3. Results and discussion

3.1. LDPE Sphere fluidization

As a benchmark, case 1 of the study investigates the fluidization behavior of LDPE particles with superficial gas velocity from 1.4U mf to 3.4U mf. Figure 5 compares the fluidization behavior of LDPE spherical particles with varying superficial gas velocity. The image frame with the maximum expanded bed height has been chosen for each superficial gas velocity for demonstration purposes (Figure 5a-d). At the lower superficial gas velocity (1.4 U mf and 2.0U mf ), slug flows are formed due to the relatively narrow bed configuration, with the maximum expanded bed height increases significantly due to the increase of superficial gas velocity from 1.4 U mf and 2.0U mf. Markedly, such a trend ceases with the further increase of superficial gas velocity. At 3.0 U mf and 3.4U mf, the maximum expanded bed height drops significantly compared to 2.0 U mf case, and two regions with visually different particle void fraction are formed. Generally similar to a spouted bed, the loosely packed fountain region is at the top of the bed while a densely packed region forms at the bottom. To quantify the overall fountain region length, the 500 frames are overlaid to generate the time-averaged bed images at these fluidization velocities. The two regions are distinct due to the grayscale value and the fountain height is measured to be 3.36 cm and 5.02 cm at a superficial gas velocity of 3.0 U mfand 3.4 U mf, respectively. The current transition from slugging to spouting is similar to the behavior observed in some of the so-called spout-fluid beds using a central jet together with an auxiliary flow through a porous or perforated distributor plate at certain flow conditions33,34.
The velocity field for 2Umf case is shown in Figure 6. The color encodes the velocity magnitude, Vmag of the particles. Due to the narrow bed of solids, at t=0s, the bubbles formed at the distributor plate grow into a flat slug which is clearly identified by the almost uniform upward velocity region of around 20 cm/s with a size of around 5 cm in length. Above the slugs, the particles from previously disintegrated slugs fall onto the slug and have a velocity close to zero. Below the slug, the particles have relatively low velocities and separate from the slug. At t=0.125s, the slug continues to move upwards, and in the meanwhile accelerate particles from previous slugs. At the bottom of the slug, the particles that cannot stick to the slug start to replenish by raining solids. The size of the slug remains almost unchanged. At t=0.313s, a large portion of the slug’s particles starts to fall which spans a length of around 10 cm, whereas the rest of the particles continue to rise and decelerate as shown in the velocity map. At t=0.556s, all the particles in the slug start to fall and reach as high as 56 cm/s. The particles at bottom of the bed start to form another slug with a small upward velocity. At t=0.763s, the particles continue to fall while another slug continues to form. In general, the dynamics of the LDPE particles at 2 Umf resembles the typical Geldart type D particles behavior, even though no complete void space or multiple slugs is formed presumably due to the relative shallow bed configuration. The rising rate of the bubble or the slug can be estimated to be around 35 cm/s by tracking the almost zero velocity band below the slug. This result is in good agreement with the correlation results proposed by Stewart and Davidson35,
U b= 0.35(gD t)0.5
where D t is the diameter of the bed, and gis the gravitational constant, which results in a value of 28 cm/s.