| OCR Text |
Show In addition to the conservation of momentum, the equation of mass continuity (Eq. 3) and conservation of energy (Eq. 4) are also solved. ppZ).o (3> o.t, Ot Ox, Ox, 0X, Ox, j- Ox, where h is the static enthalpy, k is the molecular conductivity, k, is the effective conductivity due to turbulent transport ( k,= ut/ Pr,), Jy is the diffusion flux of the species j', and the source term Sh includes heat of chemical reaction and any interphase exchange of heat. In the combustion of hydrocarbon fuels, the soot particles, gaseous C02 and H20 are usually the primary radiating species that are significantly non-gray. Consequently, emissivity or absorptivity needs to be computed accurately so as to account for their true radiative characteristics into the model. In the present simulation. Discrete Ordinate Method ( D O M ) is used to solve the radiative transfer equation (RTE) for an absorbing, emitting and scattering media. The D O M , conceptually an extension of the flux methods, converts the integro-differential equations by discretization of angular variation of radiative intensity into differential equations (Fiveland, 1984). Being differential in form, these equations can easily be coupled with flow transport equations in reacting and non-reacting flow problems. There are two types of chemical species transport models used in the combustion space, (i) the finite rate chemistry formulation, which is based on solving individual species transport equation and (ii) the mixture fraction probability density function (PDF) approach in which a single conserved scalar, mixture fraction (and its variance), is solved and the individual species concentrations are derived from the predicted mixture distribution. In this approach individual reaction mechanisms need not be defined; instead, the reacting species are treated with the chemical equilibrium approach. As noted above, the mixture fraction, / at each point in the combustion space is computed through the solution of the conservation equation for the mean (time averaged) value o f / and its variance f2 in the flow field. The mixture fraction variance is used in the closure model describing the turbulence-chemistry interactions (Fluent Users Manual, 1999). 2.2 Dispersed Phase In addition to solving transport equations for the continuous phase, a discrete second phase is solved in the Lagrangian frame of reference. The trajectories and heat and mass transfer from/to these discrete particles are coupled with the continuous phase. The trajectory of the discrete phase particle is calculated by integrating the force balance on the particle, which is given in Eq (5). - = FD(U-UP)+ g,(pp-p)/pp + F, (5) dt where F D (u -up) is the drag force per unit particle mass and 18// Co Re FD = PrDp1 24 Here, u is the fluid phase velocity, up is the particle velocity, \i is the molecular viscosity of the fluid, p is the fluid density, p p is the particle density, and D p is the particle diameter. R e is the Reynolds number, which is defined based on the relative velocity of the fluid and particle velocities. The drag coefficient C D is defined from Morsi'and Alexander's expression (1972): |
