Introduction

Reserve batteries are a special type of secondary battery in which the electrodes and electrolytes can be maintained in an inactive state, thereby preventing self-discharge and enabling storage over long durations of even 15 years or more [1–3]. Upon being activated, they are one-off batteries that can instantly produce power [4]. To store thermal batteries in an inactive state, methods such as maintaining electrolytes in a solid state or segregating and storing electrodes and electrolytes have mainly been used thus far [4]. Figure 1. shows the structure of a typical reserve battery. Each unit cell consists of a cathode, an electrolyte, an anode, a heat source, and current collectors, and many unit cells are stacked in multiple layers [1, 5, 6]. In addition, the battery insulator has several layers on the top, bottom, and sides that determine its insulation performance. Thermally activated (hereafter called simply “thermal”) reserve batteries operate as batteries when the solid electrolytes are dissolved into liquids by using a chemical heat source [7, 8]. Such batteries are widely used as special-purpose power sources because they generate high electric power within a relatively short duration. The insulation performance of thermal batteries strongly influences their operating time because the battery performance sharply decreases if the melting temperature of electrolytes becomes lower than a certain temperature [9, 10].

Fig. 1
figure 1

Structure of thermal battery and method of operation

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D. Kim et al. conducted research on the characteristics of internal electrodes through two-dimensional simulation [11], and the results were used as the basic data of the three-dimensional model design in this study. A. Yazdani et al. conducted research on the characteristics and melting temperatures of electrolytes [12], and the results were used for the as electrolyte properties in this study. J. R. Sweeney et al. performed an experiment on thermal battery performance characteristics and provided valuable information for the design of electrode materials [13]. N. D. Streeter et al. developed an axisymmetric finite element code to predict the temperature and heat flux of a thermal battery as a whole, but additional data appears to be required to predict the insulation performance of a thermal battery [14]. G. C. S. Freitas et al. conducted research on the electrode characteristics of a small thermal battery by performing two-dimensional simulation [15]. Although various studies have been conducted since the invention of thermal batteries in 1940, it is difficult to appropriate data for improving the insulation performance of thermal batteries the reason [1]. This appears to be because information and technologies have not been released as thermal batteries are mainly used for military purposes [15]. The present study aims to establish thermal analysis conditions and techniques for thermal batteries used as special-purpose power sources through comparisons with experimental data.

Setup of calculation model and boundary condition

One unit cell of a thermal battery consists of a cathode, an electrolyte, an anode, a heat source, and current collectors, and many such unit cells are stacked in multiple layers. Therefore, a battery for analysis was modeled to establish the boundary conditions and analysis techniques for thermal batteries, as shown in Fig. 2a. Here, to minimize the number of calculation grids and the computational time required, a 2° full model, which is a part of the thermal battery, was modeled(Fig. 2b.). In this model, circumferentially periodic boundary conditions were applied in the circumferential direction. Further, a 2°-part model was constructed to realize grid independence, as shown in Fig. 2c. This model was based on a unit cell, which is repeated. Therefore, this model was analyzed by applying circumferentially and axially periodic boundary conditions.

Fig. 2
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Models of thermal battery (a) Full model (b) 2° Full model (c) 2° Part model

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The material properties of the thermal battery, as listed in Table 1., were referred from a previous study [16]. The model of the thermal battery contained polyhedral meshes, and two prism layers were applied. The calculation grids were generated using the Mesher function in Star-CCM + . Table 2. shows the calculation grid setting and initial conditions [17].

Table 1 Material properties of thermal battery
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Table 2 Calculation grid setting condition and initial conditions
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One unit cell of the thermal battery was selected as the grid independence model, shown in Fig. 3. Circumferentially and axially periodic boundary conditions were applied to this model. The number of calculation grids was varied as 1,500, 3,000, 7,500, and 15,000, as shown in Fig. 4.

Fig. 3
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Grid independence model (2°-part model) (a) 1,500 (b) 3,000 (c) 7,500 (d) 15,000

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Fig. 4
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Number of calculation grids

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Here, the heating time of the heat source was 2.5 s and the calorific value was 298 cal/g, as described previously [1]. Figure 5a. shows the temperature of the heat source over time according to the number of grids. Considering the heating time of the heat source, heat transfer analysis was conducted for 4 s. Figure 5b. shows the time required to reach the maximum temperature of the heat source shown in Fig. 5a. and the error rate of the maximum temperature. The error rate was less than 1% for all numbers of grids, but the number of grids for the 2°-part model was determined to be 3,000. Specifically, when using the same grid generation method, the number of grids for the 2° full model was determined to be approximately 65,000.

Fig. 5
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Temperature and error rate (a) Temperature of heat source (b) Error rate of maximum temperature

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Heat transfer analysis was conducted by applying the convective heat transfer coefficient to the housing surface in order to apply the experiment results of the housing surface temperature to the analysis. In the experiments, the temperatures were measured at the center of the side of the housing, and the temperature change trend in a reliable time range (200–900 s) was used. Heat transfer analysis was conducted by applying different convective heat transfer coefficients (17, 20, 25, and 30 W/m2·K). The 0–200 s section was excluded from the comparison because the experimental errors in this section were considered large. Figure 6. shows the analysis results. The convective heat transfer coefficient was confirmed to be between 17 and 20 W/m2·K, and a value of 19.2 W/m2·K was obtained through numerical interpolation. Figure 7. shows a comparison of the housing surface temperatures calculated using the obtained heat transfer coefficient and measured in the experiment.

Fig. 6
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Housing surface temperatures with different convective heat transfer coefficients

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Fig. 7
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Comparison of calculated and experimentally measured housing surface temperatures

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Calculation results

Heat transfer analysis was conducted from 0 to 1,000 s by applying a convective heat transfer coefficient of 19.2 W/m2·K to the 2° full model. Figure 8. shows the temperature distribution inside the thermal battery at 3.7, 300, 600, and 870 s. In particular, Fig. 8a. shows the temperature distribution at the time when the maximum temperature occurred. The experimentally measured operating time of the thermal battery was approximately 870 s; Fig. 8d. shows the temperature distribution at this time. Theoretically, the performance of the thermal battery decreases sharply when the electrolyte temperature drops below approximately 450 °C. Therefore, the electrolyte temperature is an important factor in the operational performance of the thermal battery. Figure 9. shows the total averaged electrolyte temperature and the one-cell averaged temperatures for the top and bottom electrolyte and the middle electrolyte of the thermal battery. For an operating time of 870 s, the total averaged electrolyte temperature was 457 °C (Fig. 9a) and the one-cell averaged temperatures of the middle electrolyte and the top and bottom electrolyte were respectively 466 °C and 441 °C (Fig. 9b). These results indicate that rapid heat release occurred at the top and bottom as well as at the side of the housing. Therefore, the insulation of the top and bottom of the housing must be reinforced; the reinforcement of the side insulators is also important. To improve the operating time of the thermal batteries in the future, their insulation performance could be improved by analyzing and reinforcing the insulation of the top, bottom, and sides of the housing.

Fig. 8
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Temperature distributions inside thermal battery (a) 3.7 s (b) 300 s (c) 600 s (d) 870 s

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Fig. 9
figure 9

Electrolyte temperatures of thermal battery (a) Total averaged temperature (b) One-cell averaged temperature

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Conclusion

Although studies to improve the performance of thermal batteries by improving their materials have been conducted since 1940, literature on analysis conditions and techniques to improve insulation performance remains insufficient. The present study aimed to establish thermal analysis conditions and techniques for thermal batteries used as special-purpose power sources. Grid independence was realized to increase the accuracy of the solution, and grids with an error rate of less than 1% were applied. The experiment results of the housing surface temperature were applied to a thermal analysis through the convective heat transfer coefficient. This coefficient was determined to be 19.2 W/m2·K. The heat transfer analysis results showed that the total averaged electrolyte temperature, top and bottom electrolyte temperature, and middle electrolyte temperature were 457 °C, 441 °C, and 466 °C, respectively, with an operating time of 870 s. Assuming a minimum operating temperature of 450 °C for the electrolyte, the amount of power generated decreases rapidly from the top and bottom electrolyte layers of the housing of the thermal battery. This is because rapid heat release occurs at the top and bottom of the housing compared to the sides. Therefore, improving the insulation performance of the top and bottom of the housing could significantly improve the operational performance of the thermal battery; reinforcement of the side insulator is also required. The obtained results could serve as important basic data for improving the performance of thermal batteries and extending their operating time.

Regarding an improvement in the operating time of thermal batteries, it was confirmed that the material properties of insulation are important performance factors. In the future, research on the improvement of insulation performance will be continue to conducted using the thermal analysis techniques proposed in this study to extend the performance of thermal batteries.