025

00 02 04 06 08 1

Disk burner


rD

b

120575 = 50

120575 = 18

120575 = 6

(a)

2

18

16

14

12

10

08

06

04

02

000 03 06 09 12 15

120575 = 94

120575 = 65

120575 = 14

yh


Square burner

(b)


119887= 044




119888









60

50

40

30

20

10


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(a)

60

50

40

30

20

10

0


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(b)













Acknowledgment


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










60

50

40

30

20

10


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(a)

60

50

40

30

20

10

0


Posit

ion

(mm

)

60

50

40

30

20

10

0

Posit

ion

(mm

)

Position (mm)


Position (mm)

Counts175

125

75

25

(b)













Acknowledgment


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















Acknowledgment


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article A Comparison of the ... - Hindawi

Documents

Transcript of Research Article A Comparison of the ... - Hindawi