# Experimental Validation and Numerical Simulation of a Hybrid Sensible-Latent Thermal Energy Storage for Hot Water Provision on Ships

^{1}

^{2}

^{3}

^{4}

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## Abstract

**:**

## 1. Introduction

^{3}of a hydrate salt mixture to a 50 dm

^{3}tank.

## 2. Thermal Energy Storage Design

#### 2.1. Identification of the Hot Water Demand On-Board

#### 2.2. PCM Selection

^{3}can be achieved, which can still be considered attractive for the given application.

#### 2.3. Hybrid Sensible/Latent TES Design

^{3}cylindrical vertical tank was designed in order to maximize the inclusion of PCM macro-capsules. The tank was equipped with two internal flanges at the top and at the bottom to guarantee the proper positioning of the PCM tubes. Furthermore, in order to properly distribute the HTF inside the tank, the bottoming flange was designed including evenly distributed holes, from which the HTF passed during the charging phase, thus achieving a homogeneous temperature distribution inside the tank.

_{0}–T

_{5}) were inserted inside the tank, in contact with the water, at three different heights, as represented in Figure 4. Each pair of inserted thermocouples at each height was installed out of phase of 90°, to evaluate not only the longitudinal but also the transversal temperature distribution. Two adhesive thermocouples were attached over the tank surface at the bottom (T

_{6}) and at the top (T

_{7}). Finally, at the inlet and outlet of the charging and discharging circuits, Pt 100 platinum resistances were installed, which were used to analyze the performance of the storage during both charge and discharge.

## 3. Experimental Characterization

#### 3.1. Experimental Setup

- -
- The charging circuit, which exploits a 24-kW electric heater connected to an intermediate vessel. This vessel is heated up to the target charging temperature and then it is connected to the TES under testing, in order to provide a quite stable charging temperature. Since the tank size is of the same order of magnitude of the designed hybrid tank, a certain fluctuation is achieved during the charging phase, but smoothed compared to the possible direct connection to the HEX 1.
- -
- The discharging circuit, which exploits either a chiller or tap water to discharge the TES under testing. In this case, an intermediate plate HEX (HEX 2 in Figure 5) is used to simulate the load demand and a three-way tempering valve is installed to set the desired temperature to be delivered to the user.

#### 3.2. Testing Conditions

## 4. Experimental Results

#### 4.1. Charging Test

_{0}, T

_{2}and T

_{4}according to Figure 4), along with one of the temperatures measured over the surface of the tank and the environmental temperature.

#### 4.2. Discharging Test

#### 4.3. Performance Indicators

_{USER}(kJ), where t

_{disch}(s), is the discharging time for each step; ṁ (kg/s), is the water flow rate on the user side; cp (kJ/kgK), is the water-specific heat; T

_{USER}and T

_{TAP}(°C) are the water temperature delivered to the user and the tap water temperature, respectively.

_{USER}, which varies due to the inertia of the mixing valve, used to meet the expected 45 °C.

_{w}[kg/m

^{3}], represents the water density, considered with a nominal value of 1000 kg/m

^{3}in the calculations. T

_{USER_NOM}and T

_{TAP_NOM}(°C) are the nominal constant temperatures delivered to the user and coming from the network, respectively. They were assumed, for the calculations, to be equal to 45 °C and 15 °C, respectively.

_{loss}(W/m

^{2}K) is the convective heat transfer coefficient, considered equal to 3.76 W/m

^{2}K, for a cylinder subjected to natural convection [32]; A

_{tank}(m

^{2}) is the external surface area of the tank; T

_{tank}and T

_{env}(°C) are the surface tank temperature and environmental temperature, respectively.

_{TH}(kJ]), calculated by integrating the sensible and latent contribution, according to the operating temperature range and the integral storage curve of the PCM derived from the DSC analysis performed.

#### 4.4. Performance Indicators: Results

^{3}of hot water even if the tank itself has a volume of 100 dm

^{3}, demonstrating the possibility of strongly reducing the size of the tanks.

## 5. Numerical Simulation

#### 5.1. CFD Model

#### 5.1.1. Enthalpy Porosity Model

_{mush}is a constant fixed to 10

^{−6}following [37] and $\epsilon $ is a small number to avoid division by zero. The source term is zero when the liquid fraction is equal to 1 and assumes a high value when the liquid fraction is 0 and the material is all solid, so the velocity becomes zero. The energy equation is written in terms of enthalpy as

_{l}is the temperature at which the PCM starts to liquefy and T

_{s}the temperature at which the material starts to solidify. A linear dependence between α and T is considered along the range.

#### 5.1.2. Numerical Model

^{−4}and 10

^{−9}for energy equation. The solution is time dependent; using an implicit second-order scheme with a time step of 0.1 s for integration, laminar flow was considered.

#### 5.1.3. CFD Simulation Results

#### 5.2. ESP-r Model

#### 5.2.1. Numerical Model

_{e}the external radius and λ the conductivity of encapsulating material. The global coefficient is applied as a boundary condition to the lateral surface of PCM bar discretization. On the upper and lower faces of the PCM bars, the simple one-dimensional global-heat-exchanger condition, Equation (14), is considered.

#### 5.2.2. Simulation Results

#### 5.3. Numerical Simulation Results Discussion

## 6. Conclusions

^{3}vertical cylindrical tank, up to 20 cylindrical PCM macro-capsules, summing up to 40 dm

^{3}of PCM. The designed tank was then tested under controlled boundary conditions in the lab, by means of a testing rig, mimicking the operating conditions that could be found on board of a ship, in terms of charging and discharging temperature. The results showed that the hybrid TES maintains a discharging power comparable with the sensible TES, with an overall storage density of up to 35% higher. This behavior is due to the ability of PCM macro-capsules to reheat the surrounding water during stand-by periods, due to the slower reaction of the encapsulated PCM. In order to better investigate the operation of the TES, two numerical models were also developed and validated. Both models were tested against the experimental results and demonstrated to be capable of reproducing the main features of the charging and discharging modes of the hybrid TES. The first model has been implemented in Fluent and allows an insight into the phenomena involved in the heat exchange between the water and PCM macro-capsules. It was capable of reproducing the thermal field inside the TES during the stand-by periods, allowing an appreciation of the phenomenon of water reheating with thermal stratification. The second model is an ESP-r component plant system, and despite the simplifying assumptions being reproduced perfectly, the charging of the TES and the main features of the discharging were well represented, with the reheating effect during the stand-by periods, but with less thermal stratification. However, the model rapid execution times allows the insertion of the component into a plant network for carrying on simulations and optimizations of the performance of a whole system featuring hybrid TES.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Onset melting temperature and latent heat evaluated over the PCM S58 measured in the DSC apparatus.

**Figure 3.**Detailed exploded tri-dimensional view of the designed hybrid sensible/latent storage, left-hand side, section of the internal macro-capsules’ arrangement, center, and view of the capsules inserted inside the storage, right-hand side.

**Figure 4.**Schematic representation of the TES with the temperature sensors included (highlighted). T

_{0}–T

_{5}are thermocouples inserted in the tank. T

_{6}and T

_{7}measure the surface temperature of the storage. T

_{9}–T

_{12}are used to measure inlet/outlet temperature of each hydraulic circuit.

**Figure 5.**Schematic representation of the testing rig employed for the TES testing, highlighting the charging and discharging circuits.

**Figure 6.**Comparison between charging phases at 10 kg/min for both tested configurations in the temperature range 45–75 °C. Dynamic evolution of three reference internal temperatures along the height of the tank, the temperature of the insulation and the ambient temperature (

**a**). Comparison between charging power measured (

**b**).

**Figure 7.**Comparison between discharging phases for both TES configurations at 12 kg/min, starting from 70 °C. Dynamic evolution of three reference internal temperatures along the height of the tank, the temperature of the insulation and the ambient temperature. On the top-right corner is a detail of the time frame during which the sensible storage is fully discharged.

**Figure 8.**Comparison between discharging phases for both TES configurations at 12 kg/min, starting from 70 °C. Dynamic evolution of the discharging power measured. On the top-right corner is a detail of the time frame during which the sensible storage is fully discharged.

**Figure 9.**Comparison of the discharged energy storage (left-hand side vertical axis) and equivalent hot water production (right-hand side vertical axis) between sensible and hybrid TES configurations as a function of initial discharging temperature and varying with the heat transfer flow rate.

**Figure 10.**Average discharging power as function of initial discharging temperature and flow rate for sensible (

**a**) and hybrid (

**b**) TES configurations.

**Figure 11.**Boundary conditions for numerical simulation, inlet temperature and mass flow rate (

**a**) Test 1—charge, (

**b**) Test 2—discharge.

**Figure 12.**Geometry of the PCM enhanced Tank, (

**a**) geometry with surface grid, (

**b**) bottom grid with inlet plenum, (

**c**) mid-height section of the model.

**Figure 13.**Results obtained with the Fluent mode and comparison with experimental results, temperature at sensors and liquid fraction for. (

**a**) Test 1 charge phase, (

**b**) Test 2 discharge phase.

**Figure 14.**Temperature distribution of the fluent model during discharge at different times: (

**a**) 360 s, (

**b**) 2040 s, (

**c**) 2280 s, (

**d**) 6000 s. The timings are also reported in Figure 13b.

**Figure 15.**Liquid fraction of the fluent model during discharge at different times: (

**a**) 360 s, (

**b**) 2040 s, (

**c**) 2280 s, (

**d**) 6000 s. The timings are also reported in Figure 13b.

**Figure 16.**Numerical discretization of the PCM module with container thickness. (

**a**) Top view, (

**b**) symmetry plane view.

**Figure 17.**Results for Test 1 charge problem (

**a**) and Test 2 discharge top view; (

**b**) symmetry plane view.

**Table 1.**Nominal features of the PCM S58 [10].

PCM | Phase Change Temperature | Density | Latent Heat | Volumetric Latent Heat | Specific Heat | Thermal Conductivity | Maximum Operating Temperature |
---|---|---|---|---|---|---|---|

S58 | 58 °C | 1505 kg/m^{3} | 145 kJ/kg | 218 MJ/m^{3} | 2.55 kJ/kg K | 0.69 W/m K | 120 °C |

Overall volume [m^{3}] | 0.1 |

Tank weight [kg] | 45 |

Tank height [m] | 1.15 |

Tank diameter [m] | 0.345 |

Maximum number of PCM capsules [-] | 20 |

Maximum volume of PCM capsules (when 20 capsules are included) [m ^{3}] | 0.04 |

Theoretical TES storage capacity in sensible configuration (reference ∆T = 20 K) [kWh] | 2.15 |

Theoretical TES density in sensible configuration (reference ∆T = 20 K) [kWh/m ^{3}] | 20.5 |

Theoretical TES storage capacity in sensible/latent configuration (reference ∆T = 20 K) [kWh] | 3.62 |

Theoretical TES density in sensible/latent configuration (reference ∆T = 20 K) [kWh/m ^{3}] | 35.2 |

**Table 3.**Testing conditions applied to the two TES configurations during charging and discharging phases.

Condition | Initial Temperature [°C] | Final Temperature [°C] | Flow Rate [kg/min] |
---|---|---|---|

Charging | 45.0 | From 65.0 to 80.0 | 10.0–12.0–15.0 |

Discharging | From 65.0 to 80.0 | 45.0 | 9.0–12.0 |

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**MDPI and ACS Style**

Frazzica, A.; Manzan, M.; Palomba, V.; Brancato, V.; Freni, A.; Pezzi, A.; Vaglieco, B.M.
Experimental Validation and Numerical Simulation of a Hybrid Sensible-Latent Thermal Energy Storage for Hot Water Provision on Ships. *Energies* **2022**, *15*, 2596.
https://doi.org/10.3390/en15072596

**AMA Style**

Frazzica A, Manzan M, Palomba V, Brancato V, Freni A, Pezzi A, Vaglieco BM.
Experimental Validation and Numerical Simulation of a Hybrid Sensible-Latent Thermal Energy Storage for Hot Water Provision on Ships. *Energies*. 2022; 15(7):2596.
https://doi.org/10.3390/en15072596

**Chicago/Turabian Style**

Frazzica, Andrea, Marco Manzan, Valeria Palomba, Vincenza Brancato, Angelo Freni, Amedeo Pezzi, and Bianca M. Vaglieco.
2022. "Experimental Validation and Numerical Simulation of a Hybrid Sensible-Latent Thermal Energy Storage for Hot Water Provision on Ships" *Energies* 15, no. 7: 2596.
https://doi.org/10.3390/en15072596