Experimental and Simulation Study on Heat Accumulation Phenomenon at the Bottom of Solid Thermal Storage Electric Boilers

The "carbon peak and carbon neutrality" policy was firstly put forward in the Chinese Central Economic Work Conference 2020 which aiming at reducing the carbon emission in China. According to this policy, the carbon emissions should reach their peak before 2030 and achieve neutrality before 2060. For this purpose, the adjustment and optimization of industrial and energy structures should be accelerated to promote the efficient heating systems. Against this backdrop, using clean electricity as a heat source, adding energy storage between the electricity and heating systems, can reduce the conflict between grid peak shaving and heating supply to a certain extent while ensuring electricity supply for heating. Solid electric thermal storage technology can convert fluctuating electricity from low grid valleys, wind power, and other sources into thermal energy, which is used for heating during peak electricity demand periods. This is an advanced and efficient form of thermal storage, playing a crucial role in improving the flexibility of the power grid.

Domestic and international experts have conducted extensive research on solid thermal storage electric boilers through numerical simulations and experimental tests, focusing on thermal storage and release characteristics, economics, operation modes, evaluation indices, and system optimization. These efforts have driven the technological advancement of solid thermal storage electric boilers [1-5]. However, as a new heating method, solid thermal storage technology faces many engineering challenges in practical applications, and research in related fields is limited. This project aims to address the practical operational issues of solid thermal storage electric boilers, taking a novel approach with innovative aspects.

At the initial stage of heat release in solid thermal storage electric boilers, the temperature of the thermal storage bricks reaches 500-700℃, and the heat exchange between the air and the thermal storage bricks is efficient, resulting in good heating performance. As the heat release process continues, the average brick temperature of the thermal storage body decreases, significantly reducing energy quality and resulting in poor heating performance. In engineering practice, methods such as increasing the boiler's thermal storage temperature are commonly used to enhance the heat release capacity of the thermal storage body. However, this approach consumes large amounts of energy, presents challenges to the safe and stable operation of the electric heating system, and is economically inefficient. Therefore, it is particularly important to improve the thermal efficiency of solid thermal storage electric boilers based on the existing operating parameters.

This study mainly analyzes the heat accumulation phenomenon at the bottom of solid thermal storage electric boilers using experimental and simulation methods. Chapter 1 introduces the application background and main technical issues of solid thermal storage electric boilers. Chapter 2 presents the experimental study on the heat accumulation phenomenon at the bottom of solid thermal storage electric boilers. Chapter 3 introduces the numerical simulation study on the heat accumulation phenomenon at the bottom of solid thermal storage electric boilers. Chapter 4 compares the experimental data with simulation results and evaluates the experimental platform and numerical calculation model. Chapter 5 presents the research conclusions and suggestions for future studies.

3.1 Physical model

In order to visually observe and analyze the heat accumulation phenomenon at the bottom of the thermal storage body, this study builds a model based on the experimental setup of the solid thermal storage electric boiler, as shown in Figure 5.

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Figure 5. 3D view of solid thermal storage electric boiler model

3.2 Mathematical model

The fluid flow and heat transfer processes involved in this study follow the basic physical laws of mass conservation, momentum conservation, and energy conservation. The k-ε turbulence model is used for solving [7, 8].

(1) Mass conservation—Continuity equation

$\frac{\partial \rho}{\partial \mathrm{t}}+\frac{\partial(\rho \mathrm{u})}{\partial \mathrm{x}}+\frac{\partial(\rho v)}{\partial \mathrm{y}}+\frac{\partial(\rho \omega)}{\partial \mathrm{z}}=0$          (1)

For incompressible fluids with constant density, the continuity equation simplifies to:

$\frac{\partial(\mathrm{u})}{\partial \mathrm{x}}+\frac{\partial(\mathrm{v})}{\partial \mathrm{y}}+\frac{\partial(\omega)}{\partial \mathrm{z}}=0$          (2)

(2) Momentum conservation law—N-S equations

$\begin{aligned} u \frac{\partial(\rho u)}{\partial \mathrm{x}}+\mathrm{v} \frac{\partial(\rho \mathrm{u})}{\partial \mathrm{y}} & +\mathrm{w} \frac{\partial(\rho \mathrm{u})}{\partial \mathrm{z}} =-\frac{\partial \mathrm{p}}{\partial \mathrm{x}}+\frac{\partial}{\partial \mathrm{x}}\left(\mu \frac{\partial \mathrm{u}}{\partial \mathrm{x}}\right)+\frac{\partial}{\partial \mathrm{y}}\left(\mu \frac{\partial \mathrm{u}}{\partial \mathrm{y}}\right)  +\frac{\partial}{\partial \mathrm{z}}\left(\mu \frac{\partial \mathrm{u}}{\partial \mathrm{z}}\right)\end{aligned}$          (3)

$\begin{aligned} u \frac{\partial(\rho v)}{\partial \mathrm{x}}+\mathrm{v} \frac{\partial(\rho \mathrm{v})}{\partial \mathrm{y}} & +\mathrm{w} \frac{\partial(\rho \mathrm{v})}{\partial \mathrm{z}}  =-\frac{\partial \mathrm{p}}{\partial \mathrm{y}}+\frac{\partial}{\partial \mathrm{x}}\left(\mu \frac{\partial \mathrm{v}}{\partial \mathrm{x}}\right)+\frac{\partial}{\partial \mathrm{y}}\left(\mu \frac{\partial \mathrm{v}}{\partial \mathrm{y}}\right)  +\frac{\partial}{\partial \mathrm{v}}\left(\mu \frac{\partial \mathrm{v}}{\partial \mathrm{z}}\right)\end{aligned}$          (4)

$\begin{aligned} u \frac{\partial(\rho \mathrm{w})}{\partial \mathrm{x}}+\mathrm{v} \frac{\partial(\rho \mathrm{w})}{\partial \mathrm{y}} & +\mathrm{w} \frac{\partial(\rho \mathrm{w})}{\partial \mathrm{z}}  =-\frac{\partial \mathrm{p}}{\partial \mathrm{z}}+\frac{\partial}{\partial \mathrm{x}}\left(\mu \frac{\partial \mathrm{w}}{\partial \mathrm{x}}\right)+\frac{\partial}{\partial \mathrm{y}}\left(\mu \frac{\partial \mathrm{w}}{\partial \mathrm{y}}\right)  +\frac{\partial}{\partial \mathrm{v}}\left(\mu \frac{\partial \mathrm{w}}{\partial \mathrm{z}}\right)-\rho \mathrm{g}\end{aligned}$          (5)

(3) Energy conservation equation—Heat transfer differential equation

$\frac{\partial T}{\partial t}+\nabla \cdot(u T)=\alpha \nabla^2 T+Q^{\prime}$          (6)

For conditions without internal heat sources and constant properties, this simplifies to:

$\begin{aligned} \frac{\partial(\rho \mathrm{T})}{\partial \mathrm{t}}+\frac{\partial(\rho \mathrm{uT})}{\partial \mathrm{x}}+ & \frac{\partial(\rho \mathrm{vT})}{\partial \mathrm{y}}+\frac{\partial(\rho \mathrm{wT})}{\partial \mathrm{z}}  =\frac{\partial}{\partial \mathrm{x}}\left(\frac{\lambda}{\mathrm{C}_{\mathrm{p}}} \frac{\partial \mathrm{T}}{\partial \mathrm{x}}\right)+\frac{\partial}{\partial \mathrm{y}}\left(\frac{\lambda}{\mathrm{C}_{\mathrm{P}}} \frac{\partial \mathrm{T}}{\partial \mathrm{y}}\right)  +\frac{\partial}{\partial \mathrm{z}}\left(\frac{\lambda}{\mathrm{C}_{\mathrm{P}}} \frac{\partial \mathrm{T}}{\partial \mathrm{z}}\right)\end{aligned}$          (7)

(4) k-ε equations:

$\begin{aligned} \frac{\partial(\rho \mathrm{k})}{\partial \mathrm{t}}+\frac{\partial\left(\rho \mathrm{ku}_{\mathrm{i}}\right)}{\partial \mathrm{x}_{\mathrm{i}}}= & \frac{\partial}{\partial \mathrm{x}_{\mathrm{i}}}\left[\left(\mu+\frac{\mu_{\mathrm{t}}}{\sigma_{\mathrm{k}}}\right) \frac{\partial \mathrm{k}}{\partial \mathrm{x}_{\mathrm{j}}}\right]+\mathrm{G}_{\mathrm{k}}+\mathrm{G}_{\mathrm{b}}-\rho \varepsilon -\mathrm{Y}_{\mathrm{M}}+\mathrm{S}_{\mathrm{k}}\end{aligned}$          (8)

$\begin{aligned} \frac{\partial(\rho \varepsilon)}{\partial \mathrm{t}}+\frac{\partial\left(\rho \varepsilon \mathrm{u}_{\mathrm{i}}\right)}{\partial \mathrm{x}_{\mathrm{i}}}= & \frac{\partial}{\partial \mathrm{x}_{\mathrm{j}}}\left[\left(\mu+\frac{\mu_{\mathrm{t}}}{\sigma_{\varepsilon}}\right) \frac{\partial \varepsilon}{\partial \mathrm{x}_{\mathrm{j}}}\right] +\mathrm{C}_{1 \varepsilon} \frac{\varepsilon}{\mathrm{k}}\left(\mathrm{G}_{\mathrm{k}}+\mathrm{C}_{3 \varepsilon} \mathrm{G}_{\mathrm{b}}\right)-\mathrm{C}_{2 \varepsilon} \rho \frac{\varepsilon^2}{\mathrm{k}}+\mathrm{S}_{\varepsilon}\end{aligned}$          (9)

3.3 Simulation calculation

This study uses ANSYS software for the 3D modeling and calculation of the solid thermal storage electric boiler, with the Fluent solver calculating temperature and velocity distribution of the model. For simplification, reasonable assumptions for the solid thermal storage electric boiler model are made as follows [9-12]:

(1) Air is incompressible and viscous, and the flow in the air duct is turbulent;

(2) Radiation heat transfer is not considered in the model;

(3) The inlet air temperature and flow velocity are constant during each heat storage and release stage;

(4) Relevant system physical parameters are constant;

(5) The temperature and pressure inside the thermal storage body change over time;

(6) Heat transfer from the thermal storage body to the surroundings is ignored.

When dividing the physical model into meshes, the mesh for the thermal storage body insulation structure at the bottom is refined. After a mesh independence verification, the total mesh number is 3,549,724, with a minimum orthogonality quality of 0.2, as shown in Figure 6.

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Figure 6. Physical model mesh division

The material property parameters for the main materials involved in the calculation are as follows [13-15] (Table 3).

Table 3. Main material property parameters

Based on the experimental conditions in Section 3.2, the simulation process is set with the following inlet wind speed, wind temperature, and heat storage/release duration (Table 4).

Table 4. Inlet wind speed and wind temperature settings for each stage

3.4 Simulation results analysis

This section analyzes the temperature change of the thermal storage body and the heat accumulation issue during the three rounds of heat storage and release.

After the first round of heat storage and release, the temperature distribution of the solid thermal storage electric boiler in the central cross-section parallel to the airflow direction is shown in Figure 7.

As shown in Figure 7(a), during the first round of heat storage, the thermal storage body increases from the initial temperature (14℃) after 6.5 hours of heating with a small amount of ventilation. The highest temperature reaches 503℃, and the average temperature of the thermal storage body rises from 14℃ to 366.9℃. The heat storage center is located at the top, rear part of the thermal storage body (along the direction of airflow). The insulation structure at the bottom of the thermal storage body shows a noticeable temperature rise. As shown in Figure 7(b), after 10 hours of heat release, the average temperature of the thermal storage bricks decreases to 115.4℃. The internal temperature distribution becomes relatively uniform, and the average temperature of the insulation structure at the bottom is higher than that of the thermal storage body, indicating that heat continues to be stored in the insulation structure and should not dissipate.

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(a) After heat storage

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(b) After heat release

Figure 7. Temperature distribution of the boiler center section at the end of the first round of heat storage and heat release

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Figure 8. Temperature and ventilation speed distribution at the furnace center section after the second and third rounds of heat storage and release

Figure 8 shows the temperature and airflow velocity distribution in the central cross-section of the boiler at the end of the second and third rounds of heat storage and release. From this, we can see that, after the second round of heat storage, the highest temperature of the thermal storage body reaches 558℃, with an average temperature of 418.5℃, which is 51.6℃ higher than the average temperature of the first round of heat storage. This indicates that the first round of heat storage and release, where only the middle wind inlet was opened, resulted in slower airflow in the upper channel of the thermal storage body (as shown in Figure 8(c)). As a result, heat could not be sufficiently carried away by the air, and heat accumulated in the upper rear area of the thermal storage body, leading to an increase in the average temperature. The temperature distribution of the thermal storage body became uneven, causing the heat exchange capacity and heat exchange efficiency of certain areas to decrease, reducing the overall heat storage and release capacity, lowering the air quality, and affecting the system's heat efficiency and economy. During the third round of heat storage and release, all three air inlets were opened, and as shown in Figure 8(c), the airflow distribution inside the air ducts became more uniform. After the third round of heat storage, the average temperature of the thermal storage bricks reached 367.7℃, and the overall temperature distribution of the thermal storage body became more uniform, alleviating the heat accumulation phenomenon. The system's operational efficiency and economy were improved.

By comparing the temperature distribution of the insulation structure at the bottom of the thermal storage body after the three rounds of heat storage and release, it can be concluded that, as the heat storage and release cycles proceed, heat is transferred from the thermal storage body to the bottom insulation structure, causing the temperature of the insulation structure to gradually increase. The wind speed and uniformity of the air supply during heat storage and release do not significantly affect the temperature rise effect. The heat accumulation phenomenon is persistent and difficult to eliminate.

In order to further analyze the characteristics of heat accumulation in the insulation structure at the bottom of the heat storage body, the temperature cloud maps of the cross-sections of the insulation structure below the heat storage body, i.e., the four layers of unperforated MgO bricks, clay bricks (1), and clay bricks (2), at the end of the three rounds of heat release are summarized, as shown in Figure 9.

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Figure 9. Temperature distribution at different positions at the bottom after the heat release of the solid heat storage electric boiler

After completing the three rounds of heat storage and release, the overall temperature of the insulation structure at the bottom of the heat storage body gradually increases. Heat is transmitted from top to bottom in the vertical direction, gradually accumulating. By comparing the MgO brick cloud maps after the second and third rounds of heat release, it can be seen that although improving the air supply uniformity can slightly reduce the average temperature of the bricks and reduce the temperature gradient of the MgO brick layer, it has little effect on alleviating the heat accumulation in the insulation structure. Analyzing the temperature cloud maps of the three insulation layers after the third heat release, it is predicted that if the heat storage and release process continues for multiple rounds, the entire insulation structure will be gradually heated, with temperatures tending to equalize, and the average temperature ($\bar{t}$) will exceed 100℃, with the highest temperature exceeding 200℃.

Based on the above simulation results, the conclusion can be drawn that after several rounds of heat storage and release, a large amount of heat accumulates in the insulation structure at the bottom of the heat storage body, and this heat is of higher quality, which cannot be easily utilized by changing the airflow organization or system operation mode. Adopting other improvement measures to utilize this heat is economically viable and has research value [16, 17].

3.5 Calculation of accumulated heat at the bottom of the heat storage body

Based on the simulation results, the maximum heat generated at the furnace bottom during the three rounds of heat storage and release is considered.

$\sum \mathrm{Q}_{\max }=\sum \mathrm{Q}_1+\sum \mathrm{Q}_2+\sum \mathrm{Q}_3$         (10)

where:

$\sum \mathrm{Q}_1$ — Total heat stored in the standard MgO brick layer during the three rounds of heat storage and release, kJ

$\sum \mathrm{Q}_2$ — Total heat stored in the middle clay insulation brick layer during the three rounds of heat storage and release, kJ

$\sum \mathrm{Q}_3$ — Total heat stored in the bottom clay insulation brick layer during the three rounds of heat storage and release, kJ

The temperature variation of the three brick layers during the three rounds of heat storage and release is obtained from the simulation results. By using the physical parameters of different brick layers and the brick layer volumes, the mass of each part of the bricks is calculated. Then, by utilizing the temperature changes of the brick layers every minute, the heat stored in the brick layers per minute is obtained. The total heat stored in the brick layers at different positions at the bottom of the heat storage body during the entire heat storage and release process is summed. Taking the heat release of the standard MgO brick layer per minute as an example:

$\mathrm{Q}_1=\mathrm{C}_{\mathrm{p} 1} \mathrm{M}_1 \Delta \mathrm{t}_1$          (11)

where:

$\mathrm{Q}_1$ — Heat stored in the standard MgO brick layer per minute, kJ

$\mathrm{C}_{\mathrm{p} 1}$ — Specific heat capacity of the standard MgO brick, J/(kg·K)

$\mathrm{M}_1$ — Total mass of the standard MgO brick layer, kg

$\Delta \mathrm{t}_1$ — Average temperature change per minute of the standard MgO brick layer, K

The calculations for other brick layers are performed similarly. Finally, the results obtained are as follows:

$\sum Q_1=7.26 e^5 k J, \sum Q_2=6.57 e^4 k J, \sum Q_3=9.63 e^4 k J$

From the calculation results, it can be seen that the heat accumulation in the MgO brick layer is the largest, about 10 times that of the other two brick layers. Therefore, fully utilizing the heat stored in the MgO brick layer has a significant effect on improving the system's heat efficiency. During the three rounds of heat storage and release in the solid heat storage electric boiler, the total heat stored in the bottom standard brick layer and the clay insulation brick layer is about 5.25e⁵ kJ.

This research starts with the working principle of the solid heat storage electric boiler and, based on analyzing the physical process of heat storage and release, uses experimental and simulation methods to study the heat accumulation problem at the bottom of the heat storage body. First, a test platform was established for the heat accumulation phenomenon at the bottom of the solid heat storage boiler, and three rounds of experimental testing were conducted. Then, using the test platform as a prototype, a physical model and mathematical model for numerical simulation were established and calculated. Finally, by comparing and analyzing the experimental data and simulation results, the scientificity and accuracy of the experiments and simulations were verified. The main conclusions of this study are:

(1) Through the analysis of experimental and simulation data, the temperature of the heat storage body and the insulation structure at the bottom gradually rises as the heat storage and release process continues, and heat accumulation occurs. Improving the ventilation conditions can optimize the temperature distribution of the heat storage body and effectively reduce its temperature non-uniformity, but the effect of changing ventilation conditions on the heat utilization in the insulation structure is minimal.

(2) Calculations show that the heat accumulation phenomenon in the standard heat storage brick layer of the boiler's insulation structure is the most serious, one order of magnitude higher than in other brick layers. The total heat storage in the insulation structure is 5.25e⁵ kJ. Fully utilizing the heat stored in the standard heat storage brick is the most effective way to alleviate the heat accumulation phenomenon.

(3) By comparing the simulation results and experimental data, the experimental and simulation data match well. In the experiment, it took 5 hours and 20 minutes to heat the solid heat storage electric boiler from room temperature to 500℃. In the simulation, this heating process was calculated to take 5 hours and 30 minutes. The average error of the average temperature during the three rounds of heat storage and release was less than 10%.

The results of this study show that the heat accumulation effect at the bottom of the solid heat storage boiler cannot be effectively alleviated by changing the airflow and operation modes. Future research is recommended to design a heat recovery system at the bottom, such as setting up a coil heat exchanger in the insulation structure at the bottom, which is connected to municipal water to carry away the accumulated heat, thus effectively improving the system's heat utilization. However, the layout of the coils and the application of recovered heat still require further research.