e1Y@YS@ 

 − WS − .S S; (19)where YS is the mole fraction of NO or HCN. This equation,which is similar to the conservation equations of 4ow andheat, is coupled to the equations of 4ow and combustion.The term WS in Eq. (19), which represents the productionand consumption of NO, is the key for NO formation. Thetime-averaged reaction rates of thermal NO formation andthe fuel nitrogen homogeneous reactions R1 and R2 areWNO;Th =8:39 × 10161:5T−0:5YN2 Y 0:5O2×exp(−564:4kJ=(RT))(1 + FTh); (20)WNO;R1 = (1 × 1011) YHCNMmMHCN  YO2MmMO2 b×exp(−280:3KJ=(RT))(1 + FR1)MNOMm; (21)WNO;R2 = (3 × 1012) YHCNMmMHCN  YNOMmMNO b×exp(−251:05 KJ=(RT))(1 + FR2)MNOMm: (22) When turbulent 4uctuation is considered with no impacton the release of coal nitrogen and the char heterogeneoussurface reaction R3 for NO formation, the correspondingreaction rates areWN = .N ˙ mP=MN ; (23)WNO;R3 =41:8 × PAEPNO×exp(−142:5KJ=(RT)) MNO: (24)
The corresponding time-averaged reaction rates of NOand HCNareWNO =(WNO;R1 − WNO;R2 − WNO;R3)MNO + WNO;Th; (25)WHCN =(WN − WNO;R1 − WNO;R2)MHCN: (26)In Eqs. (20)–(22), FTh, FR1 and FR2 are functions ac-counting for the turbulence-chemistry interaction, and theirexpressions areFTh =Y  N2Y  O2YN2 YO2+ ERT 

T Y  O2TYO2+ T Y  N2TYN2+ 12  ERT 2T 2T2; (27)FR1 =Y  HCNY  O2YHCNYO2+ ERT 

T Y  O2TYO2+ T Y  HCNTYHCN+ 12  ERT 2T 2T2; (28)FR2 = Y  HCNY  NOYHCNYNO+ ERT 

T Y  NOTYNO+ T Y  HCNTYHCN+ 12  ERT 2T 2T2; (29)where these functions express the e>ect of concentration4uctuation and temperature 4uctuation on the time-averagedreaction rate. For all 4uctuation variables, the SOM closuremodels can be obtained as@@x(u’    )+ @r@r(rv’    )+ @r@ 

(w’    )= @@x 

 e1Y@’    @x+ @r@r 

r e1Y@’    @r+ @r2@ 

× 

 e1Y@’    @ 

+ c1 T 

 @’@x  @ @x +  @’r@r ×  @ r@r +  @’r@ 

@ r@ 

  − c2 ’    k+ S’  : (30)In highly shear 4ows all 4uctuation correlations can bedetermined by the following SOM closure:’    = c7k3 2@’@xj@ @xj; (31)where ’ and   denote T, YNO, YO2 or YHCN, respectively,and S’  is the source term of reaction or radiation.3. Numerical computation and discussionIn this paper, a computer code PERT-SCF (Pure Eulerian–Eulerian Model for Reacting Two-Phase Flows in a SwirlCoal Flame) is developed. The modi9ed k– –kp two-phaseturbulence model, EBU–Arrhenius gas combustion model,DO radiation heat model, two-equation coal devolatiliza-tion model, moisture evaporation model, di>usion-kineticchar combustion model and SOM NOX formation modelare incorporated into a comprehensive model. For the nu-merical solution, the di>erential equations in Eulerian co-ordinates are integrated over the control volume to obtain9nite-di>erence equations (FDEs) using the upwind scheme.The FDEs are solved using the SIMPLE algorithm with p-vcorrections, TDMA line-by-line and plane-by-plane itera-tions and under-relaxations. The criterion for convergenceis that the summation of gas-phase residual mass sourcesis less than 1 × 10−3and the summation of particle-phaseresidual mass sources is less than 1 × 10−2.3.1. Simulation of methane–air turbulent combustionIn order to verify the validation of the modi9ed k–  modeland the SOMNOX formation model, PERT-SCF is 9rst usedto simulate methane–air di>usion combustion. The standardk–  model and the presumed
PDF-9nite-reaction-rate modelare also used to calculate 4ow 9eld and NOX formation,respectively.For the presumed PDF-9nite-reaction-rate model, inwhich the instantaneous reaction rate is taken as a func-tion of two variables—temperature and oxygen concen-tration, the time-averaged reaction rate is expressed bytime-averaged variables, that isWNO;Th =  10  10ˆ WNO;Th(