| OCR Text |
Show a - e --(pU/e)- - dx, dx, k dX) de V °*J) du, du, k where C| and C 2 are the constants, and T and Tt are determined via Boussinesq approximations. In addition to the conservation of momentum, the equation of mass continuity (Eq. 6) and conservation of energy (Eq. 7) are also solved. ox, <3' d x, d Xl dXi dxij. J d x, where h is the static enthalpy, k is the molecular conductivity, k, is the effective conductivity due to turbulent transport ( k,= \ix/ Prt), Jj- is the diffusion flux of the species jj-, and the source term Sh includes the heat of chemical reaction and any interphase exchange of heat. The source term Sh is defined by Sn = Qrad (8) In the combustion of hydrocarbon fuels, the soot particles, gaseous C 0 2 and H 2 0 are usually the primary radiating species that are significantly non-gray. Consequently, emissivity or absorptivity needs to be computed accurately to account for their true radiative characteristics in 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 mtegro-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 reactmg and non-reacting flow problems. 2.1 CHEMICAL SPECIES TRANSPORT MODEL The chemical reaction process is based on 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. A s 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 off and its variance, £2, in the flow field. |
