The equations governing the pollutant flow in the incinerator
Given the air flow velocity and the dimensions of the incinerator as well as the high temperatures, the flow regime is turbulent. Neglecting the net rotating flows, since all changes along the flow and in vertical direction are important, the k-ε turbulence model is a good model for analyzing this problem. The equations required to solve the isothermal gas flow in the incinerator include time-averaged mass and momentum conservation equations [24]:
Mass conservation ∂Ui∂Xi=0 (1)
Momentum conservation2 ∂ρUi∂t+∂ρUiUj∂Xi=∂p∂Xi+ρ∂∂Xjv∂Ui∂Xi+∂Ui∂Xi−∂Ui′Ui′∂Xj+SMiWhere Ui is velocity along i, i = 1, 2, 3, Xi is x, y, z coordinates along i, Y mass fraction of gas emissions, ρ air density, υ kinematic viscosity, Ui turbulent velocity component along i’ and SMi is the momentum source along i’.As mentioned previously, since the Reynolds removal process and time-averaged equations will lead to unknown relationships for fluctuating velocity components, so a turbulent model is also needed. Thus, the k-ε model was used. This model requires the solution of two additional transport equations, one for turbulent kinetic energy, k and the other for its dissipation rate or ε [24]:3 ∂∂xiρuik=∂∂xiμ+μtδk∂k∂xi+P−ρε4 ∂∂xiρuiε=∂∂xiμ+μtδε∂ε∂xi+C1εkP−C2ρε2k
Enthalpy conservation: ∂∂xiρuih=∂∂xiμ+μtδh∂h∂xi+Sh (5)
Chemical species conservation: ∂∂xiρuims=∂∂xiμ+μtδh∂ms∂xi+Ss (6)
Equation of State: ρ=PRTσmj/Mj (7)