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Show Substituting Eq. (9) in Eq. (7) the governing equation for the radial motion of the particle with burning is given as d2R 2 TdR w +1 2-m M Q.-(l+m)/2 nn T T = Q(2i + 1) ' BoLdT- vr J (1 " S) (11) dx R Solution of Eqs. (7) and (11) can be numerically obtained. It will be seen later that the solution of Eq. (11) with burning does not yield significantly different results from the solution of Eq. (7) as far as slag rejection is concerned. This result does implicitly assume that mineral vaporization is not significant during particle burning. 4.0 RESULTS AND DISCUSSION Slag rejection is interpreted in terms of relative phenomenological time scales. To achieve wall impact of a specific initial particle size, it is required that the time from injection to impact is less than (i) particle burnup time, and (ii) combustor residence time. Equations (3) and (4) can be solved numerically to obtain the results for time to reach wall for given geometry and operating conditions of cyclone burner. A few simple explicit results for T are given in Appendix A for the cases of (i) forced vortex flow ( i= -1 in Eq. (1)) and Stoke's drag, (m = 1 in Eq. (2)) and (ii) forced vortex flow and constant friction coefficient. Further, explicit results for the radial velocity of particles are also shown in the Appendix for both the previous cases and in addition for the case of free vortex flow (? = 1 in Eq. (1)) and flow with v1 - 1/2 which approximately accounts for the viscous effects of the flow. From the results for radial velocity of the particle, one can also obtain the velocity with which the particles impinge on the slag layer of the wall. Numerical results for impact time to reach the wall and its relevance to slag rejection will be discussed in detail. The numerical results will be discussed for 1) vp = 0 and 2) vr 4 0. -15- AVCO EVERETT |