# Dynamic Simulations on Enhanced Heat Recovery Using Heat Exchange PCM Fluid for Solar Collector

^{*}

## Abstract

**:**

^{2}. Furthermore, the higher PCM content has higher latent heat. On the other hand, the lower content PCM can increase the temperature difference between the SC inlet and outlet because of the lower PCM heat capacity. For the 1 L/min flow rate, 2 wt% PCM fluid has shorter heat-storing time and larger net transportable energy than 0 wt% PCM fluid (426 kJ←403 kJ) for the SCHP unit.

## 1. Introduction

_{4}∙1/2 H

_{2}O (s) + 32.9 kJ/mol ⇌ CaSO

_{4}(s) + 1/2 H

_{2}O (g)

_{2}O (g) ⇌ H

_{2}O (l) + 41.7 kJ/mol

## 2. Methodology

#### 2.1. Descriptions of SCHP Unit

#### 2.2. Mathematical Model for Circulation Loop of HTF in the SCHP Unit

#### 2.2.1. Assumptions

- The preparation processes of the PCM fluid are not considered in the simulation.
- The solid erythritol at ambient temperature is distributed uniformly in silicone oil.
- The received solar heat flux at different positions of the SC is uniform.
- The solar irradiation absorbed by the outer glass tube is neglected.
- The heat loss caused by the evacuated glass tube is neglected.
- The thermal resistance caused by the thickness of the glass tube in SC is neglected.
- The continuum surface force model [42] in ANSYS Fluent is used to represent that the surface tension at the PCM–silicone oil interface decreases when the surfactant is adsorbed on the PCM surface.

#### 2.2.2. Initial and Boundary Conditions

#### 2.2.3. Governing Equations

^{−3}, 10

^{−3}, 10

^{−6}, 10

^{−3}, 10

^{−3}, and 10

^{−3}.

#### 2.2.4. Net Transportable Energy

## 3. Results and Discussions

#### 3.1. Grid and Time-Step Independence

#### 3.2. Verification of Simulation and Experimental Data

^{2}. The average solar irradiation from two experiments (1 L/min and 2 L/min) is 1105 W/m

^{2}and 1013 W/m

^{2}, respectively. After correcting for the effects of solar radiation on recovered heat, the recovered heat at different flow rates is 222 W at 1 L/min and 217 W at 2 L/min per 1000 W/m

^{2}solar irradiation. Different flow rates have similar recovered heat under the same solar irradiation conditions.

^{2}(1 L/min) and 227 W/m

^{2}(2 L/min) per 1000 W/m

^{2}solar irradiation. The absolute errors between the experiments and simulations are 3.6% at 1 L/min and 4.6% at 2 L/min. The amount of recovered heat in the solar collector is used to determine the accuracy of the simulation model. The results shown in Figure 2 illustrate that the previously specified boundary conditions can be used.

#### 3.3. Specific Viscosities of PCM Fluid

#### 3.4. Effects of Flow Rates on Recovered Heat

^{−6}m

^{3}/s), 1 L/min (1.6 × 10

^{−5}m

^{3}/s), 2 L/min (3.3 × 10

^{−5}m

^{3}/s), and 3 L/min (5 × 10

^{−5}m

^{3}/s). The PCM fluid used in this subsection contains 10 wt% PCM, which was tested in previous studies [37]. The Reynolds numbers are 34, 67, 130, and 195, respectively (the physical properties of the mixture are calculated by volume average).

^{2}, when solar irradiation is constant at 1000 W/m

^{2}, and after a continuous circulation of 30 min, Figure 5 presents the net transportation energy and circulation power of the loop under different flow rates at 30 min. At 30 min, the net transportation energy of PCM fluid from 0.5 L/min to 3 L/min is 415 kJ, 404 kJ, 393 kJ, and 383 kJ, respectively. Therefore, in these cases, the net transportation energy will increase as the flow rate decreases. In this case, lower flow rates (0.5 L/min and 1 L/min) can promote the recovered heat and net transportation energy.

#### 3.5. Effects of Weight Fractions of PCM on Recovered Heat

^{2}, when solar irradiation is constant at 1000 W/m

^{2}, and after a continuous circulation of 30 min, Figure 8 presents the net transportation energy and circulation power of the loop under different flow rates at 30 min. At the flow rate of 1 L/min, compared to 0 wt% PCM fluid, when using 2 wt%, 5 wt%, and 10 wt% PCM fluid, the circulation power increases by 1.004, 1.012, and 1.028 times, respectively. At 30 min, the recovered heat of 0 wt%, 2 wt%, 5 wt%, and 10 wt% PCM fluid is 414 kJ, 436 kJ, 422 kJ, and 416 kJ, respectively, and the relative theoretical circulation power of the PCM fluids is 11.4 kJ, 11.4 kJ, 11.5 kJ, and 11.7 kJ, respectively. Therefore, in these cases, 2 wt% PCM fluid achieves the highest net transportable energy due to higher recovered heat and lower circulation power.

#### 3.6. Estimation of Heat-Storing Time for SCHP Unit

^{2}and SC area of 1 m

^{2}, the pure silicone oil as the HTF requires a heat-storing time of 205 min. The shortest heat-storing time of 194 min is achieved using 2 wt% PCM fluid. As observed in this study, increasing the PCM content leads to an increase in the heat-storing time.

## 4. Conclusions

- It is necessary to maintain the weight fraction of the PCM below 10 wt% to control the impact of the increase in specific viscosity on the circulation power of the circulation.
- The melted mass and recovered heat of the PCM fluid are affected by flow rate, with a larger melted mass observed at lower flow rates due to longer residence time in the SC. A lower flow rate can enhance the PCM melted mass and the recovered heat although sensible heat amount increases with the flow rate. The best flow rate is 1 L/min when the SC area is 1 m
^{2}. - The higher PCM content has higher latent heat. On the other hand, the lower content PCM can increase the temperature difference between the SC inlet and outlet because of the lower PCM heat capacity.
- The increase in the net transportable energy illustrates that using PCM fluid can increase the recovered heat without a significant increase in the circulation power. The maximum growth in this study is achieved with 2 wt% PCM fluid.
- For the 1 L/min flow rate, 2 wt% PCM fluid has shorter heat-storing time and larger net transportable energy than 0 wt% PCM fluid (426 kJ←403 kJ) for the SCHP unit.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

T | Temperature | (K) |

q | Heat | (W) |

P | Pressure | (kPa) |

λ | Effective thermal conductivity | (W/mK) |

η | Reflectance | (-) |

τ | Transmittance | (-) |

$\sigma $ | Absorbance | (-) |

h | Heat transfer coefficient | (W/m^{2}K) |

I | Irradiation | (W/m^{2}) |

$\dot{m}$ | Mass transfer rate | (kg/m^{3}s) |

∆H | Enthalpy | (J/kg) |

ω | Weight fraction | (wt%) |

Q | Recovered heat | (W) |

$\xi $ | Net transportable energy | (kJ) |

W | Circulation power | (kJ) |

F | Flow rate | (L/min) |

S | Volumetric heat source | (W/m^{3}) |

ρ | Mixture density | (kg/m^{3}) |

${\rm Z}$ | Body force | (N/m^{3}) |

$\mu $ | Viscosity of multiphase flow | (Pas) |

∆P | Pressure drop | (kPa) |

t | Time | (min) |

$\upsilon $ | Velocity | (m/s) |

$M$ | Energy loss in the circulation | (J/kg) |

α | Volume fraction | (-) |

$\theta $ | Specific viscosity | (-) |

Subscripts | ||

atm | Atmosphere | |

g | Glass | |

r | Solar irradiation | |

th | Pipes in reactor | |

f | Frame of reactor | |

m | Melting point | |

l | Liquid phase | |

s | Solid phase | |

pump | Circulation pump | |

loss | Energy loss | |

fr | Piping friction | |

lat | Latent heat | |

lo | Local elements | |

int | Internal | |

in | Input | |

c | Circulation | |

sen | Sensible heat storing | |

chem | Chemical heat storing | |

p | Particle in reactant bed | |

h | Hot heat from chemical heat storing | |

ex | Exchange heat | |

tot | Total |

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**Figure 4.**Several melting performances at different flow rates: (

**a**) mass and melting percentage of liquid PCM over time at the SC outlet/inlet; (

**b**) recovered heat forms liquid PCM; (

**c**) total recovered heat (kJ) over temperature at the SC outlet; (

**d**) temperature of PCM fluid at the SC inlet/outlet after melting over time; (

**e**) temperature of PCM fluid at the Re inlet/outlet after melting over time; (

**f**) Effects of flow rate on total recovered heat of PCM fluid, including sensible heat of silicone oil, solid PCM, liquid PCM, and latent heat of melting.

**Figure 6.**Sectional view (YZ − Plane, X = 0.039 m) of 10 wt% PCM fluid at the Re inlet when the melted PCM is 80 g at the SC outlet.

**Figure 7.**Several melting performances at different PCM weight fractions: (

**a**) mass of liquid PCM over time; (

**b**) melting percentage of liquid PCM over time; (

**c**) recovered heat from liquid PCM; (

**d**) effects of weight fraction on total recovered heat of PCM fluid, including sensible heat of silicone oil, solid PCM, and liquid PCM as well as latent heat; (

**e**) temperature of PCM fluid at the SC inlet/outlet after melting over time; (

**f**) temperature of PCM fluid at the Re inlet/outlet after melting over time.

Component | Properties/Unit | Value |
---|---|---|

Evacuated glass tubes (Borosilicate) | Number | 6 |

Outer/inner diameter (mm) | 47.00/37.00 | |

Transmittance of outer glass | 0.92 | |

Emissivity of outer glass | 0.90 | |

Absorbance of selective coating | 0.94 | |

Emissivity of selective coating | 0.06 | |

Manifold u-pipes (copper) | Inner diameter (mm) | 6.00 |

Length (mm) | 1500 | |

CPC reflector | Reflectance | 0.94 |

Connecting pipes (SUS304) | Inner diameter (mm) | 14.60 |

Total length (mm) | 2495 |

Fluid | Properties/Unit | Value |
---|---|---|

Base of HTF (silicone oil) | Density (kg/m^{3}) | $-0.93T+1241$ |

Specific heat (J/kg/K) | $1.4T+1097$ | |

Viscosity (Pas) Thermal conductivity (W/(m·K)) | ${10}^{{10}^{-0.84\ast \mathrm{LOG}\left(\mathrm{T}\right)+2.3}}\times {10}^{-6}\xb7\mathsf{\rho}$ 0.13 | |

Solid PCM (erythritol) [41] | Density (kg/m^{3}) | 1480 |

Specific heat (J/(kg·K)) | 1350 | |

Viscosity (Pas) | 0.02895 | |

Thermal conductivity (W/(m·K)) | 0.732 | |

Liquid PCM (erythritol) [41] | Density (kg/m^{3}) | 1300 |

Specific heat (J/(kg·K)) | 2740 | |

Viscosity (Pas) | 0.01602 | |

Thermal conductivity (W/(m·K)) | 0.326 | |

Latent heat (kJ/kg) | 340 | |

Melting temperature (K) | 390.15 |

Type | Location | Formula | |
---|---|---|---|

Initial Conditions: | |||

Temperature | All domains | $\mathrm{t}=0:\mathrm{T}={\mathrm{T}}_{\mathrm{atm}}=298.15\mathrm{K}$ | (3) |

Pressure | All domains | $\mathrm{t}=0:\mathrm{P}={\mathrm{P}}_{\mathrm{atm}}=101.325\mathrm{kPa}$ | |

Velocity | All domains | $\mathrm{t}=0:\mathrm{v}=0\mathrm{m}/\mathrm{s}$ | |

Boundary Conditions: | |||

Temperature | The front of the SC | $\mathsf{\lambda}\frac{\partial \mathrm{E}}{\partial \mathrm{n}}={\mathrm{c}}_{\mathrm{p}}\xb7{\mathsf{\tau}}_{\mathrm{g}}\xb7\mathsf{\sigma}\xb7{\mathrm{I}}_{\mathrm{r}}$ | (4) |

The back of the SC | $\mathsf{\lambda}\frac{\partial \mathrm{E}}{\partial \mathrm{n}}={\mathsf{\eta}}_{\mathrm{cpc}}\xb7{\mathrm{c}}_{\mathrm{p}}\xb7{\mathsf{\tau}}_{\mathrm{g}}\xb7\mathsf{\sigma}\xb7{\mathrm{I}}_{\mathrm{r}}$ | (5) | |

The CPs | $\mathsf{\lambda}\frac{\partial \mathrm{E}}{\partial \mathrm{n}}={\mathrm{h}}_{\mathrm{cp}}\xb7{\mathrm{c}}_{\mathrm{p}}\xb7\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{atm}}\right)$ | (6) | |

The pipes in the Re | $\mathsf{\lambda}\frac{\partial \mathrm{E}}{\partial \mathrm{n}}={\mathrm{h}}_{\mathrm{th}}\xb7{\mathrm{c}}_{\mathrm{p}}\xb7\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{atm}}\right)$ | (7) | |

The frame in the Re | $\mathsf{\lambda}\frac{\partial \mathrm{E}}{\partial \mathrm{n}}={\mathrm{h}}_{\mathrm{f}}\xb7{\mathrm{c}}_{\mathrm{p}}\xb7\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{atm}}\right)$ | (8) | |

Pressure | All boundaries | $\frac{\partial \mathrm{P}}{\partial \mathrm{n}}=\mathrm{G}\left(\mathrm{t},\mathrm{x},\mathrm{y},\mathrm{z}\right)$ | (9) |

Velocity | All boundaries | ${\left.\mathrm{v}\right|}_{\mathrm{attheboundary}}={\mathrm{v}}_{\mathrm{wall}}=0$ | (10) |

^{2}); ${\mathsf{\tau}}_{\mathrm{g}}$, transmittance of the outer glass; $\mathsf{\sigma}$, absorbance of the selective coating; ${\mathsf{\eta}}_{\mathrm{cpc}}$, reflectance of the CPC reflector; $\mathrm{n}$, the normal direction of the HTF surface.

MAPE (%) | ${\mathbf{T}}_{\mathbf{r}\mathbf{e},\mathbf{i}\mathbf{n}}$ | ${\mathbf{T}}_{\mathbf{r}\mathbf{e},\mathbf{o}\mathbf{u}\mathbf{t}}$ | ${\mathbf{T}}_{\mathbf{s}\mathbf{c},\mathbf{i}\mathbf{n}}$ | ${\mathbf{T}}_{\mathbf{r}\mathbf{e},\mathbf{o}\mathbf{u}\mathbf{t}}$ | ||||
---|---|---|---|---|---|---|---|---|

${9.5\times 10}^{6}$ | ${1.5\times 10}^{7}$ | ${9.5\times 10}^{6}$ | ${1.5\times 10}^{7}$ | ${9.5\times 10}^{6}$ | ${1.5\times 10}^{7}$ | ${9.5\times 10}^{6}$ | ${1.5\times 10}^{7}$ | |

${3.0\times 10}^{7}$ | 0.86 | 0.34 | 0.75 | 0.34 | 0.98 | 0.35 | 1.06 | 0.33 |

MAPE (%) | ${\mathbf{T}}_{\mathbf{r}\mathbf{e},\mathbf{i}\mathbf{n}}$ | ${\mathbf{T}}_{\mathbf{r}\mathbf{e},\mathbf{o}\mathbf{u}\mathbf{t}}$ | ${\mathbf{T}}_{\mathbf{s}\mathbf{c},\mathbf{i}\mathbf{n}}$ | ${\mathbf{T}}_{\mathbf{r}\mathbf{e},\mathbf{o}\mathbf{u}\mathbf{t}}$ | ||||
---|---|---|---|---|---|---|---|---|

1 s | 5 s | 1 s | 5 s | 1 s | 5 s | 1 s | 5 s | |

0.1 s | 0.019 | 0.065 | 0.017 | 0.059 | 0.017 | 0.057 | 0.019 | 0.066 |

F | 1 L/min | |||
---|---|---|---|---|

ω | 0 wt% | 2 wt% | 5 wt% | 10 wt% |

${\mathrm{Q}}_{\mathrm{ex},\mathrm{re}}$ (W) | 75.9 | 80.2 | 77.2 | 76.2 |

${\mathbf{Q}}_{\mathbf{s}\mathbf{e}\mathbf{n},\mathbf{p}}\mathbf{}\mathbf{\left(}\mathbf{kJ}\right)$ | ${\mathbf{Q}}_{\mathbf{s}\mathbf{e}\mathbf{n},\mathbf{r}\mathbf{e}}\left(\mathbf{kJ}\right)$ | ${\mathbf{Q}}_{\mathbf{h}}\left(\mathbf{kJ}\right)$ |
---|---|---|

132 | 223 | 580 |

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**MDPI and ACS Style**

Ren, Y.; Ogura, H. Dynamic Simulations on Enhanced Heat Recovery Using Heat Exchange PCM Fluid for Solar Collector. *Energies* **2023**, *16*, 3075.
https://doi.org/10.3390/en16073075

**AMA Style**

Ren Y, Ogura H. Dynamic Simulations on Enhanced Heat Recovery Using Heat Exchange PCM Fluid for Solar Collector. *Energies*. 2023; 16(7):3075.
https://doi.org/10.3390/en16073075

**Chicago/Turabian Style**

Ren, Yawen, and Hironao Ogura. 2023. "Dynamic Simulations on Enhanced Heat Recovery Using Heat Exchange PCM Fluid for Solar Collector" *Energies* 16, no. 7: 3075.
https://doi.org/10.3390/en16073075