# Design Optimization of a Composite Solar Wall Integrating a PCM in a Individual House: Heating Demand and Thermal Comfort Considerations

^{*}

## Abstract

**:**

_{2}emissions. Due to their high heat storage capacity, phase change materials (PCMs) have impressed many researchers. This paper investigates the energy performance of an individual house integrating a solar Trombe wall containing PCM with respect to heating demand and thermal comfort applications. The thermal energy performance of the design house was simulated using Dymola/Modelica, the thermal building simulation tool, whereby the optimization of objective functions as regards heating demand and thermal comfort was executed using GenOpt, the generic optimization software. Optimization of the solar Trombe wall focuses on the feasibility to find the optimal PCM parameters when running GenOpt, which consist of latent heat, melting temperature, PCM thickness and thermal conductivity, in order to minimize both the annual energy consumption for heating and the number of hours of thermal discomfort. The parametric study was first conducted for each PCM parameter so as to not only observe its effect on the identified energy performance, but also ensure the absence of errors in simulation runs before performing the optimization. The ‘Coordinate Search’ Generalized Pattern Search (GPS) algorithm was applied to minimize the objective function, whereas the ‘Weighted Sum Approach’ was used to solve the multi-objective function problem. Results showed that the higher the latent heat, the lower the heating demand and the greater the thermal comfort. The results of these parametric studies show that for the effect of the parameter on heating, demand is quite limited (1–2 kWh·m${}^{-2}$·year${}^{-1}$) whereas the effect on thermal comfort is more significant. The optimal PCM melting temperature is higher for warmer climates; it is also higher for the studied case applying the optimization method to minimize the objective function by assigning the number of hours of thermal discomfort (from 32.8 ${}^{\circ}\mathrm{C}$ to 35.9 ${}^{\circ}\mathrm{C}$, depending on weather) than it is when applying the optimization method to reduce the objective function by assigning heating demand (from 31.5 ${}^{\circ}\mathrm{C}$ to 32.9 ${}^{\circ}\mathrm{C}$, again depending on weather).

## 1. Introduction

_{2}emissions [1]; it is the single largest energy consumer category in Europe. A package of energy efficiency measures (EEMs), under the guidelines of European regulations (EU) [2,3], has established various building measures to mitigate consumption, including building envelope improvements, passive techniques, building system modifications as well as measures based on sustainable energy sources. A solar Trombe wall that integrates a phase change material (PCM), which is the focus of the present study, is a passive design technique that may be considered as an EEM.

^{®}[15].

^{®}is a rather commonly used tool in the building optimization method according to the results of interviews with building optimization experts [16]. The GenOpt program runs on the source code in JAVA and is a free generic optimization tool built to execute building optimization problems (BOPs); it is thereby appropriate and reasonable to use in building performance simulations (BPS) with an acceptable level of complexity. Furthermore, GenOpt is an optimization tool to minimize the objective function $f\left(\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\right)$, as evaluated from external simulation tools that read its input from text files and write its output to text files, e.g., EnergyPlus [17], TRNSYS [18], Dymola/Modelica. Choosing optimization algorithms for a particular study condition serves to reach the optimal cost function value, leading to the best cost reduction [19]. Hence, the methodology for choosing an optimization algorithm in a given BOP normally depends on various considerations, such as design variables, constraints and nature of objective functions, analytical first- and second-order derivatives of the objective functions, static vs. dynamic problem and potential algorithm performance [20].

_{2}emission. Some of the previous literature studies regarding the PCM to reduce CO

_{2}level have been conducted [37,38,39,40,41]. It is interesting therefore to study the building energy performance based on a simulation-based optimization within an approach coupling the solar Trombe wall with PCM for the purpose of maximizing building performance.

_{2}as well.

_{pcm}, melting temperature TM

_{pcm}, storage wall thickness e

_{pcm}and thermal conductivity $\lambda $

_{pcm}, and to establish the simulation-based optimization methodology targeting the following objective functions: heating demand objective function, number of hours of thermal discomfort objective function and heading demand + number of hours of discomfort objective function.

## 2. Methodology

#### 2.1. Description of the House Model

^{2}; the 11.13 m

^{2}bedroom on the south side; and the 24.25-m

^{2}living room on the south side. The constructive features of this detached house as well as the physical characteristics of its elements are given in the table of the previous work [24].

_{fr}= 0.38). Window area and orientations have been reported in the previous work [24].

#### 2.2. Solar Trombe Wall Description and Climatic Regions

^{®}, generating a latent heat of 17.1 kJ/kg. The phase change temperature is 25.8 ${}^{\circ}\mathrm{C}$. The characterization of the thermal properties of the composite storage wall has been described in [47]. The thermal characteristics of the element used in the solar Trombe wall system are listed in table of the previous study [24]. The numerical study of the solar Trombe wall integrated along with the concrete and PCM storage wall, compared to the results of measurement data, were validated in previous studies [44,48]. It should be noted herein that the solar Trombe wall, installed at the southern wall of the house model, is exposed to both sunlight and outside air.

## 3. Parametric Study

_{pcm}, the melting temperature TM

_{pcm}and the thermal conductivity $\lambda $

_{pcm}. The variation in PCM thickness eppcm is also taken into account. Table 2 shows the definition, established range and value steps to be optimized. The bounds were chosen one-by-one to be physically plausible (since not all combinations are realistic). It should be noted that once a parametric study has been conducted, all the other parameters are held at their basic value, as given in the “Base” column of Table 2.

## 4. Effect of Solar Wall Parameters on Heating Demand

#### 4.1. Variation in Latent Heat (LA_pcm)

_{sup_LA 10000}). The power supplied, with higher latent heat, is greater, and its curve decreases slowly during the night. The total energy supplied and heating demand applied with the three latent heat values, as calculated by integrating power as a function of time, are given in Table 3.

#### 4.2. Variation in Melting Temperature (TM_pcm)

_{pcm}shifts from 30.8 ${}^{\circ}\mathrm{C}$ to 20.8 ${}^{\circ}\mathrm{C}$), which can be explained by the fact that over the period while the value of PCM melting temperature is too small, the PCM phase change is inappropriate to sufficiently charge thermal energy. According to the curve, the lowest heating demand corresponds to an optimal PCM melting temperature value of 30.8 ${}^{\circ}\mathrm{C}$.

#### 4.3. Variation in the PCM Storage Wall Thickness (e_pcm)

_{pcm}= 4 cm). The power supplied with a storage wall of 12 cm to 15 cm thick shows poorer results than a 4-cm thick wall, while the temperature curves inside the bedroom containing a 12-cm or 15-cm thick storage wall are also below those of a 4-cm thick wall. Similarly, for the variation of latent heat, it should be noted that the power supplied with a wall thickness of 4 cm decreases rapidly, while temperature inside the bedroom also decreases towards the setpoint temperature compared to the other configurations (i.e., curves of T

_{bed_e 12 cm}and T

_{bed_e 15 cm}). Conversely, the power supplied remains positive longer than the case with the thinner wall (e.g., 4 cm) at night when installing the thicker storage wall. Table 4 reports the total energy supplied and heating demand vs. three values of storage wall thickness.

#### 4.4. Variation in Thermal Conductivity ($\lambda $_pcm)

_{pcm}increases, the energy supplied by the solar Trombe wall also increases, even as heating demand decreases. Figure 11 presents the gain in power supplied and temperature inside the bedroom as thermal conductivity increases from 0.22 W/m·K to 1.02 W/m·K.

_{pcm}, TM

_{pcm}and ${\lambda}_{\mathrm{pcm}}$). Nevertheless, it does substantially influence the amplitude of these variables since it favors the direct transfer of thermal energy and power supplied to the bedroom.

## 5. Effect of Solar Wall Parameters on Building Comfort during Winter

## 6. Optimization Process Methodology

#### 6.1. Optimization Method

- Optimization of heating demand;
- Optimization of the number of hours of thermal discomfort;
- Simultaneous optimization of heating demand and number of hours of discomfort.

#### 6.2. Optimization of Heating Demand

#### 6.3. Optimization of the Number of Hours of Thermal Discomfort

_{pcm}= 40,000 J/kg. For those cases denoted “**”, the upper bound has therefore been reached.

_{pcm}= 15 cm in the defined range. The optimal values of thermal conductivity and melting temperature do lie within the defined range. Just like the results obtained from the heating demand objective function, the optimal melting temperature from the number of hours of discomfort objective function shows an increase in value relative to weather, i.e., the warmer the climate, the higher the melting temperature (32.8 ${}^{\circ}\mathrm{C}$ for Paris vs. 35.9 ${}^{\circ}\mathrm{C}$ for Nice).

#### 6.4. Simultaneous Optimization of Heating Demand and Number of Hours of Discomfort

## 7. Conclusions

- The higher the latent heat, the lower the heating demand and the better the thermal comfort in the bedroom, Figure 12;
- The optimal melting temperatures are approximately 31 ${}^{\circ}\mathrm{C}$ for heating demand and 44 ${}^{\circ}\mathrm{C}$ for number of hours of discomfort, Figure 13;
- The effect of storage wall thickness is small with respect to heating demand, whereas the higher the thickness, the lower the number of hours of discomfort and, thus, the better the thermal comfort, Figure 14;
- The higher the thermal conductivity, the lower the heating demand and the higher the number of hours of discomfort, Figure 15.

- Development of the mortar + PCM composition with higher latent heat, density and conductivity;
- Use of a macro-encapsulated PCM storage wall;
- Development of the solar wall relying on the same method, dimensions and location (e.g., living room, with a larger floor area to be heated);
- Use of a solar wall for preheating air within the entire house.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbols: | |

c | specific heat capacity, J/kg K |

c_{solid} | specific heat capacity when PCM is in the solid state, J/kg K |

c_{liquid} | specific heat capacity when PCM is in the liquid state, J/kg K |

E | energy, kW·h |

e | thickness, m |

H | height, m |

h | hour |

L_{A} | latent heat, J/kg |

nbHr | number of hours |

no | number |

P | power supplied by the composite Trombe wall, W |

T | temperature, ${}^{\circ}$C |

T_{M} | melting temperature, ${}^{\circ}$C |

T_{C} | comfort temperature, ${}^{\circ}$C |

W | width, m |

Greek symbols | |

α | absorptivity |

$\epsilon $ | emissivity |

$\lambda $ | thermal conductivity, W/m K |

$\varphi $ | flux, W/m^{2} |

$\rho $ | density, kg/m^{3} |

Subscripts | |

bed | bedroom |

c | comfort |

ext | exterior |

flc | floor concrete |

fr | frame |

glw | glass wool |

hea | heating |

lv | lower vent |

liv | living room |

max | maximum |

mid | middle |

nor | north-facing rooms |

ref | reference |

sal | salon |

sup | supply |

uv | upper vent |

Abbreviations | |

M_PCM | composite material: mortar + PCM |

PCM | phase change material |

U | frame window factor |

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**Figure 3.**Energy supplied by the solar Trombe wall and annual heating demand vs. latent heat during the cold season (7 months total: January–April and October–December).

**Figure 4.**Effect of latent heat on the power released by the solar Trombe wall and temperature inside the bedroom.

**Figure 5.**Energy released by the solar Trombe wall and heating demand in the bedroom vs. melting temperature during the cold season (7 months total: January–April and October–December).

**Figure 6.**Variations in: the power supplied by the solar Trombe wall, temperature at the center of the phase change material (PCM) storage wall and temperature inside the bedroom.

**Figure 7.**Daily amplitudes during the entire year of temperature fluctuations at the center of the PCM storage wall vs. four different values of PCM melting temperature. T

_{max_storage wall}and T

_{min_storage wall}denote respectively the daily maximum and minimum temperatures.

**Figure 8.**Energy released by the solar Trombe wall and heating demand vs. storage wall thickness during the cold season (7 months total: January–April and October–December).

**Figure 9.**Effect of PCM storage wall thickness on the power released by the solar Trombe wall and temperature inside the bedroom.

**Figure 10.**Energy released by the solar Trombe wall and heating demand vs. thermal conductivity during the cold season (7 months total: January–April and October–December).

**Figure 11.**Effect of PCM thermal conductivity on both the power released by the solar Trombe wall and temperature inside the bedroom.

**Figure 12.**Number of hours of thermal discomfort and heating demand vs. latent heat during the cold season (7 months total: January–April and October–December).

**Figure 13.**Number of hours of thermal discomfort and heating demand vs. melting temperature during the cold season (7 months total: January–April and October–December).

**Figure 14.**Number of hours of thermal discomfort and heating demand vs. storage wall thickness during the cold season (7 months total: January–April and October–December).

**Figure 15.**Number of hours of thermal discomfort and heating demand vs. thermal conductivity during the cold season (7 months total: January–April and Octobr–December).

**Figure 16.**Variation in the objective function (f(x) = Heating demand), as subsequently simulated using three initial values.

**Figure 17.**Temperature variations inside the bedroom. T

_{ext}and T

_{comfort+3.5 ${}^{\circ}\mathrm{C}$}denote respectively the outside air temperature and comfort setpoint temperature plus 3.5 ${}^{\circ}\mathrm{C}$.

**Figure 19.**Number of hours of thermal discomfort vs. latent heat parameters lying close to the upper bound of 40,000 J/kg.

**Figure 20.**Temperature variations inside the bedroom. T

_{ext}and T

_{comfort+3.5 ${}^{\circ}\mathrm{C}$}denote respectively the variation in outside air temperature and the comfort setpoint temperature plus 3.5 ${}^{\circ}\mathrm{C}$.

**Figure 22.**Comparison of the power supplied by the solar Trombe wall installed with the optimized and non-optimized PCM.

Weather | Variable | January | February | March | April | May | June | July | August | September | October | November | December |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Paris | $\varphi $, (W/m${}^{2}$) T, ${(}^{\circ}\mathrm{C})$ | 154 3.9 | 253 4.2 | 366 7 | 523 10 | 588 14.3 | 649 16.8 | 671 19.4 | 627 19.7 | 481 15.7 | 334 11.3 | 198 6.4 | 135 4.7 |

Lyon | $\varphi $, (W/m${}^{2}$) T, ${(}^{\circ}\mathrm{C})$ | 185 3.3 | 324 3.8 | 493 7.9 | 583 10.8 | 623 15.4 | 713 19 | 760 21.6 | 659 20.4 | 561 16.4 | 339 13 | 214 7.3 | 161 4 |

Nice | $\varphi $, (W/m${}^{2}$) T, ${(}^{\circ}\mathrm{C})$ | 314 9 | 432 8.8 | 541 11.5 | 675 13.1 | 724 17.5 | 779 20.6 | 841 23.9 | 793 24 | 636 20.8 | 439 16.2 | 327 11.8 | 273 9.2 |

Parameter | Definition | Units | Minimum | Base | Maximum | Steps |
---|---|---|---|---|---|---|

$L{A}_{pcm}$ | latent heat | J/kg | 10,000 | 17,100 | 40,000 | 1000 |

$T{M}_{pcm}$ | melting temperature | ${}^{\circ}\mathrm{C}$ | 18.8 | 25.8 | 55.8 | 1 |

${e}_{pcm}$ | storage wall thickness | m | 0.04 | 0.04 | 0.15 | 0.01 |

${\lambda}_{pcm}$ | thermal conductivity | W/(m.K) | 0.2 | 0.62 | 1 | 0.05 |

LA_{pcm}(J/kg) | E Supplied for 2 Whole Days | E Heating Demand for 2 Days |
---|---|---|

10,000 | 2.60 kW·h | 0.35 kW·h |

25,000 | 2.26 kW·h | 0.52 kW·h |

40,000 | 1.89 kW·h | 0.58 kW·h |

e_{pcm}(m) | E Supplied for 2 Whole Days | E Heating Demand for 2 Days |
---|---|---|

4 | 6.791 kW·h | 0.282 kW·h |

12 | 4.251 kW·h | 0.837 kW·h |

15 | 3.393 kW·h | 0.818 kW·h |

**Table 5.**Heating demand for four months of Paris weather based on three initial PCM parameter values.

Calculation Number | TM_{pcm}${}^{\circ}\mathbf{C}$ | LA_{pcm}J/kg | e_{pcm}cm | $\mathit{\lambda}$_{pcm}W/m·K | Heating Demand kWh·m${}^{-2}$·4 months${}^{-1}$ | |
---|---|---|---|---|---|---|

1 | Initial value | 20.8 | 15,000 | 4 | 0.22 | 31.69 |

Optimal value | 31.5 | 40,000 * | 9 | 1 * | 28.02 | |

2 | Initial value | 34.8 | 20,000 | 8 | 0.95 | 28.88 |

Optimal value | 31.5 | 40,000 * | 9 | 1 * | 28.02 | |

3 | Initial value | 20.8 | 39,000 | 14 | 0.95 | 30.47 |

Optimal value | 31.5 | 40,000 * | 9 | 1 * | 28.02 |

**Table 6.**Optimal parameters of three distinct weather conditions (optimization of the heating demand objective function).

Weather | TM_{pcm}${}^{\circ}\mathbf{C}$ | LA_{pcm}J/kg | e_{pcm}cm | $\mathit{\lambda}$_{pcm}W/m·K | Heating Demand kWh·m${}^{-2}$·4 months${}^{-1}$ |
---|---|---|---|---|---|

Paris | 31.5 | 40,000 * | 9.0 | 1.00 * | 28.02 |

Lyon | 32.9 | 40,000 * | 10 | 1.00 * | 24.10 |

Nice | 32.8 | 40,000 * | 15 | 1.00 * | 2.23 |

Weather Type | House Case Study | Number of Hours of Discomfort | Energy Supplied in the Cold Season (kWh·m ^{−2}·Year^{−1}) | Heating Demand Energy (kWh·m ^{−2}·Year^{−1}) |
---|---|---|---|---|

Paris-Orly | no Trombe wall | 0 | – | 66.07 |

non-optimized PCM | 170 | 18.68 | 53.42 | |

optimized PCM | 84 | 18.96 | 50.66 | |

Lyon | no Trombe wall | 0 | – | 61.24 |

non-optimized PCM | 362 | 26.73 | 48.99 | |

optimized PCM | 150 | 23.03 | 46.46 | |

Nice | no Trombe wall | 0 | – | 21.07 |

non-optimized PCM | 1031 | 50.50 | 8.64 | |

optimized PCM | 496 | 44.70 | 4.29 |

**Table 8.**Optimal parameters for the three weather conditions (optimization of the number of hours of discomfort objective function).

Weather | TM_{pcm}${}^{\circ}\mathbf{C}$ | LA_{pcm}J/kg | e_{pcm}cm | $\mathit{\lambda}$_{pcm}W/m·K | Heating Demand kWh·m${}^{-2}$·4 Months${}^{-1}$ | No. of Hours of Discomfort h/4 Months |
---|---|---|---|---|---|---|

Paris | 32.8 | 40,000 * | 15 * | 0.4 | 29.46 | 0 |

Lyon | 35.2 | 39,889 ** | 15 * | 0.2 | 26.36 | 6.7 |

Nice | 35.9 | 39,963 ** | 15 * | 0.2 | 3.44 | 11 |

**Table 9.**Optimal parameters, for three weather datasets, from the optimization of the single-objective function.

Weather | TM_{pcm}${}^{\circ}\mathbf{C}$ | LA_{pcm}J/kg | e_{pcm}cm | $\mathit{\lambda}$_{pcm}W/m·K | Heating Demand kWh·m${}^{-2}$·4 Months${}^{-1}$ | No. Hours Discomfort h/4 Months |
---|---|---|---|---|---|---|

Paris | 35.8 | 40,000 * | 15 * | 0.733 | 28.57 | 0 |

Lyon | 34.9 | 40,000 * | 14.9 ** | 0.2 | 26.33 | 7.2 |

Nice | 36 | 39,963 ** | 15 * | 0.2 | 3.44 | 11.1 |

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## Share and Cite

**MDPI and ACS Style**

Leang, E.; Tittelein, P.; Zalewski, L.; Lassue, S.
Design Optimization of a Composite Solar Wall Integrating a PCM in a Individual House: Heating Demand and Thermal Comfort Considerations. *Energies* **2020**, *13*, 5640.
https://doi.org/10.3390/en13215640

**AMA Style**

Leang E, Tittelein P, Zalewski L, Lassue S.
Design Optimization of a Composite Solar Wall Integrating a PCM in a Individual House: Heating Demand and Thermal Comfort Considerations. *Energies*. 2020; 13(21):5640.
https://doi.org/10.3390/en13215640

**Chicago/Turabian Style**

Leang, Enghok, Pierre Tittelein, Laurent Zalewski, and Stéphane Lassue.
2020. "Design Optimization of a Composite Solar Wall Integrating a PCM in a Individual House: Heating Demand and Thermal Comfort Considerations" *Energies* 13, no. 21: 5640.
https://doi.org/10.3390/en13215640