Computation of NO x emission of a methane air diffusion flame in a two-dimensional laminar jet with detailed chemistry

Transcription

1 Combust. Theory Modellng 1 (1997) Prnted n the UK PII: S (97) Computaton of NO x emsson of a methane ar dffuson flame n a two-dmensonal lamnar jet wth detaled chemstry Yguang Ju and Takash Noka Department of Aeronautcs and Space Engneerng, Tohoku Unversty, Aramak Aoba, Aoba-ku, Senda 980, Japan Insttute of Flud Scence, Tohoku Unversty, Katahra, Senda , Japan Receved 8 August 1996, n fnal form 8 August 1997 Abstract. NO x formaton from a methane ar dffuson flame n a two-dmensonal jet nvolvng hghly preheated ar, whch has recently become an mportant topc n ndustral furnaces, s nvestgated numercally usng a full chemstry approach ncludng C 2, prompt and thermal mechansms. Effects of ncreased ar temperature on NO x formaton are examned. Numercal results show that both NO formaton mechansms ncrease dramatcally wth ncreasng ar temperature. A C-shaped producton zone of NO 2, correspondng to the fuellean and fuel-rch regons of trple flame, s dentfed. It s shown that NO formaton wth hgh ar temperature can be suppressed effcently by decreasng the oxygen concentraton n the arstream. Producton rate analyses of elementary reactons are made. Formaton paths of NO x at low and hgh temperatures are obtaned and compared. The results show that the NO x formaton path depends strongly on the ar temperature. In addton to the thermal route and the HCN NO route, the HCN CN and NO CN recyclng routes are greatly enhanced at hgh ar temperature. The results show that the prompt mechansm and the thermal mechansm are strongly coupled at hgh ar temperature. Calculatons of prompt NO and thermal NO n a two-dmensonal jet and n the counterflow confguraton reveal that the conventonal method cannot gve a correct predcton of prompt NO and thermal NO, partcularly at hgh ar temperature. A method usng the concept of fxed ntrogen s presented. Numercal results ndcate that the formaton process of prompt NO and thermal NO can be evaluated properly by the present method. 1. Introducton Recently, reducton of NO x n a regeneratve burner, whch recycles the extra heat from the exhausted gas to preheat the nlet ar up to 1500 K through a ceramc storage heat exchanger, has attracted great attenton. There have been a consderable number of studes [1 6] on the NO x formaton mechansm. In hydrocarbon flames, t has been made clear that the thermal mechansm and the prompt mechansm are the man routes for NO x formaton. Hahn and Wendt [4] studed NO x formaton expermentally and numercally n a counterflow dffuson flame. A comparson between the experment and the predcton showed that formaton of NO was poorly predcted by the chemcal knetcs employed n the case of ammona addton to ar [4]. As an mprovement to ths defcency, a full chemstry model ncludng C 2 as E-mal address: ju@ju.mech.tohoku.ac.jp /97/ $19.50 c 1997 IOP Publshng Ltd 243

2 244 Y Ju and T Noka well as prompt, thermal and fuel mechansms was presented by Mller and Bowman [5]. Ther numercal results showed that expermental data can be well reproduced by ths full chemstry. Based on ths knetcs, Nshoka and co-workers [7, 8] studed the NO x formaton routes of both premxed and dffuson flames n the counterflow confguraton. Effects of stretch rate on NO x formaton have been nvestgated by Drake and Blnt [9]. Recently, the combned effect of stretch and ar temperature on NO x formaton has been examned by the frst author [10] usng counterflow dffuson flames. In fact, NO x emsson n practcal burners s mult-dmensonal. A computatonal and expermental study of NO n an axsymmetrc lamnar dffuson flame has been conducted recently by Smooke et al [16] and shows that the flame confguraton has a dramatc nfluence on the NO x emsson. However, only lmted studes on the NO x formaton n a mult-dmensonal flow are currently avalable n the lterature. Addtonally, the use of hghly preheated ar s a new challenge for reducton of NO x emsson. Therefore, an understandng of NO x emsson and the reducton of NO x formaton nvolvng hghly preheated ar n a mult-dmensonal confguraton s necessary. Fuel njecton nto a hghly preheated arstream s the basc way of burnng methane n regeneratve burners and also represents an deal confguraton for studyng the physcal processes n the mult-dmensonal problems. The purpose of the present study s to nvestgate numercally the NO x formaton mechansm of a methane ar dffuson flame n a two-dmensonal lamnar jet. Frst, formaton of NO x n the trple flame, whch s the typcal flame structure of dffuson flames n a lamnar jet and a mxng layer, s examned. Then effects of ncreased ar temperature and decreased oxygen concentraton n ar on NO x formaton are nvestgated. NO x emsson ndces correlated wth the ar temperature and the oxygen concentraton were obtaned. Ths s followed by an examnaton of flame structure and producton rate analyses. Formaton routes of NO x at both low and hgh temperatures are presented. Fnally, ndvdual contrbutons of the prompt and thermal mechansms to the total NO x emsson are dscussed. Results obtaned, respectvely, from the full chemstry and a combned mechansm of C 2 and a thermal mechansm are compared. A method usng fxed ntrogen for the evaluaton of prompt NO and thermal NO s presented and examned. 2. Governng equatons and chemcal models As shown n fgure 1, a dffuson flame of methane njected from a nozzle (5 mm n wdth) nto an nfnte ar stream s consdered. Inlet veloctes of the methane and the ar streams are 50 and 30 cm s 1, respectvely. The nlet fuel temperature s set at 300 K, whle the ar temperature s rased from 300 to 1300 K; the ntal pressure s 1 atm. The resultng Reynolds number s lower than 300. Thus the flow can be assumed to be lamnar. Wth the low Mach number approxmaton, the governng equaton can be wrtten as p = ρrt n Y j /M j (1) j=1 ρ t + (ρu j ) = 0 (2) x j ρu t + x j (ρu u j ) = p x + x j ( µ u ) x j (3)

3 Computaton of NO x emsson of a methane ar dffuson flame 245 Fgure 1. Schematc llustraton of the computatonal doman. ρc p T t ρ Y t T + ρc p u j = ( λ T ) + x j x j x j + ρu j Y x j n =1 ρy C p V j T x j n h ω (4) = x j (ρy V j ) + ω = 1,n (5) where t corresponds to tme and x j represents the stream drecton and ts vertcal coordnates (x and y). u represents the velocty n the x -drecton. ρ, p and T are densty, pressure and temperature, respectvely. Y, h and ẇ correspond to the mass fracton, enthalpy and reacton rate of speces, respectvely. R s the gas constant, C p s the specfc heat and λ s the heat conductvty. µ s the vscosty, M and V j are, respectvely, the molecular weght and the dffuson velocty of speces n the x j -drecton. n s the number of speces. The chemcal mechansm used n ths study s bascally the one presented by Mller and Bowman [5]. The data for the H+O 2 = OH+O reacton obtaned by Yu et al [11] are used. In addton, the reacton CH 3 + CH 3 = C 2 H 4 + H 2 s added to the C 2 chemstry for hgh ar temperature consderaton. The present chemstry ncludes 235 reactons and 50 speces. Reactons (1) (150) and (235) represent C 2 chemstry. Reactons (151) (231) and (232) (234), respectvely, correspond to prompt and thermal mechansms (see [5] for detals). Transport coeffcents and thermodynamc propertes are calculated usng the CHEMKIN package [13, 14]. =1 3. Numercal method The purpose of ths study s to seek a steady-state soluton of equatons (1) (5) usng the PISO method [12]. To express the above equatons n the fnte-dfference form, a fourthorder upwnd scheme s used for the convecton term. Thus the flux of the convecton term

4 246 Y Ju and T Noka can be wrtten generally as f φ/ x =f φ =f j ( φ j+2 +8φ j+1 8φ j 1 +φ j 2 )/(12δx) + f j (φ j+2 4φ j+1 + 6φ j 4φ j 1 + φ j 2 )/(4δx). (6) Here φ s a non-conservatve scalar such as T and Y. By further employng the centraldfference scheme for the vscous and dffuson terms, the governng equaton may be expressed n a fnte-dfference form at each mesh pont as 1 δt (ρn+1 ρ n ) + (ρu ) n+1 = 0 (7) 1 δt [(ρu)n+1 (ρu) n )] + A n+1 u n+1 = H n+1 (u n+1 ) p n+1 (8) 1 δt (ρc p) n+1 (T n+1 T n ) + B n+1 T n+1 = I n+1 (T n+1 ) + S n+1 T (9) 1 δt ρn+1 (Y n+1 Y n ) + Cn+1 Y n+1 = J n+1 (Y n+1 ) + S n+1. (10) In the above equatons, the operator whch s defned n equaton (6) s the fntedfference equvalent of the convectve flux. Here n and n + 1 stand for two successve nstants n tme. A, B and C are the fnte-dfference coeffcents at the central node. H, I and J denote the fnte-dfference representaton at all the nodes surroundng the central node. A detaled defnton of these quanttes s gven n [12]. In order to nclude a detaled chemstry, the source terms S T and S n the energy and the speces equatons should be treated mplctly. Therefore, a lnearzaton of the source terms s necessary. In ths study, the two source terms are lnearzed n the form ( ) S n+1 T = ST n + ST (T n+1 T n ) = ST n T + S 0T (T n+1 T n ) (11) ( ) S n+1 = S n S + (Y n+1 Y n Y ) = Sn + S 0 (Y n+1 Y n ). (12) To solve equatons (7) (10) mplctly, the orgnal PISO method [12] splt the soluton procedure nto three steps: one predcton step and two correcton steps. Snce the present nterest s n fndng a steady-state soluton, only the frst two steps are employed. At the predcton step, the temperature, speces mass fracton and veloctes are solved n the followng sequence: ( ρ n Cp n δt ( ρ n + B n S n 0T δt + Cn S0 n ( ρ n δt + An ) ( ρ n C T = I n (T p n ) + δt ) ( ρ Y = J n (Y n ) + δt Sn 0 )u = H n ρn (u ) + ) T n + S n T (13) S0T n ) Y n + S n (14) δt un p n. (15) From the old tme nstant n, superscrpt denotes the temporary feld values obtaned at the predcton step. Note that n solvng the energy equaton, the temperature rather than the enthalpy s used n ths study. Ths s because the use of enthalpy sometmes results n dvergence for dffuson flames when a detaled transport model s consdered. From the value of T, the densty ρ can be calculated from the state equaton. It should be noted here that, dfferent from the orgnal PISO method, the low Mach number approxmaton made here separated the couplng between the pressure varance and the

5 Computaton of NO x emsson of a methane ar dffuson flame 247 densty. Thus the ambent pressure rather than the pressure varant s used n calculatng the densty. To obtan the temporary pressure feld, the new velocty feld u n+1 and pressure p are sought to satsfy the contnuty equaton 1 δt (ρ ρ n ) + (ρ u n+1 ) = 0 (16) and the momentum equaton ( ) 1 δt + An ρ u n+1 ρ n = H n (u ) + ρn δt un p. (17) By takng the dvergence of equaton (17) on both sdes and usng equaton (16), the pressure equaton can be derved as 2 p = 1 δt 2 (ρ ρ n ) + 1 A n ] δt ρ n (ρ ρ n ) + [H n ρn (u ) + δt un. (18) The above equaton s of Posson type n whch 2 s the Laplacan operator n fntedfference form. The frst term on the rght-hand sde corresponds to the acoustc wave. Ths term s retaned and solved n the orgnal PISO method. However, ncluson of ths term wll make the numercal soluton very dffcult, snce a small charge of densty wll result n a large change of pressure. If one s not nterested n the acoustc wave such as n a flow wth hgh Mach number, the ncluson of ths term s not computatonally effcent. An order analyss of the wave equaton wll show that the followng relaton s justfable: 1 δt 2 (ρ ρ n )/ 2 ρ p 2 t 2 / 2 p u2 c 2 M2. (19) Here c and M are the acoustc wave speed and the Mach number, respectvely. Therefore, t s clear that at a low Mach number, the frst term on the rght-hand sde of equaton (18) s neglgble. Ths consderaton s used n ths study. At the correcton step, u n+1 s frst calculated from equaton (17) after p s obtaned. Then the coeffcents of A, B, C and those n H, I, J are updated usng these new feld data. The new temperature T n+1 and speces mass fracton Y n+1 are solved from the followng equatons: ( ρ Cp ) ( ρ C ) + B S0T T n+1 = I (T p ) + S0T T n + ST n (20) δt δt ( ρ ) ( ρ δt + C S0 Y n+1 = J (Y ) ) + δt S 0 Y n + S n. (21) Wth the results of T n+1, the new densty ρ n+1 s then calculated from the state equaton. Fnally, by updatng A/ρ and H n equaton (17), the new pressure feld p n+1 can be solved n a smlar way to equaton (18). As shown n fgure 1, the computatonal doman s a 5 cm 4.5 cm rectangle wth grd ponts. The axal length s chosen for the requrement of mesh sze (the maxmum mesh sze s 0.5 mm) and for the lmtaton of the computaton cost. A larger axal length may result n a larger total amount of NO emsson, but does not sgnfcantly change the mechansm of the NO formaton. A second-order extrapolaton s used at the ext boundary for the temperature and mass fractons. The pressure at the ext boundary s fxed at 1 atm. Zero-gradent condtons are used at the centrelne. The parameters at the nlet and top boundares are specfed at the gven values. The pressure at the nlet s extrapolated from downstream meshes.

6 248 Y Ju and T Noka 4. Numercal results and dscussons 4.1. Emsson ndex of NO x Dstrbutons of NO for low and hgh ar temperatures are shown n fgure 2, whch shows that the mole fracton of NO ncreases quckly downstream. Addtonally, an ncrease of ar temperature results n a surge of NO emsson and a thckenng of the NO producton zone. It can be seen that, at low ar temperature, NO s produced manly wthn the reacton zone, whle at hgh ar temperature the NO producton zone shfts slghtly to the ar sde. Fgure 2. Dstrbuton of mole fractons of NO for temperatures of (a) 500 and (b) 1300 K. Fgure 3. Dstrbuton of mole fractons of NO 2 for temperatures of (a) 500 and (b) 1300 K. Dstrbutons of NO 2 at 500 and 1300 K are shown n fgure 3. Very dfferent from that of NO, a C-shaped NO 2 producton zone s formed outsde the dffuson flame. Wth the ncrease of ar temperature, fgure 3 ndcates that formaton of NO 2 s enhanced n the fuel-rch regon, but decreases n the fuel-lean regon of the trple flame. Ths s a new phenomenon whch has not been found n the studes of the counterflow confguraton [7 10], where no trple flame exsts. To show the nner structure of NO x emsson, temperature and mole fractons of N and NO x n the lower half doman at x = 5 cm are plotted n fgure 4 (y = 2.25 cm s the centrelne). It can be seen that NO s sngle peaked and the jump of NO mole fracton on

7 Computaton of NO x emsson of a methane ar dffuson flame 249 Fgure 4. Structure of NO x producton and the dstrbuton of temperature at x = 5.0 cm. Fgure 5. Emsson ndces of NO x correlated wth ar temperature. the fuel sde concdes wth the postons of peak temperature and peak mole fracton of N. Snce here N only appears n the reacton zone, the jump of NO s attrbuted to the prompt NO. In addton, NO 2 s double peaked on both sdes of the dffuson flame. Moreover, the mole fracton of NO 2 on the fuel sde s hgher than that on the ar sde. Fgure 4 also shows that the N 2 O concentraton s also sngle peaked on the ar sde. However, wth the ncrease of ar temperature, another peak s dentfed at the locaton of the peak mole fracton of N. In prevous studes, the emsson ndex [7] s usually used to evaluate NO x emsson. Fgure 5 shows that the emsson ndces ( ω M dx dy/ ω CH4 M CH4 dx dy) correlate

8 250 Y Ju and T Noka wth the ar temperature. It can be seen that the emsson ndex of NO ncreases dramatcally wth an ncrease of ar temperature. Ths result agrees wth that obtaned n the counterflow dffuson flame [10]. However, the emsson ndex of NO 2 shown n fgure 5 s completely dfferent from that obtaned n the counterflow confguraton, showng an ncreasng dependence on the ar temperature. The reason for the ncrease of NO 2 n the current case s that there s an ncrease of NO formaton n the fuel-rch regon of the trple flame as the ar temperature s rased. Therefore, NO 2 formaton s an mportant ssue n mult-dmensonal dffuson flames Reducton of NO emsson As shown n fgure 5, the surge of NO x emsson at hgh ar temperature makes the regeneratve burner dffcult to use practcally. Recently, Tanaka et al [15] found that NO x emsson n regeneratve burners can be reduced by recyclng the burnt gas nto the arstream. However, the mechansm as to why NO x emsson s reduced s not properly known. In order to understand ths mechansm, NO x emsson wth a dluted arstream s examned. To avod the complexty of the chemstry and boundary condton, ntrogen s used as the dluton gas here. Fgure 6 show the flame temperature and the emsson ndex of NO as a functon of ar temperature for typcal oxygen concentratons n the arstream. It can be seen that the emsson ndex of NO decreases dramatcally wth the decrease of oxygen concentraton n the dluted arstream. In partcular, at hgh ar temperature the reducton of NO emsson s consderable. Therefore, fgure 6 shows that dluton of the preheated arstream provdes an effcent way to reduce the flame temperature and suppress the formaton of NO. Dstrbutons of temperature and mole fractons of O and OH at x = 5cmofthe lower half computaton doman are plotted n fgure 7. It can be seen that, as the oxygen mole fracton n the arstream decreases from to 0.1, the maxmum flame temperature decreases. The reacton zone becomes narrow and shfts slghtly to the arstream sde. Fgure 6. Temperature and emsson ndex of NO correlated wth ar temperature for typcal oxygen concentratons n the arstream.

9 Computaton of NO x emsson of a methane ar dffuson flame 251 Furthermore, a decrease of oxygen concentraton results n a great decrease of O and OH concentratons n the flame. As wll be dscussed below, NO formaton at hgh ar temperature s manly through the thermal mechansm. Thus, the decrease of O and OH concentratons greatly nhbts the reactons N 2 + O = NO + N and N + OH = NO + H. Therefore, the drect mechansm for NO reducton by usng dluted preheated ar s due to the decrease of flame temperature and the decrease of the concentratons of O and OH. Fgure 7. Dstrbutons of temperature and mole fracton of O and OH n a dluted arstream NO x formaton mechansm Reducton of NO x emsson needs a clear understandng of the detaled formaton process. Fgures 8 and 9 show the formaton paths of NO x at ar temperatures of 500 and 1300 K, respectvely. The arrow denotes the reacton path and ts lnewdth represents the maxmum reacton rate at the ext. The sze of the speces character represents ther maxmum mole concentratons. For brevty, only the reactons whch wll be mentoned repeatedly are gven as follows: CH + N 2 = HCN + N (151) C + N 2 = CN + N (152) CH 2 + N 2 = HCN + NH (153) CH 2 + N 2 = H 2 CN + N (154) CO + N 2 = NCO + N (194) H + N 2 = NH + N (210) N + NO = N 2 + O (232) N + O 2 = NO + O (233) N + OH = NO + H. (234)

10 252 Y Ju and T Noka Fgure 8. Formaton routes of NO x for an ar temperature of 500 K at x = 5.0 cm. Here, reactons (232) (234) represent the thermal mechansm, the others belong to the prompt mechansm. Fgure 8 clearly shows that there are only two prncpal orgns, the thermal orgn (bottom) and the prompt orgn (left), to produce a fresh N atom. In the thermal mechansm, N s produced through reacton (232) and s then converted to NO by reactons (234) and (233). In the prompt mechansm, N s manly produced through reactons (151) (154) as well as (194) and (210), and s consumed n two ways: converted to NO drectly through reactons (234) and (233) and converted to HCN through N + CH 3 = H 2 CN + H (168) H 2 CN + M = HCN + H + M. (155) Fgures 8 and 9 also show that the HCN NO route s very mportant for NO formaton. Ths route conssts of two dfferent paths, HCN NH NO and HCN NCO NO. The HCN NH NO path can be further dvded nto two sub-steps: HCN NH and NH NO. Here the HCN NH path s manly composed of the followng four sub-routes: HCN + O = NCO + H (176) NCO + H = NH + CO. (192) Ths route has been dscussed by Mller et al [3]. The other three are HCN + OH = CN + H 2 O (171) HCN + H = CN + H 2 (179) CN + OH = NCO + H (182) NCO + H = NH + CO (192)

11 Computaton of NO x emsson of a methane ar dffuson flame 253 Fgure 9. Formaton routes of NO x for an ar temperature of 1300 K at x = 5.0 cm. and HCN + OH = HOCN + H (172) HOCN + H = HNCO + H (175) HCN + OH = HNCO + H (163) HNCO + H = NH 2 + CO (199) NH 2 + H = NH + H 2 (215) NH 2 + OH = NH + H 2 O (214) and HCN + O = NH + CO. (177) Among these four routes, the frst one s the man route. Regardng the NH NO route, the followng two sub-routes are domnant; one s NH + H = N + H 2 (211) N + OH = NO + H (234) and the other s NH + OH = HNO + H (208) HNO + OH = NO + H 2 O. (229) On the other hand, the HCN NCO NO route NCO + OH = NO + CHO (195)

12 254 Y Ju and T Noka NCO + O = NO + CO (193) s very slow compared wth the HCN NH NO route. There are stll other paths for NO formaton, but they are not as mportant as those mentoned above. Addtonally, NO s manly recycled back to NH and HCN through NO + C = CN + O (156) CN + OH = NCO + H (182) NCO + H = NH + CO (192) and NO + HCCO = HCNO + CO (161) HCNO + H = HCN + OH (163) and NO + CH 2 = HCN + OH (162) NO + CH = HCN + O. (157) Among them, the last path s the most domnant one at both hgh and low temperatures. Comparson of fgures 8 and 9 ndcates that, although the overall patterns of NO formaton routes at low and hgh temperatures are smlar, there are several consderable dfferences both n the prompt mechansm and n the thermal mechansm. Frst, the rates of the HCN NO route and the three recycle paths ncrease dramatcally wth ncrease of temperature, especally the HCN CN and NO CN recycle route. Secondly, there s a dramatc change to the thermal reacton (232). At low ar temperature, reacton (232) converts NO slowly to N 2. At hgh ar temperature, however, reacton (232) quckly removes NO wthn the reacton zone, but produces NO rapdly on the ar sde. In addton to NO, NO 2 s manly produced through HO 2 + NO = NO 2 + OH (188) NO + O 2 = NO 2 + O (190) at low ar temperature and through at hgh ar temperature. NO + O + M = NO 2 + M (191)

13 Computaton of NO x emsson of a methane ar dffuson flame 255 Ths mples that NO 2 formaton at low temperature depends strongly on the mole concentraton of HO 2. Snce HO 2 s manly produced by the reacton H+O 2 +M = HO 2 +M and removed by H + HO 2 = OH + OH, at hgh temperature, the former reacton becomes slow whle the latter becomes fast, thus resultng n a very low HO 2 concentraton. Ths s why NO 2 decreases quckly on the ar sde but ncreases on the fuel sde wth the ncrease of ar temperature Evaluaton of prompt NO and thermal NO In prevous studes, the concepts of prompt NO and thermal NO have been used frequently to understand the formaton mechansm of NO. In the conventonal method [7, 9], thermal NO s calculated by usng C 2 chemstry and the thermal mechansm alone (reactons (232) (234)). Prompt NO can then be obtaned by subtractng the amount of NO calculated wth ths mechansm from the result calculated by the full chemstry. However, as shown n fgures 8 and 9, the thermal and prompt mechansms are strongly coupled through reactons (232) and (234) at hgh ar temperature. Thus the role of the thermal mechansm n the full chemstry may be very dfferent from that n the case of C 2 chemstry and the thermal mechansm alone. To show ths dfference, n addton to the full chemstry, NO emsson resultng from C 2 chemstry and the thermal mechansm alone s also calculated n the present study. A comparson of the rates of reacton (232) n, respectvely, the full chemstry and n C 2 wth the thermal mechansm alone under the same boundary condtons s shown n fgure 10. It can be seen that, on the ar sde (left), the rates of reacton (232) n these two mechansms are the same. However, n the vcnty of the flame zone, the results of the full chemstry show that reacton (232) rapdly converts NO back to N 2, whle results of C 2 chemstry and the thermal mechansm alone show a small postve producton rate of NO. Because n the conventonal method, NO predcted by C 2 chemstry and the thermal mechansm alone s smply consdered as the thermal NO n the full chemstry case, results n fgure 10 Fgure 10. Comparson of the rates of the reacton NO + N = N 2 + O n the full chemstry and n a mechansm of C 2 and the thermal mechansm at x = 5.0 cm.

14 256 Y Ju and T Noka Fgure 11. Producton rates of actve N from the prompt and the thermal mechansm. (a) Prompt mechansm; (b) thermal mechansm. show that the conventonal method over-predcts thermal NO n the full chemstry and thus under-predcts prompt NO or even yelds a negatve prompt NO n some complex cases. A detaled examnaton of ths ssue wll be made below usng the counterflow dffuson flame. To adequately evaluate the contrbuton of the thermal and prompt mechansms at hgh ar temperature, a new parameter rather than NO should be ntroduced to avod the couplng of these two mechansms. Fgures 8 and 9 showed that producton of N from N 2 through these two mechansms s ndependent. Therefore, the present study employs fxed ntrogen (whch s essentally all N-contanng compounds other than N 2 ) nstead of NO. As shown n Fgure 12. Fracton of thermal NO n total NO formaton n counterflow dffuson flames wth a stretch rate of 45 s 1.

15 Computaton of NO x emsson of a methane ar dffuson flame 257 fgure 9, the man orgn of the fxed ntrogen from the prompt mechansm s reactons (151) (154), and (194) and (210). The orgn of fxed ntrogen from the thermal mechansm s reacton (232). Fgure 11 shows the ndvdual contrbutons of these two mechansms n terms of the fxed ntrogen. It can be seen that the prompt mechansm produces fxed ntrogen only n the reacton zone. Ths dstrbuton concdes well wth that of the mole fracton of CH. In contrast, fgure 11(b) clearly ndcates that the thermal mechansm produces NO on the hgh-temperature ar sde but rapdly converts NO back to N 2 n the reacton zone. Ths results agrees well wth those shown n fgures 5 and Examnaton usng the counterflow dffuson flame To show the falure of the conventonal method n dstngushng the prompt NO from the thermal NO, computatons of NO formaton wth varous ar temperatures n counterflow dffuson flames are made. Detaled descrptons of the governng equatons and boundary condtons are gven n [10]. The stretch rate s fxed at 45 s 1 and the burner separaton dstance s 2 cm. The temperature of the fuel stream s kept at 300 K. NO formatons are calculated by usng both the full chemstry and the C 2 chemstry together wth the thermal mechansm alone. The varaton of the fracton of thermal NO n the total NO producton wth ar temperature s shown n fgure 12. (Therm) NO denotes the total NO producton predcted by the C 2 chemstry wth the thermal mechansm alone. Full NO denotes the total NO formaton predcted by the full chemstry. Therefore, (Therm) NO /Full NO represents the fracton of thermal NO n the total NO formaton of the conventonal method. On the other hand, Prompt N s the formaton of the fxed ntrogen through the prompt mechansm n the full chemstry and Full N s the total formaton of the fxed ntrogen. Fgure 12 shows that, at an ar temperature of 300 K, the conventonal method predcts that the proporton of thermal NO s about 5%. However, fgure 8 ndcates that the thermal mechansm converts NO back to N 2. These are very contradctory results. In addton, fgure 12 shows that thermal NO ncreases dramatcally wth ncreasng ar temperature. However, for ar temperatures greater than 900 K, the conventonal method yelds a fracton of thermal NO far larger than unty. Ths means that NO formaton calculated by the C 2 chemstry and the thermal mechansm alone s larger than that calculated by the full chemstry. It s even worse when the ar temperature ncreases further. Therefore, the conventonal method neglected the couplng between the prompt mechansm and the thermal mechansm and thus cannot gve a correct evaluaton of prompt NO n the most complex stuatons. However, fgure 12 shows that the method presented n ths study gves a reasonable predcton of thermal NO. It can also be seen that at low ar temperature, thermal NO s slghtly negatve, ndcatng that the thermal mechansm converts NO back to N 2. Ths s consstent wth the results shown n fgure 8. At hgh temperature, thermal NO s the man route for NO formaton. Ths s why NO formaton can be reduced effcently by decreasng the oxygen concentraton n the preheated ar. 5. Concluson The NO x formaton mechansm of a methane ar dffuson flame n a two-dmensonal lamnar jet s nvestgated numercally wth full chemstry. Numercal results showed that NO s manly produced through the prompt mechansm n the flame zone and through the thermal mechansm on the hgh-temperature ar sde. A C-shaped dstrbuton of NO 2, correspondng, respectvely, to the fuel-lean and fuel-rch

16 258 Y Ju and T Noka regons of the trple flame, s dentfed. The emsson ndex of NO ncreases dramatcally wth ncreasng ar temperature. It s shown that reducton of NO formaton nvolvng the preheated ar can be realzed by decreasng the oxygen concentraton n the ar stream. The effects of ar temperature on the NO x formaton paths are nvestgated. Key NO x producton routes and recyclng routes are obtaned for both low and hgh temperatures. Increase of ar temperature greatly enhanced the HCN NH NO route, n partcular, the HCN CN and NO CN paths. The thermal mechansm rapdly converts NO back to N 2 at the flame zone, but quckly produces NO on the hgh-temperature ar sde. The prompt mechansm and the thermal mechansm are strongly coupled. The conventonal method s shown to greatly over-predct thermal NO and under-predct prompt NO. At hgh ar temperature, ths method even becomes msleadng n dstngushng the prompt NO from the thermal NO. Numercal results ndcated that the method presented n ths study usng fxed ntrogen nstead of NO can adequately reflect the contrbuton of these two mechansms to total NO emsson. References [1] Fenmore D C th Int. Symp. on Combuston (Pttsburgh, PA: The Combuston Insttute) p 373 [2] Drake M C, Correa S M, Ptz R W, Shyy W and Fenmore C P 1987 Comb. Flame [3] Mller J A, Mclean W J, Chander D W, Smooke M D and Kee R J th Int. Symp. on Combuston (Pttsburgh, PA: The Combuston Insttute) p 673 [4] Hahn W A and Wendt J O L th Int. Symp. on Combuston (Pttsburgh, PA: The Combuston Insttute) p 121 [5] Mller J A and Bowman C T 1989 Prog. Energy Combust. Sc [6] Nakata T 1993 PhD Thess Tohoku Unversty [7] Nshoka M, Nakagawa S, Ishkawa Y and Takeno T 1994 Comb. Flame [8] Kurta A, Kondo S, Nshoka M and Takeno T th Japanese Symp. on Combuston p 209 (n Japanese) [9] Drake M C and Blnt R J 1991 Comb. Flame [10] Ju Y 1996 Trans. Japan. Soc. Mech. Eng. B [11] Yu C L, Frenklach M, Masten D A, Hanson R K and Bowman C T 1994 J. Phys. Chem [12] Issa R I, Ahmad-Befru B, Beshay K R and Gosman A D 1991 J. Comput. Phys [13] Kee R J, Dxon-Lews G, Warnatz J, Coltrn M E and Mller J A 1986 Sanda report SAND [14] Kee R J, Grcar J F, Smooke M D and Mller M D 1985 Sanda report SAND [15] Tanaka R, Kshmoto K and Hasegawa T 1994 Combust. Sc. Technol (n Japanese) [16] Smooke M D, Ern A, Tanoff M A, Valdat B A, Mohammed R K, Marran D F and Long M B 1996 The 26th Int. Symp. on Combuston (Pttsburgh, PA: The Combuston Insttute) p 2161