On Blow-Out of Jet Spray Diffusion Flames

Transcription

1 5 th ICDERS August 7, 015 Lees, UK n Blow-ut of Jet Spray Dffuson Flames N. Wenberg an J.B. Greenberg Faculty of Aerospace Engneerng, Technon Israel Insttute of Technology Hafa, Israel 1 Introucton The mechansm of gaseous jet ffuson flame blow-out an stablty has been stue both expermentally an theoretcally. The queston of prme mportance concerne the nature of the physcal an/or chemcal mechansms whereby the ffuson flame forme as a result of a jet fuel ssung nto an oxzng envronment often stablzes above the jet orfce, yet sometmes s blown out. Van quckenborne an Van Tggelen [1] stue the stablzaton of lfte, turbulent, ffuson methane flames expermentally. They foun that the base of the lfte flame anchors n a regon corresponng to the formaton of a stochometrc mxture, where the turbulent burnng velocty was equal to the flow velocty. They also observe that blow-out n jet ffuson flames s not an extncton phenomenon snce the flame can be mantane at varous heghts, prove there exsts a permanent gnton source. Kalghatg [] speculate that the blow-out velocty s a functon of the lamnar flame spee an heght of the stochometrc contour an foun a "unversal" non-mensonal formula to escrbe the blow-out stablty lmt of gaseous jet ffuson flames n stll ar. Chung an Lee [3] expermentally stue the characterstcs of lamnar lfte flames stablze n a non-premxe jet. They entfe the trbrachal structure of what was later to become known as an ege flame wth a fuel lean premxe structure on one arm connecte to a fuel lean premxe structure on a secon arm, wth a tralng ffuson flame ownstream an anchore n the aforementone flame root. They foun an expresson for lftoff heght as a functon of the flow rate, burner ameter an the Schmt number, Sc (rato of vscosty an mass ffusvty). They recognze the key role playe by Sc n the stablty mechansm for crcular jets, notng that the lft-off heght wll ncrease wth an ncrease n flow-rate for Sc < 0.5 an Sc > 1 but wll ecrease for 0.5 < Sc < 1. The basc theory utlze for prectng contons for flame blow out s summarze n [4] an [5]. It reles on the escrpton of an ncompressble jet extng from a narrow slot an the use of a smlarty soluton (etals of the evelopment are gven n [6]) for the governng bounary layer equatons. A soluton for the Schwab-Zelovtch parameters equaton s also evelope n a smlar fashon. The latter parameter enables a flame surface (nfntessmally thn) to be efne (nfnte chemcal Damkohler number). The pont(s) of concence of the flame surface an the flame spee surface (efne as those ponts where the axal velocty of the jet s equal to the local burnng velocty) ncate whether flame stablty s acheve or whether flame blow-out occurs, or, alternatvely, (see [5]) whether a lfte or a partal flame s acheve. It s of nterest to note that the crux of ths prectve capablty banks on the physcal escrpton of an ege flame wthout actually assgnng a etale mathematcal escrpton to t. It s for ths reason that Corresponence to: aer9801@technon.ac.l 1

2 Jet Spray Dffuson Flame the local premxe burnng velocty s explote even though the concept of burnng velocty has no real sgnfcance n the context of a ffuson flame. Many jet ffuson flames are actually fuele by a spray of lqu roplets. Yet the aforementone analyss has been htherto restrcte to gas flames only. In the current paper we present a new analyss whch accounts for precsely ths more realstc stuaton, an examne the way n whch the spray mpacts upon flame blow out an stablty. The Moel We conser two-mensonal jet spray ffuson flame (see Fg. 1). A -D lqu fuel spray jet emerges from a narrow slot burner port an entrans surrounng ar. Due to the mutual ffuson between the evaporatng fuel an the oxygen n the ar, a mxng layer s forme above the burner. Uner approprate operatng contons, a -D ffuson flame can be establshe throughout ths mxng layer. Fgure 1. A two-mensonal jet spray ffuson flame As mentone n the Introucton, accorng to classcal theory the behavor of a gas jet flame s etermne by the ext velocty of the fuel jet at the burner port an possble scenaros are summarze n Table 1. The queston aresse n the current work s how the summary s altere by the presence of a lqu fuel spray n the supply contons. 5 th ICDERS August -7, Lees

3 Table 1. Gaseous jet ffuson flame scenaros as escrbe n the lterature Jet Spray Dffuson Flame Jet ext velocty Lower than the burnng velocty. Slghtly hgher than the burnng velocty. Much hgher than the burnng velocty. Above the blow- out velocty. Flame characterstcs Flashback The flame enters the burner port an s mmeately extngushe ue to lack of oxygen. Complete an stable flame The flame remans attache to the burner port tp (see Fg. 1). Lfte flame The flame s etache from the burner port tp an a lfte flame s obtane above the burner. The lft-off heght s proportonal to the jet ext velocty. Blow-out The flame cannot reman stable above the burner an moves ownstream to a coler regon where t s eventually extngushe. 3 Governng equatons an soluton The mathematcal moel for the problem s base on the lamnar bounary layer theory for the jet an the sectonal approach (assumng a sngle secton for smplcty at the current stage) for the lqu roplets [7]. The mensonless governng equatons are: Contnuty an momentum conservaton equatons: u u x Mass conservaton equaton for the fuel roplets: v + = 0 y u u 1 u + v = x y Re y Y Y u v C Y x y + = Energy an speces conservaton equatons (n Schwab-Zelovch formulaton): β β 1 β u v C Y + = + α x y Re Sc y u β β 1 β v = x y Re Sc y In these equatons the nepenent varables are normalze, as are the velocty components ( u,v ), the mass fracton of lqu fuel n the spray Y an the Schwab-Zelovtch parameters ( β, β 3) whch are base on YF Y /ν an ( ) ( ) c T+ LY / Q+ 1 L / Q Y /ν, respectvely, where Y F,Y p F 5 th ICDERS August -7, Lees 3

4 Jet Spray Dffuson Flame are mass fractons of fuel vapor an oxygen, ν s the stochometrc coeffcent,t s temperature, cp s specfc heat, Q s heat of reacton an L s latent heat of vaporzaton. number, Sc s the Schmt number, ( C Re s the Reynols = C / U s normalze sectonal evaporaton coeffcent,u jet wth an average velocty, respectvely, an C the sectonal evaporaton coeffcent) an ( ) α = Y + Y / β, where the suffx refers to jet nlet contons. F,,, For the velocty u bounary contons are: symmetry at y = 0, u 0 as y an the total constant axal momentum flux, M, specfe at the nlet, x = 0. Smlar bounary contons hol for β an β 3. Also, v = 0 at y = 0. For Y a total flux conton for the lqu fuel s specfe at the nlet. The governng equatons were solve usng a smlarty soluton, wth smlarty varable ( / 3 1/ 3 ( 4 / 3 1/ 3 ))( / 3 ) η= ˆ Re M / 3 y x, an the followng solutons were obtane (for the case of Ĉ= 1, where Ĉ s a parameter relate to the evaporaton rate of the fuel roplets): ( ) ( M / Re) 1/ 3 1/ 3 1/ 3 / 3 3 Re M u,v = sec h ˆ η, 5/ 3 1/ 3 1/ 3 / 3 ( ˆ η sec h ˆ η tanh ˆ η) x 6 x In the regon wth fuel roplets, ˆ η< ˆ η : ( ) ˆ η β {( ) ˆ η ( α ( )) ˆ η} Y = A / x cosh, = D sec h Sc A / Sc+ 1 cosh / x 1/ 3 Sc 1/ 3 an wthout fuel roplets ˆ η ˆ η = = η, where ˆη s etermne from the > : Y ( 1/ 3 ) Sc 0, β ˆ B / x sech streamlne beyon whch the roplets o not travel n the transverse recton. Fnally, β ( B / x ) 1/ 3 Sc ˆ 3 3 sec h = η. In these solutons A,B,B 3,D are constants foun usng the bounary contons. The flame front s locate at those ponts where β = 0. 4 Results The shape an characterstcs of the flame are etermne by the mutual poston of two funamental surfaces the flame front surface (FFS), on whch β =, an the flame spee surface (FSS), on whch u= S ( S s the local lamnar flame spee). These are rawn n Fgs an 3 for fferent operatng contons. Note that the transverse coornate has been stretche for clarty the flames are actually rather thn. The unbroken black lne s the lmtng contour to the rght of whch no lqu roplets travel. The blue lne elneates flame spee surface. Yellow lnes are stable flame fronts. In contrast to the case of a purely gas flame, for whch only the Schmt number an the ext velocty of the fuel jet at the burner port etermne the nature of the flame, for the spray flame the roplets content of the fuel jet was also foun to play a key role. Conser Fg.. For the purely gas flame, the flame front surface (sol rea lne) les outse the flame spee surface, thereby ensurng a stable flame anchore to the burner. When the fuel s supple exclusvely as lqu roplets the flame front surface (small otte lne) les wthn the flame spee surface whereby flame blow-out occurs. For the case n whch the fuel s supple equally as vapor an lqu fuel roplets the lower part of the flame front 0 5 th ICDERS August -7, Lees 4

5 Jet Spray Dffuson Flame surface s wthn the flame spee surface but subsequently ownstream the curves cross an then the FFS les outse the FSS. Ths mples that the Fgure : The flame front an spee surfaces for Sc= 1 an U = 0.95m / sec an fferent ntal roplet loas. Fgure 3: The flame front an spee surfaces for Sc= 0.5 an U = 0.95m / sec an fferent ntal roplet loas. flame s lfte above the burner an stablzes ownstream. For a lower Schmt number of 0.5 results are shown n Fg.3. A further scenaro s observe for the case n whch the fuel s supple equally as vapor an lqu fuel roplets. Here the lower part of the flame s anchore to the burner whereas the upper part of the flame cannot be sustane. In general, as the lqu fuel content n the total fxe fuel supply ncreases, the flame shrnks (n ts heght an wth, see both Fgs an 3), ts temperature ecreases (not shown here) an the blowout velocty s reuce. These results can be unerstoo by the fact that as the ntal roplet loa ncreases 5 th ICDERS August -7, Lees 5

6 Jet Spray Dffuson Flame not all the roplets succee n vaporzng before reachng the flame front leang to a smaller, more compact FFS. Table summarzes a comparson between the spray flame an ts purely gaseous flame equvalent an ncates that n contrast to gas flames, for Sc 1 lfte spray flames may exst uner certan operatng contons. Table. Comparson between gas fuel an fuel spray jet ffuson flames Sc Pure gaseous fuel jet Fuel spray jet < 1 The flame front begns as complete, then becomes partal (open) an eventually blows out, as the velocty ncreases. velocty ncreases. = 1 The flame front begns as complete an eventually blows out, as the velocty ncreases. > 1 The flame front begns as complete, then becomes lfte an eventually blows out, as the velocty ncreases. The flame front begns as complete, then becomes partal (open) an/or lfte an eventually blows out, as the The flame front begns as complete, then becomes lfte an eventually blows out, as the velocty ncreases. The flame front begns as complete, then becomes lfte an eventually blows out, as the velocty ncreases. References [1] L. Van quckenborne an A. Van Tggelen, The stablzaton mechansm of lfte ffuson flames, Combuston an Flame, vol. 10, no. 1, pp , [] G. T. Kalghatg, Blow-out stablty of gaseous jet ffuson flames. Part I: n stll ar, Combuston Scence an Technology, vol. 6, no. 5-6, pp , [3] S. H. Chung an B. J. Lee, n the characterstcs of lamnar lfte flames n a nonpremxe jet, Combuston an Flame,vol. 86, no. 1-, pp. 6 7, [4] C.K. Law, Combuston Physcs, Cambrge Unversty Press, USA, 006. [5] K. Annamal an K. Pur, Combuston Scence an Engneerng, Taylor & Francs Group, 007. [6] H. Schlctng an K. Gersten, Bounary-Layer Theory, McGraw-Hll, NY, 008. [7] J.B. Greenberg, I. Slverman an Y. Tambour, "n the rgns of Spray Sectonal Conservaton Equatons", Combuston an Flame, vol. 93, pp , th ICDERS August -7, Lees 6