# Heat Storage and Release Performance of Cascade Phase Change Units for Solar Heating in a Severe Cold Region of China

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## Abstract

**:**

## 1. Introduction

^{2}per year. In the winter, however, there is a long heating period and significant heating demand. As a result, Inner Mongolia appears to be a promising candidate for solar heating development. However, there have been few reports on cascade phase change heat storage technology being used for heating in Inner Mongolia. In this paper, a numerical method is used to investigate the heat storage and release performances of cascade heat storage units with various PCM schemes, as well as to find the best PCM scheme for cascade heat storage in Inner Mongolia’s harsh cold region.

## 2. Modelling

#### 2.1. Solar Irradiation Data

^{−1}. $t$ is the HTF inlet temperature, K. Considering that the temperature of the heating water supply is generally 348 K, this paper sets the inlet temperature of the HTF to 348 K. To realise the variation of hourly solar irradiation, the flow rate of HTF therefore correspondingly varies, as shown in Figure 3.

#### 2.2. Materials Combination Schemes

- (1)
- The phase change temperature of the selected materials should be lower than the inlet temperature of the HTF. The phase change temperature of the material in the first stage unit should be higher than that in the second stage unit;
- (2)
- A gradient is formed by the phase change temperature difference of the specified material combinations;
- (3)
- The chosen materials should be common PCM in solar thermal utilisation systems and meet the most basic principles of phase change material screening, such as meeting thermal storage parameter requirements, good economy, environmental protection, and so on.

#### 2.3. Physical and Mathematical Model

- (1)
- The shell and tube’s wall thickness is ignored, and the shell wall is adiabatic;
- (2)
- The PCMs are homogeneous and uniformly distributed in the storage unit;
- (3)
- The thermal properties of PCMs are constant.

- (1)
- Mathematical model of HTF and model assumptionsThe following assumptions give unsteady three-dimensional flow models of heat transfer during the melting process of PCM in the cylindrical exchanger enclosure:
- The HTF flow and the liquid PCM are in the laminar pattern;
- The average temperature of inlet corresponds to the HTF inlet value;
- Term of viscous dissipation has been neglected, thus the viscous incompressible flow and the temperature distribution in the annulus are described by Navier-Stokes and thermal energy equations, respectively;
- The density is calculated using the Boussinesq approximation;
- During the transition from the solid to the liquid state, density remains constant;
- Since the term of viscous dissipation has been ignored, Navier–Stokes is used to explain the viscous incompressible flow and thermal energy equations is used to explain temperature distribution in the annulus.

_{f}is the density of the HTF, kg·m

^{−3}; c

_{f}is the specific heat of the HTF, J·(kg·K)

^{−1}; T

_{f}is the temperature of the HTF, K; v

_{x}and v

_{y}are the flow velocity of HTF in x and y direction, m/s; and k

_{f}is the thermal conductivity of the HTF, W·(m·K)

^{−1}.

^{−1}.

- (2)
- Mathematical model of phase change material

^{−3}; $\lambda $ is the thermal conductivity of the phase change material, W·(m·K)

^{−1}; ${T}_{p}$, ${T}_{r}$ are the temperature and reference temperature of the phase change material, respectively, K; $H,h,{h}_{l},{h}_{s},{h}_{r}$ are the enthalpy of the phase change material, respectively, sensible heat specific enthalpy, liquid specific enthalpy, solid specific enthalpy and reference enthalpy, kJ·kg

^{−1}; ${C}_{p}$ is the constant pressure specific heat capacity of the phase change material, kJ·(kg·K)

^{−1}; $\beta $ is the liquid phase ratio; $L$ is the latent heat of the phase change material, kJ·kg

^{−1}.

#### 2.4. Boundary and Initial Conditions

- (1)
- Boundary conditions

_{inlet}is the inlet temperature of the HTF, K.

^{−1}; is the inlet flow velocity of the HTF, m·s

^{−1}.

- (2)
- Initial conditions

#### 2.5. Numerical Simulation Method

## 3. Results and Analysis

#### 3.1. Model Validation

#### 3.1.1. Independence Verification

#### 3.1.2. Comparison and Verification with Experimental Results

#### 3.2. Heat Storage and Release Performance of Cascade Units

^{2}, 781.5 W/m

^{2}, and 913.1 W/m

^{2}, respectively. Figure 9b depicts the average heat fluxes in the heat release process. They must be constantly dropping when discharging heat. They do, however, drop faster at first due to the release of latent heat. In the heat release process of S1–S3, the average heat flux is 661.1 W/m

^{2}, 975.6 W/m

^{2}, and 807.2 W/m

^{2}, respectively.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Distribution of solar resources in China [21].

**Figure 2.**The monthly variation of solar irradiation in Baotou of Inner Mongolia [22].

**Figure 4.**Physical model and 2D simplified model of the cascaded phase change heat storage: (

**a**) Physical model; (

**b**) 2D model.

**Figure 5.**Independence analysis of grid number and time step: (

**a**) with different grid numbers; (

**b**) with different time steps.

**Figure 7.**Heat storage behaviours in cascade units with three combination schemes of PCMs: (

**a**) S1: stearic acid + lauric acid; (

**b**) S2: paraffin (C28) + paraffin (C16); (

**c**) S3: palmitic acid + polyethylene glycol.

**Figure 8.**Liquid fraction in the cascade units of S1–S3: (

**a**) heat storage process; (

**b**) heat release process.

**Figure 9.**Average heat flux in the cascade units of S1–S3: (

**a**) heat storage process; (

**b**) heat release process.

Scheme 1 | S1 | S2 | S3 | |||
---|---|---|---|---|---|---|

Material | Stearic Acid | Lauric Acid | Paraffin (C28) | Paraffin (C16) | Palmitic Acid | Polyethyle-ne Glycol |

Density/kg·m^{−3} | 913 | 867 | 780 | 776 | 989 | 1200 |

Specific Heat/J·(kg·K)^{−1} | 2175 | 2300 | 2120 | 2500 | 2480 | 2300 |

Thermal Conductivity/W·(m·K)^{−1} | 0.216 | 0.147 | 0.151 | 0.118 | 0.160 | 0.190 |

Latent Heat/kJ·kg^{−1} | 201.8 | 173.8 | 253.0 | 141.9 | 222.0 | 181.4 |

Phase Change Temperature/K | 341 | 318 | 334 | 320 | 332 | 324 |

Time | 8:00 | 9:00 | 10:00 | 11:00 | 12:00 | 13:00 |

Total Radiation Intensity on Horizontal Plane/W·m^{−2} | 21.6 | 22.2 | 147.2 | 283.3 | 369.4 | 419.4 |

Inlet velocity/m s^{−1} | 0.023 | 0.023 | 0.154 | 0.297 | 0.387 | 0.440 |

Time | 14:00 | 15:00 | 16:00 | 17:00 | 18:00 | -- |

Total Radiation Intensity on Horizontal Plane/W·m^{−2} | 419.4 | 380.6 | 297.2 | 158.3 | 22.2 | -- |

Inlet velocity/m s^{−1} | 0.440 | 0.399 | 0.316 | 0.166 | 0.023 | -- |

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**MDPI and ACS Style**

Zhang, L.; Liu, Z.; Jin, G.; Cuce, E.; Jin, J.; Guo, S.
Heat Storage and Release Performance of Cascade Phase Change Units for Solar Heating in a Severe Cold Region of China. *Energies* **2022**, *15*, 7421.
https://doi.org/10.3390/en15197421

**AMA Style**

Zhang L, Liu Z, Jin G, Cuce E, Jin J, Guo S.
Heat Storage and Release Performance of Cascade Phase Change Units for Solar Heating in a Severe Cold Region of China. *Energies*. 2022; 15(19):7421.
https://doi.org/10.3390/en15197421

**Chicago/Turabian Style**

Zhang, Li, Zhihui Liu, Guang Jin, Erdem Cuce, Jing Jin, and Shaopeng Guo.
2022. "Heat Storage and Release Performance of Cascade Phase Change Units for Solar Heating in a Severe Cold Region of China" *Energies* 15, no. 19: 7421.
https://doi.org/10.3390/en15197421