# A Fast-Reduced Model for an Innovative Latent Thermal Energy Storage for Direct Integration in Heat Pumps

^{*}

## Abstract

**:**

## Featured Application

**the latent storage unit described in this paper is suitable for application in heat pumps and chillers; either used for space heating/cooling or domestic hot water.**

## Abstract

## 1. Introduction

## 2. Latent Thermal Storage Design

## 3. Model Description

- -
- the thermo-physical properties of the refrigerant, the HTF, and the PCM are independent of temperature; however, the properties in the solid phase are different from the properties in the liquid phase;
- -
- HTF is incompressible;
- -
- the temperature of the refrigerant, HTF, and the metal walls varies only in the flow direction (x-direction) along their lengths, which are divided into n nodes;
- -
- radiative heat transfer is not considered;
- -
- the heat loss to the surroundings is negligible;
- -

^{−1}) is the mass flow rate, h (J kg

^{−1}) is the specific enthalpy, and $\dot{Q}$ (W) is the heat transfer term.

_{ref}(W m

^{−2}K

^{−1}) is the heat transfer coefficient for the refrigerant cell, A (m

^{2}) is the heat transfer area for each cell, k (W m

^{−1}K

^{−1}) is the thermal conductivity of the wall material, D

_{h}(m) is the hydraulic diameter of the channel, Re is the Reynolds number, Pr is the Prandtl number, and Nu is the Nusselt number. The friction factor j is calculated as:

^{−1}K

^{−1}) is the specific heat capacity of the heat transfer fluid. Similarly to the case of the refrigerant cell, a constant pressure drop was considered and the heat transfer was calculated as:

_{HTF}was calculated according to a Nu correlation, as in Equation (6), with:

_{p,s}(J kg

^{−1}K

^{−1}) is the specific heat of the solid, c

_{p,l}(J kg

^{−1}K

^{−1}) is the specific heat of the liquid, L (J kg

^{−1}) is the latent heat of melting, T

_{1}(°C) is the onset temperature for melting, T

_{2}(°C) is the offset temperature for the melting process, and γ is the liquid fraction, calculated as:

#### Initial and Boundary Conditions

## 4. Model Validation

- -
- charge mode: the refrigerant of the heat pump is used to solidify the PCM, there is no flow in the HTF circuit;
- -
- discharge mode: the heat pump is off, the HTF is circulated, and the PCM is melted by subtracting the latent heat from the HTF, which is cooled down and delivered to the user;
- -
- parallel charging/discharging mode: the PCM is charged and discharged at the same time. Hence, the heat pump is on and at the same time the HTF circuit is connected to the load.

## 5. Optimization through Parametric Analysis under Variable Input Conditions

## 6. Comparison with the State-of- the-Art

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Schematic layout of the lumped model of the three-fluids heat exchanger with latent thermal storage.

**Figure 3.**(

**a**) heat pump and latent heat storage system installed in the lab during the testing campaign. (

**b**) schematic representation of the three-fluid heat exchanger.

**Figure 4.**Model validation for the different operating modes. (

**a**) charge; (

**b**) discharge; (

**c**) parallel operation.

**Figure 5.**Temperatures in the PCM and refrigerant circuit during charging for different numbers of stacked PCM layers.

**Figure 7.**Average PCM temperature for different HTF flow rates during discharge for four layers and an HTF inlet at 12 °C.

**Figure 9.**Average PCM temperature for different numbers of stacked PCM layers during discharge. HTF flow rate 0.5 kg/s, HTF inlet 12 °C.

PCM | Refrigerant | Coolant | |
---|---|---|---|

volume (dm^{3}) | 52.5 | 2.2 | 5.4 |

hydraulic diameter (m) | 0.0035 | 0.0022 | 0.0024 |

cross sectional area (m^{2}) | 0.0534 | 0.0021 | 0.0054 |

heat transfer area (m^{2}) | 57.7 | 3.94 | 8.83 |

number of passages | 44 | 10 | 22 |

core length × width × depth (m) | 1 × 0.60 × 0.16 | ||

empty weight (kg) (Al) | 110 |

Phase change temperature range (°C) | 2–4 |

Density (liquid) (kg m^{−3}) | 770 |

Density (solid) (kg m^{−3}) | 880 |

Specific heat (kJ kg^{−1 }K^{−1}) | 2 |

Melting latent heat (kJ kg^{−1}) | 175 |

Volume expansion (%) | 12.5 |

Thermal conductivity (W m^{−1} K^{—1}) | 0.2 |

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**MDPI and ACS Style**

Palomba, V.; Frazzica, A. A Fast-Reduced Model for an Innovative Latent Thermal Energy Storage for Direct Integration in Heat Pumps. *Appl. Sci.* **2021**, *11*, 8972.
https://doi.org/10.3390/app11198972

**AMA Style**

Palomba V, Frazzica A. A Fast-Reduced Model for an Innovative Latent Thermal Energy Storage for Direct Integration in Heat Pumps. *Applied Sciences*. 2021; 11(19):8972.
https://doi.org/10.3390/app11198972

**Chicago/Turabian Style**

Palomba, Valeria, and Andrea Frazzica. 2021. "A Fast-Reduced Model for an Innovative Latent Thermal Energy Storage for Direct Integration in Heat Pumps" *Applied Sciences* 11, no. 19: 8972.
https://doi.org/10.3390/app11198972