Effect of the Number of Injectors on the Mixing Process in a Rapidly Mixed Type Tubular Flame Burner

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1 Journal of Aled Flud Mechancs, Vol. 1, No., , 17. Avalable onlne at ISSN , EISSN DOI: /acadub.jafm Effect of the Number of Injectors on the Mxng Process n a Radly Mxed Tye Tubular Flame Burner Y. Chouar 1, W. Kraa 1, H. Mhr 1 and P. Bournot 1 UTTPI, Natonal Engneerng School of Monastr (ENIM), Av. Ibn El Jazzar, 519 Monastr, Tunsa Unversty Insttute for Industral Thermal Systems, UMR CNRS 6595, Technoole Château Gombert, Marselle, France Corresondng Author Emal: yoldoss.chouar@yahoo.fr (Receved March 1, 16; acceted October 17, 16) ABSTRACT Three-dmensonal smulatons are erformed to study the non-reactve mxng rocess n a radly mxed tye tubular flame burner (RTFB). The current work examnes the effect of the number of njectors (N=, 4 and 6) on the mxng rocess by focusng on three crterons (Flow structure, local swrl ntensty and mxng layer thckness). The Dscrete Phase Model (DPM) s used to track the artcle trajectores. Valdaton of the numercal results s carred out by comarng the redcted artcle trajectores, central recrculaton zone (CRZ) and tangental velocty results to the exermental data. It s concluded that the model offers a satsfactory redcton of the flow feld n a RTFB. Numercal results show that, for the same geometrcal swrl number (Sw) and the same Reynolds number (ReT), the ncreasng of the number of njectors enhances the mxng rocess by generatng a larger reverse flow and reducng the mxng layer thckness. It s also concluded that the local swrl ntensty along of the RTFB can be correlated n terms of geometrc swrl number and number of njectors. Keywords: CFD; DPM; Number of njectors; Mxng layer thckness; Tubular flame burner. NOMENCLATURE AT area of the tangental nlet slts Da Damköhler number De ext dameter d artcle dameter DR CRZ dameter K mxng coeffcent N number of njectors L njector length L* total burner length LCRZ CRZ length N1 slts number of seeded ar N slts number of unseeded ar Qtotal total flow n burner Qnj flow njected Q flow njected n one slt Re flud Reynolds number n the njecton ReT flud Reynolds number n the tube Re Reynolds number of artcles S Sw St Uf U Vnj V W δ ρ ρ τm τr CRZ DPM MgO RANS RTFB swrl number geometrcal Swrl number Stokes number flud velocty artcle velocty njecton velocty tangental velocty comonent slt Wdth mxng layer thckness densty of flud densty of artcle mxng tme reacton tme Central Recrculaton Zone Dscrete Phase Model Magnesum Oxde artcles Reynolds Averaged Naver Stokes Radly mxed tye Tubular Flame Burner 1. INTRODUCTION Swrlng flows have been commonly encountered n varous ndustral alcatons such as exchangers (Cakmak et al. 11 and Vahdfar et al. 15), cyclone searators (Avc et al. 13 and Guzan et al. 14) and esecally n varous tyes of burners (Khald et al. 16 and Klančšar et al. 16).

2 Y. Chouar et al. / JAFM, Vol. 1, No., , 17. Indeed, the burners use swrlng flow for controlled mxng of reactve seces (oxdzer and fuel) wth the am to mrove flame stablty and reduce ollutants emsson (Syred and Beer 1974). Ishzuka et al. (7) have roosed the safe concet of the Radly Tubular Flame Burner (RTFB). The reactants n ths burner are searately ntroduced usng four tangental njectors. So, the mxng rocess between the reactve occurs radly under the effect of centrfugal force. Followng the gnton of combuston, a radly mxed tye tubular flame can be establshed. Ths tye of burner (RTFB) have been revewed and nvestgated exermentally by multle researchers as Zhang et al. (5) and Sh et al. (13)-(14a) (14b) (14c). Sh et al. (14b) (14c) have nvestgated the mxng rocess, the extncton lmts and the stablty under dfferent oxygen mole fractons. It was demonstrated that the mxng layer thckness (δ) and the square root of the njecton velocty are nversely roortonal. On the one hand, Sh et al. (14b) have outlned the role of ths thckness (δ). Indeed, the mxng layer thckness allows to deduce the mxng tme (τm) and to calculate the Damkhöler number (Da =τm/τr wth τr s the reacton tme). On the other hand, Sh et al. (14b) have demonstrated that the Damkhöler number s able to gve a useful ndcaton for the success or falure of the rad combuston n the RTFB. The authors have also examned the effect of geometrc swrl (Sw) and Reynolds W V nj ( Re I ) numbers on mxng n a RTFB. They have demonstrated that hgh geometrc swrl (Sw) and Reynolds (ReI) numbers are recommended to enhance the mxng n a RTFB wth four njectors. It s worth notng that Y. Zhang et al. (5) have examned exermentally the flow feld n two tubular flame burners wth a geometrcal swrl number of.1 and.78. In the tye of burner RTFB, t s essental to have a general dea on the success/falure of the tubular flame before the combuston test. However, t s worth notng that the exermental nvestgatons are often lmted by the bounds of cost and measurement technques. To surmount these lmts, the comutatonal flud dynamcs was roosed n order to analyse the mxng n dfferent burner confguratons. The CFD roose varous crterons for quantfcaton of mxng rocess (as examle the mxture fracton, coherent structures and the mxng layer). By usng the mxture fracton, Tatsum et al. (1) have examned the buoyancy and the swrl effects on mxng rocess n the mnature confned multjet. A small flow crculaton was observed n the roxmty of the baffle late. Ths regon extends toward the downstream zone as the swrl number ncreases. Tatsum et al. (1) have deduced that ths exanson may mrove the erformance of mxng control. By analysng the coherent structures, the vortex breakdown bubbles and the mean assve scalar dstrbuton, Ranga Dnesh et al. (1) have studed the swrl effects on the mxng n a coannular swrl combustor. It was found that an ncreasng swrl number leads to an ncrease n the rate of decay of axal momentum due to both vscous and nvscd effects. Ths decay romotes mxng n the vcnty of the swrl generator. In another study, the mxng layer was used by Pathak et al. (5) to examne the effects of the streamlne curvature on the mxng rocess. M. A. Azm et al. (16) have outlned the mact of oeratng condtons on the mxng of two coaxal streams. These authors have demonstrated that the reducton n the mxng thckness reflects the mrovement of the mxng of two fluds. The study of swrlng flows wth the same global arameters (Sw and ReT) has shown that ths tye of flow has a strong memory and does not easly lose ts orgnal dentty (Ktoh et al. 1991, Steenbergen et al and Martemanov et al. 4). Thus, t s necessary to note that the characterstcs of a swrlng flow deend strongly on the geometry of the swrl generator. Mantlla (1998) has noted that the number of cylndrcal nlet has a sgnfcant effect on the local swrl ntensty. Ths fact suorts the resent numercal study that rovdes a detaled nvestgaton of mxng n the radly mxed tye tubular flame Burners (RTFB). The am of the resent aer s to mrove the desgn of the RTFB by analyzng the effect of changng number of njectors on mxng rocess, to correlate the swrl decay along of the RTFB n terms of geometrcal swrl number and number of njectors and to determne the mxng coeffcent for each burner.. BURNER CONFIGURATION The tubular flame burner confguratons consdered n the resent study (Fg. 1) are dentcal to the exermental confguratons of Sh et al. (14b). The burners are oen on both sdes. For the valdaton of the CFD code, two RTFB confguratons were analyzed. The total length of burners s L* =1 D wth D s the nner dameter whch equals to 16 mm. The burners have four rectangular tangental njectors wth a wdth W=.15 D and a length L. In order to valdate our results and to analyze then the effect of number of njectors, fve RTFB confguratons were dentfed (Table 1). The swrl number S used to measure the swrl strength was defned by Beer and Chger. (197) as: S G x G uwr dr (1) R ( D / ) ( D / ) ru dr R Ths dmensonless number s the quotent of the axal flux of tangental angular momentum G and the axal flux of the axal lnear momentum Gx multled wth the ext tube radus D/. Snce t s usually defcent n the detaled exermental data of velocty rofles for a swrl burner, the geometrcal swrl number can also be defned as a functon of nut outut arameters of the burner, as follows (Alekseenko et al. 1999) : 596

3 Y. Chouar et al. / JAFM, Vol. 1, No., , 17. S w D D e () 4 AT Fg. 1. Schematc of the radly mxed tye tubular flame burner. A hexahedral mesh wth a structured boundary layer mesh near the burner wall was used snce t s much more comutatonally effcent than the tetrahedral mesh. To reduce the total cell number and avod a very large dfference n cell volume between adjacent cells, the axal mesh dstrbuton s ncreased rogressvely from the downstream slts to the outlet regon. In order to ensure the ndeendence of the soluton on the grd sze, grd denstes from cells to cells were tested for the comutatonal doman. It was notced that for a cells number varyng between to , the numercal results were smlar. So, the choce of the grd sze, whch was based on the weakest comutng tme, was fxed to cells (Fg. ). The selected grd (879 4 cells) s locally refned n the near njecton slts and boundary walls (Δy=Δz=3.1-4 ) as well as near the burner axs (Δy=Δz=1-4 ) so as to redct more accurately the trajectory of artcles and the mxng rocess. Fg. shows the overall grd structures adoted n ths research. Where De s the ext throat dameter whch defned by the followng exresson De=D-W, AT=N*L*W s the total area of the tangental nlet njectors, N s the number of njectors and L s the njector length. The two burner confguratons studed as a valdaton of the CFD code are characterzed by a geometrcal swrl number (Sw) equal to.34 and 1.37 resectvely (Table 1). ctable 1 Secfcatons of burner desgn Table 1 Secfcatons of burner desgn Area of the Number of tangental nlet Injectors, N slts, A T [m ] Cases Geometrcal swrl number, Sw Burner x Burner 4 18 x Burner x Burner 4 96 x Burner x The mxng rocess was analysed by adotng the method roosed by Sh et al. (13)-(14a) (14b) (14c) based on the njecton of Magnesum oxde artcles (MgO) (Fg. 1). Indeed, for the burner wth four njectors, seeded ar (ar + Magnesum oxde artcles (MgO)) was ntroduced nto the horzontal njectors (A), non seeded arflow was ntroduced nto the other two njectors (B). 3. GRID SYSTEM The comutatonal domans of the dfferent confguratons were frst generated and meshed by Gambt. The geometry of nterest has a symmetrcal nature. So, the smulatve doman adoted here s the half of the tubular burner. Fg.. Grd system used n the comutaton. 4. NUMERICAL MODEL A numercal nvestgaton based on Reynoldsaveraged Naver Stokes (RANS) method s erformed to examne the effect of number of njectors on the mxng rocess n Radly mxed tye Tubular Flame Burner (RTFB). The Euleran Lagrangan aroach wth a dscrete hase method (DPM) was used to descrbe the sold artcles moton n a flow feld,.e., the gas hase was consdered as a contnuum hase by solvng Naver Stokes equatons and the sold hase was calculated by trackng artcles n the flow feld Assumtons For all smulatons, the followng assumtons were consdered: - The flow s steady state and sothermal. - The flow s lamnar. Indeed, for all studed cases, the Reynolds number n the tube DU av ReT s less than the crtcal Reynolds number of 3. (R.C. Chanaud 1963 and 1965). - The consdered flud n ths study s ar and t s assumed to be ncomressble (Mach <.3). 597

4 Y. Chouar et al. / JAFM, Vol. 1, No., , The artcle hase s suffcently dluted that artcle-artcle nteractons - The effects of the artcle volume fracton on the gas hase are neglgble. - The volume fracton of dscrete hase s less than 1 1% (Elghobash 1994). - The sold artcles are shercal and nondeformable wth a same dameter d =1-6 m and densty ρ =358 kg/m 3. Snce the artcle densty s consderably larger than that of the flud,.e., ρ/ρ>>1, the Basset force, the buoyancy force, the vrtual mass force and the ressure gradent force, could be neglected (D.E. Stock et al. (1996); Wenjng Sun et al. 15). 4.. Governng Equatons Gven the recedng assumtons, the governng equatons can be wrtten as follows: U (3) x U ju x j P x x j U x j (4) The force balance on artcles has been ntegrated to determne the trajectores of the sold artcle (Fluent.6). The artcles motons are calculated wth the followng equaton: du F (5) D dt U U g Where FD s the drag force er unt of mass and velocty dfference (U-UP), U s the flud hase velocty and UP s the artcle velocty. FD s gven by: 18 CD Re FD (6) d 4 μ s the molecular vscosty of the flud, ρ s the flud densty, ρ s the densty of artcle, d s the artcle dameter, Re s the relatve Reynolds number of artcles whch s defned as U UP d Re (7) And CD s the drag coeffcent gven by: C D a a1 Re a Re 3 (8) Where the a s are constants that aly for smooth shercal artcles over several ranges of Re gven by S. A. Mors and Alexander (197). The volume flow rate of the dscrete hase d ( Q N u f ) was chosen equal to.9 4 multled by the volume flow rate of the gas hase and the number of MgO artcles ntroduced n the smulaton at the corresondng nlets s resectvely equal to 3584, 16, 56, 56 and 56 for the burners 1,, 3, 4 and 5. In ths three-dmensonal study, the MgO artcles are consdered to followng exactly the flow, ndeed for all treated cases the artcles have a very small d u f Stokes number S t N. D 4.3. Boundary Condtons and Soluton Strateges The burners consdered have four rectangular tangental njectors and two axal outlets. Snce, the geometry of nterest has a symmetrcal nature. So, the smulatve doman adoted here s the half of the RTFB. It means that the half of the total flow enters through the four tangental slots (wth a length of L/) and t comes out through a sngle axal outlet. The boundary condtons llustrated n Fg. 1, are summarzed n Table. Table Boundary Condtons Desgnaton Condtons Values Injectors of seeded ar flow (N1), (A) Mass flow-nlet Injectors of nonseeded ar flow Mass flow-nlet (N), (B) f Qs=Qnj/N Qa=Qnj/N Walls No Sl - Symmetry (C) Symmetry - Outlet (D) Outflow - Numercal comutatons were carred out usng Fluent whch s based on the fnte volume method. In order to mrove accuracy, the second order uwnd scheme was used. The SIMPLE method was aled to determne the ressure velocty coulng. It uses a relatonsh between velocty and ressure correctons to enforce mass conservaton and obtan the ressure feld. The maxmum resdual of all varables was 1-4 n the converged soluton. We noted that the N1 s the number of njectors tye A whch nject ar/mgo and the N s the number of njectors tye B whch nject ar. 5. RESULTS AND DISCUSSION 5.1. Valdaton of the Numercal Model To gve more confdence of the model, we establshed some quanttatve and qualtatve comarsons wth the exermental data of Sh et al. (14b). The valdaton of the numercal model s erformed by comarng the flow structure, mxng layer thckness, dameter of the central recrculaton zone 598

5 Y. Chouar et al. / JAFM, Vol. 1, No., , 17. (CRZ) and crcumferental veloctes results wth the exermental results of Sh et al. (14b). Three cases were consdered: - Case 1: L=64mm; Sw=.34; Qnj=.15Nm 3 /h; - Case : L=64mm; Sw=.34; Qnj =.7Nm 3 /h; - Case 3: L=16mm; Sw=1.37; Qnj =.15Nm 3 /h. The seeded ar (ar + MgO artcles) s tangentally ntroduced nto the burner by the two horzontal njectors. Or, non-seeded ar was ntroduced by the other njectors. To smlfy the flow vsualzaton, the flow structure s determned by trackng the artcles trajectores delmtng the flow njected through the horzontal slts. Case 1: L=64mm ; Sw=.34; Qnj=.15Nm 3 /h Case : L=64mm ; Sw=.34; Qnj=.7Nm 3 /h Partcles trajectores exanson (case 1 and ) and shrnkage (case 3) of the jet thckness after beng ejected outsde the njector. Moreover, t s shown that the wdth of the ar njected from the low sde gradually shrnks wth ncreasng the geometrcal swrl number. The dashed zone ndcates surface contour of negatve axal velocty whch s used to dentfy the exstence of the central recrculaton zone (CRZ). Ths zone eventually aears only for the case 3 charactersed by a geometrcal swrl number larger than the crtcal swrl number (Sw>.6). Indeed, Guta et al. (1984) have establshed that the number of swrl must be hgher than.6, value from whch the flow develos recrculaton zones. The mxng layer thckness (δ) around the ext of the njector s defned as the wdth of the non seeded ar flow from the uer rght slt. Ths thckness was measured after an angle of 45 degrees of the startng ont O (see Fg. 3) whch s defned as the nner edge of the lower rght njector. Numercal and exermental results of the mxng layer thckness and the CRZ dameter are comared n Table 3. The dscreancy between these results s less than 5%. Thus, the obtaned results agree well wth those of Sh et al. (14b). Table 3 Numercal and exermental mxng layer thckness and CRZ dameter Case 1 Case Case 3 Ex. Nu. Ex. Nu. Ex. Nu. δ (mm) DR (mm) Exerment of Sh et al. : S w =.34, Q=.15 [Nm 3 /h] Numercal: S w =.34, Q=.15 [Nm 3 /h] Exerment of Sh et al. : S w =.34, Q=.7 [Nm 3 /h] Numercal: S w =.34, Q=.7 [Nm 3 /h] Exerment of Sh et al. :S w =1.37, Q=.15 [Nm 3 /h] Numercal: S w =1.37, Q=.15 [Nm 3 /h] Case 3: L=16mm; Sw=1.37; Qnj=.15Nm 3 /h V/U av (m/s) 4 Fg. 3. Predcted and exermental results of artcle trajectores n a cross secton for the three treated cases. + : Exermental data; Gray lne: Numercal results. Fgure 3 shows a confrontaton between the redcted and exermental Sh et al. (14b) results of flow structure for the three cases treated here. It s found that a satsfactory agreement wth the exermental data (Sh et al. (14b)) was obtaned. Indeed, ths method ermts to descrbe r/d (m) Fg. 4. Numercal and exermental results of crcumferental veloctes at x/d=. In Fg. 4, we comare numercal and exermental rofles of the tangental velocty at the njectors 599

6 Y. Chouar et al. / JAFM, Vol. 1, No., , 17. outlet for the three treated cases. To analyse the statstcal accuracy of the roosed model, the determnaton coeffcent (R-square) and the P- value for the three cases have been calculated and resented n Table 4. Table 4 Summary of R-square and P-value Case 1 Case Case 3 Burner 3 R-square P-Value As t can be seen on Table 4, the results are statstcally sgnfcant wth a hgh R-square (close to 1) and a low P-value (less than 1-7 ). So, the agreement between the results s satsfactory whch means that the adoted model offers a satsfactory redcton of the tangental velocty dstrbutons. Ths comarson roves the valdty of our numercal model and justfes ts use to dscuss the effects of some arameters affectng the RTFB oeratng. 5.. Number of Injectors Effect In ths sub-secton, we attemt to reveal the effect of number of njectors on the flow structure and the mxng rocess n a RTFB. The dscussed results are thematcally resented accordng to the followng subtocs: flow structure (artcle trajectores and CRZ), local swrl ntensty and Mxng layer thckness. Three burner confguratons wth dfferent number of njectors (N=, 4, 6) have been consdered (Table 1) Flow Structure The total flow rate s fxed at a value of 41-5 Kg s -1,.e. almost the same Reynolds number (ReT). It should be noted also that all the tested burners have the same geometrcal swrl number (Sw=1.83). In Fg. 5, the artcle trajectores n the cross secton erendcular to the tube axs (x=, y, z) for dfferent numbers of njectors were resented. For all the tested burners, t s shown that the flow wdth shrnks after beng ejected outsde the njector generatng a very ntense centrfugal force. Ths strong centrfugal force causes the ressure dro n the center causng the aearance of a central recrculaton zone. Moreover, the mxng layer thckness revously defned seems to be constant for the three burners. However, ths s only true for a general observaton. In realty, an mortant decrease of the mxng coeffcent s vsble, esecally between burner 4 and burner 5. Ths result s dscussed wth more detals n the secton of the mxng layer thckness. Moreover, t s noted that the seeded ar wdth after njecton decreases and the dameter of CRZ ncreases by ncreasng the number of njectors, whch accordng to B.sh et al. (14b), results n the decrease the mxng tme n the burner (Eqs. (1) and (11)). Burner 4 Burner 5 Fg. 5. Partcles trajectores n a cross secton varyng wth number of njectors. These observatons lead to conclude that for the same geometrcal swrl (Sw) and Reynolds (ReT) numbers, the ncrease of the number of njectors romotes the mxng rocess n radly tubular flame burner. The Fg. 6 llustrated, at the left sde, the contour lot of axal velocty and streamlnes on the lane (x, y, z=m) and the so-surfaces (U=) ndcatng central recrculaton zones at the rght sde for burner 3, 4, 5 resectvely. The streamlnes resent a radal vortex bubble shft towards the nlet lane wth ncreasng the number of njectors. Ths vortex manfests on the erhery of the central recrculaton zone (CRZ). Ths zone s located n the central regon. It has the same concal form for the three burners. Ths haens due to the decrease of the swrl moton whle gong downstream of the swrl generatng devce, decreasng thus the centrfugal force and consequently the adverse ressure gradent. The sze of the CRZ becomes more extended wth ncreased number of njectors (seen Fg. 6). Ths haens due to the nlet mass flow dstrbuton effect. Ths observaton verfes that the mxng rocess s more effcent n the burner 5. 6

7 Y. Chouar et al. / JAFM, Vol. 1, No., , 17. Burner 3: LCRZ/D = 5.19, DR /D =.5 swrl decrease can be aroxmated as exonental functon (S=A ex (B* x/d); where A and B are deendng to the geometrcal swrl number and the number of njectors). Burner 4: LCRZ/D = 4.37, DR /D =.44 Burner 5: LCRZ/D = 5.375, DR/D = Fg. 8. Varatons of Ln(S/S w N ))/(N Sw )) accordng to (x/d). X Velocty [m/s] (a) (b) Fg. 6. Predcted results of axal veloctes by varyng number of njectors (a): the contour lot of axal velocty (streamlnes n black), (b): sosurfaces n blue ndcatng zero axal velocty (U=) zones Local Swrl Intensty In ths subsecton, the total flow rate and the geometrcal swrl number are fxed at a value of 41-5 Kg s -1 and 1.83, resectvely. For desgn uroses, t s major to understand the swrl decay rocess along the burner. The Swrlng moton decay s an nevtable effect n swrl flows resultng from shear stresses. To calculate Swrl decay, t s sutable to calculate the swrl number along the burner axs usng Eq. (1) In the Fg. 8, Ln( S / Sw N )) /( N S w )) s resented as a functon of (x/d). As you can see n the Fg. 8, the three curves of Fg. 7 are transformed nto a sngle lnear lne assng through the orgn wth a sloe of So, the local swrl number can be correlated n terms of geometrc swrl number and number of njectors as follows: x S Sw N ex(.15n Sw ) (x/d ) (9) D Mxng Layer Thckness The effect of the number of njectors on the mxng tme was examned. To quantfy ths effect, the mxng coeffcent K s also determned. Indeed, the coeffcent K s an essental arameter n determnng the Damkhöler number (Da= τm / τr) where τm s the mxng tme that s exressed based on K as follows: K m (1) V D nj mass Where Dmass s the mass dffusvty. The mxng coeffcent K was determned accordng to the work of Sh et al. (13, 14a, 14b, 14c) who have found that the flow near the slts s domnated by a boundary layer tye flow. So, they were demonstrated that the mxng layer thckness (δ) determned after 45 degrees from the startng ont O (see Fg. 3) can be exressed as a functon of njecton velocty, as follows: Fg. 7. Swrl ntensty dstrbutons for varous number of njectors along the e axs. Fgure 7 dects the local swrl ntensty dstrbuton along the burner axs for dfferent number of njectors. Accordng to Hay and West (1975), F. Chang and V. K. Dhr (1994) and Steenbergen and Voskam (1998), local swrl number wth an exonental manner excet for axal dstances less than two dameters downstream the nlet. The local K (11) V nj In ths subsecton, the njecton velocty was vared for the three burners (burner 3, 4 and 5). The corresondng wdth s lotted as a functon of 1 (see Fg. 9). It s shown that the flow V nj around the ext of the njector s domnated by a 61

8 Y. Chouar et al. / JAFM, Vol. 1, No., , 17. boundary layer tye flow (Sh et al. (14a) (14b) (14c)). At a constant total flow rate (QTotal) shown by the dotted lne, t has been noted the wdth gradually decreases wth ncreasng the number of njectors. good agreement was found. Thereafter, we analysed the mxng rocess for dfferent numbers of njectors and we notced that, for the same geometrcal swrl (Sw) and Reynolds (ReT) numbers, the ar wdth after njecton decreases and the dameter of CRZ ncreases wth the ncrease of the number of njectors. Ths haens due to the ncrease of the swrl number near the nlet, ncreasng thus the centrfugal force and consequently the adverse ressure gradent. Thus, the ncrease of number of njectors romotes the mxng rocess n radly tubular flame burner. On the other hand, we correlated the swrl decay along of the RTFB n terms of geometrc swrl number and number of njectors and we determned the mxng coeffcent for each burner. REFERENCES Fg. 9. Boundary layer tye flow around the ext of njector varyng wth the number of njectors. For fxed njecton velocty Vnj=1 m/s, t s shown that the mxng layer thckness reaches ts maxmum for the case wth low number of njectors (N=) (corresondng to the smaller values of total flow rate, QTotal=N* Q). Indeed, the burner 4 (N=) gves the uer lmt of mxng coeffcent (K= m 1.5 s -.5 ). By gradually ncreasng the number of njectors,.e. the total flow rate ncreases, resultng n the decrease of the mxng coeffcent. Accordng to these observatons and Eqs. (1) and (11), we can conclude that the burner wth hgher number of njectors ensures a better mxng tme. 6. CONCLUSION In ths aer, a numercal nvestgaton based on Reynolds-averaged Naver Stokes (RANS) method s erformed to examne the effect of number of njectors on the mxng rocess n Radly mxed tye Tubular Flame Burner (RTFB). To analyse the non reactve mxng rocess, the method adoted by Sh et al. (14b) based on the njecton of Magnesum oxde artcles (MgO) s used (Fg. 1). Numercal smulatons were erformed usng Fluent 6.3 whch s based on the fnte volume method. Sold artcles moton n a flow feld were descrbed by the Euleran Lagrangan aroach wth a dscrete hase method (DPM),.e., the gas hase was treated as a contnuum by solvng Naver Stokes equatons and the sold hase was calculated by trackng artcles n the Flow feld. We started our results by comarng the numercal results to the exermental data of Sh et al. (14b) n order to valdate our numercal model. The results of the flow structure, mxng layer thckness, dameter of the central recrculaton zone (CRZ) and crcumferental veloctes were comared and a Alekseenko, S. V., P. A. Kubn, V. L. Okulov and S. I. Shtork (1999). Helcal vortces n swrl flow. Journal of Flud Mechancs 38, Avc, A., I. Karagoz, A. Surmen and I. Camuz (13). Exermental Investgaton of the Natural Vortex Length n Tangental Inlet Cyclones. Searaton Scence and Technology (Phladelha) 48(1), 1-16 Azm, M. A. (16). Mxng of Co-Axal Streams: Effects of Oeratng Condtons. Journal of Aled Flud Mechancs 9(), Beer J. M. and N. A. Chger (197). Combuston Aerodynamcs. Aled Scence Publshers I., Cakmak, G., Z. Argunhan and C. Yldz (11). Effect of swrl generators wth dfferent szed roeller on heat transfer enhancement. Energy Educaton Scence and Technology Part A: Energy Scence and Research 7(), Chanaud, R. C. (1963). Exerment concernng the vortex whstle. J. Acoust. Soc. Am. 35(7), Chanaud, R. C. (1965). Observatons of oscllatory moton n certan swrlng flows. J. Flud Mech. 7, Chang, F. and V. K. Dhr (1994). Turbulent flow feld n tangentally njected swrl flows n tubes. Internatonal Journal of Heat and Flud Flow 15, Elghobash, S. (1994). On redctng artcle-laden turbulent flows. Al. Sc. Res. 5, Fluent (6). FLUENT 6.3 user s gude. Guzan, R., I. Mokn, H. Mhr and P. Bournot (14). CFD modelng and analyss of the fsh-hook effect on the rotor searator's effcency. Powder Technology 64, Guta, A. K., D. G. Llley and N. Syred (1984). Swrl Flows. Abacus Press. 6

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