# A Numerical Parametric Study of a Double-Pipe LHTES Unit with PCM Encapsulated in the Annular Space

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}/KNO

_{3}-PCM in an AISI 321 tube were studied by Zhang et al. [9]. Numerical analysis results and experimental data were in line, and inserts of metallic foam/sponge had an insignificant effect on the solidification rate of salt [9]. A high-temperature LHTES system for concentrated solar power (CSP) plants with magnesium chloride as PCM enhanced with graphite foam has also been analyzed by Zhao et al. [10]. The addition of graphite foam in the PCM increased the exergy efficiency and improved the heat transfer processes [10]. Aadmi et al. [11] studied experimentally and numerically (with Comsol Multiphysics) a hot plate apparatus with PCM composites of epoxy resin paraffin wax. It was discovered that the container geometry affected the melting of PCM and a higher PCM content improved the LHTES capacity. KNO3–NaNO3 was encapsulated in a spherical shell, and no cracking was observed in the shell in an experimental and numerical investigation [12]. In another study by Arena et al. [13], the mushy zone of a finned double-pipe LHTES with paraffin RT35 was examined in three cases of heat transfer by convection and two cases for laminar and turbulent flow. Larger values for the mushy zone constant, representing the mushy area, led to a reduction of natural convection in the charging and discharging thermal cycles. A TES system with composite epoxy resin spherical shape paraffin wax RT27 was studied by Moulahi et al. [14], and the mushy zone proved to have an impact on the melting range. A numerical study of a PCM-air heat exchanger with dodecanoic acid was conducted by Herbinger et al. [15], and a higher heat transfer rate was observed for smaller heat exchanger channels and a higher air temperature. LHTES system performance under partial load in both charging and discharging cycles has also been studied by Arena et al. [16]. At a melting fraction of 0.75 and 0.90, the duration of the thermal cycles decreased up to 50% and the stored energy up to 30% [16]. The thermal properties of a PU-PCM composite were experimentally and numerically examined by Purohit and Sistla [17], and the study output indicated nucleation and crystallization domination of salt hydrate. Afsharpanah et al. [18,19,20] focused on several enhancement methods, such as porous foams, fins, and nanomaterials. A copper foam enhancement technique [18] increased the phase change rate by 92.5%.

## 2. Materials and Methods

#### 2.1. LHTES System Design

^{2}K and air temperature of 10 °C (the fan is blowing air over the LHTES). The LHTES system was isolated from air during discharging. Type M Copper pipes were selected for both unit’s pipes with a better heat transfer rate than aluminum pipes.

#### 2.2. Numerical Model

_{1→2}around the phase change temperature was investigated experimentally and set to 5K in melting and 2.5 K in solidification processes. Within the interval ∆T

_{1→2}, there is a “mushy zone” with mixed material properties. Cases 1–3 use a double pipe unit with no fins, while cases 4–6 and 7–9 involve double pipe with internal and external fins, respectively. Case 10 addresses a double pipe with internal and external fins. Case 11 examines a single pipe encapsulating a PCM electrospun fiber matrix. An extra fine mesh was used in the Comsol model for a minimum error range, and the average element quality in all geometries was 0.81–0.89. In the discharging phase, we decided to couple together, in a time-dependent study, the two single-physics codes of turbulent flow and heat transfer in solids and liquids in a multiphysics system. This method transfers information between each module during the solution process. In the charging phase, a time-dependent study of heat transfer in solids and liquids was used. A k-ε model using the RANS (Reynolds-Averaged Navier–Stokes) equation was selected for the simulation of turbulent flow (Equation (1)). For the heat transfer in solids and liquids, the energy Equation (2) was used. The heat transfer process’s effective density, heat capacity, mass fraction, and thermal conductivity in the phase change module are described by Equation (3)–(6).

## 3. Results and Discussion

#### 3.1. Validation Model Analysis

^{3}/h and 0.35 m

^{3}/h were presented in Table 3. The double-pipe heat exchanger with encapsulated PCM in the annular space configuration previously presented [28] is the same configuration as the one analyzed in the current study. For this reason, the model created in Comsol Multiphysics was adjusted to have the same geometry and was validated with previous experimental data [24]. The parameters studied for the validation were the inlet and outlet temperature of the water, the temperature of the PCM-copper pipe wall, as well as the melting time of the PCM. The melting time of the PCM was calculated through the solid-to-liquid phase indicator for average surface in the numerical simulation. In the experimental process, an uncertainty of 30 s for the time interval was calculated. The percentage difference between the experimental and calculated melting time for the validation case is shown in Table 4. The percentage difference is calculated according to Equation (7). The percentage differences for the melting time are below 5% and 8.3%, which is considered a positive outcome.

#### 3.2. Charging and Discharging Thermal Cycles

^{2}) during the charging and discharging phases is depicted in Figure 11. The linear average energy flux for the charging (solidification) process for the right boundary PCM-wall-air is analyzed in Figure 11. For the discharging (melting) phase, the total energy flux (W/m

^{2}) of the left boundary PCM-wall-water is presented in Figure 11. The heat flux flow (W/m

^{2}) evolves quickly in the simulation’s beginning and then approaches zero. The simulated energy fluxes during charging and discharging display little variations. In the charging phase for cases 1–3 (Figure 11a), the smaller diameter LHTES (case 1) presented a lower heat flux and approached 0 more quickly at 3h. Additionally, in cases 5 and 6 with internal fins (Figure 11b), longer fins displayed lower energy flux and approached 0 at 3.3–3.6 h. the energy flux curves of cases 7–9 (Figure 11c) with external fins converge and present three times higher energy flux at the beginning of the simulation compared to other cases and reach 0 at around 4 h. Case 10 (Figure 11d) follows the same trend as cases 4–6. The energy flux of case 11 fiber matrix (Figure 11e) started at a higher value than cases with no fins and internal fins and reached 0 at 2.5 h. The discharging curves of energy flux cases 1–10 follow the same trend as the charging curves. However, the energy flux of case 11 with the electrospun fiber matrix approaches 0 at 10 s. This is explained due to direct-contact heat transfer of the water-electrospun fiber matrix. In both charging and discharging thermal cycles, external fins (cases 7–9) enhance the heat transfer of the LHTES system.

## 4. Conclusions

^{2}) are displayed in cases with external fins. Case 1, with the lowest PCM volume, and case 10, with internal and external fins, exhibit the fastest solidification time of 0.92 h and 0.84 h, respectively. The numerical simulation’s shortest discharging time is displayed for the electrospun fiber matrix case at 4 s due to the direct contact heat transfer of PCM matrix water. The phase change process was accelerated by 99.97% in the discharging cycle and by 31.12% in the charging cycle compared to the case with no fins of the same external tube diameter (case 3). A small-scale LHTES shall be constructed in future work, and an experimental evaluation should be conducted as additional research.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Parameter | Description | Unit |

ρ | Density | kg/m^{3} |

P | Pressure | Pa |

u | Velocity | m/s |

θ | Fraction/Indicator of phase transition | - |

${C}_{P}$ | Specific heat | J/kgK |

a_{m} | Mass fraction | - |

k | Thermal conductivity | W/mK |

HTF | Heat Transfer Fluid | - |

LHTES | Latent Heat Thermal Energy Storage | - |

PCM | Phase Change Material | - |

## References

- Souayfane, F.; Fardoun, F.; Biwole, H.P. Phase change materials (PCM) for cooling applications in buildings: A review. Energy Build
**2016**, 129, 396–431. [Google Scholar] [CrossRef] - Osterman, E.; Tyagi, V.V.; Butala, V.; Rahim, N.A.; Stritih, U. Review of PCM based cooling technologies for buildings. Energy Build.
**2012**, 49, 37–49. [Google Scholar] [CrossRef] - Al-Abidi, A.A.; Bin Mat, S.; Sopian, K.; Sulaiman, M.Y.; Lim, C.H. The Review of thermal energy storage for air conditioning systems. Renew. Sustain. Energy Rev.
**2012**, 16, 5802–5819. [Google Scholar] [CrossRef] - Zhai, X.Q.; Wang, X.L.; Wang, T.; Wang, R.Z. A review on phase change cold storage in air-conditioning system: Materials and applications. Renew. Sustain. Energy Rev.
**2013**, 22, 108–120. [Google Scholar] [CrossRef] - Lin, Y.; Jia, Y.; Alva, G.; Fang, G. Review on thermal conductivity enhancement, thermal properties and applications of phase change materials in thermal energy storage. Renew. Sustain. Energy Rev.
**2018**, 82, 2730–2742. [Google Scholar] [CrossRef] - Rathod, M.K.; Banerjee, J. Thermal stability of phase change materials used in latent heat energy storage systems: A review. Renew. Sustain. Energy Rev.
**2013**, 18, 246–258. [Google Scholar] [CrossRef] - Sharma, A.; Tyagi, V.V.; Chen, C.R.; Buddhi, D. Review on thermal energy storage with phase change materials and applications. Renew. Sustain. Energy Rev.
**2009**, 13, 318–345. [Google Scholar] [CrossRef] - Paroutoglou, E.; Afshari, A.; Bergsøe, N.C.; Fojan, P.; Hultmark, G. A PCM based cooling system for office buildings: A state of the art review. E3S Web Conf.
**2019**, 111, 01026. [Google Scholar] [CrossRef] [Green Version] - Zhang, H.L.; Baeyens, J.; Degrève, J.; Cáceres, G.; Segal, R.; Pitié, F. Latent heat storage with tubular-encapsulated phase change materials (PCMs). Energy
**2014**, 76, 66–72. [Google Scholar] [CrossRef] [Green Version] - Zhao, W.; France, D.M.; Yu, W.; Kim, T.; Singh, D. Phase change material with graphite foam for applications in high-temperature latent heat storage systems of concentrated solar power plants. Renew. Energy
**2014**, 69, 134–146. [Google Scholar] [CrossRef] - Aadmi, M.; Karkri, M.; El Hammouti, M. Heat transfer characteristics of thermal energy storage for PCM (phasechange material) melting in horizontal tube: Numerical andexperimental investigations. Energy
**2015**, 85, 339–352. [Google Scholar] [CrossRef] - Parrado, C.; Cáceres, G.; Bize, F.; Bubnovich, V.; Baeyens, J.; Degrève, J.; Zhang, H.L. Thermo-mechanical analysis of copper-encapsulated NaNO3-KNO3. Chem. Eng. Res. Des.
**2015**, 93, 224–231. [Google Scholar] [CrossRef] [Green Version] - Arena, S.; Casti, E.; Gasia, J.; Cabeza, L.F.; Cau, G. Numerical simulation of a finned-tube LHTES system: Influence of the mushy zone constant on the phase change behaviour. Energy Procedia
**2017**, 126, 517–524. [Google Scholar] [CrossRef] - Moulahi, C.; Trigui, A.; Boudaya, C.; Karkri, M. Smart macroencapsulated resin/wax composite for energy conservation in the built environment. J. Thermoplast. Compos. Mater.
**2017**, 30, 887–914. [Google Scholar] [CrossRef] - Herbinger, F.; Bhouri, M.; Groulx, D. Investigation of heat transfer inside a PCM-air heat exchanger: A numerical parametric study. Heat Mass Transf. Stoffuebertragung
**2018**, 54, 2433–2442. [Google Scholar] [CrossRef] - Arena, S.; Casti, E.; Gasia, J.; Cabeza, L.F.; Cau, G. Numerical analysis of a latent heat thermal energy storage system under partial load operating conditions. Renew. Energy
**2018**, 128, 350–361. [Google Scholar] [CrossRef] - Purohit, B.K.; Sistla, V.S. Studies on solution crystallization of Na2SO4·10H2O embedded in porous polyurethane foam for thermal energy storage application. Thermochim. Acta
**2018**, 668, 9–18. [Google Scholar] [CrossRef] - Afsharpanah, F.; Izadi, M.; Hamedani, F.A.; Mousavi Ajarostaghi, S.S.; Yaïci, W. Solidification of nano-enhanced PCM-porous composites in a cylindrical cold thermal energy storage enclosure. Case Stud. Therm. Eng.
**2022**, 39, 1DUMMY. [Google Scholar] [CrossRef] - Afsharpanah, F.; Mousavi Ajarostaghi, S.S.; Arıcı, M. Parametric study of phase change time reduction in a shell-and-tube ice storage system with anchor-type fin design. Int. Commun. Heat Mass Transf.
**2022**, 137, 106281. [Google Scholar] [CrossRef] - Afsharpanah, F.; Pakzad, K.; Mousavi Ajarostaghi, S.S.; Arıcı, M. Assessment of the charging performance in a cold thermal energy storage container with two rows of serpentine tubes and extended surfaces. J. Energy Storage
**2022**, 51, 104464. [Google Scholar] [CrossRef] - Shahsavar, A.; Goodarzi, A.; Mohammed, H.I.; Shirneshan, A.; Talebizadehsardari, P. Thermal performance evaluation of non-uniform fin array in a finned double-pipe latent heat storage system. Energy
**2020**, 193, 116800. [Google Scholar] [CrossRef] - Shahsavar, A.; Goodarzi, A.; Talebizadehsardari, P.; Arıcı, M. Numerical investigation of a double-pipe latent heat thermal energy storage with sinusoidal wavy fins during melting and solidification. Int. J. Energy Res.
**2021**, 45, 20934–20948. [Google Scholar] [CrossRef] - Boulaktout, N.; Mezaache, E.H.; Teggar, M.; Arici, M.; Ismail, K.A.R.; Yildiz, Ç. Effect of Fin Orientation on Melting Process in Horizontal Double Pipe Thermal Energy Storage Systems. J. Energy Resour. Technol. Trans. ASME
**2021**, 143, 1–14. [Google Scholar] [CrossRef] - Nicholls, R.A.; Moghimi, M.A.; Griffiths, A.L. Impact of fin type and orientation on performance of phase change material-based double pipe thermal energy storage. J. Energy Storage
**2022**, 50, 104671. [Google Scholar] [CrossRef] - Paroutoglou, E.; Fojan, P.; Gurevich, L.; Hultmark, G.; Afshari, A. Thermal Analysis of Organic and Nanoencapsulated Electrospun Phase Change Materials. Energies
**2021**, 14, 995. [Google Scholar] [CrossRef] - Paroutoglou, E.; Afshari, A.; Fojan, P.; Hultmark, G. Investigation of Thermal Behavior of Paraffins, Fatty Acids, Salt Hydrates and Renewable Based Oils as PCM. In Proceedings of the International Renewable Energy Storage Conference 2020 (IRES 2020), Düsseldorf, Germany, 10–12 March 2020; Volume 6, pp. 34–40. [Google Scholar] [CrossRef]
- Paroutoglou, E.; Fojan, P.; Gurevich, L. Thermal Properties of Novel Phase-Change Materials Based on Tamanu and Coconut Oil Encapsulated in Electrospun Fiber Matrices. Sustainability
**2022**, 14, 7432. [Google Scholar] [CrossRef] - Medrano, M.; Yilmaz, M.O.; Nogués, M.; Martorell, I.; Roca, J.; Cabeza, L.F. Experimental evaluation of commercial heat exchangers for use as PCM thermal storage systems. Appl. Energy
**2009**, 86, 2047–2055. [Google Scholar] [CrossRef]

**Figure 3.**Configuration of double-pipe LHTES unit with fins on the internal pipe (

**left**), LHTES unit with fins on the external pipe (

**right**).

**Figure 4.**Configuration of double-pipe LHTES unit with fins on the internal and external pipes of the LHTES unit.

**Figure 6.**Inlet and outlet water temperature in experiments/numerical simulation for mass flow rate (

**a**) m = 0.1064 kg/s, (

**b**) m = 0.098 kg/s.

**Figure 7.**Temperature of PCM-copper wall in experiments/numerical simulation for mass flow rate (

**a**) m = 0.1064 kg/s, (

**b**) m = 0.098 kg/s.

**Figure 9.**Melting fraction during charging and discharging processes (

**a**) cases 1–3, (

**b**) cases 4–6, (

**c**) cases 7–9, (

**d**) case 10, (

**e**) case 11.

**Figure 10.**PCM temperature during charging and discharging processes (

**a**) cases 1–3, (

**b**) cases 4–6, (

**c**) cases 7–9, (

**d**) case 10, (

**e**) case 11.

**Figure 11.**Energy flux (W/m2) during charging and discharging processes (

**a**) cases 1–3, (

**b**) cases 4–6, (

**c**) cases 7–9, (

**d**) case 10, (

**e**) case 11.

**Figure 12.**Total enthalpy of LHTES during charging and discharging processes (

**a**) cases 1–3, (

**b**) cases 4–6, (

**c**) cases 7–9, (

**d**) case 10, (

**e**) case 11.

Case | Copper PCM Pipe Inner Diameter (m) | Thickness of PCM Pipe (m) | PCM Mass (kg) | Internal Fins | External Fins | Fins Width (m) | Fins Height (m) | Distance between Fins (m) | |
---|---|---|---|---|---|---|---|---|---|

1 | 0.026797 m | 0.000889 m | 0.158 | - | - | - | |||

2 | 0.0327914 m | 0.0010668 m | 0.257 | - | - | - | |||

3 | 0.0387858 m | 0.0012446 m | 0.376 | - | - | - | |||

4 | 0.0387858 m | 0.0012446 m | 0.362 | x | 0.0065 m | 0.0004 m | 0.0021 m | ||

5 | 0.0387858 m | 0.0012446 m | 0.352 | x | 0.00975 m | 0.0004 m | 0.0021 m | ||

6 | 0.0387858 m | 0.0012446 m | 0.364 | x | 0.00975 m | 0.0004 m | 0.0046 m | ||

7 | 0.0387858 m | 0.0012446 m | 0.376 | x | 0.0065 m | 0.0004 m | 0.0021 m | ||

8 | 0.0387858 m | 0.0012446 m | 0.376 | x | 0.00975 m | 0.0004 m | 0.0021 m | ||

9 | 0.0387858 m | 0.0012446 m | 0.376 | x | 0.00975 m | 0.0004 m | 0.0046 m | ||

10 | 0.0387858 m | 0.0012446 m | 0.352 | x | x | Int. fins | Ext. fins | 0.0004 m | 0.0021 m |

0.00975 m | 0.0065 m | ||||||||

11 | 0.0387858 m | 0.0012446 m | 0.198 | - | - | - |

Theoretical Properties | |

Density (Solid) | 0.88 kg/L |

Density (Liquid) | 0.77 kg/L |

Heat Capacity (Solid) | 2 kJ/kg·K |

Heat Capacity (Liquid) | 2 kJ/kg·K |

Latent Heat of Fusion | 260 kJ/kg |

Thermal Conductivity | 0.2 W/m·K |

Melting Point | 18 °C |

Experimental Properties (Pure RT18) | |

Melting temperature | 17.5 °C |

Solidification temperature | 15.4 °C |

Latent heat of melting | 137.8 kJ/kg |

Latent heat of solidification | 139.3 kJ/kg |

Experimental Properties (RT18 Electrospun Fiber Matrix) | |

Melting temperature | 17.3 °C |

Solidification temperature | 15.2 °C |

Latent heat of melting | 102.1 kJ/kg |

Latent heat of solidification | 82.2 kJ/kg |

Porosity of fiber matrix | 0.474 |

Experiment | Process | Temperature Conditions | Turbulent Flow | PCM Properties | Air Temperature (°C) | ||
---|---|---|---|---|---|---|---|

Water Inlet (°C) | PCM at Start (°C) | Volumetric Flow Rate (m^{3}/h) | Latent Heat (J/g) | Phase Change Temp. (°C) | |||

1 | Charge (Melting) | 50 | 24 | 0.38 | 157 | 35 | 22–24 |

2 | Charge (Melting) | 50 | 24 | 0.35 | 157 | 35 | 22–24 |

Experiment | Mass Flow Rate (kg/s) | Experimental Melting Time | Calculated Melting Time | Percentage Difference |
---|---|---|---|---|

1 | 0.1064 | 25,200 s | 26,470 s | 5% < 10% |

2 | 0.0980 | 24,060 s | 26,060 s | 8.3% < 10% |

Case | Charging (Solidification) Time | Discharging (Melting) Time |
---|---|---|

1 | 3310 s | 3420 s |

2 | 4090 s | 7070 s |

3 | 6940 s | 13,620 s |

4 | 5500 s | 3220 s |

5 | 4060 s | 1230 s |

6 | 4500 s | 1530 s |

7 | 5830 s | 14,590 s |

8 | 5710 s | 14,070 s |

9 | 4520 s | 14,510 s |

10 | 3040 s | 1040 s |

11 | 4780 s | 4 s |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Paroutoglou, E.; Fojan, P.; Gurevich, L.; Furbo, S.; Fan, J.; Medrano, M.; Afshari, A.
A Numerical Parametric Study of a Double-Pipe LHTES Unit with PCM Encapsulated in the Annular Space. *Sustainability* **2022**, *14*, 13317.
https://doi.org/10.3390/su142013317

**AMA Style**

Paroutoglou E, Fojan P, Gurevich L, Furbo S, Fan J, Medrano M, Afshari A.
A Numerical Parametric Study of a Double-Pipe LHTES Unit with PCM Encapsulated in the Annular Space. *Sustainability*. 2022; 14(20):13317.
https://doi.org/10.3390/su142013317

**Chicago/Turabian Style**

Paroutoglou, Evdoxia, Peter Fojan, Leonid Gurevich, Simon Furbo, Jianhua Fan, Marc Medrano, and Alireza Afshari.
2022. "A Numerical Parametric Study of a Double-Pipe LHTES Unit with PCM Encapsulated in the Annular Space" *Sustainability* 14, no. 20: 13317.
https://doi.org/10.3390/su142013317