Author Contributions
L.M.: Investigation, Software, Writing—original draft. K.A.B.: Supervision, Writing—review & editing. J.A.M.K.: Conceptualization, Supervision, Writing—review & editing. N.G.D.: Conceptualization, Methodology, Supervision, Writing—review & editing. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Dimensionless axial particle and gas temperature profiles without heat production.
Figure 1.
Dimensionless axial particle and gas temperature profiles without heat production.
Figure 2.
Dimensionless axial particle and gas temperature profiles without heat production.
Figure 2.
Dimensionless axial particle and gas temperature profiles without heat production.
Figure 3.
Schematic overview of the pseudo-2D fluidized bed.
Figure 3.
Schematic overview of the pseudo-2D fluidized bed.
Figure 4.
Snapshots of instantaneous voidage patterns for varying aspect ratios: (a) H0/W = 0.5, (b) H0/W = 1, (c) H0/W = 2, and different superficial gas velocities: 0.4, 0.5 and 0.6 m/s (from left to right).
Figure 4.
Snapshots of instantaneous voidage patterns for varying aspect ratios: (a) H0/W = 0.5, (b) H0/W = 1, (c) H0/W = 2, and different superficial gas velocities: 0.4, 0.5 and 0.6 m/s (from left to right).
Figure 5.
Temporally and spatially averaged bed voidage as a function of superficial velocity and aspect ratio.
Figure 5.
Temporally and spatially averaged bed voidage as a function of superficial velocity and aspect ratio.
Figure 6.
Profiles at different heights of time-averaged vertical particle velocity for varying aspect ratios: (a) H0/W = 0.5, (b) H0/W = 1, (c) H0/W = 2. Note that all profiles are shown at z = H0.
Figure 6.
Profiles at different heights of time-averaged vertical particle velocity for varying aspect ratios: (a) H0/W = 0.5, (b) H0/W = 1, (c) H0/W = 2. Note that all profiles are shown at z = H0.
Figure 7.
Snapshots of particle temperature as a function of aspect ratio: (a) H0/W = 0.5, (b) H0/W = 1, (c) H0/W = 2, and different superficial gas velocities: 0.4, 0.5 and 0.6 m/s (from left to right).
Figure 7.
Snapshots of particle temperature as a function of aspect ratio: (a) H0/W = 0.5, (b) H0/W = 1, (c) H0/W = 2, and different superficial gas velocities: 0.4, 0.5 and 0.6 m/s (from left to right).
Figure 8.
Particle temperature standard deviation as a function of ug,0 and H0/W.
Figure 8.
Particle temperature standard deviation as a function of ug,0 and H0/W.
Figure 9.
Dimensionless particle temperature probability density function (PDF) for varying aspect ratios: 0.5, 1 and 2 (top to bottom) and different gas superficial velocities.
Figure 9.
Dimensionless particle temperature probability density function (PDF) for varying aspect ratios: 0.5, 1 and 2 (top to bottom) and different gas superficial velocities.
Figure 10.
Snapshots of gas temperature as a function of aspect ratio: (a) H0/W = 0.5, (b) H0/W = 1, (c) H0/W = 2, and different superficial gas velocities: 0.4, 0.5 and 0.6 m/s (from left to right).
Figure 10.
Snapshots of gas temperature as a function of aspect ratio: (a) H0/W = 0.5, (b) H0/W = 1, (c) H0/W = 2, and different superficial gas velocities: 0.4, 0.5 and 0.6 m/s (from left to right).
Figure 11.
Snapshots of the temperature of two types of particles as a function of aspect ratio: (a) H0/W = 0.5, (b) H0/W = 1, (c) H0/W = 2, and different superficial gas velocities: 0.4, 0.5 and 0.6 m/s (from left to right).
Figure 11.
Snapshots of the temperature of two types of particles as a function of aspect ratio: (a) H0/W = 0.5, (b) H0/W = 1, (c) H0/W = 2, and different superficial gas velocities: 0.4, 0.5 and 0.6 m/s (from left to right).
Figure 12.
Dimensionless temperature PDF of all particles, inactive particles and active particles for different gas superficial velocities and varying aspect ratios: 0.5, 1 and 2.
Figure 12.
Dimensionless temperature PDF of all particles, inactive particles and active particles for different gas superficial velocities and varying aspect ratios: 0.5, 1 and 2.
Table 1.
Particle and gas phase properties in the fixed bed verification.
Table 1.
Particle and gas phase properties in the fixed bed verification.
Property (Unit), Symbol | Value |
---|
Gas density (kg/m3), ρg | 1000 |
Inlet gas temperature (K), Tg,0 | 373 |
Gas viscosity (Pa s), µg | 1.0 × 10−3 |
Gas heat capacity (J/kg/K), Cpg | 4187 |
Gas thermal conductivity (W/m/K), kg | 0.5 |
Particle diameter (m), dp | 3.95 × 10−3 |
Particle density (kg/m3), ρp | 8400 |
Initial temperature of gas and particles (K) | 273 |
Particle heat capacity (J/kg/K), Cpp | 385 |
Table 2.
Settings for discrete element method (DEM) simulations of the fixed bed.
Table 2.
Settings for discrete element method (DEM) simulations of the fixed bed.
Setting | Value |
---|
Width of the bed (m) | 0.1 |
Depth of the bed (m) | 0.1 |
Initial particle bed height (m) | 0.5 |
Particle number | 78,125 (25 × 25 × 125) |
Δx = Δy = Δz (m) | 0.004 |
Time step of particle phase (s) | 0.0001 |
Time step of gas phase (s) | 0.002 |
Table 3.
Settings for DEM simulations of the pseudo-2D fluidized bed.
Table 3.
Settings for DEM simulations of the pseudo-2D fluidized bed.
Setting | Value |
---|
Width of the bed (m) | 0.08 |
Depth of the bed (m) | 0.01 |
Initial particle bed height (m) | 0.04/0.08/0.16 |
Particle number | 37,225/74,450/148,900 |
Δx = Δy = Δz (m) | 0.0025 |
Time step of particle phase (s) | 1.0 × 10−5 |
Time step of gas phase (s) | 2.0 × 10−4 |
Table 4.
Particle and gas phase properties in the fluidization simulations.
Table 4.
Particle and gas phase properties in the fluidization simulations.
Property (Unit), Value | Value |
---|
Gas density (kg/m3), ρg | 1.49 |
Inlet gas temperature (K), Tg,0 | 330 |
Gas viscosity (Pa s), µg | 1.0 × 10−5 |
Gas heat capacity (J/kg/K), Cpg | 1670 |
Gas thermal conductivity (W/m/K), kg | 2.09 × 10−2 |
Particle diameter (m), dp | 9.95 × 10−4 |
Particle density (kg/m3), ρp | 667 |
Particle heat capacity (J/kg/K), Cpp | 1670 |
Normal coefficient of restitution (particle–particle), e | 0.6 |
Youngs Modulus | 5.0 × 105 |
Poisson ratio | 0.45 |
Table 5.
Equilibrium temperature of the gas phase (Tg) and the active/inactive particles (Tp1/Tp2).
Table 5.
Equilibrium temperature of the gas phase (Tg) and the active/inactive particles (Tp1/Tp2).
| Non-Uniform Cases | Uniform Cases |
---|
| Tg | Tp1 | Tp2 | (Tp1-Tp2)/(Tp1-Tg,in) | Tg | Tp |
---|
0.5/0.4 | 346 | 346 | 367 | −1.28 | 346 | 346 |
0.5/0.5 | 343 | 343 | 362 | −1.5 | 343 | 343 |
0.5/0.6 | 341 | 341 | 359 | −1.7 | 341 | 341 |
1.0/0.4 | 362 | 362 | 383 | −0.64 | 362 | 363 |
1.0/0.5 | 356 | 356 | 375 | −0.75 | 356 | 356 |
1.0/0.6 | 351 | 351 | 370 | −0.85 | 351 | 352 |
2.0/0.4 | 394 | 394 | 415 | −0.32 | 394 | 395 |
2.0/0.5 | 381 | 381 | 401 | −0.37 | 381 | 382 |
2.0/0.6 | 373 | 373 | 391 | −0.42 | 373 | 373 |