# Effect of Gas Velocity Distribution on Heat Recovery Process in Packed Bed of Plate-Shaped Slag

^{*}

## Abstract

**:**

## 1. Introduction

_{2}sources among all Japanese industries, further energy savings is needed in order to reduce CO

_{2}emissions from steel works. The major Japanese steel companies have participated in the COURSE50 National Project since FY2008 under a commitment of New Energy and Industrial Technology Development Organization (NEDO) to achieve a 30% reduction in CO

_{2}from steel works [1,2,3,4]. Steelmaking slag, which is produced as a by-product of the steel refining process, possesses a great amount of heat in the molten state and is considered to be a promising heat resource for future utilization. As a part of the COURSE50 project, the authors developed a new process for heat recovery from steelmaking slag in order to utilize this huge amount of thermal energy [5]. Figure 1 shows the process drawing of the COURSE50 slag heat recovery system, including a CO

_{2}separation plant as a target process for heat utilization. In this process, molten slag, which has a temperature of above 1673 K, is solidified continuously on the surface of water-cooled rolls to produce plate-shaped slag of approximately 1373 K. These slag plates are transferred directly to the slag chamber in a high-temperature state for heat recovery, which is another feature of this process. The temperature drop during the slag transportation from the end of the apron conveyer to the slag chamber is negligible owing to its short transportation time within 25 s. In the future plan, the heat recovered from this slag will be utilized for regeneration of the CO

_{2}absorbent in the CO

_{2}separation plant, which requires a huge amount of thermal energy.

## 2. Gas Velocity Distribution in Laboratory-Scale Packed Bed of Plate-Shaped Samples

#### 2.1. Laboratory-Scale Gas Velocity Measurements

_{s}is calculated by Equation (1). The equivalent particle diameter d

_{p}(also called the Sauter mean diameter) in Equation (2) means the sphere size that has the same volume/surface area ratio as a particle of interest. When considering the effect of the surface heat transfer phenomena of irregularly-shaped particles, d

_{p}is sometimes used preferably in the modeling. Sphericity is defined by the following Equation (3), and means the irregularity of the particle shape. These values are also listed in Table 1.

#### 2.2. Laboratory-Scale Gas Velocity Measurements—Results and Discussion

#### 2.3. Laboratory-Scale CFD Simulation

_{w}and “central region” having porosity of ε

_{c}in the porous medium was adopted to simplify the model [25]. The thickness of the near-wall region (X in Figure 6) can be estimated by the following porosity function shown in Equation (6), which is defined within the distance from the column wall [26,27,28]. The parameter A decides the porosity increment in the vicinity of the wall, which is usually decided empirically.

_{w}as the region within the radial distance of 0.5d from the inner wall.

_{s}so as not to underestimate the wall effect, especially in case the sphericity is much lower than one. Accordingly, the thickness of the near-wall region x was set to be 0.5L in the following simulation. In our experimental setup, the plate-shaped samples have a relatively smaller long side length L against the plate thickness compared to that of the actual plate-shaped slag in Figure 2, which results in the small difference between L and d

_{s}in Table 1. Therefore, the model itself does not change significantly if L was used instead of d

_{s}in the laboratory-scale study. The porosity of the near-wall region ε

_{w}, which is related to the A value in Equation (6), was assumed to be 1.4 times larger than that of the central-region ε

_{c}with reference to the measured radial porosity profile in a packed bed of plate-shaped samples obtained by Montillet et al. [21]. This is equivalent to the A value of 0.4 in Figure 7. The value of the porosity of the central-region ε

_{c}in Table 2 was obtained by the bulk average porosity measured previously from the sample packing weight, packing height, and sample density.

#### 2.4. Laboratory-Scale CFD Simulation—Results and Discussion

## 3. Gas Velocity Distribution and Heat Recovery Efficiency in Pilot-Scale Slag Packed Bed

#### 3.1. Pilot-Scale Slag Heat Recovery Tests

#### 3.2. Pilot-Scale CFD Simulation

_{ht}, was solved along with the Equations (4) and (5). The Q

_{ht}was calculated by the following heat transfer equation, Equation (8), in which the heat transfer coefficient h was defined as a user-defined function. To simulate the heat recovery behavior in the packed bed of plate-shaped slag, it is important to define the proper heat transfer coefficient h in the porous medium model, which is equivalent to the actual gas-to-plate heat transfer phenomenon. In general, the local Nusselt number Nu

_{x}for heat transfer on an infinite flat plate can be estimated by Johnson-Rubesin’s equation, which is shown here as Equation (9) [29].

_{m}in Equation (10), which was obtained by integration of Equation (9) in the range from x = 0 to L. The average heat transfer coefficient h

_{m}was calculated by Equation (11), in which the average Nusselt number Nu

_{m}was multiplied by a correction factor β. In this pilot-scale model, the value of β was assumed to be 0.42, which was deduced empirically in our previous work [7].

#### 3.3. Pilot-Scale CFD Simulation—Results and Discussion

#### 3.4. Comparison with Results of Pilot-Scale Test

## 4. Conclusions

## Nomenclature

d_{s} | Equivalent spherical volume diameter |

d_{p} | Equivalent particle diameter |

ρ | Density |

m | Mass |

S | Surface area |

V | Volume |

φ | Sphericity |

p | Pressure |

t | Time |

v | Gas velocity |

τ | Shear stress |

ε | Local porosity |

ε_{0} | Bulk porosity |

d | Particle size |

R_{0} | Radius of the bed |

r | Radial position |

A | Constant |

Nu | Nusselt number |

Pr | Prandtl number |

Re | Reynolds number |

λ | Thermal conductivity of the fluid |

α | Heat transfer coefficient on the surface of the particle |

h | Heat transfer coefficient in the bed |

β | Correction factor |

L | Long side length of a slag particle |

Δp | Pressure drop in the bed |

μ | Dynamic viscosity of the fluid |

## Subscripts

a | Apparent |

f | Fluid |

p | Particle |

x | Local value at x |

m | Mean |

L | Integrated within the range from x = 0 to x = L |

s | Superficial |

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**Experimental apparatus for measurement of gas velocity distribution above packed bed of plate-shaped samples: (

**a**) schematic drawings of experimental setup; (

**b**) photo of experimental apparatus and (

**c**) top view of packed samples.

**Figure 4.**Circumferential gas velocity distribution measured by experimental apparatus: (

**a**) r = 30 mm, 50 mm; (

**b**) r = 70 mm, 100 mm and (

**c**) r = 120 mm, 140 mm.

**Figure 6.**Laboratory-scale CFD simulation model to calculate gas velocity distribution inside and outside chamber: (

**a**) schematic image of packing condition around inner wall of chamber; and (

**b**) schematic drawing of modeled region.

**Figure 8.**Results of laboratory-scale CFD simulation: (

**a**) color contours of gas velocity distribution; and (

**b**) radial gas velocity distribution obtained by experimental measurements and CFD simulation.

**Figure 12.**Result of Case 1 simulation: (

**a**) gas temperature; (

**b**) slag temperature and (

**c**) gas velocity.

**Figure 13.**Result of Case 2 simulation: (

**a**) gas temperature; (

**b**) slag temperature and (

**c**) gas velocity.

**Figure 14.**Calculated gas velocity distribution at top of slag packed bed: (a) Case 1, (b) Case 2, ◊: Average value at 5 min, ♦: Average value at 45 min.

**Figure 15.**Gas velocity measurement in pilot-scale slag heat recovery chamber (

**left**) and photo of discharged slag after heat recovery (

**right**).

Chamber | Chamber inner diameter (mm) | 300 |

Packed bed | Sample temperature (K) | 298 |

Sample packing height (mm) | 250 | |

Total weight of the sample (kg) | 25 | |

Sample | Dimensions T × W × L (mm) | 8 × 22.5 × 22.5 |

Equivalent spherical volume diameter d_{s} [mm] | 19.8 | |

Equivalent particle diameter dp (mm) | 14.0 | |

Sphericity d_{p}/d_{s} (mm) | 0.71 | |

Sample density (t/m^{3}) | 2.0 | |

Gas | Gas inlet temperature (K) | 298 |

Gas flow rate (L/min) | 200 | |

Anemometer | Radical position of the probe r (mm) | 30, 50, 70, 100, 120, 140 |

Rotation speed of the probe (rpm) | 1.71 |

Chamber | Chamber inner diameter (mm) | 300 |

Packed bed | Sample temperature (K) | 298 |

Sample packing height (mm) | 250 | |

Total weight of the sample (kg) | 25 | |

Sample bed porosity | Central ε_{c} = 0.40 | |

Near-wall ε_{w} = 0.56 | ||

Specific surface area (m^{2}/m^{3}) | Central 164.6 | |

Near-wall 86.1 | ||

Sample | Dimensions T × W × L (mm) | 8 × 22.5 × 22.5 |

Equivalent spherical volume diameter d_{s} (mm) | 19.8 | |

Equivalent particle diameter d_{p} (mm) | 14.0 | |

Sphericity d_{p}/d_{s} (mm) | 0.71 | |

Sample density (t/m^{3}) | 2.0 | |

Gas | Inlet temperature (K) | 298 |

Volumetric flow rate (L/min) | 200 | |

Mass flow rate (kg/s) | 0.00408 | |

Outlet gauge pressure (Pa) | 0 |

Equipment | Specifications | ||
---|---|---|---|

Twin-roll plant | Cooling roll | Dimensions | Φ1.6 m × W1.5 m |

Number of rolls | 2 | ||

Material | Cu | ||

Rotation speed | Max.20 rpm | ||

Cooling water flow rate | 125–130 m^{3}/h/roll | ||

Ladle tilting machine | Tilting speed | Max.6.5 °/min | |

Load | Max.140 t | ||

Conveyer | Dimensions | W1.3 m × L14.5 m | |

Lifting height | 5.5 m | ||

Speed | 25 m/min | ||

Material | SUS304 | ||

Slag heat recovery plant | Crusher | Capacity | 1.0 t/min |

Bucket elevator | Transport capacity | 1.0 t/min | |

Heat recovery chamber | Chamber size | L1.5 m × W2.0 m × H2.5 m | |

Capacity | Max.6 t | ||

Blower | Gas flow rate | Max.12000 Nm^{3}/h | |

Motor | 150 kW | ||

Cyclone | Size | Φ2.2 m × H7.5 m |

Twin-roll plant | Ladle tilting speed (mm/s) | 1.0 |

Rotation speed of the cooling rolls (rpm) | 10 | |

Cooling water flow rate (t/h/roll) | 125 | |

Conveyer speed (m/min) | 25 | |

Slag heat recovery plant | Amount of slag charged (t) | 4.8 |

Height of the slag packed bed (m) | 1.83 | |

Gas flow rate (Nm^{3}/h) | 7200 |

Chamber | Chamber cross section (m^{2}) | 2.82 |

Wall thickness (mm) | Steel inner wall 5 | |

Heat insulator 100 | ||

Steel outer wall 12 | ||

Heat transfer coefficient on walls (W/m^{2}K) | 20 | |

Wall initial temperature (K) | 298 | |

Ambient temperature (K) | 298 | |

Packed bed | Slag bed porosity | Central ε_{c} = 0.55 |

Near-wall ε_{w} = 0.77 | ||

Specific surface area (m^{2}/m^{3}) | Central 164.6 | |

Near-wall 86.1 | ||

Slag packing height (m) | (Case1) 1.83 (Case2) 3.50 | |

Slag | Dimensions of the slag T × W × L (mm) | 7 × 50 × 50 |

Equivalent spherical volume diameter d_{s} (mm) | 32.2 | |

Equivalent particle diameter d_{p} (mm) | 16.4 | |

Sphericity d_{p}/d_{s} (mm) | 0.51 | |

Initial temperature (K) | Precharged slag 298 | |

Slag for heat recovery 1373 | ||

Gas | Inlet temperature (K) | 298 |

Volumetric flow rate (Nm^{3}/h) | (Case1) 7200 (Case2) 10900 | |

Mass flow rate (kg/s) | (Case1) 2.368 (Case2) 3.592 | |

Outlet gauge pressure (Pa) | 0 |

Item | Density (g/m^{3}) | Specific Heat (J/kgK) | Thermal Conductivity (W/Mk) |
---|---|---|---|

Slag | 2200 | 1010 | λs |

Heat insulator | 100 | 1256 | 0.2 |

Steel | 8030 | 502 | 40 |

Temp (K) | 373 | 473 | 573 | 673 | 773 | 873 | 973 | 1073 | 1173 | 1273 |

λs | 0.22 | 0.45 | 0.74 | 1.13 | 1.66 | 2.37 | 3.28 | 4.40 | 5.76 | 7.35 |

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**MDPI and ACS Style**

Shigaki, N.; Ozawa, S.; Sumi, I.
Effect of Gas Velocity Distribution on Heat Recovery Process in Packed Bed of Plate-Shaped Slag. *Energies* **2017**, *10*, 755.
https://doi.org/10.3390/en10060755

**AMA Style**

Shigaki N, Ozawa S, Sumi I.
Effect of Gas Velocity Distribution on Heat Recovery Process in Packed Bed of Plate-Shaped Slag. *Energies*. 2017; 10(6):755.
https://doi.org/10.3390/en10060755

**Chicago/Turabian Style**

Shigaki, Nobuyuki, Sumito Ozawa, and Ikuhiro Sumi.
2017. "Effect of Gas Velocity Distribution on Heat Recovery Process in Packed Bed of Plate-Shaped Slag" *Energies* 10, no. 6: 755.
https://doi.org/10.3390/en10060755