| OCR Text |
Show which incorporates the key features of: boundary layer diffusion (kD ), adsorption (ka ), desorption (kd ), and internal diffusion (governed by an experimental value for f = Rsl Re where Re is the external reaction rate). Variations in the partial pressure of oxygen Ya and temperature Tp (affecting kD' ka, kd ) along the particle path produce corresponding variations in the value of Rs. Activation energies and pre-exponential factors for the rate of pyrolysis and the rates of diffusion, adsorption, and desorption for the char reaction are based on experimental data [6]. The specific reaction rate Rs is related to the unburned fraction of char Ub = ppTcl P~T~ (where Pp is particle density, Tc is particle radius, and the 0 subscripts denote initial values) by the following expression [6]: which may be obtained by writing the equation for the specific reaction rate as the sum of external and internal reaction rates: and specifying the integration path: where Q = 3(f - 1). The expression for Ub is then numerically integrated point by point to calculate the unburned fraction of each particle as it travels through the imposed temperature and oxygen concentration fields. 3 Numerical solution The vorticity transport equation is solved numerically by an alternating-direction implicit (ADI) method. The corresponding stream-function distribution is obtained by a direct, fully implicit solution of the elliptic stream function equation. The time evolution of the flow field is pursued as long as desired. Knowing the flow field at any particular time instant, we 7 |
