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# Optimization of packed-bed thermal energy storage system with PCM fillers for greenhouse application

Baoshan Xie, Nicolas Baudin, Jérôme Soto, Yilin Fan, Lingai Luo

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Baoshan Xie, Nicolas Baudin, Jérôme Soto, Yilin Fan, Lingai Luo. Optimization of packed-bed thermal energy storage system with PCM fillers for greenhouse application. EuroSun 2022, Sep 2022, Kassel, Germany. hal-03977559

HAL Id: hal-03977559

https://hal.science/hal-03977559

Submitted on 7 Feb 2023

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Distributed under a Creative Commons Attribution 4.0 International License
# Optimization of packed-bed thermal energy storage system with PCM fillers for greenhouse application

Baoshan XIE<fnref n="1" />, Nicolas BAUDIN<fnref n="1" />, Jérôme SOTO<fnref n="1" />,<fnref n="2" />, Yilin FAN<fnref n="1" />, Lingai LUO<fnref n="1" />,*

Packed-bed Thermal Energy Storage (TES) technology by using Phase Change Material (PCM) is useful to improve system capacity and stabilize temperature stratification. However, utilization and efficiency improvement through the conventional uniform layer packing structure are not enough, particularly less in global optimization.

This work aims at proposing a multi-objective genetic algorithm (MOGA) to optimize the multi-layered packing structure of the packed-bed TES tank for the greenhouse application.

## Methodology

### Model:

(For fluid)

$$ \epsilon \cdot \rho_f \cdot C_{p,f} \cdot \left( \frac{\partial T_f}{\partial t} + u_f \cdot \frac{\partial T_f}{\partial z} \right) = \frac{\partial}{\partial z} \cdot \left( \lambda_{f,eff} \cdot \frac{\partial T_f}{\partial z} \right) + h_{f,PCM} \cdot \frac{A_{PCM}}{V_{PCM}} \cdot (T'_{PCM} - T_f) + h_{f-w} \cdot \frac{A_{f-w}}{V_b} \cdot (T_w - T_f) $$

(For PCM)

$$ \rho_{PCM} \frac{\partial H_{m,PCM}}{\partial t} = \frac{1}{r^2} \cdot \frac{\partial}{\partial r} \cdot \left( r^2 \cdot \lambda_{PCM} \cdot \frac{\partial T_{PCM}}{\partial r} \right) $$

(For wall)

$$ \rho_w \cdot C_{p,w} \cdot \frac{\partial T_w}{\partial t} = \frac{\partial}{\partial z} \cdot \left( \lambda_w \cdot \frac{\partial T_w}{\partial z} \right) + h_{f-w} \cdot \frac{A_{f-w}}{V_w} \cdot (T_f - T_w) + h_{w-amb} \cdot \frac{A_{f-w}}{V_w} \cdot (T_{amb} - T_w) $$

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

* z, r: axial, radial

* t: time

* u_f: velocity

* λ: thermal conductivity

* h: heat transfer coefficient

* ε: porosity

* eff: effective value

* T: temperature

* f, w: fluid, wall

* b: bed

### Validation cases in LTeN lab

<table><thead><tr><th>Height/diameter</th><th>Polycarbonate</th><th>H/D=400/200 mm</th></tr></thead><tbody><tr><td>PCM</td><td>Paraffin expanded graphite capsule</td><td>ΔH<sub>m</sub>=230 J g<sup>-1</sup><br>T<sub>m</sub>=69±0.5</td></tr><tr><td>Operational temperatures</td><td>Water</td><td>20/75 °C</td></tr></tbody></table>

## Greenhouse design

### Greenhouse system

<figure><img src="image_6.png" /></figure>

### Tank size:

$$ V_{DES} = \frac{E_{GH}}{\left[ (1 - \epsilon) \cdot \rho_{PCM} \cdot C_{p,PCM} + \epsilon \cdot \rho_f \cdot C_{p,f} \right] \cdot \Delta T_{DES} \cdot \eta_{dis,DES}} $$

* E<sub>GH</sub> [J]: daily greenhouse (GH) consumption

* η<sub>dis,DES</sub>: designed discharging efficiency of TES system

* ΔT<sub>DES</sub> [K]: designed maximum temperature difference, T<sub>H</sub> - T<sub>C</sub>

### Greenhouse consumption

<figure><img src="image_7.png" /></figure>

### Radiation energy supply

<figure><img src="image_8.png" /></figure>

0.9 MWh/day

<table><thead><tr><th>Output (energy consumption)</th><th>Input (energy supply)</th></tr></thead><tbody><tr><td>Required gas heating energy, E<sub>GH</sub><br>(22:00-10:00)</td><td>Solar radiation<br>(10:00-18:00)</td></tr><tr><td>Total<br>136 KWh/m<sup>2</sup>/an (334 days)</td><td>967 kWh/m<sup>2</sup>/an (334 days)</td></tr><tr><td>Maximum<br>1 KWh/m<sup>2</sup>/day (12 h)</td><td>6 kWh/m<sup>2</sup>/day (10 h)</td></tr></tbody></table>

* Data: 3rd December 0:00 in 2014 to 1st November 23:00 in 2015.

* Gas heating energy consumption + radiation energy supply.

* Greenhouse surface area around S<sub>GH</sub>=900 m<sup>2</sup>.

## Optimization algorithm

### Packing configurations:

<figure><img src="image_9.png" /><figcaption>Design A</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Design A+</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Design B</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Design B+</figcaption></figure>

*x% means T<sub>m</sub>=x%·(T<sub>H</sub>-T<sub>C</sub>)

### Design variables

Layer thickness

$$ f_i^L = L_i/H $$

[0.1 0.9]

--

Phase change temperature

$$ f_i^T = \frac{T_{m,i} - T_c}{T_H - T_c} $$

[0.2 0.8]

$T_{m,i} \in [T_{20\%}, T_{80\%}]$

Thermal conductivity

$$ f_i^\lambda = \lambda_{PCM,i} / \lambda_f $$

[0 1]

$\lambda_{PCM} \in [0.2, 20]$

Mass flowrate in charging

$$ m_{f,chr} $$

[0 1]

$\dot{m}_{f,chr} \in [0.673, 1.65]$

Mass flowrate in discharging

$$ m_{f,dis} $$

[0 1]

$\dot{m}_{f,dis} \in [0.422, 1.65]$

### Indicators

### Objective functions

Overall energy efficiency

$$ F_1 = \min [-\eta_o = \eta_{ch} \cdot \eta_{disch}] $$

Capacity ratio + utilization ratio

$$ F_2 = \min [-\gamma_o = \frac{C_{ratio} + U_{ratio}}{2}] $$

### Performance indicators:

$$ \eta_o = \frac{\int_0^{t_{dis}} [\dot{m}_f \cdot C_{p,f} \cdot (T_{out} - T_0)] dt}{\int_0^{t_{ch}} [\dot{m}_f \cdot C_{p,f} \cdot (T_{in} - T_0)] dt} \qquad U_{ratio} = \frac{\Delta E_{out} - \Delta E_{in}}{\Delta E_{stored,max}} \qquad C_{ratio} = \frac{\Delta E_{stored,s} + \Delta E_{stored,f}}{\Delta E_{stored,max,s} + \Delta E_{stored,f}} $$

* T<sub>in</sub> [K] inlet temperature

* T<sub>out</sub> [K] Outlet temperature

## Optimization results

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

### Optimal variable ranges

### Pareto front

* Design A+ >> highest overall efficiency

* Max >> Overall energy efficiency 88%, Storage/utilization ability of 98%

## Conclusion

* Development a MOGA method for multi-layer packing configuration.

* PCM phase change temperature is important effect to be optimized

### Perspectives

* Economic cost and efficiency optimization

* Optimization under dynamic input condition

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<footnote n="1">¹ Nantes Université, Laboratoire de thermique et énergie de Nantes, LTeN, CNRS UMR 6607, 44000 Nantes, France</footnote>

<footnote n="2">² Institut Catholique d'Arts et Métiers de Nantes, 35 avenue du Champ de Manœuvres, 44470 Carquefou, France</footnote>