**3. Results and Discussion**

*3.1. Analytical Model Results*

The analytical model has been simulated for 30 cycles. The air is compressed from atmospheric conditions to 8 MPa in the first cycle. In the following cycles, the air pressure varies from 5 to 8 MPa at a stable mass flow rate considering an injected air temperature of 310 K and daily compression and decompression cycles. During an operation cycle, the air is compressed for 8 h at a mass flow rate of 0.22 kg s−<sup>1</sup> and stored for 6 h. Then, the air is released for 4 h at a mass flow rate of <sup>−</sup>0.45 kg s−<sup>1</sup> and stored for 6 h.

The variations in temperature for the air, sealing layer and concrete lining are shown in Figure 4 using FRP as sealing layer for 30 continuous cycles, which is equivalent to one month of operation. The results are also presented more in detail for the first cycle (Figure 4a) and the 30th cycle (Figure 4c). The air temperature increases up to 322 K during the first compression cycle. However, due to mixing with the injected air and heat exchange between the compressed air and the lining, the air temperature within the

reservoir decreases to 307 K from the fifth cycle (five days). During the discharge period the air temperature is also stable, reaching minimum values of 294 K. The temperature of the FRP and concrete during the charge period reach 305 and 303 K, respectively, decreasing to 296 and 300 K during the discharge phase. creases to 307 K from the fifth cycle (five days). During the discharge period the air temperature is also stable, reaching minimum values of 294 K. The temperature of the FRP and concrete during the charge period reach 305 and 303 K, respectively, decreasing to 296 and 300 K during the discharge phase. creases to 307 K from the fifth cycle (five days). During the discharge period the air temperature is also stable, reaching minimum values of 294 K. The temperature of the FRP and concrete during the charge period reach 305 and 303 K, respectively, decreasing to 296 and 300 K during the discharge phase.

month of operation. The results are also presented more in detail for the first cycle (Figure 4a) and the 30th cycle (Figure 4c). The air temperature increases up to 322 K during the first compression cycle. However, due to mixing with the injected air and heat exchange between the compressed air and the lining, the air temperature within the reservoir de-

month of operation. The results are also presented more in detail for the first cycle (Figure 4a) and the 30th cycle (Figure 4c). The air temperature increases up to 322 K during the first compression cycle. However, due to mixing with the injected air and heat exchange between the compressed air and the lining, the air temperature within the reservoir de-

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**Figure 4.** Temperature of air, fiber-reinforced plastic (FRP) and concrete lining for 30 charging and discharging cycles considering FRP as sealing layer. (**a**) First cycle; (**b**) 30 days of operation; (**c**) 30th cycle. **Figure 4.** Temperature of air, fiber-reinforced plastic (FRP) and concrete lining for 30 charging and discharging cycles considering FRP as sealing layer. (**a**) First cycle; (**b**) 30 days of operation; (**c**) 30th cycle. **Figure 4.** Temperature of air, fiber-reinforced plastic (FRP) and concrete lining for 30 charging and discharging cycles considering FRP as sealing layer. (**a**) First cycle; (**b**) 30 days of operation; (**c**) 30th cycle.

As shown in Figure 5, the air pressure varies from 5 to 8 MPa over the entire 30 days. Because of air temperature, the pressure decreases to 7.8 MPa during the storage period in the first cycle (Figure 5a). This reduction decreases to 7.9 MPa from the fifth cycle. The air pressure increases slightly in the storage period after the decompression stage. As shown in Figure 5, the air pressure varies from 5 to 8 MPa over the entire 30 days. Because of air temperature, the pressure decreases to 7.8 MPa during the storage period in the first cycle (Figure 5a). This reduction decreases to 7.9 MPa from the fifth cycle. The air pressure increases slightly in the storage period after the decompression stage. As shown in Figure 5, the air pressure varies from 5 to 8 MPa over the entire 30 days. Because of air temperature, the pressure decreases to 7.8 MPa during the storage period in the first cycle (Figure 5a). This reduction decreases to 7.9 MPa from the fifth cycle. The air pressure increases slightly in the storage period after the decompression stage.

**Figure 5.** Air pressure for 30 charging and discharging cycles considering FRP as sealing layer. (**a**) First cycle; (**b**) 30 days of operation; (**c**) 30th cycle. **Figure 5.** Air pressure for 30 charging and discharging cycles considering FRP as sealing layer. (**a**) First cycle; (**b**) 30 days of operation; (**c**) 30th cycle. **Figure 5.** Air pressure for 30 charging and discharging cycles considering FRP as sealing layer. (**a**) First cycle; (**b**) 30 days of operation; (**c**) 30th cycle.

The surface heat flux by convection between the compressed air and the FRP and between the FRP and concrete is shown in Figure 6. Note the thickness of the sealing layer (20 mm). Due to the temperature effect, the surface heat flux increases in the first cycle to 150 and 140 W m−<sup>2</sup> for FRP and concrete lining, respectively. The heat flux decreases to <sup>−</sup>90 W m−<sup>2</sup> in the decompression stage. As observe in Figure 6c in more detail, from second cycle the heat flux through the FRP and concrete is stable, reaching maximum values of 50 and <sup>−</sup>100 W m−<sup>2</sup> in the charge and discharge periods, respectively. The surface heat flux is decreasing rapidly during the storage periods. Due to the thickness of the sealing layer and the long air charging and discharging time, the surface heat flux in the sealing layer and the concrete lining is very similar. The surface heat flux by convection between the compressed air and the FRP and between the FRP and concrete is shown in Figure 6. Note the thickness of the sealing layer (20 mm). Due to the temperature effect, the surface heat flux increases in the first cycle to 150 and 140 W m−2 for FRP and concrete lining, respectively. The heat flux decreases to −90 W m−2 in the decompression stage. As observe in Figure 6c in more detail, from second cycle the heat flux through the FRP and concrete is stable, reaching maximum values of 50 and −100 W m−2 in the charge and discharge periods, respectively. The surface heat flux is decreasing rapidly during the storage periods. Due to the thickness of the sealing layer and the long air charging and discharging time, the surface heat flux in the sealing layer and the concrete lining is very similar.

**Figure 6.** Surface heat flux of FRP and concrete lining for 30 charging and discharging cycles considering FRP as sealing layer. (**a**) First day; (**b**) 30 days of operation; (**c**) 30th cycle. **Figure 6.** Surface heat flux of FRP and concrete lining for 30 charging and discharging cycles considering FRP as sealing layer. (**a**) First day; (**b**) 30 days of operation; (**c**) 30th cycle.

A comparative analysis for the air temperature, pressure and surface heat flux is shown in Figure 7 for the first cycle considering both FRP and steel as sealing layers. The results are also presented for cycle 30th in Figure 8. The air temperature fluctuation between the compression and decompression periods decreases when steel is employed as sealing layer. Because of the thermal conductivity, the temperature in the contact surface between the compressed air and sealing layer is lower when steel is employed as sealing layer (Figure 8a). The reduction in air pressure in the first cycle is greater during the storage period when FRP is used as sealing layer (Figure 7b). However, as shown in Figure 8b, this reduction is very similar from second cycle. Regarding the surface heat flux, the results are very similar for both sealing layers, reaching values 50 and −100 W m−2 in the compression and decompression stages (Figure 8c). The thermal energy balance in the 30th cycle (day 30) through the sealing layer reaches 25.27 and 20.48 kWh for FRP and steel, respectively. Although the system loses slightly more thermal energy in the compression stage when steel is used, the lining contributes with more energy to the compressed air in the decompression stage when steel is used as sealing layer (Figure 8c). A comparative analysis for the air temperature, pressure and surface heat flux is shown in Figure 7 for the first cycle considering both FRP and steel as sealing layers. The results are also presented for cycle 30th in Figure 8. The air temperature fluctuation between the compression and decompression periods decreases when steel is employed as sealing layer. Because of the thermal conductivity, the temperature in the contact surface between the compressed air and sealing layer is lower when steel is employed as sealing layer (Figure 8a). The reduction in air pressure in the first cycle is greater during the storage period when FRP is used as sealing layer (Figure 7b). However, as shown in Figure 8b, this reduction is very similar from second cycle. Regarding the surface heat flux, the results are very similar for both sealing layers, reaching values 50 and <sup>−</sup>100 W m−<sup>2</sup> in the compression and decompression stages (Figure 8c). The thermal energy balance in the 30th cycle (day 30) through the sealing layer reaches 25.27 and 20.48 kWh for FRP and steel, respectively. Although the system loses slightly more thermal energy in the compression stage when steel is used, the lining contributes with more energy to the compressed air in the decompression stage when steel is used as sealing layer (Figure 8c).

**Figure 7.** Comparative analysis between FRP and steel in the first cycle. (**a**) Temperature of air, FRP and steel; (**b**) Air pressure; (**c**) Surface heat flux of FRP and steel. **Figure 7.** Comparative analysis between FRP and steel in the first cycle. (**a**) Temperature of air, FRP and steel; (**b**) Air pressure; (**c**) Surface heat flux of FRP and steel. **Figure 7.** Comparative analysis between FRP and steel in the first cycle. (**a**) Temperature of air, FRP and steel; (**b**) Air pressure; (**c**) Surface heat flux of FRP and steel.

**Figure 8.** Comparative analysis between FRP and steel in the 30th cycle. (**a**) Temperature of air, FRP and steel; (**b**) Air pressure; (**c**) Surface heat flux of FRP and steel. **Figure 8.** Comparative analysis between FRP and steel in the 30th cycle. (**a**) Temperature of air, FRP and steel; (**b**) Air pressure; (**c**) Surface heat flux of FRP and steel. **Figure 8.** Comparative analysis between FRP and steel in the 30th cycle. (**a**) Temperature of air, FRP and steel; (**b**) Air pressure; (**c**) Surface heat flux of FRP and steel.

### *3.2. Numerical Model Results 3.2. Numerical Model Results 3.2. Numerical Model Results*

To validate the results of the analytical model, a 3D CFD numerical model has been performed and the results are shown in Figure 9. The numerical model has been simulated for 5 cycles, considering an injected air temperature of 310 K and stable air mass flow rates of 50 kg s−1 and −75 kg s−1 in the charge and discharge periods, respectively. The model geometry and thermal properties of air and solids are the same as those used in the analytic model. As presented in Figure 9a, the maximum air temperature decreases from 410 to 340 K between the first and fifth cycle. The air temperature fluctuation between air charging and discharging reaches 45 K in the fifth cycle. Likewise, the FRP temperature decreases from 385 to 322 K. However, the concrete lining temperature is more constant throughout the process. The surface heat flux for FRP and concrete is shown in Figure 9c. Due to convective effects, the heat flux increases in FRP during the first cycle. Then, from third cycle is stabilized in a maximum value of 1000 W m−2 in the compression period and To validate the results of the analytical model, a 3D CFD numerical model has been performed and the results are shown in Figure 9. The numerical model has been simulated for 5 cycles, considering an injected air temperature of 310 K and stable air mass flow rates of 50 kg s−1 and −75 kg s−1 in the charge and discharge periods, respectively. The model geometry and thermal properties of air and solids are the same as those used in the analytic model. As presented in Figure 9a, the maximum air temperature decreases from 410 to 340 K between the first and fifth cycle. The air temperature fluctuation between air charging and discharging reaches 45 K in the fifth cycle. Likewise, the FRP temperature decreases from 385 to 322 K. However, the concrete lining temperature is more constant throughout the process. The surface heat flux for FRP and concrete is shown in Figure 9c. Due to convective effects, the heat flux increases in FRP during the first cycle. Then, from third cycle is stabilized in a maximum value of 1000 W m−2 in the compression period and To validate the results of the analytical model, a 3D CFD numerical model has been performed and the results are shown in Figure 9. The numerical model has been simulated for 5 cycles, considering an injected air temperature of 310 K and stable air mass flow rates of 50 kg s−<sup>1</sup> and <sup>−</sup>75 kg s−<sup>1</sup> in the charge and discharge periods, respectively. The model geometry and thermal properties of air and solids are the same as those used in the analytic model. As presented in Figure 9a, the maximum air temperature decreases from 410 to 340 K between the first and fifth cycle. The air temperature fluctuation between air charging and discharging reaches 45 K in the fifth cycle. Likewise, the FRP temperature decreases from 385 to 322 K. However, the concrete lining temperature is more constant throughout the process. The surface heat flux for FRP and concrete is shown in Figure 9c. Due to convective effects, the heat flux increases in FRP during the first cycle. Then, from third cycle is stabilized in a maximum value of 1000 W m−<sup>2</sup> in the compression period and

<sup>−</sup>1000 W m−<sup>2</sup> in the decompression period. The numerical model results using steel as sealing layer are shown for five cycles in Figure 10. −1000 W m−2 in the decompression period. The numerical model results using steel as sealing layer are shown for five cycles in Figure 10. −1000 W m−2 in the decompression period. The numerical model results using steel as sealing layer are shown for five cycles in Figure 10.

**Figure 9.** Numerical model results for 5 charging and discharging cycles considering FRP as sealing layer. (**a**) Temperature of air, FRP and concrete lining; (**b**) Air pressure; (**c**) Surface heat flux of FRP and concrete lining. **Figure 9.** Numerical model results for 5 charging and discharging cycles considering FRP as sealing layer. (**a**) Temperature of air, FRP and concrete lining; (**b**) Air pressure; (**c**) Surface heat flux of FRP and concrete lining. **Figure 9.** Numerical model results for 5 charging and discharging cycles considering FRP as sealing layer. (**a**) Temperature of air, FRP and concrete lining; (**b**) Air pressure; (**c**) Surface heat flux of FRP and concrete lining.

**Figure 10.** Numerical model results for 5 charging and discharging cycles considering steel as sealing layer. (**a**) Temperature of air, steel and concrete lining; (**b**) Air pressure; (**c**) Surface heat flux of steel and concrete lining. **Figure 10.** Numerical model results for 5 charging and discharging cycles considering steel as sealing layer. (**a**) Temperature of air, steel and concrete lining; (**b**) Air pressure; (**c**) Surface heat flux of steel and concrete lining. **Figure 10.** Numerical model results for 5 charging and discharging cycles considering steel as sealing layer. (**a**) Temperature of air, steel and concrete lining; (**b**) Air pressure; (**c**) Surface heat flux of steel and concrete lining.

As in the analytical model, the air temperature fluctuation between air compression and decompression periods is reduced down to 41 K when steel is employed as sealing layer (Figure 10a). In general, the air temperature is much lower than the previous scenario. The surface heat flux is presented in Figure 10c, varying in the steel surface between 2000 W m−2 and −2000 W m−2 for the charge and discharge periods, respectively. Due to the high thermal conductivity (45 W m−1 K−1), the heat flux through the sealing layer is greater, and therefore the temperature in the steel surface is lower. The temperature in the steel coincides with the temperature on the concrete surface, reaching a maximum value of 320 K in the first cycle. As in the analytical model, the air temperature fluctuation between air compression and decompression periods is reduced down to 41 K when steel is employed as sealing layer (Figure 10a). In general, the air temperature is much lower than the previous scenario. The surface heat flux is presented in Figure 10c, varying in the steel surface between 2000 W m−2 and −2000 W m−2 for the charge and discharge periods, respectively. Due to the high thermal conductivity (45 W m−1 K−1), the heat flux through the sealing layer is greater, and therefore the temperature in the steel surface is lower. The temperature in the steel coincides with the temperature on the concrete surface, reaching a maximum value of 320 K in the first cycle. As in the analytical model, the air temperature fluctuation between air compression and decompression periods is reduced down to 41 K when steel is employed as sealing layer (Figure 10a). In general, the air temperature is much lower than the previous scenario. The surface heat flux is presented in Figure 10c, varying in the steel surface between 2000 W m−<sup>2</sup> and <sup>−</sup>2000 W m−<sup>2</sup> for the charge and discharge periods, respectively. Due to the high thermal conductivity (45 W m−<sup>1</sup> K −1 ), the heat flux through the sealing layer is greater, and therefore the temperature in the steel surface is lower. The temperature in the steel coincides with the temperature on the concrete surface, reaching a maximum value of 320 K in the first cycle.

The distribution of the air temperature within de reservoir and the detail of the temperature in the sealing layer are shown in Figure 11 after the decompression period at 5 MPa in the first cycle, using FRP as sealing layer. The distribution of the air temperature within de reservoir and the detail of the temperature in the sealing layer are shown in Figure 11 after the decompression period at 5 MPa in the first cycle, using FRP as sealing layer.

Due to the low thermal conductivity of FRP, the temperature reaches 390 K at the top of the reservoir. However, the temperature in the FRP decreases to 330 K at the bottom. A minimal increase in temperature is observed in the concrete lining. The distribution of the air temperature within de reservoir and the detail of the temperature in the sealing layer are shown in Figure 12 after the decompression period at 5 MPa in the first cycle, using steel as sealing layer. The temperature in the steel reaches 330 K at the top of reservoir. In Due to the low thermal conductivity of FRP, the temperature reaches 390 K at the top of the reservoir. However, the temperature in the FRP decreases to 330 K at the bottom. A minimal increase in temperature is observed in the concrete lining. The distribution of the air temperature within de reservoir and the detail of the temperature in the sealing layer are shown in Figure 12 after the decompression period at 5 MPa in the first cycle, using steel as sealing layer. The temperature in the steel reaches 330 K at the top of reservoir. In this scenario, a temperature increase up to 320 K has been obtained for the concrete lining.

this scenario, a temperature increase up to 320 K has been obtained for the concrete lining. The distribution of the surface heat flux around the compressed air is shown in Figure 13 after the first compression cycle at 8 MPa for both FRP and steel sealing layers. The surface heat flux reaches a maximum value of 7500 W m−2 in the steel surface, while in the FRP surface the maximum value is 3000 W m−2. The distribution of the surface heat flux around the compressed air is shown in Figure 13 after the first compression cycle at 8 MPa for both FRP and steel sealing layers. The surface heat flux reaches a maximum value of 7500 W m−<sup>2</sup> in the steel surface, while in the FRP surface the maximum value is 3000 W m−<sup>2</sup> .

MPa in the contact surface air-sealing layer.

**Figure 12.** Numerical model results in the first cycle at 5 MPa (decompression). Distribution of air temperature within the reservoir and temperature detail in the steel and concrete. **Figure 12.** Numerical model results in the first cycle at 5 MPa (decompression). Distribution of air temperature within the reservoir and temperature detail in the steel and concrete. **Figure 12.** Numerical model results in the first cycle at 5 MPa (decompression). Distribution of air temperature within the reservoir and temperature detail in the steel and concrete.

**Figure 13.** Numerical model results. Distribution of surface heat flux for FRP and steel in the first cycle at a pressure of 8 **Figure 13.** Numerical model results. Distribution of surface heat flux for FRP and steel in the first cycle at a pressure of 8 MPa in the contact surface air-sealing layer. **Figure 13.** Numerical model results. Distribution of surface heat flux for FRP and steel in the first cycle at a pressure of 8 MPa in the contact surface air-sealing layer.

### *3.3. Comparative Analysis 3.3. Comparative Analysis*

*3.3. Comparative Analysis*  A comparative analysis between the analytical and numerical models have been carried out. Air mass flow rates of 50 kg s−1 and −75 kg s−1 were also considered in the analytical model to carry out the comparative study. As indicated previously, although both A comparative analysis between the analytical and numerical models have been carried out. Air mass flow rates of 50 kg s−1 and −75 kg s−1 were also considered in the analytical model to carry out the comparative study. As indicated previously, although both A comparative analysis between the analytical and numerical models have been carried out. Air mass flow rates of 50 kg s−<sup>1</sup> and <sup>−</sup>75 kg s−<sup>1</sup> were also considered in the analytical model to carry out the comparative study. As indicated previously, although

both analytical and numerical models use the same model geometry, the air mass flow rates of the numerical model are higher to reduce the computational time. Figure 14 shows a comparative analysis for five cycles between analytical and CFD results using FRP as sealing layer. A comparison between FRP and steel is shown afterwards in Figure 15 for one cycle. The obtained heat transfer coefficient is also indicated in Figure 15b. In general, good agreements have been obtained between both analytical and numerical simulations. analytical and numerical models use the same model geometry, the air mass flow rates of the numerical model are higher to reduce the computational time. Figure 14 shows a comparative analysis for five cycles between analytical and CFD results using FRP as sealing layer. A comparison between FRP and steel is shown afterwards in Figure 15 for one cycle. The obtained heat transfer coefficient is also indicated in Figure 15b. In general, good agreements have been obtained between both analytical and numerical simulations. the numerical model are higher to reduce the computational time. Figure 14 shows a comparative analysis for five cycles between analytical and CFD results using FRP as sealing layer. A comparison between FRP and steel is shown afterwards in Figure 15 for one cycle. The obtained heat transfer coefficient is also indicated in Figure 15b. In general, good agreements have been obtained between both analytical and numerical simulations.

analytical and numerical models use the same model geometry, the air mass flow rates of

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**Figure 14.** Comparative analysis between analytical and numerical models for 5 charging and discharging cycles considering FRP as sealing layer. (**a**) Temperature of air and FRP; (**b**) Air pressure; (**c**) Surface heat flux of FRP and concrete **Figure 14.** Comparative analysis between analytical and numerical models for 5 charging and discharging cycles considering FRP as sealing layer. (**a**) Temperature of air and FRP; (**b**) Air pressure; (**c**) Surface heat flux of FRP and concrete lining. ering FRP as sealing layer. (**a**) Temperature of air and FRP; (**b**) Air pressure; (**c**) Surface heat flux of FRP and concrete lining.

**Figure 15.** Comparative analysis between analytical and numerical models in the first cycle considering FRP and steel as **Figure 15.** Comparative analysis between analytical and numerical models in the first cycle considering FRP and steel as sealing layers. (**a**) Air temperature; (**b**) Heat transfer coefficient; (**c**) Surface heat flux. **Figure 15.** Comparative analysis between analytical and numerical models in the first cycle considering FRP and steel as sealing layers. (**a**) Air temperature; (**b**) Heat transfer coefficient; (**c**) Surface heat flux.

sealing layers. (**a**) Air temperature; (**b**) Heat transfer coefficient; (**c**) Surface heat flux. To justify the accuracy of the simulations, the results obtained in the analytical model have been compared with experimental and numerical models. Figure 16 shows the comparison of results obtained for air temperature (Figure 16a) and pressure (Figure 16b) during the first cycle with an experimental model developed by Jiang et al. [24]. Dot points, corresponding to the experimental values, are compared with the results obtained in solid blue lines in Figure 16. In addition, Figure 17 shows the comparison of results obtained To justify the accuracy of the simulations, the results obtained in the analytical model have been compared with experimental and numerical models. Figure 16 shows the comparison of results obtained for air temperature (Figure 16a) and pressure (Figure 16b) during the first cycle with an experimental model developed by Jiang et al. [24]. Dot points, corresponding to the experimental values, are compared with the results obtained in solid blue lines in Figure 16. In addition, Figure 17 shows the comparison of results obtained To justify the accuracy of the simulations, the results obtained in the analytical model have been compared with experimental and numerical models. Figure 16 shows the comparison of results obtained for air temperature (Figure 16a) and pressure (Figure 16b) during the first cycle with an experimental model developed by Jiang et al. [24]. Dot points, corresponding to the experimental values, are compared with the results obtained in solid blue lines in Figure 16. In addition, Figure 17 shows the comparison of results obtained for air and wall temperatures (Figure 17a) and air pressure (Figure 17b) during the first cycle with a numerical model conducted by Zhou et al. [25]. The analytical model (solid lines)

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has been employed to reproduce the numerical model considered by Zhou et al. (dashed lines), reporting good accuracy as shown in Figure 17. cycle with a numerical model conducted by Zhou et al. [25]. The analytical model (solid lines) has been employed to reproduce the numerical model considered by Zhou et al. (dashed lines), reporting good accuracy as shown in Figure 17. cycle with a numerical model conducted by Zhou et al. [25]. The analytical model (solid lines) has been employed to reproduce the numerical model considered by Zhou et al. (dashed lines), reporting good accuracy as shown in Figure 17.

for air and wall temperatures (Figure 17a) and air pressure (Figure 17b) during the first

for air and wall temperatures (Figure 17a) and air pressure (Figure 17b) during the first

**Figure 16.** Comparison of results obtained during the first cycle with an experimental model developed by Jiang et al. [24]. (**a**) Air temperature; (**b**) Air pressure. **Figure 16.** Comparison of results obtained during the first cycle with an experimental model developed by Jiang et al. [24]. (**a**) Air temperature; (**b**) Air pressure. **Figure 16.** Comparison of results obtained during the first cycle with an experimental model developed by Jiang et al. [24]. (**a**) Air temperature; (**b**) Air pressure.

**Figure 17.** Comparison of results obtained during the first cycle with a numerical model conducted by Zhou et al. [25]. (**a**) Air and wall temperatures; (**b**) Air pressure. **Figure 17.** Comparison of results obtained during the first cycle with a numerical model conducted by Zhou et al. [25]. (**a**) Air and wall temperatures; (**b**) Air pressure. **Figure 17.** Comparison of results obtained during the first cycle with a numerical model conducted by Zhou et al. [25]. (**a**) Air and wall temperatures; (**b**) Air pressure.

### **4. Conclusions 4. Conclusions 4. Conclusions**

Analytical and numerical models were established to investigate the thermodynamic performance of an underground reservoir located in abandoned mines for A-CAES plants. Analyzing air temperature and pressure fluctuations during the operation time in A-CAES plants is essential to design the underground reservoir volume and the turbomachinery. Typical operating pressures from 5 to 8 MPa were considered in the air charging and discharging periods. A 20 mm thick sealing layer, 35 cm thick concrete lining and 2.5 m thick sandstone rock mass have been considered around the compressed air. In addition, FRP and steel have been employed as sealing layer. Unlike other research works, in which the heat transfer coefficient is considered constant during the operation time, in Analytical and numerical models were established to investigate the thermodynamic performance of an underground reservoir located in abandoned mines for A-CAES plants. Analyzing air temperature and pressure fluctuations during the operation time in A-CAES plants is essential to design the underground reservoir volume and the turbomachinery. Typical operating pressures from 5 to 8 MPa were considered in the air charging and discharging periods. A 20 mm thick sealing layer, 35 cm thick concrete lining and 2.5 m thick sandstone rock mass have been considered around the compressed air. In addition, FRP and steel have been employed as sealing layer. Unlike other research works, in which the heat transfer coefficient is considered constant during the operation time, in Analytical and numerical models were established to investigate the thermodynamic performance of an underground reservoir located in abandoned mines for A-CAES plants. Analyzing air temperature and pressure fluctuations during the operation time in A-CAES plants is essential to design the underground reservoir volume and the turbomachinery. Typical operating pressures from 5 to 8 MPa were considered in the air charging and discharging periods. A 20 mm thick sealing layer, 35 cm thick concrete lining and 2.5 m thick sandstone rock mass have been considered around the compressed air. In addition, FRP and steel have been employed as sealing layer. Unlike other research works, in which the heat transfer coefficient is considered constant during the operation time, in the present investigation a correlation based on both unsteady Reynolds and Rayleigh numbers is employed for the heat transfer coefficient.

The results obtained show greater variations in air temperature between the air compression and decompression when FRP is used as sealing layer. Thus, significant temperature variations in the sealing layer and only a 15 cm thickness of the concrete lining is affected by a temperature rise during operation when steel is employed as sealing layer. The volume of concrete affected is reduced when FRP is used as sealing layer around the fluid. Regarding the sandstone rock mass, no temperature fluctuation was observed in the simulations. In addition, the heat flux increases and the air temperature within the reservoir is lower when steel is employed as sealing layer.

Finally, the thermal energy balance in the 30th cycle through the sealing layer considering air mass flow rates of 0.22 and <sup>−</sup>0.45 kg s−<sup>1</sup> reached 25.27 and 20.48 kWh for FRP and steel, respectively. In general, good agreements were obtained between analytical and numerical simulations. Unlike a 1D analytical model, in the 3D CFD numerical model it is possible to analyze the distribution of the thermodynamic responses in the entire domain, assuming a significant advantage to design the reservoir.

**Author Contributions:** Conceptualization, L.Á.d.P., J.M., A.B.-S., and J.M.F.-O.; Methodology, L.Á.d.P., J.M., and J.M.F.-O.; Software, L.Á.d.P., J.M., M.G., and J.M.F.-O.; Investigation, L.Á.d.P., J.M., M.G., A.B.-S., and J.M.F.-O.; Validation, J.M., M.G., and J.F-O; Writing—original draft preparation, L.Á.d.P., J.M., and J.M.F.-O.; Writing—review and editing, J.M., M.G., A.B.-S., and J.M.F.-O.; Visualization, J.M.F.-O. and J.L.; Supervision, A.B.-S., J.L., and J.M.F.-O.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** N/A.

**Informed Consent Statement:** N/A.

**Conflicts of Interest:** The authors declare no conflict of interest.
