**3. Experimental Design**

The buried tube granular bed heat transfer experimental equipment included a cooling water pipeline system, a buried tube granular bed heat exchanger, a secondary heat exchanger, a granular bed system, and a programmable logic controller (PLC) control panel system. The equipment is illustrated in Figure 1. The combustion air and the gas in the combustion chamber were ignited by an electronic igniter to reach the experimental temperature. The high-temperature gas flowed through the buried tube granular bed and secondary heat exchangers, exchanged heat with the buried tube in the heat exchanger, and then discharged. Armored thermocouples and sensors were set between the cooling water inlet and outlet, the flue gas inlet and outlet, and the granular bed and secondary heat exchangers. The real-time cooling water flow rate, bed pressure drop, and temperatures of flue gas and cooling water were measured by the PLC control panel system.

The buried tube granular bed and secondary heat exchangers had a square structure, with section sizes of 1120 × 1000 and 1200 × 450 mm, respectively. The diameter of the heat exchange tube was 32 mm, and the thickness of the tube wall was 3 mm. To improve the heat transfer process in the buried tube granular bed heat exchanger, 60 tubes were arranged in a staggered way, for a total of 8 rows, as depicted in Figure 2.

**Figure 1.** Schematic of the experimental flow and location of measuring points.

**Figure 2.** Schematic of the arrangemen<sup>t</sup> of heat exchange tubes.

#### **4. Experiment and Result Analysis**

Filled particles were added to the designed thickness, and an experiment was performed to study the heat transfer process. Moreover, the influences of gas temperature and cooling water flow rate on heat transfer were studied.

#### *4.1. Analysis of Heat Transfer Experimental Results*

The experiment was conducted at 1073.15 K. The environmental air temperature was 318.15 K, and the cooling water flow rate was 4.5 m<sup>3</sup>/h. The flue gas temperature, cooling water temperature, bed pressure drop, and waste heat recovery rate are demonstrated in Figure 3. The temperatures of flue gas and cooling water remained stable, thereby indicating that the equipment operated stably. At the initial stage of the experiment, the heat storage of the corundum particles was incomplete, and the waste heat recovery rate of the equipment increased gradually. After 100 min, the heat storage of the particles was completed, and the recovery of waste heat stabilized gradually, at more than 72%. The bed pressure drop initially rose slowly and remained stable. At 520–550 min, 35 kg of particles were slowly and uniformly discharged, while the bed pressure drop decreased from 2000 Pa to 700 Pa.

#### *4.2. Influence of Inlet Flue Gas Temperature on Waste Heat Recovery*

After the stable operation of the equipment, the combustion air and gas flow were adjusted to change the inlet gas temperature. The cooling water flow rate was 4.5 m<sup>3</sup>/h. The waste heat recovery rate of the equipment and the heat transfer coefficient of the granular bed are plotted in Figure 4.

The results show that the inlet flue gas temperature increased from 1096.65 to 1286.45 K, and the waste heat recovery rate of the equipment increased by 1.7% with the increase in the heat transfer coefficient of the granular bed by 26.6%. The heat of the gas brought into the equipment increased with the inlet gas temperature. The waste heat recovery rate of the equipment and the heat transfer coefficient of the granular bed also increased gradually and remained stable after the inlet gas temperature reached a critical value.

In Figure 4b, the variation curve of the heat transfer coefficient of the granular bed was fitted, and the experimental correlation formula was proposed as follows:

$$k\_{ht} = \frac{755.22}{4.19e^{-0.01t} + 0.22} - 3363.45\tag{7}$$

**Figure 3.** Variation curves of heat exchange in the buried tube granular bed. (**a**) Variation curve of flue gas temperature. (**b**) Variation curve of cooling water temperature. (**c**) Variation curve of waste heat recovery rate. (**d**) Variation curve of bed pressure drop.

**Figure 4.** Influence curves of flue gas temperature on heat transfer. (**a**) Influence on waste heat recovery. (**b**) Influence on the heat transfer coefficient.

#### *4.3. Influence of Cooling Water Flow on Waste Heat Recovery*

After the stable operation of the experimental equipment, the cooling water pipeline valve was manually adjusted to change the cooling water flow rate. The flue gas inlet temperature was 1093.15 K and the flue gas flow was 350 Nm<sup>3</sup>/h. The initial cooling water flow rate was 2.6 m<sup>3</sup>/h. The influence curve of the waste heat recovery rate is exhibited in Figure 5.

**Figure 5.** Influence curves of cooling water flow on waste heat recovery. (**a**) Influence on the recovery rate of waste heat. (**b**) Influence on the heat transfer coefficient.

The experimental results showed that the recovery of waste heat and the heat transfer coefficient of the granular bed increased with the cooling water flow rate. The cooling water flow increased from 2.6 m<sup>3</sup>/<sup>h</sup> to 5.1 m<sup>3</sup>/h, and the waste heat recovery rate of the equipment increased by 1.9% with the increase in the heat transfer coefficient of the granular bed by 4.4%. The increase in the cooling water flow rate promoted the convection between the cooling water inside the heat exchange tube and the tube wall. Thus, the total heat transfer coefficient of the granular bed and heat transfer process was promoted. In accordance with the experimental data displayed in Figure 5b, the changing curve of the heat transfer coefficient of the granular bed was fitted, and the experimental correlation formula was obtained as follows:

$$k\_{ht} = \frac{36.69}{7974.34e^{-2q} + 10.78} + 60.92. \tag{8}$$

#### **5. Numerical Simulation and Analysis**

The CFD method was adopted to build a grid model using the Integrated Computer Engineering and Manufacturing (ICEM), and the grid was imported into Fluent for related settings. The granular layer was handled as a porous medium. At present, the equivalent heat transfer coefficient of porous media is generally calculated by the macroscopic induction method to study the heat transfer process of porous media. The Nikitin equation considering the influence of solid particle contact thermal resistance, gas thermal conductivity, and radiation heat transfer was used in this paper. The Nikitin equation is expressed as follows:

$$k\_{\varepsilon} = k\_{\mathcal{S}} \Big[ 1 + 3.91(1 - \varphi)k\_{\mathcal{S}}^{0.1} \ln \frac{k\_{\varepsilon}}{k\_{\mathcal{S}}} \Big] \Big[ 1 + \frac{7\rho\_{\mathcal{S}}}{\rho\_{\varepsilon} + \rho\_{\mathcal{S}}} \left( \frac{L}{d} \right)^{0.55} \Big]^{-1} + \frac{3.46\sigma T^3 \left[ 3\rho \underline{\epsilon}\_{\mathcal{S}} + (1 - \rho)\underline{\epsilon}\_{\mathcal{S}} \right]}{1 + (1 - \varphi)(1 - \underline{\xi}\_{\mathcal{S}})} + k\_{\mathcal{S}} \tag{9}$$

The fluent porous medium model was used to conduct the simulation, with the relevant parameters listed in Table 1. The hydraulic diameter and turbulence intensity were determined by the size of tubes in the bed. The viscous resistance coefficient and the inertial resistance coefficient of porous media were determined by Ergun equation. The thermal conductivity of porous media was determined by the Nikitin equation, with the relevant parameters listed in Table 1.


**Table 1.** Fluent simulation parameter setting.

To verify the grid independence, three grid sizes in the same simulation conditions were set up in this work. The inlet gas temperature was 800 K and the velocity was 1.5 m/s. The cooling water inlet temperature was 300 K and the total flow rate was 0.86 m<sup>3</sup>/s. The grid independence verification is shown in Table 2. The errors of the three grid sizes were less than 3%, which indicated that the grid independence was verified.

**Table 2.** Grid independence verification.


To analyze the temperature distribution in the granular bed intuitively, three planes were taken in the radial and vertical directions of the particle bed, as presented in Figure 6.

**Figure 6.** Schematic of the section position of the granular bed.

#### *5.1. Heat Transfer under Di*ff*erent Inlet Flue Gas Temperatures*

The inlet flue gas temperatures were adjusted and other experimental conditions were provided as follows: The inlet flue gas velocity was 1.5 m/s; the cooling water flow rate in a single heat exchange tube was 0.025 m/s, that is, the overall cooling water flow rate was 4.3 m<sup>3</sup>/h; and the inlet water temperature was 300 K. The simulation results of the temperature distribution in the granular bed are illustrated in Figure 7. The heat transfer coefficient and waste heat recovery rate of the granular bed heat exchanger with changes in inlet flue gas temperature were calculated using Tecplot, as depicted in Figure 8. The flue gas brought more heat into the bed, and the total heat transfer coefficient and the waste heat recovery rate of the bed increased to different degrees with the increase in the inlet flue gas temperature. The increasing trend slowed down with the rise in the inlet flue gas temperature, and the heat transfer process in the bed remained stable after reaching the critical value.

**Figure 7.** Temperature distribution under different inlet flue gas temperatures in granular bed. (**a**) Inlet flue gas temperature was 1100 K. (**b**) Inlet flue gas temperature was 1150 K. (**c**) Inlet flue gas temperature was 1200 K. (**d**) Inlet flue gas temperature was 1250 K

**Figure 8.** Influence of flue gas temperature on the heat transfer in granular bed. (**a**) Influence on the waste heat recovery rate. (**b**) Influence on the heat transfer coefficient.

To analyze the difference between the experimental and simulation results, the effect of flue gas temperature on the heat transfer coefficient of the granular bed was studied. The temperatures of the inlet flue gas were 1100, 1150, 1200, and 1250 K and the speed of inlet flue gas was 1.5 m/s.The flow rate of the cooling water was 4.3 m<sup>3</sup>/<sup>h</sup> and the temperature of the inlet cooling water was 300 K. The comparison curves between the experimental and simulated results of the granular bed heat transfer change with the inlet flue gas temperature are plotted in Figure 9.

The relative errors of the heat transfer coefficient and the waste heat recovery were less than 2%, thereby indicating that the simulation and experimental results were reasonable.

**Figure 9.** Comparison of experimental and simulation results. (**a**) The influence of gas temperature on the coefficient. (**b**) Variation curve of relative error.

**Figure 10.** Temperature distribution under different cooling water flow rates. (**a**). Cooling water flow rate was 2.6 m<sup>3</sup>/h. (**b**) Cooling water flow rate was 3.5 m<sup>3</sup>/h. (**c**) Cooling water flow rate was 4.3 m<sup>3</sup>/h. (**d**) Cooling water flow rate was 5.2 m<sup>3</sup>/h. (**e**) Cooling water flow rate was 6.1 m<sup>3</sup>/h.

#### *5.2. Heat Transfer under Di*ff*erent Cooling Water Flow Rates*

The cooling water flow rate was adjusted and the other experimental conditions were presented as follows: The inlet flue gas temperature was 1200 K, the inlet flue gas velocity was 1.5 m/s, and the inlet cooling water temperature was 300 K. The simulation results are demonstrated in Figure 10.

The heat transfer coefficient and waste heat recovery rate of the granular bed heat exchanger with changes in inlet flue gas temperature were calculated using Tecplot, as exhibited in Figure 11. The increase in the cooling water flow rate slightly promoted the heat transfer in the bed, and the increasing trend slowed down with the rise in the cooling water flow rate. After reaching the critical value, the heat transfer process in the bed remained stable.

**Figure 11.** Influence of cooling water flow rate on the heat transfer in granular bed. (**a**) Influence on the waste heat recovery rate. (**b**) Influence on the heat transfer coefficient.
