# Enhancing the Power Performance of Latent Heat Thermal Energy Storage Systems: The Adoption of Passive, Fractal Supports

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## Abstract

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## 1. Introduction

- Realization of optimized blends of PCMs: blends can be formulated in the attempt to get the desired PCM thermal properties to better suit the designed application [10];
- Adoption of highly conductive thermal supports: realized in the forms of fins, blades, heat pipes, and foams [11]. Their exploitation strongly enhances thermal conductivity (>200×, when embedding the PCM in porous graphite [12,13]), but can lead to detachment phenomena between the PCM and the thermal support. This phenomenon is due to the volumetric variation during melting/solidification and causes poor performance in repeated cycles [14];
- Addition of micro-/nano-particles: the adoption of micro/nano-particles, nano-fibers, nano-tubes, and other nano-scale fillers can actually provide remarkable enhancements in specific heat, thermal conductivity, and thermal diffusivity (pristine graphene allows an increase in thermal conductivity up to $2800\%$ [15,16]);

## 2. Materials and Methods

`f`

_{+}and

`f`

_{−}are frequency factors (basically, the inverse time scale for melting and solidification, respectively), and ${K}^{+}$ and ${K}^{-}$ are switch functions to control the the onset of melting and solidification, respectively, around the critical temperature ${T}_{cr}$.

- $\tilde{\ell}$ is a relaxation parameter, chosen to be on the order of 0.5 to ensure that the relaxation of ${\mathcal{F}}_{Drag}$ is faster than the other dynamics;
- $\mathrm{St}$ is the non-dimensional Stefan number, given by $\mathrm{St}=\mathrm{c}\phantom{\rule{4pt}{0ex}}\frac{{T}_{liq}-{T}_{sol}}{\mathcal{L}}$, with $\mathrm{c}$ the specific heat and $\mathcal{L}$ the latent heat;
- $\mathrm{\Delta}T$ is the characteristic temperature difference: we fix $\mathrm{\Delta}T={T}_{liquid}-{T}_{solid}$, as in [7].

## 3. Validation, Results, and Discussion

**Figure 3.**Evolution in time of the liquefied mass fraction inside the computational domain. The effect of the different $\mathrm{Ra}$ numbers and of the solid thermal support morphology is apparent.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Sketch of the different morphologies of solid thermal support: (

**a**) thin fins; (

**b**) thick blades; (

**c**) branched fractal structure. The three structures are characterized by the same mass, the same thermal conductivity, and the same temperature.

**Figure 4.**Evolution in time of the phase field parameter $\varphi $ as a function of the non-dimensional time $\theta $. All panels refer to the cases at $\mathrm{Ra}=0$.

**Figure 5.**Evolution in time of the phase field parameter $\varphi $ as a function of the non-dimensional time $\theta $. All panels refer to the regime at $\mathrm{Ra}=$ 10,000.

**Figure 6.**Evolution in time of the phase field parameter $\varphi $ as a function of the non-dimensional time $\theta $. All panels refer to the regime at $\mathrm{Ra}=$ 50,000.

**Figure 7.**(

**a**–

**c**) Snapshots of the melting front position at $\mathrm{Ra}=$ 500,000 and $\theta =5\times {10}^{-3}$.

**Figure 8.**Contours of the velocity magnitude inside the computational domain for the three investigated geometries (

**a**–

**c**) at $\mathrm{Ra}=$ 500,000 and $\theta =5\times {10}^{-3}$.

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**MDPI and ACS Style**

Amati, G.; Succi, S.; Falcucci, G.
Enhancing the Power Performance of Latent Heat Thermal Energy Storage Systems: The Adoption of Passive, Fractal Supports. *Energies* **2023**, *16*, 6764.
https://doi.org/10.3390/en16196764

**AMA Style**

Amati G, Succi S, Falcucci G.
Enhancing the Power Performance of Latent Heat Thermal Energy Storage Systems: The Adoption of Passive, Fractal Supports. *Energies*. 2023; 16(19):6764.
https://doi.org/10.3390/en16196764

**Chicago/Turabian Style**

Amati, Giorgio, Sauro Succi, and Giacomo Falcucci.
2023. "Enhancing the Power Performance of Latent Heat Thermal Energy Storage Systems: The Adoption of Passive, Fractal Supports" *Energies* 16, no. 19: 6764.
https://doi.org/10.3390/en16196764