*2.2. The DRI-Flap Distributor*

The pathway of DRI particles in the DRI-flap distributor is shown in Figure 4. The mass of the particle is *m*. At the bottom of the vertical pipe, the particle attains the velocity of *V*<sup>1</sup> (*m*/*s*) normal to the inclined pipe and it attains the velocity of *V*<sup>2</sup> (*m*/*s*) at the end of the inclined pipe, then the particle collides with DRI-flap and attains the bouncing velocity of *V*<sup>3</sup> (*m*/*s*). The friction coefficient between particle and inclined-pipe is μ, and the length of inclined pipe is *l*1. The angle between the inclined pipe and the horizontal direction is α1, and that between *V*<sup>3</sup> and the vertical direction is α2.

**Figure 4.** Pathway of direct reduction iron (DRI) in DRI-flap distributor.

DRI particles stored in the upper hopper fall onto the bottom of vertical pipe. This motion is simplified by assuming the flow of a bulk stream similar to that of an individual particle, which is stationary when leaving the upper hopper and gains an exit velocity *V*<sup>1</sup> along the direction normal to the inclined pipe.

$$V\_1 = k\_{\rm 1,DRI} \cos \alpha\_1 \sqrt{2g(H\_1 + h\_1)} \tag{1}$$

where a correction coefficient, *k*1,DRI, is introduced to take into account the imperfect elastic collision of the falling particles.

Since the moving direction of DRI particles from the vertical pipe is normal to the inclined pipe, the initial particle velocity along the inclined pipe is zero. Therefore, the velocity at the end of the inclined pipe is obtained as

$$V\_2 = \sqrt{2g(\cos \alpha\_1 - \mu \sin \alpha\_1)l\_1} \tag{2}$$

The velocity *V*<sup>3</sup> after colliding with the flap is

$$V\_3 = k\_{2, \text{DRI}} V\_2 \tag{3}$$

where a correction coefficient, *k*2,DRI, is introduced to take into account the imperfect elastic collision between the particles and flap.

Upon leaving the flap, the velocity of the bulk stream is decomposed into two components in the vertical direction (*V*<sup>3</sup> sinα2) and the horizontal direction (*V*<sup>3</sup> cosα2). After this, the bulk stream will form a parabolic motion similar to the free falling of a particle from a chute tip.
