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Show These results are based on the assumption that anyular momentum of gas is conserved. However, the gas supplies rotational momentum to the particles and some momentum is lost because of wall friction. Also, gas turbulent exchange is typically significant. Hence, a free vortex flow law is not followed. Thus, with viscous effects, l ~ 0.5 (cf. Eq. (1)) and curve CnD, in Figure 5 corresponds to this case. The shift in the intersection point of the initial separation and burning time curves (from P to Pj) is not significant. 4.2 CONSTANT GAS RADIAL VELOCITY AND NEGLIGIBLE BURNING The gas injected at the wall has to escape through the re-entrant throat. Moreover, the gas itself is given an inward radial motion at the entry. Consistent with assumption (v), we will assume a constant radial velocity. If it is idealized that the gas has to travel from tne wall to the center of cyclone within the available residence time (~ 40 ms) then a limiting estimation can be made for the radial velocity. Such an estimate yields v = 5 m/s while tangential velocity Vt = 100 m/s. In Figure 5, curve C?P?D? shows the effect of gas radial velocity. The inward radial velocity of gas gives a higher travel time scale (line C^D^). Such a curve intersects the burn time line at P„ giving a particle size limit of about 26 ym for wall capture. The effect on particle travel time scale is significant. The particles accelerate to a high radial velocity due to centrifugal force. Since vp - 5 m/s while initial vf - 100 m/s, the drag force is mostly due to particle velocity. As the particles approach the wall, the centrifugal force drops down due to decreasing tangential velocity of gas. Further, the particle radial velocity is slowed down due to the drag force. A point is reached at which centrifugal force is equal to the drag force at which the particle velocity is maximum. Further approach to the wall results in less centrifugal force and dominant drag force both due to inward flowing gases and particle velocity. The resulting lower radial velocity of the particle increases the time scale to reach the wall. For certain particle <;i?ps d < d V = 0 at r = r .. < r and these particles resizes ap < u p > c n t ) v r crit w volve around at a fixed orbit never reaching the wall. Such a size is given by letting d2R/dt2 = 0 and dR/dt = 0 in Eq. (7). -21- ^7AVCO EVERETT |