(w’)= @@x  

’@’@x + @r@r r 

’@’@r + @r2@ 

’@’@ 

 + S’ + S’p; (1)@@x(pup’p)+ @r@r(rpvp’p)+ @r@ 

(pwp’p)= @@x  

’p@’p@x + @r@r r 

’p@’p@r + @r2@ 

’p@’p@ 

 + S’p + S’pg; (2)where Eqs. (1) and (2) are the generalized forms for thegas and particle phases respectively, and the two-phaseturbulence model is k– –kp (Zhou, 1993). The standardk– –kp model adopts an isotropic viscosity model basedon the Boussinesq assumption and tends to eliminate theanisotropic free-vortex region of the turbulent 4ow, espe-cially swirling 4ow. The question mainly focuses on the  equation. The reason for this is that it overrates the di>usionrate of the jet and does not consider the Eddy structure.In this paper, the turbulent-time-scale model is adopted tomodify the source term S  of the   equation. The typicalturbulent kinetic energy (TKE) dissipation rate equation ( equation) is@@x(u )+ @r@r(rv )+ @r@ 

(w )= @@x  

 @ @x + @r@r r 

 @ @r + @r2@ 

 @ @ 

 +c 1 k(Gk + Gp + GR) − c 2 2k; (3)whereGk =2 T  @u@x 2+ @v@r 2+  @wr@ 

+ vr 2 + T  @w@x+ @ur@ 

 2+ @u@r+ @v@x 2+  @vr@ 

+ @w@r− wr 2 ;Gp = − p i2p rp(Cbp kkp − k);GR = −2k pnp ˙ mp: The source term S  of the   equation isS  = c 1 k(Gk + Gp + GR) − c 2 2k:After modi9cation, S  is written asS  = c 1 k(Gk + Gp + GR) − c 2(1 − cgsRigs) 2k;where the turbulent-time-scale model Rigs isRigs = k2 2wr2@@r(rw)= k2 2wr @w@r+ wr :2.2. Gas combustion and radiation modelsAlthough investigations of coal devolatilization havegiven rise to a number of kinetic models and consideredvolatiles including a lot of 4ammable components (Solomonet al., 1990; Therssen et al., 1995), these models need ratherlarge computation time in a three-dimensional procedure.When volatile is only CH4, some reasonable results canalso be gained. For volatile (CH4) and CO combustion, theconventional EBU–Arrhenius model (Zhou, 1993) is used,and WS = min(WEBU;WArr ),whereWEBU = cE kmin YS ;YOX# ; (4)WArr = BS 2YS YOX exp(−ES =RT); (5)where s stands for CH4 (volatile) or CO. For radiative heattransfer, the discrete-ordinate (DO) model is used. The lit-erature (Fiveland, 1988) gives a detailed derivation of theDO model.2.3. Single coal particle mass change modelA single reacting coal particle is considered to consistof dry and free (daf) coal, moisture, char and ash. Apartfrom ash, which is an inert material without mass change,the other three parts change due to moisture evaporation,devolatilization and char combustion. The total mass changeof a single coal particle can be obtained as˙ mp =˙ mw;p +˙ mv;p +˙ mc;p; (6)where ˙ mw;p is the moisture evaporation rate, ˙ mv;p is thevolatile fuel releasing rate, and ˙ mc;p is the char reaction rate.These mass transfer rates are described by the sub-modelsoutlined in the following sections.2.3.1. Moisture evaporation rateThe moisture evaporation rate is calculated by a di>usionmodel in a way similar to the droplet evaporation rate (Zhou,1993). Assuming that the moisture in a coal particle di>usesto the surface of the coal particle to form a liquid 9lm andtreating this liquid 9lm as a surface layer of a water dropletwith the same diameter, the moisture evaporation rate canbe determined as˙ mw;p =                      −&dpNup)SCpsln 1+ Cps(T − Tp)1 − LW ; (Tp ¿Tb);−&dpNupDS Sln 1+ YH2O;S − YH2O;g1 − YH2O;S ; (Tp ¡Tb);(7)where YH2O;S is the mass fraction of vapor at the surfaceof the coal particles, given by YH2O;S =BW exp(−EW =RTp),and YH2O;g is the mass fraction of vapor surrounding the coalparticle, which is equal to the vapor concentration in thecalculation grid