| OCR Text |
Show duced at different locations in the fluid jet experience different local fluid velocities and drag and, therefore, follow different paths. As the path of an individual particle depends on its size and input location, the reaction history depends on the path through the imposed temperature and oxygen concentration fields. The rate of volatile release at each position of the path depends on the particle temperature, which is determined by a local energy balance. When 99 percent of the volatile matter is released, char reaction begins. The rate of reaction depends on the local temperature and oxygen concentration at each position of the path. Isotherms for the imposed temperature field are shown in Fig. 7. The temperature at the furnace entrance is 300 K and rises along the axis to a peak temperature of 1800 K at a distance 2x/d = 2.0 from the entrance. The imposed oxygen field has a maximum value of 21 percent at the furnace entrance and declines along the axis. The present fluid flow calculations use a constant density approximation, which uncouples the flow from the flame. This approximation does impose a limitation on the analysis. A local correction for density can be used but is not applied in this development. Also in this model, the effect of radiative heat transfer is taken into account by the imposed temperature field. The flow is axisymmetric and two dimensional, and at the present time, we do not account for the effects of the particle momentum on the flow field. Even with these simplifications, several new and important phenomena are explained from this analysis. 2.1 The gaseous phase The fluid flow in the combustion chamber is represented mathematically by the time-dependent Navier-Stokes equations for an incompressible fluid expressed as a transport equation for the vorticity vector wand the stream function 'f/;. The vorticity transport equation is -OmW + (V· V)w = (w· V)V - -R1(e V x V x w) (1) 4 |
