Experimental study of scalar filtered mass density function in turbulent partially premixed flames

Transcription

1 Proeedings of the Comustion Institute 31 (7) Proeedings of the Comustion Institute Experimentl study of slr filtered mss density funtion in turulent prtilly premixed flmes Dnhong Wng, Chenning Tong, *, R.S. Brlow, A.N. Krpetis Deprtment of Mehnil Engineering, Clemson University, Clemson, SC 93-91, USA Comustion Reserh Fility, Sndi Ntionl Lortories, Livermore, CA , USA Deprtment of Aerospe Engineering, Texs A&M Univesity, College Sttion, TX 773, USA Astrt The mixture frtion filtered mss density funtion () used in lrge eddy simultion (LES) of turulent omustion is studied experimentlly using line imges otined in turulent prtilly premixed methne flmes (Sndi flmes D nd E). Cross-strem filtering is employed to otin the nd other filtered vriles. The mens of the onditionl on the sugrid-sle (SGS) slr vrine t given lotion re found to vry from lose to Gussin to imodl, inditing well-mixed nd nonpremixed SGS mixing regimes, respetively. The imodl SGS slr hs struture (rmp liff) similr to the ounter-flow model for lminr flmelets. Therefore, while the urden on mixing models to predit the well-mixed SGS slr is expeted to lessen with deresing filter sle, the urden to predit the imodl one is not. These SGS slr strutures n result in flututions of the SGS flme struture etween distriuted retion zones nd lminr flmelets, ut for resons different from the slr dissiption rte flututions ssoited with the turulene sde. Furthermore, the imodl SGS slr ontriutes signifint mount of the slr dissiption in the retion zones, highlighting its importne nd the need for mixing models to predit the imodl s. Ó The Comustion Institute. Pulished y Elsevier In. All rights reserved. Keywords: Turulent flmes; Lrge-eddy simultion; Filtered density funtion; Turulent mixing 1. Introdution In LES of turulent omustion the sugridsle (SGS) slr mixing nd the resulting instntneous (density-weighted) distriution of slr vlues in eh grid volume, the filtered mss density funtion (), must e fithfully represented in order to predit urtely the hemil retion rtes [1 3]. An importnt modeling pproh uses the trnsport * Corresponding uthor. Fx: E-mil ddress: tong@es.lemson.edu (C. Tong). eqution, in whih the retion soure term is in losed form, while the mixing of SGS slrs requires modeling. As step towrd understnding the mixing of multiple retive SGS slrs nd towrd developing improved mixing models, the present work investigtes the mixing of the SGS mixture frtion, whih plys n importnt role in determining the mixture frtion nd onsequently the omustion regimes nd lol extintion/reignition hrteristis. The is lso n importnt model vrile in severl other LES pprohes for nonpremixed omustion, suh s the lminr flmelet method nd onditionl moment losure /$ - see front mtter Ó The Comustion Institute. Pulished y Elsevier In. All rights reserved. doi:1.11/j.proi..7.99

2 153 D. Wng et l. / Proeedings of the Comustion Institute 31 (7) The urrent understnding of onserved slr SGS mixing is lrgely sed on the Kolmogorov Oukhov Corrsin theory, in whih the SGS slr is onsidered to possess ertin self-similr properties. Therefore, the SGS slr is expeted to hve self-similr distriutions. However, our reent investigtion of SGS mixing in nonreting jets [ 7] showed, for the first time, tht the SGS slr hs qulittively different distriutions nd strutures, depending on the instntneous SGS slr vrine. When the SGS vrine is smll ompred to its men vlue, the SGS slr on verge hs lose-to-gussin distriutions, similr to the slr proility density funtion (PDF) in fully developed slr field, nd the slr dissiption depends wekly on the SGS slr, inditing well-mixed SGS slr fields. However, when the SGS vrine is lrge ompred to its men vlue, the SGS slr on verge hs imodl distriutions, inditing highly nonpremixed SGS slr fields. The onditionlly filtered slr dissiption hs ell-shped dependene on the slr. In nonpremixed flme suh SGS struture would indite regions of highly segregted fuel nd oxidizer seprted y shrp interfe, resemling the struture of ounter-flow diffusion flme, whih is model for lminr flmelets []. The imodl FDFs re similr to the slr PDF in the erly stges of inry mixing, nd re ontrry to the generl onsidertions sed on Kolmogorov s hypothesis. The well-mixed nd the highly nonpremixed SGS mixture frtion fields n potentilly hve strong influenes on the flme struture. For the former the SGS slr flututions t the dissiption sles (Corrsin sle, (D 3 /) 1/ ) must e lrger thn the retion zone width in the mixture frtion spe to support lminr flmelets, where D nd re the moleulr diffusivity nd the energy dissiption rte, respetively. This ondition is similr to tht given y Bilger [9]. For the imodl SGS fields, however, the slr vlue jump etween the highly nonpremixed SGS regions re generlly of the order of the instntneous SGS rms vlue, nd hene is muh lrger thn the flututions predited y the Oukhov Corrsin sling. Furthermore, the jump often ours over distne of the order of the Corrsin sle, therey limiting the retion zone to lyer thinner thn the Corrsin length sle nd resulting in lminr flmelets. This ondition for lminr flmelets is similr to tht given y Peters [1]. In this work, we study experimentlly the SGS mixing of the mixture frtion in turulent prtilly premixed flmes nd exmine the different SGS mixture frtion distriutions nd strutures. We investigte the hrteristis of the filtered mss density funtion () of the mixture frtion, F nl ð^n; x; tþ ¼hqðx; tþdðn ^n; x; tþi Z ¼ qðx ; tþdðn ^n; x ; tþgðx x Þdx ; ð1þ nd the onditionlly filtered slr dissiption rte, hvjni ¼hD on on jni ox j ox ; ðþ j whih is the mixing term in the trnsport eqution, where n nd q re the mixture frtion nd the fluid density, respetively. The susripts nd L denote onventionl nd Fvre filtered vriles, respetively. The filter funtion G is hosen to e top-ht, for whih the SGS distriution () nd the (Fvre) filtered men vriles n e lerly interpreted. The integrtes to the filtered mixture density.. Experimentl dt We use experimentl dt otined in piloted turulent prtilly premixed methne flmes with 1:3 rtio of CH to ir y volume (Sndi flmes D nd E, see Ref. [11 13]). The mesurements employed omined line-imging of Rmn sttering, Ryleigh sttering, nd lser-indued CO fluoresene. Simultneous mesurements of mjor speies (CO,O, CO, N,CH,H O, nd H ), mixture frtion (otined from ll mjor speies), temperture, nd the rdil omponent of slr dissiption rte were mde. The mixture frtion is lulted using vrition of Bilger s definition, whih hs een modified y exluding the oxygen terms [11]. The issue of mesurement unertinty ws ddressed in Ref. [11], whih onluded tht the uries of the mesured speies mss frtions, temperture, nd mixture frtion re suffiient. For exmple, the mesured vlues of the slr vrine in uniform lirtion flows were 1 in ir nd 1 5 in flt stoihiometri flme produts nd in jet fluid, respetively. The length of the imging line is. mm with mesurement sping of. mm. The tul mesurement resolution my e lrger (.3 mm) due to the lurring effets of the optil system. Brlow nd Krpetis (, 5) ddressed the issue of the sptil resolution on the mesured men slr dissiption rte nd onluded tht for flme D the resolution is generlly dequte eyond x/d = 7.5. This resolution n still under-resolve very lrge dissiption flututions, therey under-estimting the onditionlly filtered dissiption rte in liffs. Therefore, the onlusion regrding the imodl onditionl my e slightly onservtive. Computing the nd SGS vriles from experimentl dt requires sptil filtering

3 D. Wng et l. / Proeedings of the Comustion Institute 31 (7) of slr fields. In this work, one-dimensionl filtering is employed. While in LES the filtering is generlly performed in three dimensions, our previous results hve shown tht the slr filtered density funtion (FDF) otined with one-dimensionl filters is similr to tht otined with twodimensionl filters [,5], whih hs een shown to e very good pproximtion of three-dimensionl filtering, with errors of pproximtely 5% for the rms resolvle- nd sugrid-sle vriles [1]. For similr level of imodlity for the FDF, the SGS slr vrine is somewht lrger for one-dimensionl filters, whih re therefore expeted to yield similr results. The filter sizes D employed in this work re 3. nd. mm, respetively, to ensure tht the results re relevnt to LES, i.e., they should e signifintly lrger ompred to the dissiptive sles, llowing physis of the SGS mixing nd its intertion with hemistry n e linked to inertil-rnge dynmis. In our nlyses line imges re used t eh mesurement lotion. We use in width of Dln Æn æ =.3 to ensure suffiient sttistil onvergene. While the preise level of sttistil unertinty is diffiult to predit due to the omplexity of the onditioning proedures, the degree of sttistil onvergene is inferred empirilly using our lrge dt set otined in non-reting jets [5]. We find tht while the unertinty is somewht higher when the dt size is redued to tht omprle to the urrent flme dt, the results for the imodl remin unhnged. Further redution of the in size slightly inreses the imodlity of the imodl onditionl SGS slr. Therefore, the onlusion regrding the imodl is gin somewht onservtive. 3. Results nd disussions In this setion the results of the mesured nd the onditionlly filtered dissiption re presented. Unlike PDF nd the onditionl dissiption, the nd the onditionlly filtered dissiption re rndom vriles, nd re therefore nlyzed here using their onditionl verges. We use the Fvre filtered mixture frtion, hni L ¼hqni =hqi ; ð3þ nd the Fvre SGS slr vrine, hn i L 1 Z F nl ð^n; x; tþð^n hni hqi L Þ d^n ¼hqn i =hqi hni L ðþ (lso rndom vriles) s onditioning vriles, whih provide mesure of the unmixedness of the mixture frtion. The ltter is lso n importnt vrile in the inertil-rnge dynmis, nd therefore n relte the to the inertilrnge dynmis. Suh linkge is importnt for modeling SGS mixing The onditionl slr The onditionl mixture frtion, ÆF nl jænæ L, Æn æ L æ, for flme D t x/d = 15 for severl SGS vrine vlues is shown in Fig. 1. The filter sle is D = 3. mm nd Ænæ L is set to the stoihiometri mixture frtion, n s (=.35), to mximize the proility of the SGS field ontining retion zones. For smll SGS vrine, e.g. Æn æ L., the onditionl is unimodl nd generlly not fr from Gussin. Suh distriution is similr to those otined in nonreting flows nd to the slr PDF in fully developed turulent flow, inditing tht the SGS mixture frtion is well mixed. Previous results [,5] hve shown tht the SGS slr under suh onditions is in spetrl equilirium, suggesting Fig. 1. Conditionl in flme D for D = 3. mm nd Ænæ L =.35. () x/d = 7.5; () x/d = 15; () x/d = 3.

4 153 D. Wng et l. / Proeedings of the Comustion Institute 31 (7) tht the SGS slr is onsistent with Kolmogorov s sde piture. Therefore, the verge SGS slr flututions dereses with the filter sle, suggesting tht the urden on the SGS mixing models is lessened. As the SGS vrine inreses, the eomes imodl, with the imodlity stronger for lrger SGS vrine, inditing tht the rih nd len mixtures in the SGS field (i.e., grid ell) re essentilly segregted. Furthermore, there is shrp interfe (diffusion-lyer) seprting the two regions, ross whih there is lrge slr vlue jump (see the disussion on the onditionlly filtered slr dissiption rte elow). This SGS slr struture is essentilly rmp liff struture (see Ref. [15]), with the rih nd len mixtures forming the rmps nd the diffusion lyer s the liff. The imodl is lso similr to the slr FDF for lrge SGS vrine oserved in nonreting flows []. Our previous results lso showed tht the SGS slr with lrge vrine is in spetrl nonequilirium, whih, long with the presene of the rmp liff struture, suggests tht the imodl SGS slr is not well desried y Kolmogorov s turulene sde piture. Beuse the rmp liff struture exists in the sugrid sles for ll filter sizes signifintly lrger thn the Corrsin sle, s is the se in most LES, the urden on mixing models to pture the imodl does not lessen with deresing filter sle. The vlue of the Fvre filtered mixture frtion hs different effets on the unimodl nd imodl onditionl s. For unimodl, the shpe remins pproximtely unhnged when Ænæ L inreses from.35 to.5 (Fig. ), ut the position of the pek shifts rightwrd to pproximtely. (leftwrd to. for Ænæ L =.5, not shown). The lose-to-gussin distriutions indite tht the onditionl SGS mixture frtion fields re still well-mixed nd diffuse towrd Ænæ L. For Ænæ L vlues suffiiently wy from n s, the SGS field might not ontin ny retion zones. Therefore, the s of suh fields re of less interest nd not shown. For imodl, the positions of the two peks move muh less thn tht of unimodl s Ænæ L inreses, ut with the left nd right pek vlues deresing nd inresing respetively, refleting the inrese in the Ænæ L vlue. This result indites tht vritions of the Ænæ L vlue only lter the frtion of the fuel-len region reltive to tht of the fuel-rih region in the onditionlly smpled SGS field. The onditionl s t different downstrem lotions (Fig. 1) exhiit similr hrteristis to tht t x/d = 15. The mximum vlue of the onditionl SGS mixture frtion dereses somewht with inresing downstrem distne. Fr downstrem the mximum will e signifintly less thn unity (no pure fuel left). However, the Fig.. Conditionl t x/d = 15. () Flme D, D = 3. mm, Ænæ L =.5; () flme D, D =. mm, Ænæ L =.35; () flme E, D = 3. mm, Ænæ L =.35. qulittive hrteristis of lose-to-gussin nd imodl distriutions re expeted to remin the sme, s oserved in non-reting jets[,1]. The filter sle is n importnt prmeter in LES nd it is importnt to understnd how the vries with it. The results for the two filter sles (3. nd. mm) t x/d =15(Figs. 1 nd ) re very similr, further demonstrting tht the imodl is n inherent property of the SGS slr with lrge SGS vrine nd tht the urden on the mixing model to predit the imodl distriutions does not lessen with deresing filter sle. The results lso show tht the trnsition from unimodl to imodl for the two filter sles (defined here s the point t whih the top of the eomes flt) ours t pproximtely Æn æ L =.1 nd., respetively. This differene is relted to the men SGS vrine for D = 3. mm (.5) eing smller thn tht for D =. mm (.3).

5 D. Wng et l. / Proeedings of the Comustion Institute 31 (7) Previous results [,1] hve shown tht in the fully developed region of non-reting jet the slr FDF essentilly n e ollpsed y the normlized SGS vrine, Æn æ L /Æn æ, regrdless of the filter size (s long s it is suffiiently lrge ompred to the Corrsin sle). The results in Figs. 1 nd re qulittively onsistent with the previous results. However, in developing flow this might not e true. Compring Fig. 1 nd we find tht in oth ses the trnsition to imodl ours pproximtely t Æn æ L =.1, lthough the men vlues of the SGS vrine differ y nerly ftor of (.5 vs.3). These results might e euse the turulene is evolving rpidly ner the nozzle. The results show tht the sttistil struture of the SGS mixture frtion is qulittively different for smll nd lrge SGS vrine vlues. For imodl, the differene etween the n vlues for its peks is often lrger thn the ner-equilirium (or mildly strined flmelets) retion zone width in the n spe for these methne flmes, Dn R (.3), defined y the len nd rih limits tht orrespond to 1% of the pek CO oxidtion retion rte in lminr flmes [17]. Therefore, suh mixture frtion struture is likely to limit the retion zones in thin diffusion lyers, therey resulting in lminr flmelets. By ontrst, for the well-mixed SGS mixture frtion field, the turulene sde is likely to dominte nd the dissiption-sle slr flututions lrgely follow the Kolmogorov Oukhov Corrsin preditions. Therefore, suh SGS slr is likely to result in distriuted retion zones. 3.. The onditionlly filtered slr dissiption The onditionlly filtered slr dissiption, ÆÆvjnæ jænæ L, Æn æ L æ, for the sme onditions s Fig. 1 is shown in Fig. 3. Similr to the, Ævjnæ lso hs qulittively different funtionl forms for smll nd lrge SGS vrine. For smll Æn æ L it shows wek dependene on n, onsistent with the onditionl eing unimodl nd not fr from Gussin, providing further evidene tht the SGS mixture frtion is well-mixed. For lrge Æn æ L, the onditionlly filtered dissiption eomes ell-shped, with the mximum vlue inresing with the SGS vrine vlue. Furthermore, the mximum vlue ours t the n vlue where the imodl hs the minimum, inditing tht there is shrp interfe etween the highly segregted SGS mixture frtion regions, whih is essentilly diffusion lyer (liff) with thikness of the order of the Corrsin sle. Beuse the diffusion is towrd the slr vlue t the enter of the diffusion lyer (liff), independent of the hemistry, mixing models suh s the intertion y exhnge with the men (IEM) model n led to unphysil mixing ross n s (the retion zone). χ L χ L χ L e.1e.e 1.1e.e The nd the onditionlly filtered dissiption results suggest tht the SGS mixture frtion struture under the ondition of lrge SGS vrine is similr to tht in the ounter-flow model for lminr flmelets. However, Rjgopln nd Tong [1] noted tht the len nd rih mixtures in imodl SGS slr generlly do not hve n vlues of nd 1 respetively, sitution similr to tht noted y Bish nd Dhm [1]. Therefore, the lminr flmelets resulted re not simple flmelets otined using n = nd 1 s oundry onditions. The results show tht the oundry onditions for these flmelets re essentilly the n vlues for the two peks. The oserved reltionship etween the slr nd onditionlly filtered dissiption for smll nd lrge SGS vrine is lso similr to tht etween the slr PDF nd the onditionl dissiption [,5]. This is remrkle euse while the slr PDF nd the onditionl dissiption re relted through the slr PDF eqution, there is.e.1e.e 1.1e.e e.1e.e 1.1e.e 5.e Fig. 3. Conditionlly filtered slr dissiption, ÆÆvjnæ jænæ L, Æn æ L æ, in flme D. Conditions sme s in Fig. 1.

6 153 D. Wng et l. / Proeedings of the Comustion Institute 31 (7) no nlogous eqution relting the onditionl nd the onditionlly filtered dissiption. Therefore, the reltionship suggests tht the dynmis of the onditionl SGS fields re very similr to fully developed nd rpidly evolving slr fields, respetively. The similrities etween the ove results nd those otined in nonreting flows lso suggest tht het relese does not hnge qulittively the struture of the SGS mixture frtion fields, lthough other spets of the SGS slr my still e influened y het relese. The onditionlly filtered dissiption t x/ D = 15 for the lrger filter sle D =. mm in Fig.. hs similr hrteristis to those for D = 3. mm, ut the mximum vlue is muh lower for the sme lrge SGS vrine vlue. For exmple, for Æn æ L =.5, the mximum vlue of Ævjnæ is ove s 1 for D = 3. mm while it is only ner 15 s 1 for D =. mm. We rgue tht this differene is due to two ftors. First, the trnsition from unimodl to imodl ours t smller SGS vrine vlue for χ L χ L χ L e.1e.e 1.1e.e 5.e.e.1e.e 1.1e.e 5.e e.1e.e 1.1e.e 5.e Fig.. Conditionlly filtered slr dissiption, ÆÆvjnæ jænæ L, Æn æ L æ. Conditions sme s in Fig.. D = 3. mm (Figs. 1 nd ). Therefore, we expet tht for given SGS vrine, the imodlity is stronger, nd therefore the dissiption is higher. Seond, euse of the reltively low Reynolds numer of the flme, the filter sizes employed re not very lrge ompred to the slr dissiption sles (.5 mm in liffs). Consequently, for the sme SGS vrine vlue, the verge width of the diffusion lyer smpled must e smller in when the filter size dereses, resulting in higher in-lyer dissiption rte. The onditionlly filtered dissiption for Ænæ L =.5 (Fig. ) hs similr funtionl forms to those for Ænæ L =.35, in ontrst with the lrger hnges in the, espeilly for lrge SGS vrine vlues. Beuse the pek region of the onditionlly filtered dissiption is dominted y the liff, its weker dependene on Ænæ L indites tht essentilly the sme liff is ptured y the onditionl smpling proedure. The rmps re smpled differently (see Fig. for ), ut they orrespond to muh lower dissiption vlues, nd therefore do not ffet the overll funtionl form of Ævjnæ. Comprisons mong the results for the onditionlly filtered dissiption t the three downstrem lotions (Fig. 3) show tht the mximum vlue for Ævjnæ with lrge SGS vrine dereses from x/d = 7.5 to 15, whih is due to two resons. First, the dissiption length sle generlly inreses with the downstrem distne, resulting in lrger diffusion lyer thikness nd smller Ævjnæ. Seond, for lrge SGS vrine there re extintion events t x/d = 15 ompred to nerly no extintion t x/d = 7.5 [19], therey reduing the slr diffusivity, nd onsequently the onditionlly filtered dissiption. From x/ D = 15 to 3 the dissiption length sle further inreses, whih tends to redue the Ævjnæ. However, most extinguished fluid prels hve reignited t this lotion, whih tend to inrese Ævjnæ. Due to these ompeting effets, the mximum vlue for the onditionl Ævjnæ t x/d =3 inreses slightly ompred to tht t x/d = 15. The results for the onditionl (Fig. ) nd Ævjnæ (Fig. ) for flme E re similr to those for flme D. The jet veloity is higher in flme E, resulting in higher strin rtes nd more lol extintion events. The higher strin rtes tend to result in higher slr dissiption rtes. In ddition, lol extintion my led to stronger entrinment sine het relese tends to suppress entrinment [], therey enhning the dissiption in liffs. However, lol extintion lso tends to redue the diffusivity nd dissiption. Moreover, the higher Reynolds numer nd possily the lol extintion redue the lol slr dissiption length sle, potentilly resulting in insuffiient mesurement resolution nd lower mesured dissiption rte. Proly s result of these ompeting effets, the mximum vlue

7 D. Wng et l. / Proeedings of the Comustion Institute 31 (7) for Ævjnæ for flme E (Fig. ) is pproximtely equl to (or slightly smller thn) tht for flme D. Further understnding of the effets my require mesurements of flme E t higher resolution. The ove results indite tht the SGS mixture frtion fields hve different sptil strutures for smll nd lrge SGS vrine vlues. We provide in Fig. 5 severl exmples of onditionl SGS mixture frtion nd mixture frtion-slr dissiption profiles. For smll SGS vrine, the v n profiles hve no ler strutures, onsistent with the well-mixed SGS mixture frtion. The rms (the instntneous stndrd devition) nd dissiption-sle SGS mixture frtion flututions re smller thn the retion zone width Dn R (.3). The mesured slr dissiption vlues (even fter multiplying them y ftor of three using the ssumption of lol isotropy) re smller thn the extintion dissiption rte for stedy lminr flme (v q = s 1 for the fuel onsidered), inditing tht the onditionl SGS flme is in the form of qusi-equilirium distriuted χ retion zones. For lrge SGS vrine, the SGS n profiles show lrge jumps in mixture frtion (the liff), effetively limiting the retion zone to within the struture nd resulting in lminr flmelets. The v n profiles re lso onsistent with this struture. For severl profiles the dissiption (even one omponent) exeeds the extintion vlue. Therefore, the lol extintion events under suh onditions re most likely in the form of flmelet extintion. The results lso suggest tht t given lotion in turulent flme, the SGS retion zones flutute etween distriuted retion zones nd lminr flmelets due to the ourrenes of the well mixed nd highly nonpremixed SGS mixture frtion fields. This use for the ourrenes of oth flme strutures is different from previous rguments sed on the flututions in the slr dissiption rte due to the turulene sde. The slr dissiption rte t point, y itself, does not provide suffiient informtion out the struture of the lol mixture frtion field. The vritions of the flme struture with the SGS mixture frtion struture suggest tht mixing models need to e le to pture the wellmixed nd imodl distriutions to ount for these flme strutures. To further understnd the impt of the SGS mixture frtion struture on the flme struture, it is importnt to quntify the potentil ontriutions to the het relese from eh type of flme struture. We first quntify the portion of the SGS fields ontining rmp liff strutures y plotting the PDF of lnæn æ L in flme D t x/ D =15 (Fig. ). The PDFs re pproximtely log-normlly distriuted with the peks loted t out Æn æ L =.7 nd.1, respetively. The onditionl (Fig. 1) is lredy imodl for the Æn æ L vlues t the pek lotion of the lnæn æ) L PDF, inditing tht well over 3% of the SGS slr field ontins rmp liff r (mm).35.3 Δ=3.mm Δ=.mm χ PDF of ln( ) Fig. 5. Conditionl profiles in flme D for Ænæ L =.35. x/d = 15, D = 3. mm. () nd () v n; () n Fig.. PDF of ln(æn æ L ) in flme D t x/d = 15. Ænæ L =.35.

8 15 D. Wng et l. / Proeedings of the Comustion Institute 31 (7) Tle 1 Contriutions to the slr dissiption rte from the rmp liff struture (Æn æ L > V) within the retion zone for different V vlues Flme D (mm) V D D E E strutures (Æn æ L >.5 nd.1 for D = 3 nd mm, respetively). These results re essentilly independent of the hemistry. Among these SGS fields, only those ontining slr vlue jumps lrger thn Dn R n result in lminr flmelets. To quntify the potentil ontriutions to the het relese from the imodl SGS fields, whih is hemistry (retion zone width) dependent, we lulte the rtio of the ontriutions to the slr dissiption rte from the portion of the rmp liff struture where the retion zone resides (n s Dn R < n < n s þ Dn R) to those from ll the retion zones s, R 1 V R ns þ Dn R n s Dn R hhvdðn ^nþi L jhn i L ip hn i L d^ndhn i L R ns þ Dn R hvdðn ^nþid^n ; n s Dn R ð5þ euse het relese is, to the first order pproximtion, proportionl to the slr dissiption rte, where P hn i L is the PDF of Æn æ L. The results for severl V vlues re given in Tle 1. For oth filter sles the slr dissiption for lrge SGS vrine (Æn æ L >.5 nd.1, respetively) ounts for more thn 5% of the totl slr dissiption within the retion zones, suggesting tht signifint mount of the het relese omes from the rmp liff struture, lthough it only oupies smll frtion of the sptil volume. These results indite tht imodl SGS mixture frtion ssoited with the rmp liff struture nd the resulting lminr flmelets ply importnt roles in nonpremixed/prtilly premixed flmes nd must e properly ounted for y mixing models.. Conlusions We use dt otined in turulent prtilly premixed flmes (Sndi flmes D nd E) to study the SGS mixing of mixture frtion. The Fvre filtered mixture frtion nd the Fvre SGS slr vrine re used s onditioning vriles for nlyzing the slr nd the onditionlly filtered slr dissiption. The results show tht for smll SGS slr vrine, the is unimodl regrdless of the filter sle, the mesurement lotion, nd the filtered mixture frtion vlue. However, the pek position of the shifts with the filtered mixture frtion. The onditionlly filtered slr dissiption rte depends wekly on the SGS slr, inditing tht the SGS slr is well mixed nd the turulene sde is likely to dominte the SGS mixing proess. Therefore, suh SGS mixture frtion is likely to result in distriuted retion zones. For lrge SGS vrine, however, the eomes imodl nd the onditionlly filtered slr dissiption is ell-shped, inditing the existene of rmp liff struture, whih is similr to the mixture frtion profile in the ounter-flow model for lminr flmelets. The mixture frtion struture ptured does not depend on the filtered mixture frtion vlue. For the mesurement lotions onsidered the differene in mixture frtion vlues for the two peks re generlly lrger thn the retion zone width in the mixture frtion spe, therefore the SGS mixing field under suh onditions support flmelets. These findings re similr to our previous results otined in nonreting jets, inditing tht het relese does not lter the qulittive hrteristis of the SGS mixture frtion fields. These results suggest tht t given lotion the SGS flme flututes etween distriuted retion zones nd lminr flmelets, ut for resons different from previous rguments sed on slr dissiption flututions resulted from the turulene sde. The strong effets of the imodl SGS slr on the flme struture indite tht mixing models need to e le to pture its distriutions to ount for the different flme strutures. The results for the ontriutions to the het relese from imodl SGS fields suggest tht signifint mount of het relese omes from the rmp liff struture, further highlighting its importne in flmes nd the need for mixing models to pture the imodl. The results for the with two filter sizes suggest tht or smll SGS vrine, the urden on the SGS mixing models lessens with deresing filter sle euse the SGS slr is likely to follow the Kolmogorov s sde piture. For lrger SGS vrine, lrge slr vlue jumps exist in the SGS slr for ll filter sles signifintly lrger thn the Corrsin sle, therefore the urden on the mixing model does not lessen with deresing filter size. Aknowledgments The work t Clemson ws supported y the Air Fore Offie of Sientifi Reserh under Grnt FA (Dr. Julin M. Tishkoff,

9 D. Wng et l. / Proeedings of the Comustion Institute 31 (7) progrm mnger) nd y the Ntionl Siene Foundtion under grnt CTS-9353 (CAREER wrd). The work t Sndi ws supported y the Division of Chemil Sienes, Geosienes, nd Biosienes, the Offie of Bsi Energy Sienes, the U.S. Deprtment of Energy. We thnk Professor Stephen B. Pope for reding the drft pper nd providing vlule omments. Referenes [1] S.B. Pope, Pro. Comust. Inst. 3 (199) [] P.J. Colui, F.A. Jeri, P. Givi, S.B. Pope, Phys. Fluids 1 (199) [3] M. Sheikhi, T. Drozd, P. Givi, F. Jeri, S. Pope, Pro. Comust. Inst. 3 (5) [] C. Tong, Phys. Fluids 13 (1) [5] D. Wng, C. Tong, Phys. Fluids 1 () [] D. Wng, C. Tong, S.B. Pope, Phys. Fluids 1 () [7] D. Wng, C. Tong, Pro. Comust. Inst. 3 (5) [] N. Peters, Prog. Eng. Comust. Si. 1 (19) [9] R.W. Bilger, Pro. Comust. Inst. (19) 75. [1] N. Peters, Turulent Comustion, Cmridge University press, Cmridge, Englnd,. [11] R.S. Brlow, A.N. Krpetis, Flow, Tur. Comust. 7 () 7. [1] A.N. Krpetis, R.S. Brlow, Pro. Comust. Inst. 3 (5) 5 7. [13] R.S. Brlow, A.N. Krpetis, Pro. Comust. Inst. 3 (5) 73. [1] C. Tong, J.C. Wyngrd, S. Khnn, J.G. Brsseur, J. Atmos. Si. 55 (199) [15] C. Tong, Z. Wrhft, Phys. Fluids (199) [1] A.G. Rjgopln, C. Tong, Phys. Fluids 15 (3) 7. [17] J.H. Frnk, S.A. Kiser, M.B. Long, Pro. Comust. Inst. 9 () 7 9. [1] E.S. Bish, W.J.A. Dhm, Comust. Flme 1 (1995) 57. [19] D. Wng, Ph.D. disserttion, Clemson University, Deprtment of Mehnil Engineering (July 5). [] A.N. Krpetis, R.S. Brlow, Pro. Comust. Inst. 9 ()