Numerical Study of the Swirl Effect on a Coaxial Jet Combustor Flame Including Radiative Heat Transfer

This article was downloaded by: [Gassoumi, Taoufik] On: 23 December 2009 Access details: Access Details: [subscription number 918007158] Publisher Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 3741 Mortimer Street, London W1T 3JH, UK Numerical Heat Transfer, Part A: Applications Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713657973 Numerical Study of the Swirl Effect on a Coaxial Jet Combustor Flame Including Radiative Heat Transfer Taoufik Gassoumi a; Kamel Guedri a; Rachid Said a Unité de Recherche: Etude des Milieux Ionisés et Réactifs (EMIR), IPEIM, Monastir, Tunisie a Online publication date: 21 December 2009 To cite this Article Gassoumi, Taoufik, Guedri, Kamel and Said, Rachid(2009) 'Numerical Study of the Swirl Effect on a Coaxial Jet Combustor Flame Including Radiative Heat Transfer', Numerical Heat Transfer, Part A: Applications, 56: 11, 897 — 913 To link to this Article: DOI: 10.1080/10407780903466535 URL: http://dx.doi.org/10.1080/10407780903466535 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article may be used for research, teaching and private study purposes. 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The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Numerical Heat Transfer, Part A, 56: 897–913, 2009 Copyright # Taylor & Francis Group, LLC ISSN: 1040-7782 print=1521-0634 online DOI: 10.1080/10407780903466535 NUMERICAL STUDY OF THE SWIRL EFFECT ON A COAXIAL JET COMBUSTOR FLAME INCLUDING RADIATIVE HEAT TRANSFER Taoufik Gassoumi, Kamel Guedri, and Rachid Said Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 Unité de Recherche: Etude des Milieux Ionisés et Réactifs (EMIR), IPEIM, Monastir, Tunisie A numerical study of the swirl effect on a coaxial jet combustor flame including radiative heat transfer is presented. In this work, the standard k-e model is applied to investigate the turbulence effect, and the eddy dissipation model (EDM) is used to model combustion. The radiative heat transfer and the properties of gases and soot are considered using a coupled of the finite-volume method (FVM), and the narrow-band based weighted-sumof-gray gases (WSGG-SNB) model. The results of this work are validated by experiment data. The results clearly show that radiation must be taken into account to obtain good accuracy for turbulent diffusion flame in combustor chamber. Flame is very influenced by the radiation of gases, soot, and combustor wall. However, swirl is an important controlling variable on the combustion characteristics and pollutant formation. 1. INTRODUCTION Combustion chambers designs have been optimized for years to increase efficiency and minimize pollution for steady regimes. Currently, one of the challenges of computational combustion in real engines is the radiative heat transfer. In the literature, three approaches are used to simulate turbulence. First, the direct numerical simulation (DNS) approach treats the complete equations of Navier-Stokes which are solved without any closure model. The DNS has an expensive computational time, but it is used as a reference to test other forms of simulation of turbulence [1]. Secondly, the large eddy simulation (LES) is used to calculate directly the large eddy or scale and to model the small scale. In combustion technology, LES is useful for combustion instabilities [2] and flame stabilization [3], but, it is very expensive and needs high performance processors for calculation. Finally, the Reynolds-averaged Navier-stokes (RANS) is also developed [1]. Many closure models are available, but they divide into two categories depending on the modeling of turbulence stresses, based either on an eddy-viscosity model (EVM) or a Reynolds-stresses model (RSM). The EVM, for example the standard k-e model described by Launder and Spalding [4], and the Renormalization Group theory (RNG k-e) model [5, 6], are used to treat the isotropic turbulence. However, the Received 30 June 2009; accepted 15 October 2009. Address correspondence to Taoufik Gassoumi, Etude des Milieux Ionisés et Réactifs (EMIR), IPEIM, Rue Ibn El-Jazzar, 5019, Monastir, Tunisie. E-mail: Taoufik_Gassoumi@yahoo.fr 897 898 T. GASSOUMI ET AL. NOMENCLATURE A Cp Ce1 ; Ce2 ; Cm Dmn fv G Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 h I i K k q < RF S SW T u, v, w us x, r Y yþ Z a amn1=2 b C/ e ew f j m mmn, gmn, nmn t q rs s U area of control volume face, m2 constant pressure specific heat constants of the standard k-e model directional weight soot volumetric fraction production term of turbulent kinetic energy enthalpy radiant intensity, W=m2
sr stoichiometric oxygen to fuel mass ratio Van-Karman constant turbulent energy, m2=s2 radiative heat flux, W=m2 incident radiation, W=m2 reaction rate, kg=m3
s source term swirl number temperature, K axial, radial and tangential velocity component, respectively, m=s wall friction velocity, m=s coordinate axes in cylindrical geometry mass fraction adimensional distance in wall coordinate mixture fraction Prandtl number coefficient of the angular derivative term extinction coefficient ¼ j þ rs, m1 diffusion coefficient for transport variable dissipation rate of energy, m2=s3 wall emissivity equivalence ratio absorption coefficient, m1 viscosity, kg=m
s direction cosines wave number, m1 density, kg=m3 scattering coefficient, m1 shear stress Scattering phase function / ! X DXmn x Subscripts b cr, cx E, W, T, B e, w, t, b eff F g i k l O P pr r s t t Superscripts m, n, m0 , n0 w þ, Abbreviations CFD DNS DOM EVM FVM LES RANS RNG RSM RTE WSGG- SNB general dependent variable direction discrete control angle scattering albedo blackbody radial and axial direction, respectively east, west, top and bottom neighbors points of P east, west, top, and bottom control faces effective exchange coefficient fuel gas species kth gray gas laminar transport coefficient oxygen nodal point in which intensities are located product radiation soot turbulent transport coefficient spectral parameter radiation direction wall leaving and arriving intensity directions, respectively computational fluid dynamic direct numerical simulation discrete ordinate method eddy-viscosity model finite volume method large eddy simulation Reynolds-averaged NavierStokes Renormalization Group Reynolds-stresses model radiative transfer equation narrow-band based weighted-sum-of-gray-gases RSM are more adapted to anisotropic turbulence, as in bed flows [7]. The RSM are tested to isothermal flows without chemical reaction and heat transfer. The standard wall-function approach is used to solve the near-wall region to achieve a better Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 SWIRL EFFECT ON A COAXIAL JET COMBUSTOR FLAME 899 prediction of wall effects. The wall functions are available in the literature [8]; there is a semi-empirical formula expressing the well known logarithmic law [9]. Generally, flames are influenced by the radiative properties of combustion gases and their surroundings [10]. A computational analysis of radiation avoids an under-or over-prediction of the temperature distribution in combustion systems. Zimberg et al. [11] showed, in the case of a cylindrical non-premixed flame, that there is a strong interaction between chemistry, turbulence, and radiation. For that reason, to obtain a coherent work radiation must be taken into account. In such work, when combustion and radiation are coupled we must choose the suitable methods and models for simulation. When radiation dominates in combustion systems, we must also take into account the geometry and the computational time cost. In the literature, there are many methods cited to solve the radiative transfer equation: the discrete ordinate, the discrete transfer, the flux, the Monte Carlo, the zone, the P–N, and the finite-volume methods (FVM). Several researchers, like Kim et al. [12], showed that FVM has the best accuracy and performance by comparing it with DOM. In addition, FVM shares the same computational grid with computational fluid dynamics solvers (CFD). Previously, FVM has been is used in structured grids, particularly with cylindrical coordinates [13], but it is also applied in unstructured grids for axisymmetric geometries [14]. In the present article, to solve the radiative transfer equation (ETR), the finite-volume method (FVM) will be coupled to the narrow-band based weightedsum-of-gray gases (WSGG-SNB) model of Kim and Song [15]. This radiation procedure is implemented on a combustion code using the eddy dissipation model (EDM) proposed by Magnussen and Hjertager [17] for combustion and a combination between k-e model and wall function for turbulence. The swirl is produced by adding a tangential component on the injection of the fluid (fuel or air). Thus, the effect of the swirl number is investigated. The results showed that radiation of the combustor wall, gases, soot, and swirl number played an important role in combustion. 2. MATHEMATICAL MODEL 2.1. Governing Equations In this article, to simulate the turbulent flow and chemical reaction in the burner, a two-dimensional axisymmetric mathematical model is applied. In the axisymmetric coordinate, a generalized form of the equations of motion can be expressed as 

 1 q q q q/ q q/ ðrqu/Þ þ ðrqv/Þ  rCeff rCeff ð1Þ  ¼ S/ r qx qr qx qx qr qr The diffusion coefficients Ceff and the source terms S/ of conservation law of each dependent variable / with the correspondent laminar a/l, and turbulent, a/t, Prandtl numbers are shown in Table 1. Ceff is the sum of both the laminar and turbulent transport coefficients. It is interpreted as the effective viscosity for / ¼ u, v, w, and the effective diffusivity for / ¼ h, Z, Yi. In Eq. (1), Ceff is calculated as Ceff ¼ ml m þ t a/l a/t ð2aÞ 900 T. GASSOUMI ET AL. Table 1. Diffusion coefficients, laminar, and turbulent Prandtl numbers and source terms of conservation laws [10] Equation Continuity / Ceff a/l 1 0 1.0 a/t 1.0 Axial momentum u meff 0.7 0.9 Radial momentum v meff 0.7 0.9 Tangential momentum w meff 1.0 1.0 Kinetic energy of turbulence k Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 Dissipation of turbulence energy e Energy (enthalpy) h Fuel mass fraction YF Mixture fraction Z meff rk meff re meff rh meff rYF meff rZ 0.7 0.7 S/ 0.0

 q qu 1q qv qp meff rmeff þ  qx qx r qr qx qx

 q qu 1q qv v meff rmeff þ  2meff 2 qx qr r qr qr r 
 qw2 qp q 2 2 qu qv qk þ meff þ   þ r qr qr 3 3 qx qr 2q  ðrwmeff Þ r qr mt G  1.0 Cm q 2 k 2 mt 2 2 K pffiffiffiffiffi C GCm qk  Ce2 qek ðCe2 Ce1 Þ Cm e1 0.5 r
qr 0.7 0.5 Rf 0.7 0.5 0.0 0.7 The constants of the standard k-e model are Cm ¼ 0.09, Ce1 ¼ 1:44, and Ce2 ¼ 1:92. K ¼ 0.4187 is the Van-Karman constant. with meff ¼ ml þ mt ð2bÞ where ml and mt represent, respectively, the laminar and the turbulent viscosity. a/l and a/t are the laminar and turbulent Prandtl number corresponding to the variable /, respectively. 2.2. Turbulence Model To compute turbulence, the two equations (k-e) model, developed by Launder and Spalding [4] was used. The turbulent viscosity is determined from the time-mean values of the kinetic energy of turbulence, k, and the volumetric turbulent kinetic energy dissipation rate, e, by the expression mt ¼ C m q k2 e ð3Þ where Cm is a constant and the quantities k and e are determined from Eq. (1). Where for the k equation Sk ¼ mt G  Cm q2 k2 mt ð4Þ and for the e equation Se ¼ Ce1 GCm qk  Ce2 qe2 k ð5Þ SWIRL EFFECT ON A COAXIAL JET COMBUSTOR FLAME 901 In Eqs. (4) and (5), G represents the production of turbulent kinetic energy by the mean motion and given by G ¼2
"
qu qx  2
2   #

2  qv v 2 qu qv 2 qw q w 2 þ þ þ þ þ þ r qr r qr qx qx qr r ð6Þ Boundary Conditions: Wall Function Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 The treatment of the region near the wall is very necessary, because the standard k-e model is a high-Reynolds model and cannot be applied in this region due to viscous effects. The wall distance in wall coordinate yþ is defined as [4] yþ ¼ qyp us ml ð7Þ where, yP is the normal distance from the center of the cell at the point P to the wall. us is the wall friction velocity rffiffiffiffiffi sw ð8Þ us ¼ q yþ represents the grid adimensional distance from the wall and it is given according to Launder and Spalding [4] at node P, as ! 1=4 pffiffiffi qCm ky þ y ¼ ð9Þ ml P Knowing that the laminar sublayer extends from the wall to yþ ¼ 11.63 [4]. Using the logarithmic law, the axial velocity in wall coordinate, uþ, is given by uþ 1 ¼ LnðEyþ Þ us K ð10Þ
 u s w ¼ ml y P ð11Þ Then, the shear stress is given by Otherwise, the point P is within the turbulent flow region and the shear stress is calculated using the logarithmic law of the wall so that   pffiffiffi u ð12Þ sw ¼ qCm1=2 K k lnðEyþ Þ P with K ¼ 0.4187 and E ¼ 9.0 are the Van-Karman and the smooth wall constants [4], respectively. In Table 2, the source terms of the turbulent kinetic energy k and the 902 T. GASSOUMI ET AL. Table 2. Boundary wall conditions [4] k / e 3=4 Cm kp3=2 sp 1=2 Kyp qCm S/   lnðEyþ Þ for yþ  11:63 mt G  Cm3=4 qk3=2 ðKyÞ P   yþ for yþ < 11:63 mt G  Cm3=4 qk3=2 y P 1030þ1030eP Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 turbulent dissipation rate e are given. The shear stress evaluated above is used in the generation term G to compute ðmðquÞ=ðqyÞÞ. Se is computed by assuming that the rates of the turbulent kinetic energy generation and dissipation are equal, and the value of e is given at the edge of the Couette flow region. 2.2. Combustion Model For combustion, a single step reaction of methane (CH4) and air is considered. To simplify calculations, the argon is not included. The equation for combustion of a lean mixture is given as [16]
 2 1f 7:52 CH4 þ ðO2 þ 3:76N2 Þ ! CO2 þ 2H2 O þ 2 N2 for 0  f  1 O2 þ f f f ð13Þ The fuel mass fraction, YF, is obtained using Eq. (1) where SYF ¼ RF ð14Þ h ¼ YF
HR þ Cp;m
T ð15Þ The enthalpy, h, is defined as when Cp,m is the mean specific heat and it is obtained, with the summation over all species, from X Cp;m ¼ Yk Cp;k ð16Þ k The eddy dissipation model (EDM) proposed by Magnussen et Hjertager [17], is used to calculate the reaction rate Rf from   YO Ypr e RF ¼ CR CA q min YF ; 2 ; CB k 1þi i ð17Þ where CR ¼ 4.0 (for collision mixing model), CA ¼ 1.0 (for infinite rate chemistry), and CB ¼ 0.5 (an empirical mixing constant). After obtaining YF, the mixture fraction model is used to calculate the mass fraction of other species. SWIRL EFFECT ON A COAXIAL JET COMBUSTOR FLAME 903 2.4. Radiation Model In this work, the finite-volume method (FVM), known by its simplicity and its adaptation to flows simulation particularly to turbulent combustion code, is used. The radiative transfer equation (RTE) in an absorbing-emitting and scattering gray medium can be written as [18, 19] ðX
rÞIðr; XÞ ¼ jðrÞIb ðrÞ  bðrÞIðr; XÞ þ rs ðrÞ 4p Z X0 ¼4p UðX0 ! XÞIðr; X0 ÞdX0 ð18Þ Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 However, in non-gray medium when the absorption j, the extinction b, and the scattering rs, coefficients depend on frequency t, the RTE becomes ðX
rÞIt ðr; XÞ ¼ jt ðrÞIbt ðrÞ  bt ðrÞIt ðr; XÞ þ rs ðrÞ 4p Z X0 ¼4p Ut ðX0 ! XÞIt ðr; X0 ÞdX0 ð19Þ where It(r, X) is the spectral radiation intensity at any position r and along a direction X. Ibt is the spectral blackbody radiation intensity. Ut(X0 ! X) represents the spectral scattering phase function from the incoming direction X0 to the outgoing direction X. Knowing that using the weighted-sum-of-gray gases (WSGG), the total intensity I is obtained by summing up all the kth gray gas intensities, represented in the following expression. I mn ¼ X Ikmn k ð20Þ For a two-dimensional axisymmetric problem, the spatial derivative term in Eq. (18) in the cylindrical coordinates becomes according to reference [18] ðX
rÞI mn ðr; XÞ ¼ mmn qðrI mn Þ 1 qðgmn I mn Þ qI mn  þ nmn qr r qW r qx ð21Þ where mmn, gmn, and nmn are the direction cosines, and W is the azimuthal angle measured from the direction, as shown in Figure 1. The direction cosines are defined by mmn ¼ sin h cos W ð22aÞ gmn ¼ sin h sin W ð22bÞ nmn ¼ cos h ð22cÞ The integration of the RTE for an absorbing-emmiting-scattering medium over a volume cell and a solid angle, and its discretization in spatial and angular domains and along a discrete direction Xmn ¼ (mmn, gmn, nmn) using the finite-volume method, Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 904 T. GASSOUMI ET AL. Figure 1. Direction cosines and control solid angle. can be obtained in the point P at the control volume according to reference [20] as mn
1=2 IPmn ¼ mn mn mn mn Aw Dmn þ SmP DV DXmn cr IW þ Ab Dcx IB
ðAe
Aw Þamn
1=2 IP mn mn mn mn Ae Dcr IW þ At Dcx
ðAe
Aw Þamnþ1=2 þ bmod DV DXmn ð23Þ with DXmn ¼ Z hmþ1=2 Z Wmþ1=2 sinh dh dW  Dh 1 h    i amnþ1=2 ¼
sin Wnþ1=2
sin 2hmþ1=2
sin 2hm
1=2 2 4 Z r 0 0 0 0 0 0 s Um n

>mn IPm n dXm n SPmn ¼ jIbPþ 0 0 4p Xm n ¼ 4p Z ðX  er ÞdX Dmn cr ¼ mn ZDX ðX  ex ÞdX Dmn cx ¼ hm
1=2 wm
1=2 DXmn ð24aÞ ð24bÞ ð24cÞ ð24dÞ ð24eÞ and At ¼Ab ¼ p r2e
r2w Ae ¼ 2pDxre Aw ¼ 2pDxrw
ð24f Þ ð24gÞ ð24hÞ mn In these equations, Dmn cr and Dcx are the direction cosines regarding the r and x directions, respectively. At, Ab, Aw, and Ae are the top, bottom, west, and east faces SWIRL EFFECT ON A COAXIAL JET COMBUSTOR FLAME 905 of the control volume, respectively, as shown in Figure 2. DV is the control volume and bmn mod is the modified extinction coefficient [20]. The combustor wall is assumed gray surface characterized by an emissivity ew and nw its unit normal vector. This surface emits and reflects diffusely, and then the radiative boundary condition for Eq. (18) is written as [18] Z ð1
ew Þ Iðrw ; Xþ Þ ¼ ew Ib ðrw Þ þ ð25Þ Iðrw ; Xþ Þjnw  X
jdX
p nw  X
0 when X
and Xþ indicate the arriving and leaving radiative intensity directions, respectively. The radiative heat flux at the wall can be estimated by X qwr ¼ IPmn Dmn ð26Þ cwall Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 mn The radiation source term, Sr, is given by Z 1 jt ð4pIbt
<n Þdn Sr ¼
r  qr ¼
ð27Þ 0 where the incident radiation, <, is written as Z 1 Z 1Z <¼ It dXdn <n dn ¼ 0 0 ð28Þ 4p In the present work, the narrow-band based weighted-sum-of-gray-gases (WSGG-SNB) model of Kim and Song [15] is used. This model uses the design of the weighted-sum-of-gray-gases model (WSGGM) with the database of the statistical narrow band model (SNB) to model the radiative properties of gas mixture [15, 21]. At present, this new model is one of the best models which offers a good compromise Figure 2. Variables related to grid system. 906 T. GASSOUMI ET AL. between precision and computing time [15, 21]. The extinction coefficient is bt ¼ jt þ rst ð29aÞ and the single scattering albedo, xt, is defined as xt ¼ rst rst ¼ jt þ rst bt ð29bÞ For the kth gray gas, the absorption coefficient is jk ¼ jg;k þ js;k ð30aÞ Here, soot are treated as gray so Eq. (30a) becomes Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 jk ¼ jg;k þ js ð30bÞ Indeed, the WSGG model assigns to a non-gray gas an equivalent finite number of gray gases with appropriate weighting factors strongly dependent on the local temperature [22]. Radiative Properties of Gases and Soot The absorption coefficient of any gas species i for the partial pressure P and temperature T is given by [21] ji ¼ j0i P ai =T e T2 ð31Þ where j0i and ai are the modeling parameters for species i. In this work, the soot absorption coefficient is taken in the Rayleigh scattering limit and it is defined like references [21–24] as js ¼ 3:72fv C0 T C2 ð32Þ where C0 ¼ 36pnk=[(n2  k2 þ 2)2 þ 4n2k2], n ¼ 1.85 C2 ¼ 1.4388 cm
K. n represents the real part of the complex index of refraction, and k ¼ 0.22 represents the absorptive index. fv is the soot volumetric fraction. In this article, fv ¼ 105. 3. RESULTS AND DISCUSSION To validate our numerical model, the experiment of Spadaccini et al. [25] is considered (Figure 3). The experimental inputs are summarized in Table 3. The swirl is produced by adding a tangential component on the injection of air. The most commonly used parameter is the swirl number, SW, and it is defined as the ratio of axial flux of angular momentum and axial flux of linear momentum [26]. SW ¼ R 2p wrqurdr R 2pR uqurdr ð33Þ SWIRL EFFECT ON A COAXIAL JET COMBUSTOR FLAME 907 Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 Figure 3. Coordinate system of the coaxial jet combustor (the dimensions are not to scale). where w represents the tangential component of velocity. In this study, the level of swirl strength is represented in terms of swirl number. 3.1. Gas Temperature Figure 4 shows the temperature contours with without radiation. Two cases are illustrated: a case without swirl (SW ¼ 0.0) and a case with swirl where SW ¼ 0.6. It is shown that the temperature is very influenced by the swirl. Indeed, the maximum temperature was increased from 2000 K to 2200 K when the swirl number, SW, was increased from 0.0 to 0.6. In addition, radiation heat transfer has an important effect on flame. The effect of radiation heat losses from hot gases to cold wall is less remarkable when swirl is applied. It is also shown that radiation reaches the injection zone and overheats the fuel which facilitates, consequently, its ignition. Table 3. Dimensions and flow conditions The Dimensions (cm) Central pipe radius (r1) Annular inner radius (r2) Annular wall thickness (r2r1) Annular outer radius (r3) Combustor radius r4 Combustor length (L) Flow conditions Mass flow rate (kg=s) Bulk velocity u(m=s) Temperature T (K) Swirl number SW CH4 mass fraction YCH4 O2 mass fraction YO2 N2 mass fraction YN2 Overall equivalence ratio f Combustor pressure (atm) 3.157 3.175 0.018 4.685  R 6.115 100.0 Inner jet (fuel) Outer jet (air) 0.00720 0.9287 300 0.0 1 0.0 0.0 0.137 20.63  U 750 0.6 0.0 0.2329 0.7671 0.9 1.0 Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 908 T. GASSOUMI ET AL. Figure 4. Isotherm contours in the combustor chamber with and without radiation for two different swirl number: SW ¼ 0.0 (case without swirl) and SW ¼ 0.6 (case with swirl). (a) Temperature contours without radiation: up without swirl and down with swirl; (b) isotherm contours without radiation: up without swirl and down with swirl; (c) temperature contours with radiation: up without swirl and down with swirl; and (d) isotherm contours with radiation: up without swirl and down with swirl. In the case without swirl (SW ¼ 0.0), Figures 4b and 4d clearly show the disparaition of the isotherm 2000 K when radiation is taken into account (Figures 4b and 4d: up). However, when swirl is introduced (SW ¼ 0.6), the 2200 K isotherm (Figure 4b: down) is still there when radiation is applied but in a reduced zone (4d: down). In light of these observations, one can conclude that swirl offers a good mixing of the mixture, which increases the temperature significantly. This is observed in Figure 4, when temperature increases about 200 K when swirl is applied. Indeed, swirl can create a recirculation zone: this offers a good mixing of the fuel and air. In addition, a portion of the unburned gases will go back to the combustion zone where temperature reaches its maximum and will be in a favorable condition of ignition. However, the intensity of turbulence and the flame speed vary proportionally with the swirl number. So, we must take care because a high swirl number can lead to the lift-off or even to the occurrence of flame flashback. Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 SWIRL EFFECT ON A COAXIAL JET COMBUSTOR FLAME 909 Figure 5. Temperature contours with swirl (SW ¼ 1.0): without radiation (up) and with radiation (down). When the swirl number increases, the intensity of turbulence increases and the flame length decreases. However, the use of high swirl number can lead to flame flashback. With swirl, there is a compensation of the radiative heat transfer effect. However, it is important to note that the computational power of any numerical code can be evaluated near the bluff-body by solving any scale motion. Figure 5 clearly shows that the size of the high temperature regions of the flame was reduced significantly when radiation is taken into account. Figure 6 illustrates the radial profile of temperature compared with experimental data [24] at four different axial locations and for a swirl number SW ¼ 0.6. At the two positions x=R ¼ 0.887 and x=R ¼ 1.57, convection is the important transfer mode because of strong fluctuations in this region. The error found in Figures 6a and 6b is due to this strong dynamic behavior. The reflections about the centerline of data points taken on the opposite side of the combustor are considered. For the third station, x=R ¼ 4.52, and the fourth station, x=R ¼ 5.19, the profiles agree with the experimental data. The radiative heat transfer effect is clearly observed from the main combustion zone, where temperature reaches its maximum towards the combustor outlet (see Figures 6c and 6d). 3.2. CO2 Mass Fraction Figure 7 presents the CO2 mass fraction contours with and without radiation for two different swirl numbers: SW ¼ 0.6 and SW ¼ 1.0. It shows the good mixing due to swirl and the variation of the CO2 mass fraction in the same location due to the recirculation zone where fluctuations are important (see Figure 8). Figure 7 clearly shows the recirculation of products from reactions occurring farther downstream. The important observation is that the CO2 mass fraction decreases from the main combustion zone towards the combustor outlet when the swirl number increases. It is shown in the literature, that the decrease was very small compared Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 910 T. GASSOUMI ET AL. Figure 6. Radial profile of temperature compared with experimental data. (a) Temperature at x=R ¼ 0.887; (b) temperature at x=R ¼ 1.57; (c) temperature at x=R ¼ 4.52; and (d) temperature at x= R ¼ 5.19. Figure 7. CO2 mass fraction contours with and without radiation for SW ¼ 0.6 and SW ¼ 1.0. (a) Case without radiation: up SW ¼ 0.6 and down SW ¼ 1.0; (b) case with radiation: up SW ¼ 0.6 and down SW ¼ 1.0. Downloaded By: [Gassoumi, Taoufik] At: 20:45 23 December 2009 SWIRL EFFECT ON A COAXIAL JET COMBUSTOR FLAME 911 Figure 8. The different recirculation zones in the combustor. to the reduction of NOx emissions [27]. Generally, the swirl can stabilize the flame and increase the combustion efficiency. Furthermore, the good mixing significantly reduces the NOx emissions. 4. CONCLUSION A numerical simulation of the swirl effect in a combustor chamber is investigated. To correctly judge the influence of swirl, radiation is taken into account by solving the radiative transfer equation using the finite-volume method and the narrow-band based weighted-sum-of-gray gases (WSGG-SNB) model. In this work, the effect of swirl is analyzed, including radiative heat transfer, which helps us understand the behavior of the flame under various operating conditions and avoids the under- or over-prediction of heat transfer in a combustion system. The results show that the convective exchange in swirling flow is very important in the region close to the inlet. For more accuracy, radiation of gases, soot, and wall must be taken into account from the high temperature regions of the flame towards the combustor outlet. The results show that applying swirl can be a solution to improving combustion efficiency and, consequently, reducing NOx emission. REFERENCES 1. C. Bailly and G. Comte-Bellot, Turbulence, CNRS Editions, 2003. 2. S. Roux, G. Lartigue, T. Poinsot, U. 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