Particulate Flow in a Bend

When a dilute gas-solid suspension flow passes through a curved pipe, the particle velocity is lowered by the wall friction, the effects of gravitation, and collision with the wall. The analysis of flows in pipe bends may be represented by three typical arrangements of bends  

Without losing generality, in this section we only consider case (3), where the pipe bend is located in the vertical plane with a vertical gas-solid suspension flow at the inlet, as shown in Fig. 11.10. It is assumed that the carried mass and the Basset force are neglected. In addition, the particles slide along the outer surface of the bend by centrifugal force and by the inertia effect of particles. The rebounding effect due to particle collisions with the wall is neglected. 

The equation of motion of a single particle in the direction of the pipe axis is expressed by 

once the local gas velocity and drag coefficient are given, the variation of the particle velocity along the bend can be obtained by numerical integration of Eq. (11.51). 

In order to estimate the extent of decrease in the particle velocity due to the pipe curvature, it is assumed that the drag force is negligible in comparison with the sliding force of the particle on the bend surface. With this consideration, Eq. (11.51) is reduced to 

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