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Show METHOD OF CALCULATION Gas Phase Transport Equations Pun and Spalding demonstrated that a general steady-state transport equation for an (r-z) geometry can be written for any conserved variable in the form: !_ (pu#) + 1 1 _ ( p r v „ . {|_ (r ii) +1|_ (r r# |i,} + s# (D where <p is the dependent variable, T. is the effective diffusion <P coefficient and S , is the source of d> per unit volume. <P The conservation equations (mass, three components of momentum, and others) are elliptic. Spalding and his co-workers have discussed the numerical solution of these equations based on a control volume formulation. Gas Phase Fluid Mechanics. Table 1 lists the values of 0, T , and S, for the conservation equations of mass and the three components of momentum. Table 2 lists the appropriate modeling constants. The source term, S , for the continuity equation represents the mass of gas added due to the mass transfer from the particles. Sources of momentum are also listed in the table and occur as a result of fluid mechanic terms (e.g. Coriolis forces, pressure terms) and due to interaction with the particle phase. Turbulence Model. In writing Equation 1 for momentum, we have assumed that the effective diffusion coefficient can be represented by: Ueff - Mj, + Vt (2) where u and u are the laminar and turbulent viscosities, respectively. 1 t (7) Following recommendations by Launder, et al. , the turbulent viscosity is modeled as: -4- |
