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Developing a concentrated solar power (CSP) technology is one of the most effective methods to solve energy shortage and environmental pollution all over the world. Thermal energy storage (TES) system coupling with phase change materials (PCM) is one of the most significant methods to mitigate the intermittence of solar energy. In this paper, firstly, a 2D physical and mathematical model of a novel truncated cone shell-and-tube TES tank has been proposed based on enthalpy method. Secondly, the performance during the charging/discharging process of the truncated cone tank has been compared with the traditional cylindrical tank. Finally, the effects of inlet conditions of heat transfer fluid (HTF), and thickness of tube on the charging/discharging process, stored/released energy capacity; energy storage/release rate and heat storage efficiency have been investigated. The results show that the performance of truncated cone tank is better, and the charging/discharging time reduces 32.08% and 21.59%, respectively, compared with the cylindrical tank. The effect of wall thickness on the truncated cone TES tank can be ignored. And the inlet temperature and velocity of HTF have the significant influence on the charging/discharging performance of TES tank. And the maximum heat storage efficiency of the truncated cone TES tank can reach 93%. However, some appropriate methods should be taken for improving the thermal energy utilization rate of HTF in the future. This research will provide insights and significant reference towards geometric design and operating conditions in TES system.

The sustainable development of low-carbon economy has become the inevitable choice to realize the win-win situation of economic development and environmental protection around the world. To alleviate the associated environmental problems, reduction of the use of fossil fuels by developing more cost-effective renewable energy technologies becomes increasingly significant. Among various types of renewable energy sources, solar energy takes a large proportion [

The thermal energy can be stored in different forms, such as sensible heat, latent heat, thermochemical, or a combination of these [

Avci, Dadollahi, Tao et al. [

Many researchers found that the natural convection had a great influence on the charging process in TES system. Seddegh et al. [

In general, the molten salt is one of the most promising PCM used in CSP plant; however, the main shortcomings of them are low thermal conductivity, and a lot of works have been studied to overcome this issue and to enhance the heat transfer rate of TES tank in CSP system. Parsazadeh, Yang et al. [

In addition, the packed bed LHTES system with spherical capsules has been studied in recent years for enhancing the heat transfer rate in CSP plants. Bellan et al. [

It is clear from the literature reviewed above that the natural convection accelerated the thermal energy transport in the upper region and weakened the heat transfer in the bottom region during the charging process [

The physical model is shown in Figure _{3} and 46% KNO_{3}. The length (_{in}) is 20 mm, and the material of the inner tube is steel. In addition, the container external surface is treated as an adiabatic boundary with the radius of the top and bottom as 60 mm (

Schematic diagram of a truncated cone shell-and-tube TES model.

Thermophysical properties of PCM.

PCM (NaNO_{3}/KNO_{3}) | |
---|---|

^{3}) |
2040(s), 1950(l) |

0.5(s), 0.3(l) | |

_{p} |
1420(s), 1500(l) |

_{m} (K) |
497 |

Δ |
105.8 |

In order to simplify the physical and mathematical model, the following assumptions are adopted [

The HTF flow entering the tube was laminar and simultaneously developing

The thermal conduction and viscous dissipation in the axial direction is neglected for PCM

The thermal properties of PCM in both solid and liquid phase do not change with the temperature

Adiabatic wall was assumed

The models are simplified to 2D axisymmetric

The enthalpy method is adopted to deal with the moving boundary problem in a solid-liquid phase change process. The corresponding governing equations are shown as follows [

For the HTF,

where _{a}_{m} is the melting temperature.

For the PCM,

where

The energy equation (

To calculate the stored energy of the PCM, the stored energy capacity of the TES system is given by [

Meanwhile, the released energy capacity of the TES system is given by

where

The finite volume solver ANSYS Fluent 16.0 is used to discrete the governing equations. Due to the coupled energy transfer process between the HTF and PCM, the energy equation both for HTF and for PCM is integrated solving in the whole computational domain. Accordingly, to calculate the Reynolds number of HTF (_{max} = 1654 < 2300, _{max} = 1.2 m/s), the laminar is selected as the flow model. And the coupled fluid dynamic and energy equations are solved by SIMPLEC algorithm. The second order upwind method is applied as the spatial discretization method for pressure, momentum, and energy. In order to ensure the accuracy of the calculation, the residual of the energy equation is less than 10^{−6}.

In order to validate the reliability of the physical model, the setting, calculation, and simulation results based on Fluent 16.0 software, the comparisons between the present numerical predictions, and the literature results which is the theoretical analysis by C language in MATLAB software [

Comparison between the present result and the result of literature Ref. [

The mesh of this model consists of the quadrilateral cells. To ensure mesh independent result, mesh independence test was conducted by systematically increasing the number of cell and the results as shown in Table

The results of mesh independent and time step independent test.

Total mesh | Total melting time (s) | Time step (s) | Total melting time (s) |
---|---|---|---|

12,400 | 6926 | 0.05 | 6939 |

24,080 | 6936 | 0.1 | 6941 |

46,224 | 6942 | 0.5 | 6942 |

92,017 | 6953 | 1 | 6953 |

179,177 | 6961 | 2 | 6979 |

In order to compare the TES performance between traditional cylindrical and truncated cone TES tanks, the inlet temperature and velocity of HTF are 797 K and 1.2 m/s, respectively.

The contour of the PCM liquid fraction and temperature flied in the cylindrical and truncated cone tank during the melting process are shown in Figure

Contour of the PCM temperature (left) and liquid fraction (right) in the (a) cylindrical and (b) truncated cone model during the charging process.

According to the melting time and liquid fraction in Figure

Figure

The simulated liquid PCM velocity field with cylindrical (a) and truncated cone (b) TES unit during the melting process.

In order to study the effect of thickness of tube on the TES performance during the charging process, the inlet temperature and velocity of HTF are 797 K and 1.2 m/s, respectively, and the initial temperature of PCM and tube is 487 K. Meanwhile, the radius for the inner tube (_{in}) is always 20 mm.

Figure

Effects of thickness of tube on liquid fraction.

The initial temperature of PCM with 487 K, and the inlet velocity of HTF with 1.2 m/s is chose to study the effects of inlet temperature of HTF on the melting process. And the inlet temperature of the HTF is six temperature gradients, including 597 K, 647 K, 697 K, 747 k, 797 K, and 847 K.

The effects of inlet temperature of HTF on melting process are shown in Figure

Effects of inlet temperature of HTF on liquid fraction.

The effects of initial inlet temperature of HTF on the outlet temperature of HTF are presented in Figure

Effects of inlet temperature of HTF on outlet temperature of HTF.

Figure

Effects of inlet temperature of HTF on the total stored energy capacity and energy storage rate.

where the

The histogram indicates that the total stored energy capacity and initial inlet temperature of HTF has notable positive correlation, and the initial inlet temperature of HTF increasing from 597 K to 847 K, the total stored energy capacity will increase from 506.55 kJ to 753.21 kJ, which increases about 48.69%. However, the increment of stored energy capacity decreases with the increase of inlet temperature. Meanwhile, the curve shows that the total energy storage rate increases significantly with the increase of inlet temperature, and the inlet temperature increasing from 597 K to 847 K, the energy storage rate will increase from 33.52 J/s to 120.28 J/s, which increases about four times.

It is shown that the inlet temperature of HTF has the significant influence on the TES system for a truncated cone shell-and-tube tank. The increase of inlet temperature can not only shorten the total charging time but also increase the total stored energy capacity and energy storage rate. Therefore, it is very important to select the proper inlet temperature of HTF according to the actual operating conditions to improve the storage efficiency of the TES system in the CSP plant.

In order to study the effect of the inlet velocity of HTF on the charging process of the TES tank, the initial temperature of the PCM and HTF is 487 K and 797 K, respectively. And the inlet velocity of the HTF is six temperature gradients, including 0.2 m/s, 0.4 m/s, 0.6 m/s, 0.8 m/s, 1.0 m/s, and 1.2 m/s.

Figure

Effects of inlet velocity of HTF on liquid fraction.

The effect of inlet velocity on outlet temperature of HTF is presented in Figure

Effects of inlet velocity of HTF on outlet temperature of HTF.

Figure

Effects of inlet velocity of HTF on the total stored energy capacity and energy storage rate.

In order to compare the thermal energy release performance between traditional cylindrical and truncated cone TES tanks, the inlet temperature and velocity of HTF are 377 K and 1.2 m/s, respectively, and the initial temperature of PCM and steel is 507 K.

The contour of the PCM liquid fraction and temperature field in the cylindrical and truncated cone model during the discharging process are shown in Figure

Contour of the PCM temperature (left) and liquid fraction (right) in the (a) cylindrical and (b) truncated cone model during the solidification process.

From the total discharging process, the truncated cone tank can solidify slightly faster than the cylindrical tank at the same operating condition during the discharging process. The liquid fraction difference of them is only 0.64% at 3600 s, which shows the thermal energy release rate is almost parallel at the beginning. After that, the liquid fraction of a truncated cone tank is decreasing faster than a cylindrical tank. It can be found that the discharging rate of a truncated cone unit is faster than a cylindrical tank, and the discharging time reduces about 21.59% compared to the cylindrical model. This indicates that the thermal energy release performance of truncated cone TES tank is slightly better than the traditional cylindrical tank for CSP plant under the same operating condition.

And Figure

The simulated liquid PCM velocity field with truncated cone TES unit during discharging process.

In order to investigate the effects of initial inlet temperature of HTF on discharging process, the inlet velocity of HTF is 1.2 m/s, the initial temperature of PCM is 507 K, and the inlet temperature of the HTF is six temperature gradients, including 377 K, 387 K, 397 K, 407 K, 417 K, and 427 K. The thickness of tube is neglected due to its slight effect on thermal energy storage performance.

Figure

Effects of initial inlet temperature of HTF on liquid fraction.

When the inlet temperature of the HTF is 377 K, it takes 12,920 s for the cylindrical tank to complete the discharging process and only 10,130 s for the truncated cone tank, which reduces 21.59%. For the truncated cone TES tank, the discharging time increases with the increasing inlet temperature. When the inlet temperature of HTF increase from 377 K to 427 K, the discharging time will increase from 10,130 s to 15,380 s, which increases about 51.82%. It can be seen that the inlet temperature of HTF has great influence on the discharging process of the TES tank in the CSP system, and the thermal energy release performance of the truncated cone TES tank is better than the cylindrical tank.

Figure

Effects of inlet temperature of HTF on the total released energy capacity and energy release rate.

where the

When the inlet temperature is 377 K, it can be seen that the total released energy capacity of the cylindrical tank (537.91 kJ) is much larger than that of the truncated cone TES tank (469.53 kJ). However, the energy release rate of the truncated cone tank is greater than that of the cylindrical tank, which increases 9.87% compared to the cylindrical tank. It can be found that the heat energy utilization rate from the PCM of the truncated cone TES tank is higher than that of the cylindrical tank.

For truncated cone TES tank, the total released energy capacity decreases with the increase of the inlet temperature of HTF in Figure

In order to investigate the influence of inlet velocity of HTF on the discharging process of a truncated cone TES tank, according to the results of the inlet temperature for HTF on the heat discharging process, the inlet temperature of 397 K is selected to the study. The initial temperature of PCM is 507 K, and the inlet velocity of the HTF is six temperature gradients, including 0.2 m/s, 0.4 m/s, 0.6 m/s, 0.8 m/s, 1.0 m/s, and 1.2 m/s.

The effect of inlet velocity of HTF on liquid fraction and discharging process is shown in Figure

Effects of inlet velocity of HTF on liquid fraction.

Figure

Effects of inlet velocity of HTF on the total released energy capacity and energy release rate.

In order to analyze the heat storage efficiency of the truncated cone TES tank, firstly, the heat storage efficiency is calculated by following equation.

where the

Then, according to the above results, the stored and released energy capacity in a truncated cone TES tank has been calculated. In this process, the influence of the inlet temperature and velocity of the HTF on the heat storage efficiency of the truncated cone TES tank can be compared and analyzed.

Figure

Effect of inlet temperature of HTF on heat storage efficiency.

From the diagram, it can be found that the heat storage efficiency decreases with the increase of the inlet temperature of HTF in the charging process. And the maximum heat storage efficiency of the TES tank can reach 93% and the minimum is about 58%, which indicated that the inlet temperature of the HTF has a great influence on the heat storage efficiency of the TES system in CSP plant.

When the inlet temperature of the HTF is constant during the charging process, the higher the inlet temperature of the HTF during the discharging process is, the lower the heat storage efficiency of the TES tank is. Meanwhile, when the inlet temperature of the HTF is constant during the discharging process, the higher the inlet temperature of the HTF during the charging process is, the lower the heat storage efficiency of the TES tank is. Compared with the discharging process, the inlet temperature of HTF in the charging process has the more significant effect on the heat storage efficiency. As a whole, the lower the inlet temperature of the HTF is, the higher the thermal energy utilization efficiency is, that is, the higher the heat storage efficiency of the TES tank is.

The influence of the inlet velocity of the HTF on the storage efficiency of the TES tank is shown in Figure

Effect of inlet velocity of HTF on heat storage efficiency.

It can be found that the heat storage efficiency decreases with the increase of the inlet velocity of HTF in the charging process. In the calculation range, the range of heat storage efficiency of a truncated cone TES tank is 80% ~ 65%, and the effect of velocity on the heat storage efficiency of TES tank is slighter than the influence of the inlet temperature of HTF on it.

When the inlet velocity of the HTF is constant during the charging process, the higher the inlet velocity of the HTF during the discharging process is, the higher the heat storage efficiency of the heat storage tank is. However, when the inlet velocity of the HTF is constant during the discharging process, the higher the inlet velocity of the HTF during the charging process is, the lower the heat storage efficiency of the TES tank is. And compared with the discharging process, the inlet velocity of HTF in the charging process has also the more significant effect on the heat storage efficiency. As a whole, the lower the inlet velocity of the HTF is during the charging process and the higher the inlet velocity of HTF is during the discharging process, the higher the thermal energy utilization efficiency is, that is, the higher the heat storage efficiency of the TES tank is in the CSP system. It can be concluded that the inlet condition (temperature and velocity) of HTF in the charging process has the more obvious impact on the heat storage efficiency of TES system in CSP technology.

Developing CSP technology is one of the most effective ways to solve energy shortage all over the world. And the TES system is the key to improve the performance of CSP system. In this paper, a two dimensional physical and mathematical model for a novel truncated cone shell-and-tube TES tank has been established based on enthalpy method. Then, the charging/discharging process of the cylindrical tank and the novel tank has been compared. Meanwhile, the effects of inlet conditions of HTF, and thickness of tube on the charging/discharging process, and heat storage efficiency have been investigated. The following conclusions can be drawn.

Comparing the performance between cylindrical and truncated cone TES tank, it can be seen that the performance of truncated cone tank is better under the same operating condition, which reduces the charging/discharging time about 32.08% and 21.59%, respectively. And the velocity field of liquid PCM during the charging/discharging process shows clockwise/anticlockwise convection circulation

The effect of thickness of tube on the charging process of PCM is slight, so the effect of wall thickness on the TES system can be ignored

During the charging process, with the increase of the inlet temperature of HTF, the charging time reduces about 58.56%, and the stored energy capacity and energy storage rate increase about 48.69% and four times. With the increasing inlet velocity, the melting time reduces about 38.48%, and the stored energy capacity and energy storage rate increase about 17.08% and double. However, the thermal energy utilization rate of HTF is very low

During the discharging process, with the increase of inlet temperature of HTF, the discharging time increases 51.82%, and the released energy capacity and energy release rate reduce about 6.49% and 38.34%, respectively. With the increasing velocity, the discharging time reduces about 36.95%, and the released energy capacity and energy release rate will increase about 3.27% and 65.17%, respectively

For the heat storage efficiency, the maximum heat storage efficiency of the truncated cone TES tank can reach 93% in the range of the simulation

Therefore, the initial operating condition of HTF is the significant factor in the practical applications of the CSP system. Particularly, some appropriate methods should be studied for reducing the loss of energy and improving the thermal energy utilization rate of HTF in the next study. And this researcher will provide the significant reference towards geometric design and operating conditions by considering the effect of natural convection on the TES system in the CSP plants

Specific heat, J/(kg·K)

Liquid fraction

Heat transfer coefficient, W/m^{2}·K

Velocity, m/s

_{max}:

The maximum velocity, m/s

_{r}

Prandtl number

_{e}

Reynolds number

_{max}:

The maximum Reynolds number

Total stored energy capacity, J

Total released energy capacity, J

Charging/discharging time, s

Total energy storage rate, J/s

Total energy release rate, J/s

The mass of the PCM, kg

_{in}:

The radius of the inner tube, mm

The radius of the shell side or the top of the truncated cone model, mm

The radius of the bottom of the truncated cone model, mm

The thickness of the tube, mm

The length of the PCM unit, mm

Temperature, K

_{m}

Melting point temperature of PCM, K

_{a}

The average temperature of PCM, K

_{0}:

The initial temperature, K

Concentrated solar power

Phase change material

Thermal energy storage

Heat transfer fluid

Latent heat thermal energy storage

Density, kg/m^{3}

Thermal conductivity, W/m·K

_{p}

Thermal conductivity of PCM in

Thermal conductivity of PCM in

Enthalpy, kJ/kg

Heat storage efficiency

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by the National Natural Science Foundation of China (Nos. 51876147 and 51406033). Besides, a very special acknowledgement is made to the editors and referees who made important comments to improve this paper.